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35A27, 58J15]", "value": 100, "id": "38"}, {"name": "Normal analytic spaces", "value": 100, "id": "20"}, {"name": "Applications to physics", "value": 100, "id": "81"}]}, {"id": "B", "name": "Local analytic geometry [See also 13-XX and 14-XX]", "children": [{"name": "Germs of analytic sets, local parametrization", "value": 100, "id": "10"}, {"name": "Analytic subsets of affine space", "value": 100, "id": "15"}, {"name": "Triangulation and related questions", "value": 100, "id": "25"}, {"name": "Analytic algebras and generalizations, preparation theorems", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Semi-analytic sets and subanalytic sets [See also 14P15]", "value": 100, "id": "20"}]}, {"id": "E", "name": "Holomorphic convexity", "children": [{"name": "Stein spaces, Stein manifolds", "value": 100, "id": "10"}, {"name": "Polynomial convexity", "value": 100, "id": "20"}, {"name": "Holomorphically convex complex spaces, 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the complex domain", "children": [{"name": "Approximation in the complex domain", "value": 100, "id": "10"}, {"name": "Asymptotic representations in the complex domain", "value": 100, "id": "15"}, {"name": "Boundary value problems [See also 45Exx]", "value": 100, "id": "25"}, {"name": "Moment problems, interpolation problems", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]", "value": 100, "id": "20"}]}, {"id": "D", "name": "Entire and meromorphic functions, and related topics", "children": [{"name": "Representations of entire functions by series and integrals", "value": 100, "id": "10"}, {"name": "Bloch functions, normal functions, normal families", "value": 100, "id": "45"}, {"name": "Entire functions, general theory", "value": 100, "id": "20"}, {"name": "Functional equations in the complex domain, iteration and 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"id": "20"}]}, {"id": "D", "name": "Genetics and population dynamics", "children": [{"name": "Genetics {For genetic algebras, see 17D92}", "value": 100, "id": "10"}, {"name": "Problems related to evolution", "value": 100, "id": "15"}, {"name": "Population dynamics (general)", "value": 100, "id": "25"}, {"name": "Epidemiology", "value": 100, "id": "30"}, {"name": "Animal behavior", "value": 100, "id": "50"}, {"name": "Ecology", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Protein sequences, DNA sequences", "value": 100, "id": "20"}]}, {"id": "F", "name": "Other natural sciences (should also be assigned at least one other classification number in this section)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other natural sciences (should also be assigned at least one other classification number in section 92)", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}, {"name": "Computational methods", "value": 100, "id": "08"}]}]}, {"id": "85", "name": "Astronomy and astrophysics {For celestial mechanics, see 70F15}", "children": [{"id": "A", "name": "Astronomy and astrophysics {For celestial mechanics, see 70F15}", "children": [{"name": "Radiative transfer", "value": 100, "id": "25"}, {"name": "Planetary atmospheres", "value": 100, "id": "20"}, {"name": "General", "value": 100, "id": "04"}, {"name": "Galactic and stellar dynamics", "value": 100, "id": "05"}, {"name": "Hydrodynamic and hydromagnetic problems [See also 76Y05]", "value": 100, "id": "30"}, {"name": "Statistical astronomy", "value": 100, "id": "35"}, {"name": "Miscellaneous topics", "value": 100, "id": "99"}, {"name": "Cosmology {For relativistic cosmology, see 83F05}", "value": 100, "id": "40"}, {"name": "Galactic and stellar structure", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}, {"name": "Experimental work", "value": 100, "id": "05"}, {"name": "Computational methods", "value": 100, "id": "08"}]}]}]}, {"id": "DEQ", "name": "Differential & Integral Equations, Operators", "children": [{"id": "58", "name": "Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}", "children": [{"id": "A", "name": "General theory of differentiable manifolds [See also 32Cxx]", "children": [{"name": "Topos-theoretic approach to differentiable manifolds", "value": 100, "id": "03"}, {"name": "de Rham theory [See also 14Fxx]", "value": 100, "id": "12"}, {"name": "Exterior differential systems (Cartan theory)", "value": 100, "id": "15"}, {"name": "Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]", "value": 100, "id": "14"}, {"name": "Pfaffian systems", "value": 100, "id": "17"}, {"name": "Differential forms", "value": 100, "id": "10"}, {"name": "Natural bundles", "value": 100, "id": "32"}, {"name": "Differentiable manifolds, foundations", "value": 100, "id": "05"}, {"name": "Supermanifolds and graded manifolds [See also 14A22, 32C11]", "value": 100, "id": "50"}, {"name": "Stratified sets [See also 32S60]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Currents [See also 32C30, 53C65]", "value": 100, "id": "25"}, {"name": "Vector distributions (subbundles of the tangent bundles)", "value": 100, "id": "30"}, {"name": "Jets", "value": 100, "id": "20"}, {"name": "Differential spaces", "value": 100, "id": "40"}, {"name": "Real-analytic and Nash manifolds [See also 14P20, 32C07]", "value": 100, "id": "07"}]}, {"id": "C", "name": "Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]", "children": [{"name": "Holomorphic maps [See also 32-XX]", "value": 100, "id": "10"}, {"name": "Set valued and function-space valued mappings [See also 47H04, 54C60]", "value": 100, "id": "06"}, {"name": "Implicit function theorems; global Newton methods", "value": 100, "id": "15"}, {"name": "Continuity properties of mappings", "value": 100, "id": "07"}, {"name": "Real-valued functions", "value": 100, "id": "05"}, {"name": "Fixed point theorems on manifolds [See also 47H10]", "value": 100, "id": "30"}, {"name": "Analysis on supermanifolds or graded manifolds", "value": 100, "id": "50"}, {"name": "Integration on manifolds; measures on manifolds [See also 28Cxx]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Differentiable maps", "value": 100, "id": "25"}, {"name": "Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]", "value": 100, "id": "20"}, {"name": "Spectral theory; eigenvalue problems [See also 47J10, 58E07]", "value": 100, "id": "40"}]}, {"id": "B", "name": "Infinite-dimensional manifolds", "children": [{"name": "Differentiability questions", "value": 100, "id": "10"}, {"name": "Questions of holomorphy [See also 32-XX, 46G20]", "value": 100, "id": "12"}, {"name": "Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]", "value": 100, "id": "20"}, {"name": "Homotopy and topological questions", "value": 100, "id": "05"}, {"name": "Geometry of quantum groups", "value": 100, "id": "32"}, {"name": "Noncommutative geometry (a la Connes)", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]", "value": 100, "id": "25"}, {"name": "Fredholm structures [See also 47A53]", "value": 100, "id": "15"}]}, {"id": "E", "name": "Variational problems in infinite-dimensional spaces", "children": [{"name": "Critical metrics", "value": 100, "id": "11"}, {"name": "Applications to the theory of geodesics (problems in one independent variable)", "value": 100, "id": "10"}, {"name": "Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]", "value": 100, "id": "12"}, {"name": "Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.", "value": 100, "id": "15"}, {"name": "Abstract bifurcation theory", "value": 100, "id": "07"}, {"name": "Pareto optimality, etc., applications to economics [See also 90C29]", "value": 100, "id": "17"}, {"name": "Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)", "value": 100, "id": "05"}, {"name": "Group-invariant bifurcation theory", "value": 100, "id": "09"}, {"name": "Applications", "value": 100, "id": "50"}, {"name": "Variational inequalities (global problems)", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications to control theory [See also 49-XX, 93-XX]", "value": 100, "id": "25"}, {"name": "Variational principles", "value": 100, "id": "30"}, {"name": "Harmonic maps [See also 53C43], etc.", "value": 100, "id": "20"}, {"name": "Group actions", "value": 100, "id": "40"}]}, {"id": "D", "name": "Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]", "children": [{"name": "Spaces of imbeddings and immersions", "value": 100, "id": "10"}, {"name": "Moduli problems for differential geometric structures", "value": 100, "id": "27"}, {"name": "Manifolds of mappings [See also 46T10, 54C35]", "value": 100, "id": "15"}, {"name": "Groups and semigroups of nonlinear operators [See also 17B65, 47H20]", "value": 100, "id": "07"}, {"name": "Manifolds of metrics (esp. Riemannian)", "value": 100, "id": "17"}, {"name": "Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]", "value": 100, "id": "05"}, {"name": "Group actions and symmetry properties", "value": 100, "id": "19"}, {"name": "Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)", "value": 100, "id": "30"}, {"name": "Moduli problems for topological structures", "value": 100, "id": "29"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]", "value": 100, "id": "25"}, {"name": "Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]", "value": 100, "id": "20"}]}, {"id": "H", "name": "Pseudogroups, differentiable groupoids and general structures on manifolds", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]", "value": 100, "id": "10"}, {"name": "Deformations of structures [See also 32Gxx, 58J10]", "value": 100, "id": "15"}, {"name": "Pseudogroups and differentiable groupoids [See also 22A22, 22E65]", "value": 100, "id": "05"}]}, {"id": "K", "name": "Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]", "children": [{"name": "Monodromy", "value": 100, "id": "10"}, {"name": "Singularities of vector fields, topological aspects", "value": 100, "id": "45"}, {"name": "Algebraic and analytic properties of mappings", "value": 100, "id": "20"}, {"name": "Stability", "value": 100, "id": "25"}, {"name": "Asymptotic behavior", "value": 100, "id": "55"}, {"name": "Global theory", "value": 100, "id": "30"}, {"name": "Normal forms", "value": 100, "id": "50"}, {"name": "Catastrophe theory", "value": 100, "id": "35"}, {"name": "Deformation of singularities", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Classification; finite determinacy of map germs", "value": 100, "id": "40"}, {"name": "Symmetries, equivariance", "value": 100, "id": "70"}, {"name": "Topological properties of mappings", "value": 100, "id": "15"}, {"name": "Critical points of functions and mappings", "value": 100, "id": "05"}, {"name": "Topological invariants", "value": 100, "id": "65"}]}, {"id": "J", "name": "Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]", "children": [{"name": "Noncommutative global analysis, noncommutative residues", "value": 100, "id": "42"}, {"name": "Relations with special manifold structures (Riemannian, Finsler, etc.)", "value": 100, "id": "60"}, {"name": "Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]", "value": 100, "id": "65"}, {"name": "Isospectrality", "value": 100, "id": "53"}, {"name": "Elliptic genera", "value": 100, "id": "26"}, {"name": "Index theory and related fixed point theorems [See also 19K56, 46L80]", "value": 100, "id": "20"}, {"name": "Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]", "value": 100, "id": "22"}, {"name": "Elliptic equations on manifolds, general theory [See also 35-XX]", "value": 100, "id": "05"}, {"name": "Propagation of singularities; initial value problems", "value": 100, "id": "47"}, {"name": "Hyperbolic equations [See also 35Lxx]", "value": 100, "id": "45"}, {"name": "Eta-invariants, Chern-Simons invariants", "value": 100, "id": "28"}, {"name": "Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Correspondences and other transformation methods (e.g. Lie-Backlund) [See also 35A22]", "value": 100, "id": "72"}, {"name": "Invariance and symmetry properties [See also 35A30]", "value": 100, "id": "70"}, {"name": "Applications", "value": 100, "id": "90"}, {"name": "Differential complexes [See also 35Nxx]; elliptic complexes", "value": 100, "id": "10"}, {"name": "Relations with hyperfunctions", "value": 100, "id": "15"}, {"name": "Bifurcation [See also 35B32]", "value": 100, "id": "55"}, {"name": "Boundary value problems on manifolds", "value": 100, "id": "32"}, {"name": "Spectral flows", "value": 100, "id": "30"}, {"name": "Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity", "value": 100, "id": "51"}, {"name": "Spectral problems; spectral geometry; scattering theory [See also 35Pxx]", "value": 100, "id": "50"}, {"name": "Heat and other parabolic equation methods", "value": 100, "id": "35"}, {"name": "Determinants and determinant bundles, analytic torsion", "value": 100, "id": "52"}, {"name": "Perturbations; asymptotics", "value": 100, "id": "37"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "Z", "name": "Applications to physics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications to physics", "value": 100, "id": "05"}]}]}, {"id": "49", "name": "Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]", "children": [{"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "K", "name": "Optimality conditions", "children": [{"name": "Free problems in two or more independent variables", "value": 100, "id": "10"}, {"name": "Problems in abstract spaces [See also 90C48, 93C25]", "value": 100, "id": "27"}, {"name": "Problems involving partial differential equations", "value": 100, "id": "20"}, {"name": "Problems involving 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"Optimal control problems involving relations other than differential equations", "value": 100, "id": "21"}, {"name": "Free problems in one independent variable", "value": 100, "id": "05"}, {"name": "Problems involving randomness [See also 93E20]", "value": 100, "id": "55"}, {"name": "Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)", "value": 100, "id": "30"}, {"name": "Methods involving semicontinuity and convergence; relaxation", "value": 100, "id": "45"}, {"name": "Minimax problems", "value": 100, "id": "35"}, {"name": "Frechet and Gateaux differentiability [See also 46G05, 58C20]", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Variational methods including variational inequalities [See also 47J20]", "value": 100, "id": "40"}, {"name": "Optimal control problems involving ordinary differential equations", "value": 100, "id": "15"}, {"name": "Nonsmooth analysis [See also 46G05, 58C50, 90C56]", "value": 100, "id": "52"}, {"name": "Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]", "value": 100, "id": "53"}]}, {"id": "M", "name": "Numerical methods [See also 90Cxx, 65Kxx]", "children": [{"name": "Discrete approximations", "value": 100, "id": "25"}, {"name": "Decomposition methods", "value": 100, "id": "27"}, {"name": "Methods of relaxation type", "value": 100, "id": "20"}, {"name": "Methods based on necessary conditions", "value": 100, "id": "05"}, {"name": "Other methods", "value": 100, "id": "30"}, {"name": "Methods of nonlinear programming type [See also 90C30, 65Kxx]", "value": 100, "id": "37"}, {"name": "Methods involving duality", "value": 100, "id": "29"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Newton-type methods", "value": 100, "id": "15"}]}, {"id": "L", "name": "Hamilton-Jacobi theories, including dynamic programming", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Viscosity solutions", "value": 100, "id": "25"}, {"name": "Dynamic programming method", "value": 100, "id": "20"}]}, {"id": "N", "name": "Miscellaneous topics", "children": [{"name": "Linear-quadratic problems", "value": 100, "id": "10"}, {"name": "Inverse problems", "value": 100, "id": "45"}, {"name": "Periodic optimization", "value": 100, "id": "20"}, {"name": "Impulsive optimal control problems", "value": 100, "id": "25"}, {"name": "Problems with incomplete information [See also 93C41]", "value": 100, "id": "30"}, {"name": "Optimal feedback synthesis [See also 93B52]", "value": 100, "id": "35"}, {"name": "Regularity of solutions", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Pursuit and evasion games", "value": 100, "id": "75"}, {"name": "Differential games", "value": 100, "id": "70"}, {"name": "Duality theory", "value": 100, "id": "15"}, {"name": "Linear optimal control problems [See also 93C05]", "value": 100, "id": "05"}, {"name": "Applications of optimal control and differential games [See also 90C90, 93C95]", "value": 100, "id": "90"}]}, {"id": "Q", "name": "Manifolds [See also 58Exx]", "children": [{"name": "Optimization of shapes other than minimal surfaces [See also 90C90]", "value": 100, "id": "10"}, {"name": "Sensitivity analysis", "value": 100, "id": "12"}, {"name": "Variational problems in a geometric measure-theoretic setting", "value": 100, "id": "20"}, {"name": "Minimal surfaces [See also 53A10, 58E12]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]", "value": 100, "id": "15"}]}, {"id": "S", "name": "Variational principles of physics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Variational 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47A75]", "value": 100, "id": "05"}]}, {"id": "B", "name": "Fredholm integral equations", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Fredholm integral equations", "value": 100, "id": "05"}]}, {"id": "E", "name": "Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]", "value": 100, "id": "10"}, {"name": "Integral equations with kernels of Cauchy type [See also 35J15]", "value": 100, "id": "05"}]}, {"id": "D", "name": "Volterra integral equations [See also 34A12]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Volterra integral equations [See also 34A12]", "value": 100, "id": "05"}]}, {"id": "G", "name": "Nonlinear integral equations [See also 47H30, 47Jxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other nonlinear integral equations", "value": 100, "id": "10"}, {"name": "Systems of nonlinear integral equations", "value": 100, "id": "15"}, {"name": "Singular nonlinear integral equations", "value": 100, "id": "05"}]}, {"id": "F", "name": "Systems of linear integral equations", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Dual, triple, etc., integral and series equations", "value": 100, "id": "10"}, {"name": "Systems of singular linear integral equations", "value": 100, "id": "15"}, {"name": "Systems of nonsingular linear integral equations", "value": 100, "id": "05"}]}, {"id": "H", "name": "Miscellaneous special kernels [See also 44A15]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Miscellaneous special kernels [See also 44A15]", "value": 100, "id": "05"}]}, {"id": "K", "name": "Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]", "value": 100, "id": "05"}]}, {"id": "J", "name": "Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]", "value": 100, "id": "05"}]}, {"id": "M", "name": "Qualitative behavior", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Stability theory", "value": 100, "id": "10"}, {"name": "Asymptotics", "value": 100, "id": "05"}, {"name": "Periodic solutions", "value": 100, "id": "15"}, {"name": "Positive solutions", "value": 100, "id": "20"}]}, {"id": "L", "name": "Theoretical approximation of solutions {For numerical analysis, see 65Rxx}", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Theoretical approximation of solutions {For numerical analysis, see 65Rxx}", "value": 100, "id": "05"}]}, {"id": "N", "name": "Abstract integral equations, integral equations in abstract spaces", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Abstract integral equations, integral equations in abstract spaces", "value": 100, "id": "05"}]}, {"id": "Q", "name": "Inverse problems", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inverse problems", "value": 100, "id": "05"}]}, {"id": "P", "name": "Integral operators [See also 47B38, 47G10]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integral operators [See also 47B38, 47G10]", "value": 100, "id": "05"}]}, {"id": "R", "name": "Random integral equations [See also 60H20]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Random integral equations [See also 60H20]", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "37", "name": "Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]", "children": [{"id": "A", "name": "Ergodic theory [See also 28Dxx]", "children": [{"name": "One-parameter continuous families of measure-preserving transformations", "value": 100, "id": "10"}, {"name": "Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}", "value": 100, "id": "30"}, {"name": "Orbit equivalence, cocycles, ergodic equivalence relations", "value": 100, "id": "20"}, {"name": "Homogeneous flows [See also 22Fxx]", "value": 100, "id": "17"}, {"name": "Ergodicity, mixing, rates of mixing", "value": 100, "id": "25"}, {"name": "Relations with the theory of $C^*$-algebras [See mainly 46L55]", "value": 100, "id": "55"}, {"name": "Relations with number theory and harmonic analysis [See also 11Kxx]", "value": 100, "id": "45"}, {"name": "Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]", "value": 100, "id": "50"}, {"name": "Entropy and other invariants, isomorphism, classification", "value": 100, "id": "35"}, {"name": "Dynamical systems in statistical mechanics [See also 82Cxx]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonsingular (and infinite-measure preserving) transformations", "value": 100, "id": "40"}, {"name": "General groups of measure-preserving transformations [See mainly 22Fxx]", "value": 100, "id": "15"}, {"name": "Measure-preserving transformations", "value": 100, "id": "05"}]}, {"id": "C", "name": "Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]", "children": [{"name": "Vector fields, flows, ordinary differential equations", "value": 100, "id": "10"}, {"name": "Dimension theory of dynamical systems", "value": 100, "id": "45"}, {"name": "Periodic orbits of vector fields and flows", "value": 100, "id": "27"}, {"name": "Topological and differentiable equivalence, conjugacy, invariants, moduli, classification", "value": 100, "id": "15"}, {"name": "Fixed points, periodic points, fixed-point index theory", "value": 100, "id": "25"}, {"name": "Periodic and quasiperiodic flows and diffeomorphisms", "value": 100, "id": "55"}, {"name": "Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems", "value": 100, "id": "30"}, {"name": "Homoclinic and heteroclinic orbits", "value": 100, "id": "29"}, {"name": "Orbit growth", "value": 100, "id": "35"}, {"name": "Approximate trajectories (pseudotrajectories, shadowing, etc.)", "value": 100, "id": "50"}, {"name": "Nonautonomous smooth dynamical systems [See also 37B55]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Stability theory", "value": 100, "id": "75"}, {"name": "Smooth ergodic theory, invariant measures [See also 37Dxx]", "value": 100, "id": "40"}, {"name": "Attractors and repellers, topological structure", "value": 100, "id": "70"}, {"name": "Generic properties, structural stability", "value": 100, "id": "20"}, {"name": "Symmetries, equivariant dynamical systems", "value": 100, "id": "80"}, {"name": "Dynamics of group actions other than ${\\bf Z}$ and ${\\bf R}$, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]", "value": 100, "id": "85"}, {"name": "Smooth mappings and diffeomorphisms", "value": 100, "id": "05"}, {"name": "Monotone flows", "value": 100, "id": "65"}]}, {"id": "B", "name": "Topological dynamics [See also 54H20]", "children": [{"name": "Symbolic dynamics [See also 37Cxx, 37Dxx]", "value": 100, "id": "10"}, {"name": "Continua theory in dynamics", "value": 100, "id": "45"}, {"name": "Notions of recurrence", "value": 100, "id": "20"}, {"name": "Lyapunov functions and stability; attractors, repellers", "value": 100, "id": "25"}, {"name": "Nonautonomous dynamical systems", "value": 100, "id": "55"}, {"name": "Index theory, Morse-Conley indices", "value": 100, "id": "30"}, {"name": "Multi-dimensional shifts of finite type, tiling dynamics", "value": 100, "id": "50"}, {"name": "Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Topological entropy", "value": 100, "id": "40"}, {"name": "Cellular automata [See also 68Q80]", "value": 100, "id": "15"}, {"name": "Transformations and group actions with special properties (minimality, distality, proximality, etc.)", "value": 100, "id": "05"}]}, {"id": "E", "name": "Low-dimensional dynamical systems", "children": [{"name": "Maps of the circle", "value": 100, "id": "10"}, {"name": "Rotation numbers and vectors", "value": 100, "id": "45"}, {"name": "Universality, renormalization [See also 37F25]", "value": 100, "id": "20"}, {"name": "Maps of trees and graphs", "value": 100, "id": "25"}, {"name": "Homeomorphisms and diffeomorphisms of planes and surfaces", "value": 100, "id": "30"}, {"name": "Flows on surfaces", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Twist maps", "value": 100, "id": "40"}, {"name": "Combinatorial dynamics (types of periodic orbits)", "value": 100, "id": "15"}, {"name": "Maps of the interval (piecewise continuous, continuous, smooth)", "value": 100, "id": "05"}]}, {"id": "D", "name": "Dynamical systems with hyperbolic behavior", "children": [{"name": "Invariant manifold theory", "value": 100, "id": "10"}, {"name": "Strange attractors, chaotic dynamics", "value": 100, "id": "45"}, {"name": "Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)", "value": 100, "id": "20"}, {"name": "Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)", "value": 100, "id": "25"}, {"name": "Partially hyperbolic systems and dominated splittings", "value": 100, "id": "30"}, {"name": "Hyperbolic systems with singularities (billiards, etc.)", "value": 100, "id": "50"}, {"name": "Thermodynamic formalism, variational principles, equilibrium states", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)", "value": 100, "id": "40"}, {"name": "Morse-Smale systems", "value": 100, "id": "15"}, {"name": "Hyperbolic orbits and sets", "value": 100, "id": "05"}]}, {"id": "G", "name": "Local and nonlocal bifurcation theory [See also 34C23, 34K18]", "children": [{"name": "Bifurcations of singular points", "value": 100, "id": "10"}, {"name": "Hyperbolic singular points with homoclinic trajectories", "value": 100, "id": "20"}, {"name": "Bifurcations connected with nontransversal intersection", "value": 100, "id": "25"}, {"name": "Infinite nonwandering sets arising in bifurcations", "value": 100, "id": "30"}, {"name": "Attractors and their bifurcations", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Symmetries, equivariant bifurcation theory", "value": 100, "id": "40"}, {"name": "Bifurcations of limit cycles and periodic orbits", "value": 100, "id": "15"}, {"name": "Normal forms", "value": 100, "id": "05"}]}, {"id": "F", "name": "Complex dynamical systems [See also 30D05, 32H50]", "children": [{"name": "Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]", "value": 100, "id": "10"}, {"name": "Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations", "value": 100, "id": "45"}, {"name": "Combinatorics and topology", "value": 100, "id": "20"}, {"name": "Renormalization", "value": 100, "id": "25"}, {"name": "Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as dynamical systems", "value": 100, "id": "30"}, {"name": "Small divisors, rotation domains and linearization; Fatou and Julia sets", "value": 100, "id": "50"}, {"name": "Conformal densities and Hausdorff dimension", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]", "value": 100, "id": "75"}, {"name": "Geometric limits", "value": 100, "id": "40"}, {"name": "Expanding maps; hyperbolicity; structural stability", "value": 100, "id": "15"}, {"name": "Relations and correspondences", "value": 100, "id": "05"}]}, {"id": "H", "name": "Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]", "value": 100, "id": "10"}, {"name": "Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]", "value": 100, "id": "05"}, {"name": "Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]", "value": 100, "id": "15"}, {"name": "Bifurcation theory [See also 37Gxx]", "value": 100, "id": "20"}]}, {"id": "K", "name": "Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]", "children": [{"name": "Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)", "value": 100, "id": "10"}, {"name": "Stability problems", "value": 100, "id": "45"}, {"name": "Relations with algebraic geometry, complex analysis, special functions [See also 14H70]", "value": 100, "id": "20"}, {"name": "Relations with differential geometry", "value": 100, "id": "25"}, {"name": "Perturbations, KAM for infinite-dimensional systems", "value": 100, "id": "55"}, {"name": "Relations with infinite-dimensional Lie algebras and other algebraic structures", "value": 100, "id": "30"}, {"name": "Bifurcation problems", "value": 100, "id": "50"}, {"name": "Lie-Backlund and other transformations", "value": 100, "id": "35"}, {"name": "Lattice dynamics [See also 37L60]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Soliton theory, asymptotic behavior of solutions", "value": 100, "id": "40"}, {"name": "Integration of completely integrable systems by inverse spectral and scattering methods", "value": 100, "id": "15"}, {"name": "Hamiltonian structures, symmetries, variational principles, conservation laws", "value": 100, "id": "05"}, {"name": "Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics", "value": 100, "id": "65"}]}, {"id": "J", "name": "Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]", "children": [{"name": "Symplectic mappings, fixed points", "value": 100, "id": "10"}, {"name": "Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods", "value": 100, "id": "45"}, {"name": "Bifurcation problems", "value": 100, "id": "20"}, {"name": "Stability problems", "value": 100, "id": "25"}, {"name": "Contact systems [See also 53D10]", "value": 100, "id": "55"}, {"name": "Obstructions to integrability (nonintegrability criteria)", "value": 100, "id": "30"}, {"name": "Action-minimizing orbits and measures", "value": 100, "id": "50"}, {"name": "Completely integrable systems, topological structure of phase space, integration methods", "value": 100, "id": "35"}, {"name": "Nonholonomic dynamical systems [See also 70F25]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion", "value": 100, "id": "40"}, {"name": "Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]", "value": 100, "id": "15"}, {"name": "General theory, relations with symplectic geometry and topology", "value": 100, "id": "05"}]}, {"id": "M", "name": "Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]", "children": [{"name": "Time series analysis", "value": 100, "id": "10"}, {"name": "Symplectic integrators", "value": 100, "id": "15"}, {"name": "Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)", "value": 100, "id": "25"}, {"name": "Simulation", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Computational methods for bifurcation problems", "value": 100, "id": "20"}]}, {"id": "L", "name": "Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]", "children": [{"name": "Normal forms, center manifold theory, bifurcation theory", "value": 100, "id": "10"}, {"name": "Hyperbolicity; Lyapunov functions", "value": 100, "id": "45"}, {"name": "Symmetries", "value": 100, "id": "20"}, {"name": "Inertial manifolds and other invariant attracting sets", "value": 100, "id": "25"}, {"name": "Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]", "value": 100, "id": "55"}, {"name": "Attractors and their dimensions, Lyapunov exponents", "value": 100, "id": "30"}, {"name": "Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems", "value": 100, "id": "50"}, {"name": "Invariant measures", "value": 100, "id": "40"}, {"name": "Lattice dynamics [See also 37K60]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Special approximation methods (nonlinear Galerkin, etc.)", "value": 100, "id": "65"}, {"name": "Stability problems", "value": 100, "id": "15"}, {"name": "General theory, nonlinear semigroups, evolution equations", "value": 100, "id": "05"}]}, {"id": "N", "name": "Applications", "children": [{"name": "Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]", "value": 100, "id": "10"}, {"name": "Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)", "value": 100, "id": "20"}, {"name": "Dynamical systems in biology [See mainly 92-XX, but also 91-XX]", "value": 100, "id": "25"}, {"name": "Dynamical systems in numerical analysis", "value": 100, "id": "30"}, {"name": "Dynamical systems in control", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Dynamical systems in optimization and economics", "value": 100, "id": "40"}, {"name": "Dynamical systems in solid mechanics [See mainly 74Hxx]", "value": 100, "id": "15"}, {"name": "Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "P", "name": "Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45]", "children": [{"name": "Analytic and meromorphic maps", "value": 100, "id": "10"}, {"name": "Families and moduli spaces", "value": 100, "id": "45"}, {"name": "Non-Archimedean local ground fields", "value": 100, "id": "20"}, {"name": "Finite ground fields", "value": 100, "id": "25"}, {"name": "Arithmetic dynamics on general algebraic varieties", "value": 100, "id": "55"}, {"name": "Height functions; Green functions; invariant measures [See also 11G50, 14G40]", "value": 100, "id": "30"}, {"name": "Dynamical systems on Berkovich spaces", "value": 100, "id": "50"}, {"name": "Arithmetic properties of periodic points", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Non-Archimedean Fatou and Julia sets", "value": 100, "id": "40"}, {"name": "Global ground fields", "value": 100, "id": "15"}, {"name": "Polynomial and rational maps", "value": 100, "id": "05"}]}]}, {"id": "35", "name": "Partial differential equations", "children": [{"id": "A", "name": "General topics", "children": [{"name": "Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness", "value": 100, "id": "02"}, {"name": "Cauchy-Kovalevskaya theorems", "value": 100, "id": "10"}, {"name": "Existence problems: global existence, local existence, non-existence", "value": 100, "id": "01"}, {"name": "Variational methods", "value": 100, "id": "15"}, {"name": "Propagation of singularities", "value": 100, "id": "21"}, {"name": "Parametrices", "value": 100, "id": "17"}, {"name": "Inequalities involving derivatives and differential and integral operators, inequalities for integrals", "value": 100, "id": "23"}, {"name": "Wave front sets", "value": 100, "id": "18"}, {"name": "Fundamental solutions", "value": 100, "id": "08"}, {"name": "Topological and monotonicity methods", "value": 100, "id": "16"}, {"name": "Transform methods (e.g. integral transforms)", "value": 100, "id": "22"}, {"name": "Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx}", "value": 100, "id": "35"}, {"name": "Analytic methods, singularities", "value": 100, "id": "20"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]", "value": 100, "id": "27"}, {"name": "Classical solutions", "value": 100, "id": "09"}, {"name": "Methods of ordinary differential equations", "value": 100, "id": "24"}, {"name": "Geometric theory, characteristics, transformations [See also 58J70, 58J72]", "value": 100, "id": "30"}, {"name": "Other special methods", "value": 100, "id": "25"}]}, {"id": "C", "name": "Representations of solutions", "children": [{"name": "Polynomial solutions", "value": 100, "id": "11"}, {"name": "Series solutions", "value": 100, "id": "10"}, {"name": "Self-similar solutions", "value": 100, "id": "06"}, {"name": "Traveling wave solutions", "value": 100, "id": "07"}, {"name": "Solutions in closed form", "value": 100, "id": "05"}, {"name": "Soliton solutions", "value": 100, "id": "08"}, {"name": "Trigonometric solutions", "value": 100, "id": "09"}, {"name": "Asymptotic expansions", "value": 100, "id": "20"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integral representations of solutions", "value": 100, "id": "15"}]}, {"id": "B", "name": "Qualitative properties of solutions", "children": [{"name": "A priori estimates", "value": 100, "id": "45"}, {"name": "Maximum principles", "value": 100, "id": "50"}, {"name": "Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]", "value": 100, "id": "60"}, {"name": "Liouville theorems, Phragmen-Lindelof theorems", "value": 100, "id": "53"}, {"name": "Singular perturbations", "value": 100, "id": "25"}, {"name": "Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]", "value": 100, "id": "27"}, {"name": "Perturbations", "value": 100, "id": "20"}, {"name": "Axially symmetric solutions", "value": 100, "id": "07"}, {"name": "Oscillation, zeros of solutions, mean value theorems, etc.", "value": 100, "id": "05"}, {"name": "Entire solutions", "value": 100, "id": "08"}, {"name": "Positive solutions", "value": 100, "id": "09"}, {"name": "Inertial manifolds", "value": 100, "id": "42"}, {"name": "Asymptotic behavior of solutions", "value": 100, "id": "40"}, {"name": "Attractors", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Symmetries, invariants, etc.", "value": 100, "id": "06"}, {"name": "Periodic solutions", "value": 100, "id": "10"}, {"name": "Critical points", "value": 100, "id": "38"}, {"name": "Almost and pseudo-almost periodic solutions", "value": 100, "id": "15"}, {"name": "Critical exponents", "value": 100, "id": "33"}, {"name": "Bifurcation [See also 37Gxx, 37K50]", "value": 100, "id": "32"}, {"name": "Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]", "value": 100, "id": "30"}, {"name": "Comparison principles", "value": 100, "id": "51"}, {"name": "Pattern formation", "value": 100, "id": "36"}, {"name": "Stability", "value": 100, "id": "35"}, {"name": "Resonances", "value": 100, "id": "34"}, {"name": "Blow-up", "value": 100, "id": "44"}, {"name": "Smoothness and regularity of solutions", "value": 100, "id": "65"}]}, {"id": "E", "name": "Equations and systems with constant coefficients [See also 35N05]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Convexity properties", "value": 100, "id": "10"}, {"name": "Fundamental solutions", "value": 100, "id": "05"}, {"name": "Initial value problems", "value": 100, "id": "15"}, {"name": "General theory", "value": 100, "id": "20"}]}, {"id": "D", "name": "Generalized solutions", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Weak solutions", "value": 100, "id": "30"}, {"name": "Viscosity solutions", "value": 100, "id": "40"}, {"name": "Strong solutions", "value": 100, "id": "35"}]}, {"id": "G", "name": "General higher-order equations and systems", "children": [{"name": "Initial value problems for linear higher-order equations", "value": 100, "id": "10"}, {"name": "Boundary value problems for nonlinear higher-order equations", "value": 100, "id": "30"}, {"name": "Nonlinear higher-order equations", "value": 100, "id": "20"}, {"name": "Initial-boundary value problems for linear higher-order equations", "value": 100, "id": "16"}, {"name": "Initial-boundary value problems for linear higher-order systems", "value": 100, "id": "46"}, {"name": "Initial-boundary value problems for nonlinear higher-order equations", "value": 100, "id": "31"}, {"name": "Boundary value problems for linear higher-order systems", "value": 100, "id": "45"}, {"name": "Initial-boundary value problems for nonlinear higher-order systems", "value": 100, "id": "61"}, {"name": "Nonlinear higher-order systems", "value": 100, "id": "50"}, {"name": "Linear higher-order systems", "value": 100, "id": "35"}, {"name": "Boundary value problems for nonlinear higher-order systems", "value": 100, "id": "60"}, {"name": "Initial value problems for nonlinear higher-order systems", "value": 100, "id": "55"}, {"name": "Initial value problems for nonlinear higher-order equations", "value": 100, "id": "25"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Boundary value problems for linear higher-order equations", "value": 100, "id": "15"}, {"name": "Initial value problems for linear higher-order systems", "value": 100, "id": "40"}, {"name": "Linear higher-order equations", "value": 100, "id": "05"}]}, {"id": "F", "name": "General first-order equations and systems", "children": [{"name": "Initial value problems for linear first-order equations", "value": 100, "id": "10"}, {"name": "Boundary value problems for nonlinear first-order equations", "value": 100, "id": "30"}, {"name": "Nonlinear first-order equations", "value": 100, "id": "20"}, {"name": "Hamilton-Jacobi equations", "value": 100, "id": "21"}, {"name": "Initial-boundary value problems for linear first-order equations", "value": 100, "id": "16"}, {"name": "Initial-boundary value problems for linear first-order systems", "value": 100, "id": "46"}, {"name": "Initial-boundary value problems for nonlinear first-order equations", "value": 100, "id": "31"}, {"name": "Boundary value problems for linear first-order systems", "value": 100, "id": "45"}, {"name": "Initial-boundary value problems for nonlinear first-order systems", "value": 100, "id": "61"}, {"name": "Nonlinear first-order systems", "value": 100, "id": "50"}, {"name": "Linear first-order systems", "value": 100, "id": "35"}, {"name": "Boundary value problems for nonlinear first-order systems", "value": 100, "id": "60"}, {"name": "Initial value problems for nonlinear first-order systems", "value": 100, "id": "55"}, {"name": "Initial value problems for nonlinear first-order equations", "value": 100, "id": "25"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Boundary value problems for linear first-order equations", "value": 100, "id": "15"}, {"name": "Initial value problems for linear first-order systems", "value": 100, "id": "40"}, {"name": "Linear first-order equations", "value": 100, "id": "05"}]}, {"id": "H", "name": "Close-to-elliptic equations and systems", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Hypoelliptic equations", "value": 100, "id": "10"}, {"name": "Quasi-elliptic equations", "value": 100, "id": "30"}, {"name": "Subelliptic equations", "value": 100, "id": "20"}]}, {"id": "K", "name": "Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]", "children": [{"name": "Nonlinear initial value problems for linear parabolic equations", "value": 100, "id": "60"}, {"name": "Nonlinear initial-boundary value problems for nonlinear parabolic equations", "value": 100, "id": "61"}, {"name": "Degenerate parabolic equations", "value": 100, "id": "65"}, {"name": "Singular parabolic equations", "value": 100, "id": "67"}, {"name": "Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "86"}, {"name": "Systems of parabolic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "87"}, {"name": "Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "85"}, {"name": "Higher-order parabolic equations", "value": 100, "id": "25"}, {"name": "Initial-boundary value problems for second-order parabolic equations", "value": 100, "id": "20"}, {"name": "Heat equation", "value": 100, "id": "05"}, {"name": "Initial value problems for higher-order parabolic systems", "value": 100, "id": "46"}, {"name": "Heat kernel", "value": 100, "id": "08"}, {"name": "Initial value problems for second-order parabolic systems", "value": 100, "id": "45"}, {"name": "Second-order parabolic systems", "value": 100, "id": "40"}, {"name": "Higher-order parabolic systems", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ultraparabolic equations, pseudoparabolic equations, etc.", "value": 100, "id": "70"}, {"name": "Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian", "value": 100, "id": "91"}, {"name": "Quasilinear parabolic equations", "value": 100, "id": "59"}, {"name": "Quasilinear parabolic equations with mean curvature operator", "value": 100, "id": "93"}, {"name": "Quasilinear parabolic equations with $p$-Laplacian", "value": 100, "id": "92"}, {"name": "Parabolic Monge-Ampere equations", "value": 100, "id": "96"}, {"name": "Second-order parabolic equations", "value": 100, "id": "10"}, {"name": "Initial value problems for second-order parabolic equations", "value": 100, "id": "15"}, {"name": "Semilinear parabolic equations", "value": 100, "id": "58"}, {"name": "Nonlinear parabolic equations", "value": 100, "id": "55"}, {"name": "Reaction-diffusion equations", "value": 100, "id": "57"}, {"name": "Initial value problems for higher-order parabolic equations", "value": 100, "id": "30"}, {"name": "Initial-boundary value problems for second-order parabolic systems", "value": 100, "id": "51"}, {"name": "Initial-boundary value problems for higher-order parabolic equations", "value": 100, "id": "35"}, {"name": "Initial-boundary value problems for higher-order parabolic systems", "value": 100, "id": "52"}, {"name": "Abstract parabolic equations", "value": 100, "id": "90"}]}, {"id": "J", "name": "Elliptic equations and systems [See also 58J10, 58J20]", "children": [{"name": "Boundary value problems for first-order elliptic systems", "value": 100, "id": "56"}, {"name": "Nonlinear elliptic equations", "value": 100, "id": "60"}, {"name": "Semilinear elliptic equations", "value": 100, "id": "61"}, {"name": "Quasilinear elliptic equations", "value": 100, "id": "62"}, {"name": "Nonlinear boundary value problems for linear elliptic equations", "value": 100, "id": "65"}, {"name": "Nonlinear boundary value problems for nonlinear elliptic equations", "value": 100, "id": "66"}, {"name": "Boundary values of solutions to elliptic equations", "value": 100, "id": "67"}, {"name": "Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "86"}, {"name": "Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "87"}, {"name": "Boundary value problems for second-order elliptic equations", "value": 100, "id": "25"}, {"name": "Variational methods for second-order elliptic equations", "value": 100, "id": "20"}, {"name": "Higher-order elliptic systems", "value": 100, "id": "48"}, {"name": "Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]", "value": 100, "id": "05"}, {"name": "First-order elliptic systems", "value": 100, "id": "46"}, {"name": "Second-order elliptic systems", "value": 100, "id": "47"}, {"name": "Green's functions", "value": 100, "id": "08"}, {"name": "Boundary value problems for higher-order elliptic equations", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Singular elliptic equations", "value": 100, "id": "75"}, {"name": "Degenerate elliptic equations", "value": 100, "id": "70"}, {"name": "Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian", "value": 100, "id": "91"}, {"name": "Quasilinear elliptic equations with mean curvature operator", "value": 100, "id": "93"}, {"name": "Quasilinear elliptic equations with $p$-Laplacian", "value": 100, "id": "92"}, {"name": "Elliptic Monge-Ampere equations", "value": 100, "id": "96"}, {"name": "Schrodinger operator [See also 35Pxx]", "value": 100, "id": "10"}, {"name": "Second-order elliptic equations", "value": 100, "id": "15"}, {"name": "Boundary value problems for higher-order elliptic systems", "value": 100, "id": "58"}, {"name": "Boundary value problems for second-order elliptic systems", "value": 100, "id": "57"}, {"name": "Higher-order elliptic equations [See also 31A30, 31B30]", "value": 100, "id": "30"}, {"name": "Variational methods for elliptic systems", "value": 100, "id": "50"}, {"name": "Variational methods for higher-order elliptic equations", "value": 100, "id": "35"}, {"name": "Systems of elliptic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "88"}]}, {"id": "M", "name": "Equations and systems of special type (mixed, composite, etc.)", "children": [{"name": "Initial value problems for equations of mixed type", "value": 100, "id": "11"}, {"name": "Equations of mixed type", "value": 100, "id": "10"}, {"name": "Initial-boundary value problems for equations of mixed type", "value": 100, "id": "13"}, {"name": "Boundary value problems for equations of mixed type", "value": 100, "id": "12"}, {"name": "Initial-boundary value problems for systems of mixed type", "value": 100, "id": "33"}, {"name": "Boundary value problems for systems of mixed type", "value": 100, "id": "32"}, {"name": "Initial value problems for systems of mixed type", "value": 100, "id": "31"}, {"name": "Systems of mixed type", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40]", "value": 100, "id": "86"}, {"name": "Systems of variational inequalities of mixed type [See also 35R35, 49J40]", "value": 100, "id": "87"}, {"name": "Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40]", "value": 100, "id": "85"}]}, {"id": "L", "name": "Hyperbolic equations and systems [See also 58J45]", "children": [{"name": "Initial value problems for higher-order hyperbolic systems", "value": 100, "id": "56"}, {"name": "Nonlinear first-order hyperbolic equations", "value": 100, "id": "60"}, {"name": "Initial-boundary value problems for second-order hyperbolic systems", "value": 100, "id": "53"}, {"name": "Shocks and singularities [See also 58Kxx, 76L05]", "value": 100, "id": "67"}, {"name": "Pseudohyperbolic equations", "value": 100, "id": "82"}, {"name": "Degenerate hyperbolic equations", "value": 100, "id": "80"}, {"name": "Singular hyperbolic equations", "value": 100, "id": "81"}, {"name": "Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "86"}, {"name": "Unilateral problems and variational inequalities for hyperbolic systems [See also 35R35, 49J40]", "value": 100, "id": "87"}, {"name": "Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]", "value": 100, "id": "85"}, {"name": "First-order hyperbolic equations", "value": 100, "id": "02"}, {"name": "Initial value problems for first-order hyperbolic equations", "value": 100, "id": "03"}, {"name": "Initial-boundary value problems for second-order hyperbolic equations", "value": 100, "id": "20"}, {"name": "Initial-boundary value problems for first-order hyperbolic equations", "value": 100, "id": "04"}, {"name": "Wave equation", "value": 100, "id": "05"}, {"name": "Initial value problems for first-order hyperbolic systems", "value": 100, "id": "45"}, {"name": "First-order hyperbolic systems", "value": 100, "id": "40"}, {"name": "Higher-order hyperbolic equations", "value": 100, "id": "25"}, {"name": "Quasilinear higher-order hyperbolic equations", "value": 100, "id": "77"}, {"name": "Semilinear higher-order hyperbolic equations", "value": 100, "id": "76"}, {"name": "Nonlinear higher-order hyperbolic equations", "value": 100, "id": "75"}, {"name": "Quasilinear second-order hyperbolic equations", "value": 100, "id": "72"}, {"name": "Semilinear second-order hyperbolic equations", "value": 100, "id": "71"}, {"name": "Nonlinear second-order hyperbolic equations", "value": 100, "id": "70"}, {"name": "Abstract hyperbolic equations", "value": 100, "id": "90"}, {"name": "Second-order hyperbolic equations", "value": 100, "id": "10"}, {"name": "Initial value problems for second-order hyperbolic equations", "value": 100, "id": "15"}, {"name": "Higher-order hyperbolic systems", "value": 100, "id": "55"}, {"name": "Initial-boundary value problems for higher-order hyperbolic systems", "value": 100, "id": "57"}, {"name": "Initial value problems for higher-order hyperbolic equations", "value": 100, "id": "30"}, {"name": "Second-order hyperbolic systems", "value": 100, "id": "51"}, {"name": "Initial-boundary value problems for first-order hyperbolic systems", "value": 100, "id": "50"}, {"name": "Initial-boundary value problems for higher-order hyperbolic equations", "value": 100, "id": "35"}, {"name": "Initial value problems for second-order hyperbolic systems", "value": 100, "id": "52"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Conservation laws", "value": 100, "id": "65"}]}, {"id": "N", "name": "Overdetermined systems [See also 58Hxx, 58J10, 58J15]", "children": [{"name": "Overdetermined systems with variable coefficients", "value": 100, "id": "10"}, {"name": "Overdetermined initial value problems", "value": 100, "id": "20"}, {"name": "Overdetermined boundary value problems", "value": 100, "id": "25"}, {"name": "Overdetermined initial-boundary value problems", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$\\overline\\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]", "value": 100, "id": "15"}, {"name": "Overdetermined systems with constant coefficients", "value": 100, "id": "05"}]}, {"id": "Q", "name": "Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]", "children": [{"name": "Navier-Stokes equations [See also 76D05, 76D07, 76N10]", "value": 100, "id": "30"}, {"name": "PDEs in connection with optics and electromagnetic theory", "value": 100, "id": "60"}, {"name": "Maxwell equations", "value": 100, "id": "61"}, {"name": "PDEs in connection with statistics", "value": 100, "id": "62"}, {"name": "KdV-like equations (Korteweg-de Vries) [See also 37K10]", "value": 100, "id": "53"}, {"name": "PDEs in connection with computer science", "value": 100, "id": "68"}, {"name": "Vlasov-like equations", "value": 100, "id": "83"}, {"name": "PDEs in connection with geophysics", "value": 100, "id": "86"}, {"name": "Fokker-Planck equations", "value": 100, "id": "84"}, {"name": "PDEs in connection with astronomy and astrophysics", "value": 100, "id": "85"}, {"name": "Boltzmann equations", "value": 100, "id": "20"}, {"name": "Euler-Poisson-Darboux equations", "value": 100, "id": "05"}, {"name": "PDEs in connection with statistical mechanics", "value": 100, "id": "82"}, {"name": "PDEs in connection with quantum mechanics", "value": 100, "id": "40"}, {"name": "Time-dependent Schrodinger equations, Dirac equations", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Einstein equations", "value": 100, "id": "76"}, {"name": "PDEs in connection with relativity and gravitational theory", "value": 100, "id": "75"}, {"name": "PDEs in connection with mechanics of deformable solids", "value": 100, "id": "74"}, {"name": "PDEs in connection with mechanics of particles and systems", "value": 100, "id": "70"}, {"name": "PDEs in connection with game theory, economics, social and behavioral sciences", "value": 100, "id": "91"}, {"name": "PDEs in connection with mathematical programming", "value": 100, "id": "90"}, {"name": "PDEs in connection with control and optimization", "value": 100, "id": "93"}, {"name": "PDEs in connection with biology and other natural sciences", "value": 100, "id": "92"}, {"name": "PDEs in connection with information and communication", "value": 100, "id": "94"}, {"name": "PDEs in connection with classical thermodynamics and heat transfer", "value": 100, "id": "79"}, {"name": "Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]", "value": 100, "id": "15"}, {"name": "NLS-like equations (nonlinear Schrodinger) [See also 37K10]", "value": 100, "id": "55"}, {"name": "Euler equations [See also 76D05, 76D07, 76N10]", "value": 100, "id": "31"}, {"name": "Ginzburg-Landau equations", "value": 100, "id": "56"}, {"name": "Soliton-like equations [See also 37K40]", "value": 100, "id": "51"}, {"name": "PDEs in connection with fluid mechanics", "value": 100, "id": "35"}]}, {"id": "P", "name": "Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]", "children": [{"name": "Completeness of eigenfunctions, eigenfunction expansions", "value": 100, "id": "10"}, {"name": "Asymptotic distribution of eigenvalues and eigenfunctions", "value": 100, "id": "20"}, {"name": "Scattering theory [See also 47A40]", "value": 100, "id": "25"}, {"name": "Nonlinear eigenvalue problems, nonlinear spectral theory", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Estimation of eigenvalues, upper and lower bounds", "value": 100, "id": "15"}, {"name": "General topics in linear spectral theory", "value": 100, "id": "05"}]}, {"id": "S", "name": "Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]", "children": [{"name": "Initial-boundary value problems for pseudodifferential operators", "value": 100, "id": "11"}, {"name": "Initial value problems for pseudodifferential operators", "value": 100, "id": "10"}, {"name": "Boundary value problems for pseudodifferential operators", "value": 100, "id": "15"}, {"name": "Pseudodifferential operators", "value": 100, "id": "05"}, {"name": "Fourier integral operators", "value": 100, "id": "30"}, {"name": "Paradifferential operators", "value": 100, "id": "50"}, {"name": "Topological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "R", "name": "Miscellaneous topics {For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15}", "children": [{"name": "Partial differential equations on graphs and networks (ramified or polygonal spaces)", "value": 100, "id": "02"}, {"name": "Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.", "value": 100, "id": "03"}, {"name": "Fuzzy partial differential equations", "value": 100, "id": "13"}, {"name": "Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx]", "value": 100, "id": "01"}, {"name": "Partial differential equations with measure", "value": 100, "id": "06"}, {"name": "Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]", "value": 100, "id": "60"}, {"name": "Partial differential equations with discontinuous coefficients or data", "value": 100, "id": "05"}, {"name": "Inverse problems", "value": 100, "id": "30"}, {"name": "Moving boundary problems", "value": 100, "id": "37"}, {"name": "Partial differential inequalities", "value": 100, "id": "45"}, {"name": "Free boundary problems", "value": 100, "id": "35"}, {"name": "Partial differential equations of infinite order", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Impulsive partial differential equations", "value": 100, "id": "12"}, {"name": "Integro-partial differential equations [See also 45Kxx]", "value": 100, "id": "09"}, {"name": "Partial differential equations with multivalued right-hand sides", "value": 100, "id": "70"}, {"name": "Fractional partial differential equations", "value": 100, "id": "11"}, {"name": "Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 4", "value": 100, "id": "20"}, {"name": "Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]", "value": 100, "id": "15"}, {"name": "Improperly posed problems", "value": 100, "id": "25"}, {"name": "Partial functional-differential equations", "value": 100, "id": "10"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "34", "name": "Ordinary differential equations", "children": [{"id": "A", "name": "General theory", "children": [{"name": "Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]", "value": 100, "id": "25"}, {"name": "Geometric methods in differential equations", "value": 100, "id": "26"}, {"name": "Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions", "value": 100, "id": "12"}, {"name": "Fuzzy differential equations", "value": 100, "id": "07"}, {"name": "Explicit solutions and reductions", "value": 100, "id": "05"}, {"name": "Lattice differential equations", "value": 100, "id": "33"}, {"name": "Fractional differential equations", "value": 100, "id": "08"}, {"name": "Implicit equations, differential-algebraic equations [See also 65L80]", "value": 100, "id": "09"}, {"name": "Differential equations with impulses", "value": 100, "id": "37"}, {"name": "Discontinuous equations", "value": 100, "id": "36"}, {"name": "Differential equations of infinite order", "value": 100, "id": "35"}, {"name": "Nonlinear equations and systems, general", "value": 100, "id": "34"}, {"name": "Differential inclusions [See also 49J21, 49K21]", "value": 100, "id": "60"}, {"name": "Inverse problems", "value": 100, "id": "55"}, {"name": "Hybrid systems", "value": 100, "id": "38"}, {"name": "Differential inequalities [See also 26D20]", "value": 100, "id": "40"}, {"name": "Linear equations and systems, general", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Theoretical approximation of solutions {For numerical analysis, see 65Lxx}", "value": 100, "id": "45"}]}, {"id": "M", "name": "Differential equations in the complex domain [See also 30Dxx, 32G34]", "children": [{"name": "Linear equations and systems", "value": 100, "id": "03"}, {"name": "Differential equations on complex manifolds", "value": 100, "id": "45"}, {"name": "Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)", "value": 100, "id": "15"}, {"name": "Formal solutions, transform techniques", "value": 100, "id": "25"}, {"name": "Painleve and other special equations; classification, hierarchies;", "value": 100, "id": "55"}, {"name": "Isomonodromic deformations", "value": 100, "id": "56"}, {"name": "Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)", "value": 100, "id": "50"}, {"name": "Singularities, monodromy, local behavior of solutions, normal forms", "value": 100, "id": "35"}, {"name": "Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Stokes phenomena and connection problems (linear and nonlinear)", "value": 100, "id": "40"}, {"name": "Asymptotics, summation methods", "value": 100, "id": "30"}, {"name": "Entire and meromorphic solutions", "value": 100, "id": "05"}, {"name": "Oscillation, growth of solutions", "value": 100, "id": "10"}]}, {"id": "C", "name": "Qualitative theory [See also 37-XX]", "children": [{"name": "Qualitative investigation and simulation of models", "value": 100, "id": "60"}, {"name": "Periodic solutions", "value": 100, "id": "25"}, {"name": "Relaxation oscillations", "value": 100, "id": "26"}, {"name": "Almost and pseudo-almost periodic solutions", "value": 100, "id": "27"}, {"name": "Transformation and reduction of equations and systems, normal forms", "value": 100, "id": "20"}, {"name": "Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)", "value": 100, "id": "07"}, {"name": "Location of integral curves, singular points, limit cycles", "value": 100, "id": "05"}, {"name": "Multifrequency systems", "value": 100, "id": "46"}, {"name": "Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)", "value": 100, "id": "08"}, {"name": "Invariant manifolds", "value": 100, "id": "45"}, {"name": "Complex behavior, chaotic systems [See also 37Dxx]", "value": 100, "id": "28"}, {"name": "Averaging method", "value": 100, "id": "29"}, {"name": "Equations and systems on manifolds", "value": 100, "id": "40"}, {"name": "Equivalence, asymptotic equivalence", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Growth, boundedness", "value": 100, "id": "11"}, {"name": "Oscillation theory, zeros, disconjugacy and comparison theory", "value": 100, "id": "10"}, {"name": "Monotone systems", "value": 100, "id": "12"}, {"name": "Nonlinear oscillations, coupled oscillators", "value": 100, "id": "15"}, {"name": "Symmetries, invariants", "value": 100, "id": "14"}, {"name": "Hysteresis", "value": 100, "id": "55"}, {"name": "Bifurcation [See also 37Gxx]", "value": 100, "id": "23"}, {"name": "Homoclinic and heteroclinic solutions", "value": 100, "id": "37"}]}, {"id": "B", "name": "Boundary value problems {For ordinary differential operators, see 34Lxx}", "children": [{"name": "Sturm-Liouville theory [See also 34Lxx]", "value": 100, "id": "24"}, {"name": "Nonlocal and multipoint boundary value problems", "value": 100, "id": "10"}, {"name": "Green functions", "value": 100, "id": "27"}, {"name": "Nonlinear boundary value problems", "value": 100, "id": "15"}, {"name": "Linear boundary value problems with nonlinear dependence on the spectral parameter", "value": 100, "id": "07"}, {"name": "Linear boundary value problems", "value": 100, "id": "05"}, {"name": "Positive solutions of nonlinear boundary value problems", "value": 100, "id": "18"}, {"name": "Parameter dependent boundary value problems", "value": 100, "id": "08"}, {"name": "Boundary eigenvalue problems", "value": 100, "id": "09"}, {"name": "Boundary value problems with impulses", "value": 100, "id": "37"}, {"name": "Boundary value problems on graphs and networks", "value": 100, "id": "45"}, {"name": "Boundary value problems on infinite intervals", "value": 100, "id": "40"}, {"name": "Applications", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Singular nonlinear boundary value problems", "value": 100, "id": "16"}, {"name": "Special equations (Mathieu, Hill, Bessel, etc.)", "value": 100, "id": "30"}, {"name": "Weyl theory and its generalizations", "value": 100, "id": "20"}]}, {"id": "E", "name": "Asymptotic theory", "children": [{"name": "Perturbations, asymptotics", "value": 100, "id": "10"}, {"name": "Multiple scale methods", "value": 100, "id": "13"}, {"name": "Singular perturbations, general theory", "value": 100, "id": "15"}, {"name": "Canard 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Textbook research", "value": 100, "id": "20"}, {"name": "Teachers' manuals and planning aids", "value": 100, "id": "30"}, {"name": "Computer assisted instruction; e-learning", "value": 100, "id": "50"}, {"name": "Problem books. Competitions. 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also 62Cxx, 91B06, 90B50]", "value": 100, "id": "35"}]}, {"id": "C", "name": "Social and behavioral sciences: general topics {For statistics, see 62-XX}", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Clustering [See also 62H30]", "value": 100, "id": "20"}, {"name": "One- and multidimensional scaling", "value": 100, "id": "15"}, {"name": "Measurement theory", "value": 100, "id": "05"}]}, {"id": "B", "name": "Mathematical economics {For econometrics, see 62P20}", "children": [{"name": "Trade models", "value": 100, "id": "60"}, {"name": "Statistical methods; economic indices and measures", "value": 100, "id": "82"}, {"name": "Growth models", "value": 100, "id": "62"}, {"name": "Macro-economic models (monetary models, models of taxation)", "value": 100, "id": "64"}, {"name": "Multisectoral models", "value": 100, "id": "66"}, {"name": "Matching models", "value": 100, "id": "68"}, {"name": "Heterogeneous agent models", "value": 100, 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"Environmental economics (natural resource models, harvesting, pollution, etc.)", "value": 100, "id": "76"}, {"name": "Production theory, theory of the firm", "value": 100, "id": "38"}, {"name": "Spatial models", "value": 100, "id": "72"}, {"name": "Stochastic models", "value": 100, "id": "70"}, {"name": "Group preferences", "value": 100, "id": "10"}, {"name": "Voting theory", "value": 100, "id": "12"}, {"name": "Welfare economics", "value": 100, "id": "15"}, {"name": "Social choice", "value": 100, "id": "14"}, {"name": "Utility theory", "value": 100, "id": "16"}, {"name": "Economic dynamics", "value": 100, "id": "55"}, {"name": "Special types of economies", "value": 100, "id": "54"}, {"name": "Risk theory, insurance", "value": 100, "id": "30"}, {"name": "Dynamic stochastic general equilibrium theory", "value": 100, "id": "51"}, {"name": "General equilibrium theory", "value": 100, "id": "50"}, {"name": "Special types of equilibria", "value": 100, "id": "52"}, {"name": "Models of real-world systems", "value": 100, "id": "74"}, {"name": "Resource and cost allocation", "value": 100, "id": "32"}, {"name": "Informational economics", "value": 100, "id": "44"}]}, {"id": "E", "name": "Mathematical psychology", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Cognitive psychology", "value": 100, "id": "10"}, {"name": "Psychophysics and psychophysiology; perception", "value": 100, "id": "30"}, {"name": "Measurement and performance", "value": 100, "id": "45"}, {"name": "Memory and learning [See also 68T05]", "value": 100, "id": "40"}]}, {"id": "D", "name": "Mathematical sociology (including anthropology)", "children": [{"name": "Models of societies, social and urban evolution", "value": 100, "id": "10"}, {"name": "Mathematical geography and demography", "value": 100, "id": "20"}, {"name": "Spatial models [See also 91B72]", "value": 100, "id": "25"}, {"name": "Social networks", "value": 100, "id": "30"}, {"name": "Manpower systems [See also 91B40, 90B70]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "G", "name": "Mathematical finance", "children": [{"name": "Portfolio theory", "value": 100, "id": "10"}, {"name": "Derivative securities", "value": 100, "id": "20"}, {"name": "Interest rates (stochastic models)", "value": 100, "id": "30"}, {"name": "Corporate finance", "value": 100, "id": "50"}, {"name": "Credit risk", "value": 100, "id": "40"}, {"name": "Numerical methods (including Monte Carlo methods)", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Statistical methods, econometrics", "value": 100, "id": "70"}, {"name": "Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)", "value": 100, "id": "80"}]}, {"id": "F", "name": "Other social and behavioral sciences (mathematical treatment)", "children": 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"value": 100, "id": "85"}, {"name": "Systems in abstract spaces", "value": 100, "id": "25"}, {"name": "Systems governed by partial differential equations", "value": 100, "id": "20"}, {"name": "Systems governed by functional-differential equations [See also 34K35]", "value": 100, "id": "23"}, {"name": "Fuzzy control systems", "value": 100, "id": "42"}, {"name": "Adaptive control", "value": 100, "id": "40"}, {"name": "Problems with incomplete information", "value": 100, "id": "41"}, {"name": "Linear systems", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Perturbations", "value": 100, "id": "73"}, {"name": "Time-scale analysis and singular perturbations", "value": 100, "id": "70"}, {"name": "Applications", "value": 100, "id": "95"}, {"name": "Nonlinear systems", "value": 100, "id": "10"}, {"name": "Systems governed by ordinary differential equations [See also 34H05]", "value": 100, "id": "15"}, {"name": "Discrete-time systems", "value": 100, "id": "55"}, {"name": "Sampled-data systems", "value": 100, "id": "57"}, {"name": "Systems governed by functional relations other than differential equations (such as hybrid and switching systems)", "value": 100, "id": "30"}, {"name": "Multivariable systems", "value": 100, "id": "35"}]}, {"id": "B", "name": "Controllability, observability, and system structure", "children": [{"name": "Synthesis problems", "value": 100, "id": "50"}, {"name": "Eigenvalue problems", "value": 100, "id": "60"}, {"name": "Attainable sets", "value": 100, "id": "03"}, {"name": "Geometric methods", "value": 100, "id": "27"}, {"name": "Minimal systems representations", "value": 100, "id": "20"}, {"name": "Observability", "value": 100, "id": "07"}, {"name": "Controllability", "value": 100, "id": "05"}, {"name": "Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]", "value": 100, "id": "28"}, {"name": "Computational methods", "value": 100, "id": "40"}, {"name": "Algebraic methods", "value": 100, "id": "25"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "System structure simplification", "value": 100, "id": "11"}, {"name": "Canonical structure", "value": 100, "id": "10"}, {"name": "Variable structure systems", "value": 100, "id": "12"}, {"name": "Realizations from input-output data", "value": 100, "id": "15"}, {"name": "Transformations", "value": 100, "id": "17"}, {"name": "Pole and zero placement problems", "value": 100, "id": "55"}, {"name": "Linearizations", "value": 100, "id": "18"}, {"name": "System identification", "value": 100, "id": "30"}, {"name": "Design techniques (robust design, computer-aided design, etc.)", "value": 100, "id": "51"}, {"name": "$H^\\infty$-control", "value": 100, "id": "36"}, {"name": "Sensitivity (robustness)", "value": 100, "id": "35"}, {"name": "Feedback control", "value": 100, "id": "52"}]}, {"id": "E", "name": "Stochastic systems and control", "children": [{"name": "Filtering 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100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "94", "name": "Information and communication, circuits", "children": [{"id": "A", "name": "Communication, information", "children": [{"name": "Application of orthogonal and other special functions", "value": 100, "id": "11"}, {"name": "Coding theorems (Shannon theory)", "value": 100, "id": "24"}, {"name": "Detection theory", "value": 100, "id": "13"}, {"name": "Signal theory (characterization, reconstruction, filtering, etc.)", "value": 100, "id": "12"}, {"name": "Information theory, general [See also 62B10, 81P45]", "value": 100, "id": "15"}, {"name": "Modulation and demodulation", "value": 100, "id": "14"}, {"name": "Measures of information, entropy", "value": 100, "id": "17"}, {"name": "Communication theory [See also 60G35, 90B18]", "value": 100, "id": "05"}, {"name": "Shift register sequences and sequences over finite alphabets", "value": 100, "id": "55"}, {"name": "Image processing (compression, reconstruction, etc.) [See also 68U10]", "value": 100, "id": "08"}, {"name": "Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]", "value": 100, "id": "45"}, {"name": "Source coding [See also 68P30]", "value": 100, "id": "29"}, {"name": "Channel models (including quantum)", "value": 100, "id": "40"}, {"name": "Rate-distortion theory", "value": 100, "id": "34"}, {"name": "Cryptography [See also 11T71, 14G50, 68P25, 81P94]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Authentication and secret sharing [See also 81P94]", "value": 100, "id": "62"}, {"name": "Sampling theory", "value": 100, "id": "20"}, {"name": "Theory of questionnaires", "value": 100, "id": "50"}]}, {"id": "C", "name": "Circuits, networks", "children": [{"name": "Switching theory, application of Boolean algebra; Boolean functions [See also 06E30]", "value": 100, "id": "10"}, {"name": "Fault detection; testing", "value": 100, "id": "12"}, {"name": "Applications of graph theory [See also 05Cxx, 68R10]", "value": 100, "id": "15"}, {"name": "Analytic circuit theory", "value": 100, "id": "05"}, {"name": "Applications of design theory [See also 05Bxx]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "B", "name": "Theory of error-correcting codes and error-detecting codes", "children": [{"name": "Convolutional codes", "value": 100, "id": "10"}, {"name": "Combined modulation schemes (including trellis codes)", "value": 100, "id": "12"}, {"name": "Burst-correcting codes", "value": 100, "id": "20"}, {"name": "Linear codes, general", "value": 100, "id": "05"}, {"name": "Majority codes", "value": 100, "id": "30"}, {"name": "Synchronization error-correcting codes", "value": 100, "id": "50"}, {"name": "Decoding", "value": 100, "id": "35"}, {"name": "Other types of codes", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31, 11H71]", "value": 100, "id": "75"}, {"name": "Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]", "value": 100, "id": "27"}, {"name": "Combinatorial codes", "value": 100, "id": "25"}, {"name": "Error probability", "value": 100, "id": "70"}, {"name": "Cyclic codes", "value": 100, "id": "15"}, {"name": "Arithmetic codes [See also 11T71, 14G50]", "value": 100, "id": "40"}, {"name": "Bounds on codes", "value": 100, "id": "65"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, 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"Non-Newtonian fluids", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Liquid crystals [See also 82D30]", "value": 100, "id": "15"}]}, {"id": "B", "name": "Incompressible inviscid fluids", "children": [{"name": "Existence, uniqueness, and regularity theory [See also 35Q35]", "value": 100, "id": "03"}, {"name": "Ship waves", "value": 100, "id": "20"}, {"name": "Free-surface potential flows", "value": 100, "id": "07"}, {"name": "Solitary waves [See also 35C11]", "value": 100, "id": "25"}, {"name": "Internal waves", "value": 100, "id": "55"}, {"name": "Vortex flows", "value": 100, "id": "47"}, {"name": "Capillarity (surface tension) [See also 76D45]", "value": 100, "id": "45"}, {"name": "Atmospheric waves [See also 86A10]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Flow control and optimization [See also 49Q10, 93C20, 93C95]", "value": 100, "id": "75"}, {"name": "Rossby waves [See also 86A05, 86A10]", "value": 100, "id": "65"}, {"name": "Stratification effects in inviscid fluids", "value": 100, "id": "70"}, {"name": "Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]", "value": 100, "id": "15"}, {"name": "Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing", "value": 100, "id": "10"}]}, {"id": "E", "name": "Hydrodynamic stability", "children": [{"name": "Stability and instability of magnetohydrodynamic and electrohydrodynamic flows", "value": 100, "id": "25"}, {"name": "Nonlinear effects", "value": 100, "id": "30"}, {"name": "Absolute and convective instability and stability", "value": 100, "id": "15"}, {"name": "Rotation", "value": 100, "id": "07"}, {"name": "Interfacial stability and instability", "value": 100, "id": "17"}, {"name": "Parallel shear flows", "value": 100, "id": "05"}, {"name": "Compressibility effects", "value": 100, "id": "19"}, {"name": "Stability and instability of nonparallel flows", "value": 100, "id": "09"}, {"name": "Stability and instability of geophysical and astrophysical flows", "value": 100, "id": "20"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Convection", "value": 100, "id": "06"}]}, {"id": "D", "name": "Incompressible viscous fluids", "children": [{"name": "Existence, uniqueness, and regularity theory [See also 35Q30]", "value": 100, "id": "03"}, {"name": "Other free-boundary flows; Hele-Shaw flows", "value": 100, "id": "27"}, {"name": "Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]", "value": 100, "id": "06"}, {"name": "Stokes and related (Oseen, etc.) flows", "value": 100, "id": "07"}, {"name": "Viscous vortex flows", "value": 100, "id": "17"}, {"name": "Navier-Stokes equations [See also 35Q30]", "value": 100, "id": "05"}, {"name": "Waves", "value": 100, "id": "33"}, {"name": "Lubrication theory", "value": 100, "id": "08"}, {"name": "Viscous-inviscid interaction", "value": 100, "id": "09"}, {"name": "Capillarity (surface tension) [See also 76B45]", "value": 100, "id": "45"}, {"name": "Stratification effects in viscous fluids", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Flow control and optimization [See also 49Q10, 93C20, 93C95]", "value": 100, "id": "55"}, {"name": "Wakes and jets", "value": 100, "id": "25"}, {"name": "Boundary-layer theory, separation and reattachment, higher-order effects", "value": 100, "id": "10"}]}, {"id": "G", "name": "General aerodynamics and subsonic flows", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "General aerodynamics and subsonic flows", "value": 100, "id": "25"}]}, {"id": "F", "name": "Turbulence [See also 37-XX, 60Gxx, 60Jxx]", "children": [{"name": "Fundamentals", "value": 100, "id": "02"}, {"name": "Shear flows", "value": 100, "id": "10"}, {"name": "Renormalization and other field-theoretical methods [See also 81T99]", "value": 100, "id": "30"}, {"name": "Dynamical systems approach to turbulence [See also 37-XX]", "value": 100, "id": "20"}, {"name": "Turbulent transport, mixing", "value": 100, "id": "25"}, {"name": "Statistical turbulence modeling [See also 76M35]", "value": 100, "id": "55"}, {"name": "Stratification effects", "value": 100, "id": "45"}, {"name": "Compressibility effects", "value": 100, "id": "50"}, {"name": "Convective turbulence [See also 76E15, 76Rxx]", "value": 100, "id": "35"}, {"name": "$k$-$\\varepsilon$ modeling", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Turbulent boundary layers", "value": 100, "id": "40"}, {"name": "Control of turbulent flows", "value": 100, "id": "70"}, {"name": "Transition to turbulence", "value": 100, "id": "06"}, {"name": "Isotropic turbulence; 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"Spectral methods", "value": 100, "id": "22"}, {"name": "Vortex methods", "value": 100, "id": "23"}, {"name": "Dimensional analysis and similarity", "value": 100, "id": "55"}, {"name": "Variational methods", "value": 100, "id": "30"}, {"name": "Particle methods and lattice-gas methods", "value": 100, "id": "28"}, {"name": "Asymptotic methods, singular perturbations", "value": 100, "id": "45"}, {"name": "Stochastic analysis", "value": 100, "id": "35"}, {"name": "Homogenization", "value": 100, "id": "50"}, {"name": "Symmetry analysis, Lie group and algebra methods", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Visualization algorithms", "value": 100, "id": "27"}, {"name": "Other numerical methods", "value": 100, "id": "25"}, {"name": "Finite difference methods", "value": 100, "id": "20"}, {"name": "Complex-variables methods", "value": 100, "id": "40"}]}, {"id": "L", "name": "Shock waves and blast waves [See also 35L67]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Shock waves and blast waves [See also 35L67]", "value": 100, "id": "05"}]}, {"id": "N", "name": "Compressible fluids and gas dynamics, general", "children": [{"name": "Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]", "value": 100, "id": "10"}, {"name": "Gas dynamics, general", "value": 100, "id": "15"}, {"name": "Viscous-inviscid interaction", "value": 100, "id": "17"}, {"name": "Flow control and optimization", "value": 100, "id": "25"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Boundary-layer theory", "value": 100, "id": "20"}]}, {"id": "Q", "name": "Hydro- and aero-acoustics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Hydro- and aero-acoustics", "value": 100, "id": "05"}]}, {"id": "P", "name": "Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]", "value": 100, "id": "05"}]}, {"id": "S", "name": "Flows in porous media; filtration; seepage", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Flows in porous media; filtration; seepage", "value": 100, "id": "05"}]}, {"id": "R", "name": "Diffusion and convection", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Free convection", "value": 100, "id": "10"}, {"name": "Diffusion [See also 60J60]", "value": 100, "id": "50"}, {"name": "Forced convection", "value": 100, "id": "05"}]}, {"id": "U", "name": "Rotating fluids", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Rotating fluids", "value": 100, "id": "05"}]}, {"id": "T", "name": "Two-phase and multiphase flows", "children": [{"name": "Liquid-gas two-phase flows, bubbly flows", "value": 100, "id": "10"}, {"name": "Dusty-gas two-phase flows", "value": 100, "id": "15"}, {"name": "Granular flows [See also 74C99, 74E20]", "value": 100, "id": "25"}, {"name": "Three or more component flows", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Suspensions", "value": 100, "id": "20"}]}, {"id": "W", "name": "Magnetohydrodynamics and electrohydrodynamics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Magnetohydrodynamics and electrohydrodynamics", "value": 100, "id": "05"}]}, {"id": "V", "name": "Reaction effects in flows [See also 80A32]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Reaction effects in flows [See also 80A32]", "value": 100, "id": "05"}]}, {"id": "Y", "name": "Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]", "value": 100, "id": "05"}]}, {"id": "X", "name": "Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]", "value": 100, "id": "05"}]}, {"id": "Z", "name": "Biological fluid mechanics [See also 74F10, 74L15, 92Cxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Biopropulsion in water and in air", "value": 100, "id": "10"}, {"name": "Physiological flows [See also 92C35]", "value": 100, "id": "05"}]}]}, {"id": "74", "name": "Mechanics of deformable solids", "children": [{"id": "A", "name": "Generalities, axiomatics, foundations of continuum mechanics of solids", "children": [{"name": "Stress", "value": 100, "id": "10"}, {"name": "Theories of fracture and damage", "value": 100, "id": "45"}, {"name": "Theory of constitutive functions", "value": 100, "id": "20"}, {"name": "Molecular, statistical, and kinetic theories", "value": 100, "id": "25"}, {"name": "Theories of friction (tribology)", "value": 100, "id": "55"}, {"name": "Nonsimple materials", "value": 100, "id": "30"}, {"name": "Structured surfaces and interfaces, coexistent phases", "value": 100, "id": "50"}, {"name": "Polar materials", "value": 100, "id": "35"}, {"name": "Micromechanical theories", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Random materials and composite materials", "value": 100, "id": "40"}, {"name": "Thermodynamics", "value": 100, "id": "15"}, {"name": "Kinematics of deformation", "value": 100, "id": "05"}, {"name": "Reactive materials", "value": 100, "id": "65"}]}, {"id": "C", "name": "Plastic materials, materials of stress-rate and internal-variable type", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Small-strain, rate-dependent theories (including theories of viscoplasticity)", "value": 100, "id": "10"}, {"name": "Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)", "value": 100, "id": "05"}, {"name": "Large-strain, rate-independent theories (including nonlinear plasticity)", "value": 100, "id": "15"}, {"name": "Large-strain, rate-dependent theories", "value": 100, "id": "20"}]}, {"id": "B", "name": "Elastic materials", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Linear elasticity with initial stresses", "value": 100, "id": "10"}, {"name": "Classical linear elasticity", "value": 100, "id": "05"}, {"name": "Equations linearized about a deformed state (small deformations superposed on large)", "value": 100, "id": "15"}, {"name": "Nonlinear elasticity", "value": 100, "id": "20"}]}, {"id": "E", "name": "Material properties given special treatment", "children": [{"name": "Anisotropy", "value": 100, "id": "10"}, {"name": "Granularity", "value": 100, "id": "20"}, {"name": "Texture", "value": 100, "id": "25"}, {"name": "Composite and mixture properties", "value": 100, "id": "30"}, {"name": "Random structure", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Chemical structure", "value": 100, "id": "40"}, {"name": "Crystalline structure", "value": 100, "id": "15"}, {"name": "Inhomogeneity", "value": 100, "id": "05"}]}, {"id": "D", "name": "Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonlinear constitutive equations", "value": 100, "id": "10"}, {"name": "Linear constitutive equations", "value": 100, "id": "05"}]}, {"id": "G", "name": "Equilibrium (steady-state) problems", "children": [{"name": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)", "value": 100, "id": "10"}, {"name": "Bounds for solutions", "value": 100, "id": "45"}, {"name": "Local existence of solutions (near a given solution)", "value": 100, "id": "20"}, {"name": "Global existence of solutions", "value": 100, "id": "25"}, {"name": "Qualitative behavior of solutions", "value": 100, "id": "55"}, {"name": "Uniqueness of solutions", "value": 100, "id": "30"}, {"name": "Saint-Venant's principle", "value": 100, "id": "50"}, {"name": "Multiplicity of solutions", "value": 100, "id": "35"}, {"name": "Bifurcation and buckling", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inverse problems", "value": 100, "id": "75"}, {"name": "Regularity of solutions", "value": 100, "id": "40"}, {"name": "Stress concentrations, singularities", "value": 100, "id": "70"}, {"name": "Numerical approximation of solutions", "value": 100, "id": "15"}, {"name": "Explicit solutions", "value": 100, "id": "05"}, {"name": "Energy minimization", "value": 100, "id": "65"}]}, {"id": "F", "name": "Coupling of solid mechanics with other effects", "children": [{"name": "Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)", "value": 100, "id": "10"}, {"name": "Electromagnetic effects", "value": 100, "id": "15"}, {"name": "Chemical and reactive effects", "value": 100, "id": "25"}, {"name": "Thermal effects", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Mixture effects", "value": 100, "id": "20"}]}, {"id": "H", "name": "Dynamical problems", "children": [{"name": "Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)", "value": 100, "id": "10"}, {"name": "Vibrations", "value": 100, "id": "45"}, {"name": "Existence of solutions", "value": 100, "id": "20"}, {"name": "Uniqueness of solutions", "value": 100, "id": "25"}, {"name": "Stability", "value": 100, "id": "55"}, {"name": "Regularity of solutions", "value": 100, "id": "30"}, {"name": "Random vibrations", "value": 100, "id": "50"}, {"name": "Singularities, blowup, stress concentrations", "value": 100, "id": "35"}, {"name": "Dynamical bifurcation", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Long-time behavior of solutions", "value": 100, "id": "40"}, {"name": "Numerical approximation of solutions", "value": 100, "id": "15"}, {"name": "Explicit solutions", "value": 100, "id": "05"}, {"name": "Chaotic behavior", "value": 100, "id": "65"}]}, {"id": "K", "name": "Thin bodies, structures", "children": [{"name": "Rods (beams, columns, shafts, arches, rings, etc.)", "value": 100, "id": "10"}, {"name": "Plates", "value": 100, "id": "20"}, {"name": "Shells", "value": 100, "id": "25"}, {"name": "Junctions", "value": 100, "id": "30"}, {"name": "Thin films", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Membranes", "value": 100, "id": "15"}, {"name": "Strings", "value": 100, "id": "05"}]}, {"id": "J", "name": "Waves", "children": [{"name": "Bulk waves", "value": 100, "id": "10"}, {"name": "Wave scattering", "value": 100, "id": "20"}, {"name": "Inverse problems", "value": 100, "id": "25"}, {"name": "Nonlinear waves", "value": 100, "id": "30"}, {"name": "Solitary waves", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Shocks and related discontinuities", "value": 100, "id": "40"}, {"name": "Surface waves", "value": 100, "id": "15"}, {"name": "Linear waves", "value": 100, "id": "05"}]}, {"id": "M", "name": "Special kinds of problems", "children": [{"name": "Friction", "value": 100, "id": "10"}, {"name": "Contact", "value": 100, "id": "15"}, {"name": "Micromechanics", "value": 100, "id": "25"}, {"name": "Control, switches and devices (``smart materials'') [See also 93Cxx]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Impact", "value": 100, "id": "20"}]}, {"id": "L", "name": "Special subfields of solid mechanics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Soil and rock mechanics", "value": 100, "id": "10"}, {"name": "Biomechanical solid mechanics [See also 92C10]", "value": 100, "id": "15"}, {"name": "Geophysical solid mechanics [See also 86-XX]", "value": 100, "id": "05"}]}, {"id": "N", "name": "Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]", "children": [{"name": "Displacive transformations", "value": 100, "id": "10"}, {"name": "Dynamics of phase boundaries", "value": 100, "id": "20"}, {"name": "Transformations involving diffusion", "value": 100, "id": "25"}, {"name": "Problems involving hysteresis", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Analysis of microstructure", "value": 100, "id": "15"}, {"name": "Crystals", "value": 100, "id": "05"}]}, {"id": "Q", "name": "Homogenization, determination of effective properties", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Homogenization and oscillations in dynamical problems", "value": 100, "id": "10"}, {"name": "Homogenization in equilibrium problems", "value": 100, "id": "05"}, {"name": "Effective constitutive equations", "value": 100, "id": "15"}, {"name": "Bounds on effective properties", "value": 100, "id": "20"}]}, {"id": "P", "name": "Optimization [See also 49Qxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Optimization of other properties", "value": 100, "id": "10"}, {"name": "Compliance or weight optimization", "value": 100, "id": "05"}, {"name": "Topological methods", "value": 100, "id": "15"}, {"name": "Geometrical methods", "value": 100, "id": "20"}]}, {"id": "S", "name": "Numerical methods [See also 65-XX, 74G15, 74H15]", "children": [{"name": "Finite volume methods", "value": 100, "id": "10"}, {"name": "Finite difference methods", "value": 100, "id": "20"}, {"name": "Spectral and related methods", "value": 100, "id": "25"}, {"name": "Other numerical methods", "value": 100, "id": "30"}, {"name": "Stochastic methods", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Complex variable methods", "value": 100, "id": "70"}, {"name": "Boundary element methods", "value": 100, "id": "15"}, {"name": "Finite element methods", "value": 100, "id": "05"}]}, {"id": "R", "name": "Fracture and damage", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Brittle fracture", "value": 100, "id": "10"}, {"name": "Brittle damage", "value": 100, "id": "05"}, {"name": "High-velocity fracture", "value": 100, "id": "15"}, {"name": "Anelastic fracture and damage", "value": 100, "id": "20"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}, {"name": "Experimental work", "value": 100, "id": "05"}]}]}, {"id": "70", "name": "Mechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX}", "children": [{"id": "A", "name": "Axiomatics, foundations", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Axiomatics, foundations", "value": 100, "id": "05"}]}, {"id": "C", "name": "Statics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Statics", "value": 100, "id": "20"}]}, {"id": "B", "name": "Kinematics [See also 53A17]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Kinematics of a rigid body", "value": 100, "id": "10"}, {"name": "Mechanisms, robots [See also 68T40, 70Q05, 93C85]", "value": 100, "id": "15"}, {"name": "Kinematics of a particle", "value": 100, "id": "05"}]}, {"id": "E", "name": "Dynamics of a rigid body and of multibody systems", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Perturbation methods for rigid body dynamics", "value": 100, "id": "20"}, {"name": "Motion of a rigid body with a fixed point", "value": 100, "id": "17"}, {"name": "Motion of the gyroscope", "value": 100, "id": "05"}, {"name": "Dynamics of multibody systems", "value": 100, "id": "55"}, {"name": "Motion of a rigid body in contact with a solid surface [See also 70F25]", "value": 100, "id": "18"}, {"name": "Higher-dimensional generalizations", "value": 100, "id": "45"}, {"name": "Stability problems", "value": 100, "id": "50"}, {"name": "Integrable cases of motion", "value": 100, "id": "40"}, {"name": "Robot dynamics and control [See also 68T40, 70Q05, 93C85]", "value": 100, "id": "60"}, {"name": "Free motion of a rigid body [See also 70M20]", "value": 100, "id": "15"}]}, {"id": "G", "name": "General models, approaches, and methods [See also 37-XX]", "children": [{"name": "Generalized coordinates; event, impulse-energy, configuration, state, or phase space", "value": 100, "id": "10"}, {"name": "Algebraic geometry methods", "value": 100, "id": "55"}, {"name": "Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]", "value": 100, "id": "45"}, {"name": "Topological and differential-topological methods", "value": 100, "id": "40"}, {"name": "Dynamical systems methods", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Variational methods", "value": 100, "id": "75"}, {"name": "Symmetries, Lie-group and Lie-algebra methods", "value": 100, "id": "65"}, {"name": "Functional-analytic methods", "value": 100, "id": "70"}]}, {"id": "F", "name": "Dynamics of a system of particles, including celestial mechanics", "children": [{"name": "$n$-body problems", "value": 100, "id": "10"}, {"name": "Celestial mechanics", "value": 100, "id": "15"}, {"name": "Three-body problems", "value": 100, "id": "07"}, {"name": "Inverse problems", "value": 100, "id": "17"}, {"name": "Collisions in celestial mechanics, regularization", "value": 100, "id": "16"}, {"name": "Infinite particle systems", "value": 100, "id": "45"}, {"name": "Collision of rigid or pseudo-rigid bodies", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonholonomic systems", "value": 100, "id": "25"}, {"name": "Holonomic systems", "value": 100, "id": "20"}, {"name": "Problems with friction", "value": 100, "id": "40"}, {"name": "Two-body problems", "value": 100, "id": "05"}]}, {"id": "H", "name": "Hamiltonian and Lagrangian mechanics [See also 37Jxx]", "children": [{"name": "Adiabatic invariants", "value": 100, "id": "11"}, {"name": "Lagrange's equations", "value": 100, "id": "03"}, {"name": "Periodic and almost periodic solutions", "value": 100, "id": "12"}, {"name": "Completely integrable systems and methods of integration", "value": 100, "id": "06"}, {"name": "Nonintegrable systems", "value": 100, "id": "07"}, {"name": "Hamilton's equations", "value": 100, "id": "05"}, {"name": "Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction", "value": 100, "id": "33"}, {"name": "Nearly integrable Hamiltonian systems, KAM theory", "value": 100, "id": "08"}, {"name": "Perturbation theories", "value": 100, "id": "09"}, {"name": "Constrained dynamics, Dirac's theory of constraints [See also 70F20, 70F25, 70Gxx]", "value": 100, "id": "45"}, {"name": "Relativistic dynamics", "value": 100, "id": "40"}, {"name": "Higher-order theories", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Hamilton's principle", "value": 100, "id": "25"}, {"name": "Other variational principles", "value": 100, "id": "30"}, {"name": "Hamilton-Jacobi equations", "value": 100, "id": "20"}, {"name": "Canonical and symplectic transformations", "value": 100, "id": "15"}, {"name": "Stability problems", "value": 100, "id": "14"}]}, {"id": "K", "name": "Nonlinear dynamics [See also 34Cxx, 37-XX]", "children": [{"name": "Free motions", "value": 100, "id": "25"}, {"name": "Normal forms", "value": 100, "id": "45"}, {"name": "Stability", "value": 100, "id": "20"}, {"name": "Phase plane analysis, limit cycles", "value": 100, "id": "05"}, {"name": "Transition to stochasticity (chaotic behavior) [See also 37D45]", "value": 100, "id": "55"}, {"name": "Equilibria and periodic trajectories", "value": 100, "id": "42"}, {"name": "Homoclinic and heteroclinic trajectories", "value": 100, "id": "44"}, {"name": "Nonlinear resonances", "value": 100, "id": "30"}, {"name": "Parametric resonances", "value": 100, "id": "28"}, {"name": "Quasi-periodic motions and invariant tori", "value": 100, "id": "43"}, {"name": "Forced motions", "value": 100, "id": "40"}, {"name": "Bifurcations and instability", "value": 100, "id": "50"}, {"name": "General perturbation schemes", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonlinear modes", "value": 100, "id": "75"}, {"name": "Averaging of perturbations", "value": 100, "id": "65"}, {"name": "Systems with slow and fast motions", "value": 100, "id": "70"}]}, {"id": "J", "name": "Linear vibration theory", "children": [{"name": "Modal analysis", "value": 100, "id": "10"}, {"name": "Stability", "value": 100, "id": "25"}, {"name": "Free motions", "value": 100, "id": "30"}, {"name": "Systems arising from the discretization of structural vibration problems", "value": 100, "id": "50"}, {"name": "Parametric resonances", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Forced motions", "value": 100, "id": "35"}]}, {"id": "M", "name": "Orbital mechanics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Orbital mechanics", "value": 100, "id": "20"}]}, {"id": "L", "name": "Random vibrations [See also 74H50]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Random vibrations [See also 74H50]", "value": 100, "id": "05"}]}, {"id": "Q", "name": "Control of mechanical systems [See also 60Gxx, 60Jxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Control of mechanical systems", "value": 100, "id": "05"}]}, {"id": "P", "name": "Variable mass, rockets", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Variable mass, rockets", "value": 100, "id": "05"}]}, {"id": "S", "name": "Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Symmetries and conservation laws", "value": 100, "id": "10"}, {"name": "Lagrangian formalism and Hamiltonian formalism", "value": 100, "id": "05"}, {"name": "Yang-Mills and other gauge theories", "value": 100, "id": "15"}, {"name": "More general nonquantum field theories", "value": 100, "id": "20"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or 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"value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "26", "name": "Real functions [See also 54C30]", "children": [{"id": "A", "name": "Functions of one variable", "children": [{"name": "Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]", "value": 100, "id": "24"}, {"name": "Foundations: limits and generalizations, elementary topology of the line", "value": 100, "id": "03"}, {"name": "Denjoy and Perron integrals, other special integrals", "value": 100, "id": "39"}, {"name": "Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]", "value": 100, "id": "12"}, {"name": "Continuity and related 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100, "id": "46"}, {"name": "Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives", "value": 100, "id": "27"}, {"name": "Functions of bounded variation, generalizations", "value": 100, "id": "45"}, {"name": "Singular functions, Cantor functions, functions with other special properties", "value": 100, "id": "30"}, {"name": "One-variable calculus", "value": 100, "id": "06"}, {"name": "Convexity, generalizations", "value": 100, "id": "51"}]}, {"id": "C", "name": "Polynomials, rational functions", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Polynomials: location of zeros [See also 12D10, 30C15, 65H05]", "value": 100, "id": "10"}, {"name": "Rational functions [See also 14Pxx]", "value": 100, "id": "15"}, {"name": "Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]", "value": 100, "id": "05"}]}, {"id": "B", "name": "Functions of several variables", "children": 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"$C^\\infty$-functions, quasi-analytic functions [See also 58C25]", "value": 100, "id": "10"}, {"name": "Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]", "value": 100, "id": "20"}, {"name": "Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx}", "value": 100, "id": "25"}, {"name": "Non-Archimedean analysis [See also 12J25]", "value": 100, "id": "30"}, {"name": "Fuzzy real analysis [See also 03E72, 28E10]", "value": 100, "id": "50"}, {"name": "Nonstandard analysis [See also 03H05, 28E05, 54J05]", "value": 100, "id": "35"}, {"name": "Means [See also 47A64]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Constructive real analysis [See also 03F60]", "value": 100, "id": "40"}, {"name": "Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains see 34N05}", "value": 100, "id": "70"}, {"name": "Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]", "value": 100, "id": "15"}, {"name": "Real-analytic functions [See also 32B05, 32C05]", "value": 100, "id": "05"}]}, {"id": "D", "name": "Inequalities {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15}", "children": [{"name": "Inequalities involving derivatives and differential and integral operators", "value": 100, "id": "10"}, {"name": "Other analytical inequalities", "value": 100, "id": "20"}, {"name": "Inequalities involving other types of functions", "value": 100, "id": "07"}, {"name": "Inequalities for trigonometric functions and polynomials", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inequalities for sums, series and integrals", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition 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"10"}, {"name": "Other connections with logic and set theory", "value": 100, "id": "15"}, {"name": "Nonstandard measure theory [See also 03H05, 26E35]", "value": 100, "id": "05"}]}, {"id": "D", "name": "Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "One-parameter continuous families of measure-preserving transformations", "value": 100, "id": "10"}, {"name": "Measure-preserving transformations", "value": 100, "id": "05"}, {"name": "General groups of measure-preserving transformations", "value": 100, "id": "15"}, {"name": "Entropy and other invariants", "value": 100, "id": "20"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "39", "name": "Difference and functional equations", "children": [{"id": "A", "name": "Difference equations {For dynamical systems, see 37-XX; for dynamic equations on time scales, see 34N05}", "children": [{"name": "Almost periodic solutions", "value": 100, "id": "24"}, {"name": "Difference equations, additive", "value": 100, "id": "10"}, {"name": "Difference equations, scaling ($q$-differences) [See also 33Dxx]", "value": 100, "id": "13"}, {"name": "Discrete version of topics in analysis", "value": 100, "id": "12"}, {"name": "Linear equations", "value": 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"Function-theoretic methods (including power series methods and semicontinuous methods)", "value": 100, "id": "15"}, {"name": "Matrix methods", "value": 100, "id": "05"}]}, {"id": "B", "name": "Multiple sequences and series", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Multiple sequences and series (should also be assigned at least one other classification number in this section)", "value": 100, "id": "05"}]}, {"id": "E", "name": "Inversion theorems", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Growth estimates", "value": 100, "id": "10"}, {"name": "Tauberian theorems, general", "value": 100, "id": "05"}, {"name": "Lacunary inversion theorems", "value": 100, "id": "15"}, {"name": "Tauberian constants", "value": 100, "id": "20"}]}, {"id": "D", "name": "Direct theorems on summability", "children": [{"name": "Tauberian constants and oscillation limits", "value": 100, "id": 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"Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}]}, {"id": "TOF", "name": "Complex Analysis & Function Theory", "children": [{"id": "46", "name": "Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}", "children": [{"id": "A", "name": "Topological linear spaces and related structures {For function spaces, see 46Exx}", "children": [{"name": "Graded Frechet spaces and tame operators", "value": 100, "id": "61"}, {"name": "Topological invariants ((DN), ($\\Omega$), 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completeness (including $B$-, $B_r$-completeness)", "value": 100, "id": "30"}, {"name": "Compactness in topological linear spaces; angelic spaces, etc.", "value": 100, "id": "50"}, {"name": "Summability and bases [See also 46B15]", "value": 100, "id": "35"}, {"name": "Convex sets in topological linear spaces; Choquet theory [See also 52A07]", "value": 100, "id": "55"}]}, {"id": "C", "name": "Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}", "children": [{"name": "Spaces with indefinite inner product (Kreiin spaces, Pontryagin spaces, etc.) [See also 47B50]", "value": 100, "id": "20"}, {"name": "Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]", "value": 100, "id": "07"}, {"name": "Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)", "value": 100, "id": "05"}, {"name": "Generalizations of inner products (semi-inner products, partial inner products, etc.)", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Characterizations of Hilbert spaces", "value": 100, "id": "15"}]}, {"id": "B", "name": "Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}", "children": [{"name": "Isomorphic theory (including renorming) of Banach spaces", "value": 100, "id": "03"}, {"name": "Nonseparable Banach spaces", "value": 100, "id": "26"}, {"name": "Banach sequence spaces [See also 46A45]", "value": 100, "id": "45"}, {"name": "Asymptotic theory of Banach spaces [See also 52A23]", "value": 100, "id": "06"}, {"name": "Local theory of Banach spaces", "value": 100, "id": "07"}, {"name": "Isometric theory of Banach spaces", "value": 100, "id": "04"}, {"name": "Duality and reflexivity [See also 46A25]", "value": 100, "id": "10"}, {"name": "Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]", "value": 100, "id": "28"}, {"name": "Ultraproduct techniques in Banach space theory [See also 46M07]", "value": 100, "id": "08"}, {"name": "Probabilistic methods in Banach space theory [See also 60Bxx]", "value": 100, "id": "09"}, {"name": "Banach lattices [See also 46A40, 46B40]", "value": 100, "id": "42"}, {"name": "Compactness in Banach (or normed) spaces", "value": 100, "id": "50"}, {"name": "Ordered normed spaces [See also 46A40, 46B42]", "value": 100, "id": "40"}, {"name": "Geometry and structure of normed linear spaces", "value": 100, "id": "20"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Classical Banach spaces in the general theory", "value": 100, "id": "25"}, {"name": "Interpolation between normed linear spaces [See also 46M35]", "value": 100, "id": "70"}, {"name": "Radon-Nikod{y}m, Kreiin-Milman and related properties [See also 46G10]", "value": 100, "id": "22"}, {"name": "Summability and bases [See also 46A35]", "value": 100, "id": "15"}, {"name": "Nonlinear classification of Banach spaces; nonlinear quotients", "value": 100, "id": "80"}, {"name": "Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx]", "value": 100, "id": "85"}]}, {"id": "E", "name": "Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}", "children": [{"name": "Topological linear spaces of continuous, differentiable or analytic functions", "value": 100, "id": "10"}, {"name": "Sobolev (and similar kinds of) spaces of functions of discrete variables", "value": 100, "id": "39"}, {"name": "Spaces of measures [See also 28A33, 46Gxx]", "value": 100, "id": "27"}, {"name": "Hilbert spaces of continuous, differentiable or analytic functions", "value": 100, "id": "20"}, {"name": "Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]", "value": 100, "id": "22"}, {"name": "Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}", "value": 100, "id": "25"}, {"name": "Lattices of continuous, differentiable or analytic functions", "value": 100, "id": "05"}, {"name": "Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]", "value": 100, "id": "50"}, {"name": "Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Spaces of vector- and operator-valued functions", "value": 100, "id": "40"}, {"name": "Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)", "value": 100, "id": "30"}, {"name": "Banach spaces of continuous, differentiable or analytic functions", "value": 100, "id": "15"}]}, {"id": "G", "name": "Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]", "children": [{"name": "Vector-valued measures and integration [See also 28Bxx, 46B22]", "value": 100, "id": "10"}, {"name": "Measures and integration on abstract linear spaces [See also 28C20, 46T12]", "value": 100, "id": "12"}, {"name": "Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]", "value": 100, "id": "20"}, {"name": "(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]", "value": 100, "id": "25"}, {"name": "Derivatives [See also 46T20, 58C20, 58C25]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Functional analytic lifting theory [See also 28A51]", "value": 100, "id": "15"}]}, {"id": "F", "name": "Distributions, generalized functions, distribution spaces [See also 46T30]", "children": [{"name": "Operations with distributions", "value": 100, "id": "10"}, {"name": "Integral transforms in distribution spaces [See also 42-XX, 44-XX]", "value": 100, "id": "12"}, {"name": "Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]", "value": 100, "id": "20"}, {"name": "Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]", "value": 100, "id": "05"}, {"name": "Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Distributions on infinite-dimensional spaces [See also 58C35]", "value": 100, "id": "25"}, {"name": "Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]", "value": 100, "id": "15"}]}, {"id": "H", "name": "Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}", "children": [{"name": "Ideals and subalgebras", "value": 100, "id": "10"}, {"name": "Structure, classification of topological algebras", "value": 100, "id": "20"}, {"name": "Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)", "value": 100, "id": "25"}, {"name": "Functional calculus in topological algebras [See also 47A60]", "value": 100, "id": "30"}, {"name": "Topological algebras of operators [See mainly 47Lxx]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Automatic continuity", "value": 100, "id": "40"}, {"name": "Nonassociative topological algebras [See also 46K70, 46L70]", "value": 100, "id": "70"}, {"name": "Representations of topological algebras", "value": 100, "id": "15"}, {"name": "General theory of topological algebras", "value": 100, "id": "05"}]}, {"id": "K", "name": "Topological (rings and) algebras with an involution [See also 16W10]", "children": [{"name": "Representations of topological algebras with involution", "value": 100, "id": "10"}, {"name": "Hilbert algebras", "value": 100, "id": "15"}, {"name": "General theory of topological algebras with involution", "value": 100, "id": "05"}, {"name": "Nonselfadjoint (sub)algebras in algebras with involution", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonassociative topological algebras with an involution [See also 46H70, 46L70]", "value": 100, "id": "70"}]}, {"id": "J", "name": "Commutative Banach algebras and commutative topological algebras [See also 46E25]", "children": [{"name": "Banach algebras of continuous functions, function algebras [See also 46E25]", "value": 100, "id": "10"}, {"name": "Radical Banach algebras", "value": 100, "id": "45"}, {"name": "Ideals, maximal ideals, boundaries", "value": 100, "id": "20"}, {"name": "Representations of commutative topological algebras", "value": 100, "id": "25"}, {"name": "Subalgebras", "value": 100, "id": "30"}, {"name": "Structure, classification of commutative topological algebras", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]", "value": 100, "id": "15"}, {"name": "General theory of commutative topological algebras", "value": 100, "id": "05"}]}, {"id": "M", "name": "Methods of category theory in functional analysis [See also 18-XX]", "children": [{"name": "Projective and injective objects [See also 46A22]", "value": 100, "id": "10"}, {"name": "Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]", "value": 100, "id": "20"}, {"name": "Ultraproducts [See also 46B08, 46S20]", "value": 100, "id": "07"}, {"name": "Tensor products [See also 46A32, 46B28, 47A80]", "value": 100, "id": "05"}, {"name": "Homological methods (exact sequences, right inverses, lifting, etc.)", "value": 100, "id": "18"}, {"name": "Abstract interpolation of topological vector spaces [See also 46B70]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inductive and projective limits [See also 46A13]", "value": 100, "id": "40"}, {"name": "Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}", "value": 100, "id": "15"}]}, {"id": "L", "name": "Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx]", "children": [{"name": "Decomposition theory for $C^*$-algebras", "value": 100, "id": "45"}, {"name": "Noncommutative measure and integration", "value": 100, "id": "51"}, {"name": "Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]", "value": 100, "id": "60"}, {"name": "Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]", "value": 100, "id": "89"}, {"name": "Noncommutative probability and statistics", "value": 100, "id": "53"}, {"name": "$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]", "value": 100, "id": "80"}, {"name": "Noncommutative differential geometry [See also 58B32, 58B34, 58J22]", "value": 100, "id": "87"}, {"name": "Noncommutative topology [See also 58B32, 58B34, 58J22]", "value": 100, "id": "85"}, {"name": "Tensor products of $C^*$-algebras", "value": 100, "id": "06"}, {"name": "Operator spaces and completely bounded maps [See also 47L25]", "value": 100, "id": "07"}, {"name": "General theory of $C^*$-algebras", "value": 100, "id": "05"}, {"name": "$C^*$-modules", "value": 100, "id": "08"}, {"name": "Free products of $C^*$-algebras", "value": 100, "id": "09"}, {"name": "Automorphisms", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]", "value": 100, "id": "70"}, {"name": "General theory of von Neumann algebras", "value": 100, "id": "10"}, {"name": "Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]", "value": 100, "id": "55"}, {"name": "Free probability and free operator algebras", "value": 100, "id": "54"}, {"name": "Derivations, dissipations and positive semigroups in $C^*$-algebras", "value": 100, "id": "57"}, {"name": "States", "value": 100, "id": "30"}, {"name": "Subfactors and their classification", "value": 100, "id": "37"}, {"name": "Classification of factors", "value": 100, "id": "36"}, {"name": "Classifications of $C^*$-algebras", "value": 100, "id": "35"}, {"name": "Noncommutative function spaces", "value": 100, "id": "52"}, {"name": "Quantizations, deformations", "value": 100, "id": "65"}]}, {"id": "N", "name": "Miscellaneous applications of functional analysis [See also 47Nxx]", "children": [{"name": "Applications in optimization, convex analysis, mathematical programming, economics", "value": 100, "id": "10"}, {"name": "Applications to differential and integral equations", "value": 100, "id": "20"}, {"name": "Applications in statistical physics", "value": 100, "id": "55"}, {"name": "Applications in probability theory and statistics", "value": 100, "id": "30"}, {"name": "Applications in quantum physics", "value": 100, "id": "50"}, {"name": "Applications in numerical analysis [See also 65Jxx]", "value": 100, "id": "40"}, {"name": "Applications in biology and other sciences", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "S", "name": "Other (nonclassical) types of functional analysis [See also 47Sxx]", "children": [{"name": "Functional analysis over fields other than ${\\bf R}$ or ${\\bf C}$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]", "value": 100, "id": "10"}, {"name": "Nonstandard functional analysis [See also 03H05]", "value": 100, "id": "20"}, {"name": "Constructive functional analysis [See also 03F60]", "value": 100, "id": "30"}, {"name": "Functional analysis in probabilistic metric linear spaces", "value": 100, "id": "50"}, {"name": "Fuzzy functional analysis [See also 03E72]", "value": 100, "id": "40"}, {"name": "Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "T", "name": "Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]", "children": [{"name": "Manifolds of mappings", "value": 100, "id": "10"}, {"name": "Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]", "value": 100, "id": "12"}, {"name": "Continuous and differentiable maps [See also 46G05]", "value": 100, "id": "20"}, {"name": "Holomorphic maps [See also 46G20]", "value": 100, "id": "25"}, {"name": "Distributions and generalized functions on nonlinear spaces [See also 46Fxx]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]", "value": 100, "id": "05"}]}]}, {"id": "47", "name": "Operator theory", "children": [{"id": "A", "name": "General theory of linear operators", "children": [{"name": "Norms (inequalities, more than one norm, etc.)", "value": 100, "id": "30"}, {"name": "Functional calculus", "value": 100, "id": "60"}, {"name": "Equations involving linear operators, with operator unknowns", "value": 100, "id": "62"}, {"name": "Operator inequalities", "value": 100, "id": "63"}, {"name": "Operator means, shorted operators, etc.", "value": 100, "id": "64"}, {"name": "(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]", "value": 100, "id": "53"}, {"name": "Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators", "value": 100, "id": "66"}, {"name": "Representation theory", "value": 100, "id": "67"}, {"name": "Factorization theory (including Wiener-Hopf and spectral factorizations)", "value": 100, "id": "68"}, {"name": "Tensor products of operators [See also 46M05]", "value": 100, "id": "80"}, {"name": "Spectral sets", "value": 100, "id": "25"}, {"name": "Linear relations (multivalued linear operators)", "value": 100, "id": "06"}, {"name": "Forms (bilinear, sesquilinear, multilinear)", "value": 100, "id": "07"}, {"name": "Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.", "value": 100, "id": "48"}, {"name": "General (adjoints, conjugates, products, inverses, domains, ranges, etc.)", "value": 100, "id": "05"}, {"name": "Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.", "value": 100, "id": "46"}, {"name": "Canonical models for contractions and nonselfadjoint operators", "value": 100, "id": "45"}, {"name": "Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Eigenvalue problems [See also 47J10, 49R05]", "value": 100, "id": "75"}, {"name": "(Generalized) eigenfunction expansions; rigged Hilbert spaces", "value": 100, "id": "70"}, {"name": "Dilations, extensions, compressions", "value": 100, "id": "20"}, {"name": "Local spectral properties", "value": 100, "id": "11"}, {"name": "Spectrum, resolvent", "value": 100, "id": "10"}, {"name": "Several-variable operator theory (spectral, Fredholm, etc.)", "value": 100, "id": "13"}, {"name": "Numerical range, numerical radius", "value": 100, "id": "12"}, {"name": "Invariant subspaces [See also 47A46]", "value": 100, "id": "15"}, {"name": "Operator approximation theory", "value": 100, "id": "58"}, {"name": "Cyclic vectors, hypercyclic and chaotic operators", "value": 100, "id": "16"}, {"name": "Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]", "value": 100, "id": "55"}, {"name": "Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]", "value": 100, "id": "57"}, {"name": "Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)", "value": 100, "id": "56"}, {"name": "Equations and inequalities involving linear operators, with vector unknowns", "value": 100, "id": "50"}, {"name": "Ergodic theory [See also 28Dxx, 37Axx]", "value": 100, "id": "35"}, {"name": "Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]", "value": 100, "id": "52"}, {"name": "Structure theory", "value": 100, "id": "65"}]}, {"id": "C", "name": "Individual linear operators as elements of algebraic systems", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Operators in ${}^*$-algebras", "value": 100, "id": "10"}, {"name": "Operators in $C^*$- or von Neumann algebras", "value": 100, "id": "15"}, {"name": "Operators in algebras", "value": 100, "id": "05"}]}, {"id": "B", "name": "Special classes of linear operators", "children": [{"name": "Operators on spaces with an indefinite metric [See also 46C50]", "value": 100, "id": "50"}, {"name": "Operators on ordered spaces", "value": 100, "id": "60"}, {"name": "Positive operators and order-bounded operators", "value": 100, "id": "65"}, {"name": "Random operators [See also 47H40, 60H25]", "value": 100, "id": "80"}, {"name": "Symmetric and selfadjoint operators (unbounded)", "value": 100, "id": "25"}, {"name": "Subnormal operators, hyponormal operators, etc.", "value": 100, "id": "20"}, {"name": "Operators defined by compactness properties", "value": 100, "id": "07"}, {"name": "Operators on Banach algebras", "value": 100, "id": "48"}, {"name": "Transformers, preservers (operators on spaces of operators)", "value": 100, "id": "49"}, {"name": "Commutators, derivations, elementary operators, etc.", "value": 100, "id": "47"}, {"name": "Accretive operators, dissipative operators, etc.", "value": 100, "id": "44"}, {"name": "Spectral operators, decomposable operators, well-bounded operators, etc.", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators", "value": 100, "id": "06"}, {"name": "Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]", "value": 100, "id": "10"}, {"name": "Difference operators [See also 39A70]", "value": 100, "id": "39"}, {"name": "Operators on function spaces (general)", "value": 100, "id": "38"}, {"name": "Hermitian and normal operators (spectral measures, functional calculus, etc.)", "value": 100, "id": "15"}, {"name": "Composition operators", "value": 100, "id": "33"}, {"name": "Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]", "value": 100, "id": "32"}, {"name": "Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)", "value": 100, "id": "37"}, {"name": "Jacobi (tridiagonal) operators (matrices) and generalizations", "value": 100, "id": "36"}, {"name": "Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]", "value": 100, "id": "35"}, {"name": "Kernel operators", "value": 100, "id": "34"}]}, {"id": "E", "name": "Ordinary differential operators [See also 34Bxx, 34Lxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)", "value": 100, "id": "05"}]}, {"id": "D", "name": "Groups and semigroups of linear operators, their generalizations and applications", "children": [{"name": "Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}", "value": 100, "id": "03"}, {"name": "One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]", "value": 100, "id": "06"}, {"name": "Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}", "value": 100, "id": "07"}, {"name": "Schrodinger and Feynman-Kac semigroups", "value": 100, "id": "08"}, {"name": "Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]", "value": 100, "id": "09"}, {"name": "$C$-semigroups, regularized semigroups", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integrated semigroups", "value": 100, "id": "62"}]}, {"id": "G", "name": "Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integral operators [See also 45P05]", "value": 100, "id": "10"}, {"name": "Pseudodifferential operators [See also 35Sxx, 58Jxx]", "value": 100, "id": "30"}, {"name": "Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]", "value": 100, "id": "20"}, {"name": "Potential operators [See also 31-XX]", "value": 100, "id": "40"}]}, {"id": "F", "name": "Partial differential operators [See also 35Pxx, 58Jxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)", "value": 100, "id": "05"}]}, {"id": "H", "name": "Nonlinear operators and their properties {For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx}", "children": [{"name": "Degree theory [See also 55M25, 58C30]", "value": 100, "id": "11"}, {"name": "Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]", "value": 100, "id": "10"}, {"name": "Particular nonlinear operators (superposition, Hammerstein, Nemytskiii, Uryson, etc.) [See also 45Gxx, 45P05]", "value": 100, "id": "30"}, {"name": "Accretive operators, dissipative operators, etc.", "value": 100, "id": "06"}, {"name": "Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces", "value": 100, "id": "07"}, {"name": "Set-valued operators [See also 28B20, 54C60, 58C06]", "value": 100, "id": "04"}, {"name": "Monotone operators and generalizations", "value": 100, "id": "05"}, {"name": "Measures of noncompactness and condensing mappings, $K$-set contractions, etc.", "value": 100, "id": "08"}, {"name": "Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.", "value": 100, "id": "09"}, {"name": "Random operators [See also 47B80, 60H25]", "value": 100, "id": "40"}, {"name": "Multilinear and polynomial operators [See also 46G25]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]", "value": 100, "id": "25"}, {"name": "Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]", "value": 100, "id": "20"}, {"name": "Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15]", "value": 100, "id": "14"}]}, {"id": "J", "name": "Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}", "children": [{"name": "Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]", "value": 100, "id": "10"}, {"name": "Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]", "value": 100, "id": "06"}, {"name": "Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]", "value": 100, "id": "15"}, {"name": "Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]", "value": 100, "id": "07"}, {"name": "Variational and other types of inclusions [See also 34A60, 49J21, 49K21]", "value": 100, "id": "22"}, {"name": "Equations involving nonlinear operators (general) [See also 47H10, 47J25]", "value": 100, "id": "05"}, {"name": "Variational methods [See also 58Exx]", "value": 100, "id": "30"}, {"name": "Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Iterative procedures [See also 65J15]", "value": 100, "id": "25"}, {"name": "Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]", "value": 100, "id": "20"}, {"name": "Equations with hysteresis operators [See also 34C55, 74N30]", "value": 100, "id": "40"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "L", "name": "Linear spaces and algebras of operators [See also 46Lxx]", "children": [{"name": "Algebras of operators on Banach spaces and other topological linear spaces", "value": 100, "id": "10"}, {"name": "Dual algebras; weakly closed singly generated operator algebras", "value": 100, "id": "45"}, {"name": "Operator ideals [See also 47B10]", "value": 100, "id": "20"}, {"name": "Convex sets and cones of operators [See also 46A55]", "value": 100, "id": "07"}, {"name": "Ideals of polynomials and of multilinear mappings", "value": 100, "id": "22"}, {"name": "Linear spaces of operators [See also 46A32 and 46B28]", "value": 100, "id": "05"}, {"name": "Representations of (nonselfadjoint) operator algebras", "value": 100, "id": "55"}, {"name": "Abstract operator algebras on Hilbert spaces", "value": 100, "id": "30"}, {"name": "Dual spaces of operator algebras", "value": 100, "id": "50"}, {"name": "Nest algebras, CSL algebras", "value": 100, "id": "35"}, {"name": "Algebras of unbounded operators; partial algebras of operators", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other nonselfadjoint operator algebras", "value": 100, "id": "75"}, {"name": "Operator spaces (= matricially normed spaces) [See also 46L07]", "value": 100, "id": "25"}, {"name": "Nonassociative nonselfadjoint operator algebras", "value": 100, "id": "70"}, {"name": "Operator algebras with symbol structure", "value": 100, "id": "15"}, {"name": "Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)", "value": 100, "id": "80"}, {"name": "Limit algebras, subalgebras of $C^*$-algebras", "value": 100, "id": "40"}, {"name": "Applications of operator algebras to physics", "value": 100, "id": "90"}, {"name": "Crossed product algebras (analytic crossed products)", "value": 100, "id": "65"}]}, {"id": "N", "name": "Miscellaneous applications of operator theory [See also 46Nxx]", "children": [{"name": "Applications in optimization, convex analysis, mathematical programming, economics", "value": 100, "id": "10"}, {"name": "Applications to differential and integral equations", "value": 100, "id": "20"}, {"name": "Applications in probability theory and statistics", "value": 100, "id": "30"}, {"name": "Applications in the physical sciences", "value": 100, "id": "50"}, {"name": "Applications in numerical analysis [See also 65Jxx]", "value": 100, "id": "40"}, {"name": "Applications in chemistry and life sciences", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications in systems theory, circuits, and control theory", "value": 100, "id": "70"}]}, {"id": "S", "name": "Other (nonclassical) types of operator theory [See also 46Sxx]", "children": [{"name": "Operator theory over fields other than ${\\bf R}$, ${\\bf C}$ or the quaternions; non-Archimedean operator theory", "value": 100, "id": "10"}, {"name": "Nonstandard operator theory [See also 03H05]", "value": 100, "id": "20"}, {"name": "Constructive operator theory [See also 03F60]", "value": 100, "id": "30"}, {"name": "Operator theory in probabilistic metric linear spaces [See also 54E70]", "value": 100, "id": "50"}, {"name": "Fuzzy operator theory [See also 03E72]", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}]}, {"id": "44", "name": "Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms i", "children": [{"id": "A", "name": "Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms i", "children": [{"name": "Laplace transform", "value": 100, "id": "10"}, {"name": "Radon transform [See also 92C55]", "value": 100, "id": "12"}, {"name": "Transforms of special functions", "value": 100, "id": "20"}, {"name": "General transforms [See also 42A38]", "value": 100, "id": "05"}, {"name": "Discrete operational calculus", "value": 100, "id": "55"}, {"name": "Multiple transforms", "value": 100, "id": "30"}, {"name": "Classical operational calculus", "value": 100, "id": "45"}, {"name": "Convolution", "value": 100, "id": "35"}, {"name": "Moment problems", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Calculus of Mikusi{n}ski and other operational calculi", "value": 100, "id": "40"}, {"name": "Special transforms (Legendre, Hilbert, etc.)", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "42", "name": "Harmonic analysis on Euclidean spaces", "children": [{"id": "A", "name": "Harmonic analysis in one variable", "children": [{"name": "Summability and absolute summability of Fourier and trigonometric series", "value": 100, "id": "24"}, {"name": "Trigonometric approximation", "value": 100, "id": "10"}, {"name": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "value": 100, "id": "38"}, {"name": "Convergence and absolute convergence of Fourier and trigonometric series", "value": 100, "id": "20"}, {"name": "Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}", "value": 100, "id": "16"}, {"name": "Lacunary series of trigonometric and other functions; Riesz products", "value": 100, "id": "55"}, {"name": "Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)", "value": 100, "id": "32"}, {"name": "Trigonometric polynomials, inequalities, extremal problems", "value": 100, "id": "05"}, {"name": "Multipliers", "value": 100, "id": "45"}, {"name": "Conjugate functions, conjugate series, singular integrals", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Probabilistic methods", "value": 100, "id": "61"}, {"name": "Classical almost periodic functions, mean periodic functions [See also 43A60]", "value": 100, "id": "75"}, {"name": "Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization", "value": 100, "id": "63"}, {"name": "Completeness of sets of functions", "value": 100, "id": "65"}, {"name": "Trigonometric moment problems", "value": 100, "id": "70"}, {"name": "Positive definite functions", "value": 100, "id": "82"}, {"name": "Trigonometric interpolation", "value": 100, "id": "15"}, {"name": "Convolution, factorization", "value": 100, "id": "85"}]}, {"id": "C", "name": "Nontrigonometric harmonic analysis", "children": [{"name": "Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)", "value": 100, "id": "10"}, {"name": "Other transformations of harmonic type", "value": 100, "id": "20"}, {"name": "Uniqueness and localization for orthogonal series", "value": 100, "id": "25"}, {"name": "Completeness of sets of functions", "value": 100, "id": "30"}, {"name": "Wavelets and other special systems", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "General harmonic expansions, frames", "value": 100, "id": "15"}, {"name": "Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]", "value": 100, "id": "05"}]}, {"id": "B", "name": "Harmonic analysis in several variables {For automorphic theory, see mainly 11F30}", "children": [{"name": "Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type", "value": 100, "id": "10"}, {"name": "Singular and oscillatory integrals (Calderon-Zygmund, etc.)", "value": 100, "id": "20"}, {"name": "Fourier series and coefficients", "value": 100, "id": "05"}, {"name": "Summability", "value": 100, "id": "08"}, {"name": "$H^p$-spaces", "value": 100, "id": "30"}, {"name": "Harmonic analysis and PDE [See also 35-XX]", "value": 100, "id": "37"}, {"name": "Function spaces arising in harmonic analysis", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Maximal functions, Littlewood-Paley theory", "value": 100, "id": "25"}, {"name": "Multipliers", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "43", "name": "Abstract harmonic analysis {For other analysis on topological and Lie groups, 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and multipliers of function spaces on groups, semigroups, etc.", "value": 100, "id": "22"}, {"name": "Measures on groups and semigroups, etc.", "value": 100, "id": "05"}, {"name": "Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)", "value": 100, "id": "46"}, {"name": "Spectral synthesis on groups, semigroups, etc.", "value": 100, "id": "45"}, {"name": "Character groups and dual objects", "value": 100, "id": "40"}, {"name": "Analysis on general compact groups", "value": 100, "id": "77"}, {"name": "Analysis on specific compact groups", "value": 100, "id": "75"}, {"name": "Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]", "value": 100, "id": "70"}, {"name": "Spherical functions [See also 22E45, 22E46, 33C55]", "value": 100, "id": "90"}, {"name": "Categorical methods [See also 46Mxx]", "value": 100, "id": "95"}, {"name": "Measure algebras on groups, semigroups, etc.", "value": 100, "id": "10"}, {"name": "$L^p$-spaces and other function spaces on groups, semigroups, etc.", "value": 100, "id": "15"}, {"name": "Analysis on ordered groups, $H^p$-theory", "value": 100, "id": "17"}, {"name": "Summability methods on groups, semigroups, etc. [See also 40J05]", "value": 100, "id": "55"}, {"name": "Other transforms and operators of Fourier type", "value": 100, "id": "32"}, {"name": "Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.", "value": 100, "id": "30"}, {"name": "Convergence of Fourier series and of inverse transforms", "value": 100, "id": "50"}, {"name": "Positive definite functions on groups, semigroups, etc.", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}]}, {"id": "GEO", "name": "Geometry & Topology", "children": [{"id": "55", "name": "Algebraic topology", "children": [{"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 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"05"}]}, {"id": "N", "name": "Homology and cohomology theories [See also 57Txx]", "children": [{"name": "Singular theory", "value": 100, "id": "10"}, {"name": "Products and intersections", "value": 100, "id": "45"}, {"name": "Generalized (extraordinary) homology and cohomology theories", "value": 100, "id": "20"}, {"name": "Steenrod-Sitnikov homologies", "value": 100, "id": "07"}, {"name": "Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]", "value": 100, "id": "22"}, {"name": "\\v Cech types", "value": 100, "id": "05"}, {"name": "Intersection homology and cohomology", "value": 100, "id": "33"}, {"name": "Orbifold cohomology", "value": 100, "id": "32"}, {"name": "Sheaf cohomology [See also 18F20, 32C35, 32L10]", "value": 100, "id": "30"}, {"name": "Other homology theories", "value": 100, "id": "35"}, {"name": "Elliptic cohomology", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Homology with local coefficients, equivariant cohomology", "value": 100, "id": "25"}, {"name": "Equivariant homology and cohomology [See also 19L47]", "value": 100, "id": "91"}, {"name": "$K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}", "value": 100, "id": "15"}, {"name": "Axioms for homology theory and uniqueness theorems", "value": 100, "id": "40"}]}, {"id": "Q", "name": "Homotopy groups", "children": [{"name": "Stable homotopy groups", "value": 100, "id": "10"}, {"name": "Homotopy groups of wedges, joins, and simple spaces", "value": 100, "id": "20"}, {"name": "Shape groups", "value": 100, "id": "07"}, {"name": "Hopf invariants", "value": 100, "id": "25"}, {"name": "Cohomotopy groups", "value": 100, "id": "55"}, {"name": "Stable homotopy of spheres", "value": 100, "id": "45"}, {"name": "$v_n$-periodicity", "value": 100, "id": "51"}, {"name": "$J$-morphism [See also 19L20]", "value": 100, "id": "50"}, {"name": "Operations in homotopy groups", "value": 100, "id": "35"}, {"name": "Homotopy groups of special spaces", "value": 100, "id": "52"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Homotopy groups of spheres", "value": 100, "id": "40"}, {"name": "Homotopy groups of special types [See also 55N05, 55N07]", "value": 100, "id": "70"}, {"name": "Equivariant homotopy groups [See also 19L47]", "value": 100, "id": "91"}, {"name": "Whitehead products and generalizations", "value": 100, "id": "15"}, {"name": "Homotopy groups, general; sets of homotopy classes", "value": 100, "id": "05"}]}, {"id": "P", "name": "Homotopy theory {For simple homotopy type, see 57Q10}", "children": [{"name": "Localization and completion", "value": 100, "id": "60"}, {"name": "Rational homotopy theory", "value": 100, "id": "62"}, {"name": "Homotopy functors", "value": 100, "id": "65"}, {"name": "Spanier-Whitehead duality", "value": 100, "id": "25"}, {"name": "Eilenberg-Mac Lane spaces", "value": 100, "id": "20"}, {"name": "Loop space machines, operads [See also 18D50]", "value": 100, "id": "48"}, {"name": "Homotopy extension properties, cofibrations", "value": 100, "id": "05"}, {"name": "Infinite loop spaces", "value": 100, "id": "47"}, {"name": "$H$-spaces and duals", "value": 100, "id": "45"}, {"name": "Stable homotopy theory, spectra", "value": 100, "id": "42"}, {"name": "Spectra with additional structure ($E_\\infty$, $A_\\infty$, ring spectra, etc.)", "value": 100, "id": "43"}, {"name": "Suspensions", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Equivariant homotopy theory [See also 19L47]", "value": 100, "id": "91"}, {"name": "Relations between equivariant and nonequivariant homotopy theory", "value": 100, "id": "92"}, {"name": "Homotopy equivalences", "value": 100, "id": "10"}, {"name": "Classification of homotopy type", "value": 100, "id": "15"}, {"name": "Shape theory [See also 54C56, 55Q07]", "value": 100, 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of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}", "value": 100, "id": "50"}, {"name": "Classifying spaces of groups and $H$-spaces", "value": 100, "id": "35"}, {"name": "Microbundles and block bundles [See also 57N55, 57Q50]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Sphere bundles and vector bundles", "value": 100, "id": "25"}, {"name": "Fibrewise topology", "value": 100, "id": "70"}, {"name": "Equivariant fiber spaces and bundles [See also 19L47]", "value": 100, "id": "91"}, {"name": "Classification", "value": 100, "id": "15"}, {"name": "Discriminantal varieties, configuration spaces", "value": 100, "id": "80"}, {"name": "Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]", "value": 100, "id": "40"}, {"name": "Generalizations of fiber spaces and bundles", "value": 100, "id": "65"}]}, {"id": "U", "name": "Applied homological algebra and category theory [See also 18Gxx]", "children": [{"name": "Simplicial sets and complexes", "value": 100, "id": "10"}, {"name": "Universal coefficient theorems, Bockstein operator", "value": 100, "id": "20"}, {"name": "Homology of a product, Kunneth formula", "value": 100, "id": "25"}, {"name": "Duality", "value": 100, "id": "30"}, {"name": "Abstract and axiomatic homotopy theory", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Topological categories, foundations of homotopy theory", "value": 100, "id": "40"}, {"name": "Chain complexes", "value": 100, "id": "15"}, {"name": "Abstract complexes", "value": 100, "id": "05"}]}, {"id": "T", "name": "Spectral sequences [See also 18G40, 55R20]", "children": [{"name": "Serre spectral sequences", "value": 100, "id": "10"}, {"name": "Adams spectral sequences", "value": 100, "id": "15"}, {"name": "Generalized cohomology", "value": 100, "id": "25"}, {"name": "General", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Eilenberg-Moore spectral sequences [See also 57T35]", "value": 100, "id": "20"}]}]}, {"id": "54", "name": "General topology {For the topology of manifolds of all dimensions, see 57Nxx}", "children": [{"id": "A", "name": "Generalities", "children": [{"name": "Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)", "value": 100, "id": "10"}, {"name": "Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)", "value": 100, "id": "20"}, {"name": "Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}", "value": 100, "id": "25"}, {"name": "Topological spaces and generalizations (closure spaces, etc.)", "value": 100, "id": "05"}, {"name": "Consistency and independence results [See also 03E35]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Fuzzy topology [See also 03E72]", "value": 100, "id": "40"}, {"name": "Syntopogeneous structures", "value": 100, "id": "15"}]}, {"id": "C", "name": "Maps and general types of spaces defined by maps", "children": [{"name": "Special maps on topological spaces (open, closed, perfect, etc.)", "value": 100, "id": "10"}, {"name": "Real-valued functions [See also 26-XX]", "value": 100, "id": "30"}, {"name": "Extension of maps", "value": 100, "id": "20"}, {"name": "Embedding", "value": 100, "id": "25"}, {"name": "Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]", "value": 100, "id": "55"}, {"name": "Weak and generalized continuity", "value": 100, "id": "08"}, {"name": "Shape theory [See also 55P55, 57N25]", "value": 100, "id": "56"}, {"name": "$C$- and $C^*$-embedding", "value": 100, "id": "45"}, {"name": "Function spaces [See also 46Exx, 58D15]", "value": 100, "id": "35"}, {"name": "Special sets defined by functions [See also 26A21]", "value": 100, "id": "50"}, {"name": "Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Algebraic properties of function spaces [See also 46J10]", "value": 100, "id": "40"}, {"name": "Entropy", "value": 100, "id": "70"}, {"name": "Retraction", "value": 100, "id": "15"}, {"name": "Continuous maps", "value": 100, "id": "05"}, {"name": "Selections [See also 28B20]", "value": 100, "id": "65"}]}, {"id": "B", "name": "Basic constructions", "children": [{"name": "Product spaces", "value": 100, "id": "10"}, {"name": "Hyperspaces", "value": 100, "id": "20"}, {"name": "Adjunction spaces and similar constructions", "value": 100, "id": "17"}, {"name": "Subspaces", "value": 100, "id": "05"}, {"name": "Categorical methods [See also 18B30]", "value": 100, "id": "30"}, {"name": "Spectra", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Presheaves and sheaves [See also 18F20]", "value": 100, "id": "40"}, {"name": "Quotient spaces, decompositions", "value": 100, "id": "15"}]}, {"id": "E", "name": "Spaces with richer structures", "children": [{"name": "Semimetric spaces", "value": 100, "id": "25"}, {"name": "Compact (locally compact) metric spaces", "value": 100, "id": "45"}, {"name": "Stratifiable spaces, cosmic spaces, etc.", "value": 100, "id": "20"}, {"name": "Nearness spaces", "value": 100, "id": "17"}, {"name": "Proximity structures and generalizations", "value": 100, "id": "05"}, {"name": "Bitopologies", "value": 100, "id": "55"}, {"name": "$p$-spaces, $M$-spaces, $\\sigma$-spaces, etc.", "value": 100, "id": "18"}, {"name": "Moore spaces", "value": 100, "id": "30"}, {"name": "Complete metric spaces", "value": 100, "id": "50"}, {"name": "Metric spaces, metrizability", "value": 100, "id": "35"}, {"name": "Baire category, Baire spaces", "value": 100, "id": "52"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Special maps on metric spaces", "value": 100, "id": "40"}, {"name": "Probabilistic metric spaces", "value": 100, "id": "70"}, {"name": "Uniform structures and generalizations", "value": 100, "id": "15"}]}, {"id": "D", "name": "Fairly general properties", "children": [{"name": "Lower separation axioms ($T_0$--$T_3$, etc.)", "value": 100, "id": "10"}, {"name": "Local compactness, $\\sigma$-compactness", "value": 100, "id": "45"}, {"name": "Noncompact covering properties (paracompact, Lindelof, etc.)", "value": 100, "id": "20"}, {"name": "``$P$-minimal'' and ``$P$-closed'' spaces", "value": 100, "id": "25"}, {"name": "Sequential spaces", "value": 100, "id": "55"}, {"name": "Compactness", "value": 100, "id": "30"}, {"name": "$k$-spaces", "value": 100, "id": "50"}, {"name": "Extensions of spaces (compactifications, supercompactifications, completions, etc.)", "value": 100, "id": "35"}, {"name": "Realcompactness and realcompactification", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Remainders", "value": 100, "id": "40"}, {"name": "Base properties", "value": 100, "id": "70"}, {"name": "Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)", "value": 100, "id": "15"}, {"name": "Special constructions of spaces (spaces of ultrafilters, etc.)", "value": 100, "id": "80"}, {"name": "Connected and locally connected spaces (general aspects)", "value": 100, "id": "05"}, {"name": "Separability", "value": 100, "id": "65"}]}, {"id": "G", "name": "Peculiar spaces", "children": [{"name": "$P$-spaces", "value": 100, "id": "10"}, {"name": "Scattered spaces", "value": 100, "id": "12"}, {"name": "Counterexamples", "value": 100, "id": "20"}, {"name": "Extremally disconnected spaces, $F$-spaces, etc.", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Pathological spaces", "value": 100, "id": "15"}]}, {"id": "F", "name": "Special properties", "children": [{"name": "Continua and generalizations", "value": 100, "id": "15"}, {"name": "Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]", "value": 100, "id": "05"}, {"name": "Unicoherence, multicoherence", "value": 100, "id": "55"}, {"name": "Dimension theory [See also 55M10]", "value": 100, "id": "45"}, {"name": "Spaces of dimension $\\leq 1$; curves, dendrites [See also 26A03]", "value": 100, "id": "50"}, {"name": "Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Topological characterizations of particular spaces", "value": 100, "id": "65"}]}, {"id": "H", "name": "Connections with other structures, applications", "children": [{"name": "Topological groups [See also 22A05]", "value": 100, "id": "11"}, {"name": "Topological representations of algebraic systems [See also 22-XX]", "value": 100, "id": "10"}, {"name": "Topological fields, rings, etc. [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80}", "value": 100, "id": "13"}, {"name": "Topological lattices, etc. [See also 06B30, 06F30]", "value": 100, "id": "12"}, {"name": "Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]", "value": 100, "id": "15"}, {"name": "Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Fixed-point and coincidence theorems [See also 47H10, 55M20]", "value": 100, "id": "25"}, {"name": "Topological dynamics [See also 28Dxx, 37Bxx]", "value": 100, "id": "20"}]}, {"id": "J", "name": "Nonstandard topology [See also 03H05]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonstandard topology [See also 03H05]", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "57", "name": "Manifolds and cell complexes {For complex manifolds, see 32Qxx}", "children": [{"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "M", "name": "Low-dimensional topology", "children": [{"name": "Covering spaces", "value": 100, "id": "10"}, {"name": "Special coverings, e.g. branched", "value": 100, "id": "12"}, {"name": "Two-dimensional complexes", "value": 100, "id": "20"}, {"name": "Topological methods in group theory", "value": 100, "id": "07"}, {"name": "Fundamental group, presentations, free differential calculus", "value": 100, "id": "05"}, {"name": "Wild knots and surfaces, etc., wild embeddings", "value": 100, "id": "30"}, {"name": "Geometric structures on low-dimensional manifolds", "value": 100, "id": "50"}, {"name": "Dehn's lemma, sphere theorem, loop theorem, asphericity", "value": 100, "id": "35"}, {"name": "Group actions in low dimensions", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Invariants of knots and 3-manifolds", "value": 100, "id": "27"}, {"name": "Knots and links in $S^3$ {For higher dimensions, see 57Q45}", "value": 100, "id": "25"}, {"name": "Relations with graph theory [See also 05Cxx]", "value": 100, "id": "15"}, {"name": "Characterizations of $E^3$ and $S^3$ (Poincare conjecture) [See also 57N12]", "value": 100, "id": "40"}]}, {"id": "N", "name": "Topological manifolds", "children": [{"name": "Cellularity", "value": 100, "id": "60"}, {"name": "Algebraic topology of manifolds", "value": 100, "id": "65"}, {"name": "Stratifications", "value": 100, "id": "80"}, {"name": "Shapes [See also 54C56, 55P55, 55Q07]", "value": 100, "id": "25"}, {"name": "Topology of infinite-dimensional manifolds [See also 58Bxx]", "value": 100, "id": "20"}, {"name": "Topology of $E^2$, $2$-manifolds", "value": 100, "id": "05"}, {"name": "Flatness and tameness", "value": 100, "id": "45"}, {"name": "Neighborhoods of submanifolds", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "General position and transversality", "value": 100, "id": "75"}, {"name": "Cobordism and concordance", "value": 100, "id": "70"}, {"name": "Topology of general $3$-manifolds [See also 57Mxx]", "value": 100, "id": "10"}, {"name": "Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]", "value": 100, "id": "13"}, {"name": "Topology of $E^3$ and $S^3$ [See also 57M40]", "value": 100, "id": "12"}, {"name": "Topology of $E^n$, $n$-manifolds ($4 \\less n \\less \\infty$)", "value": 100, "id": "15"}, {"name": "Topology of topological vector spaces", "value": 100, "id": "17"}, {"name": "Geometric structures on manifolds [See also 57M50]", "value": 100, "id": "16"}, {"name": "Microbundles and block bundles [See also 55R60, 57Q50]", "value": 100, "id": "55"}, {"name": "Engulfing", "value": 100, "id": "30"}, {"name": "Isotopy and pseudo-isotopy", "value": 100, "id": "37"}, {"name": "$S^{n-1}\\subset E^n$, Schoenflies problem", "value": 100, "id": "50"}, {"name": "Embeddings and immersions", "value": 100, "id": "35"}]}, {"id": "Q", "name": "PL-topology", "children": [{"name": "Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]", "value": 100, "id": "10"}, {"name": "Wall finiteness obstruction for CW-complexes", "value": 100, "id": "12"}, {"name": "Cobordism", "value": 100, "id": "20"}, {"name": "General topology of complexes", "value": 100, "id": "05"}, {"name": "Approximations", "value": 100, "id": "55"}, {"name": "Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}", "value": 100, "id": "45"}, {"name": "Isotopy", "value": 100, "id": "37"}, {"name": "Microbundles and block bundles [See also 55R60, 57N55]", "value": 100, "id": "50"}, {"name": "Embeddings and immersions", "value": 100, "id": "35"}, {"name": "Cobordism and concordance", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Comparison of PL-structures: classification, Hauptvermutung", "value": 100, "id": "25"}, {"name": "Engulfing", "value": 100, "id": "30"}, {"name": "Equivariant PL-topology", "value": 100, "id": "91"}, {"name": "Triangulating manifolds", "value": 100, "id": "15"}, {"name": "Regular neighborhoods", "value": 100, "id": "40"}, {"name": "General position and transversality", "value": 100, "id": "65"}]}, {"id": "P", "name": "Generalized 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transformations", "value": 100, "id": "15"}]}, {"id": "R", "name": "Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}", "children": [{"name": "Topological quantum field theories", "value": 100, "id": "56"}, {"name": "Homotopy spheres, Poincare conjecture", "value": 100, "id": "60"}, {"name": "Surgery and handlebodies", "value": 100, "id": "65"}, {"name": "Surgery obstructions, Wall groups [See also 19J25]", "value": 100, "id": "67"}, {"name": "$h$- and $s$-cobordism", "value": 100, "id": "80"}, {"name": "Equivariant cobordism", "value": 100, "id": "85"}, {"name": "Vector fields, frame fields", "value": 100, "id": "25"}, {"name": "Controllability of vector fields on $C^\\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]", "value": 100, "id": "27"}, {"name": "Characteristic classes and numbers", "value": 100, "id": "20"}, {"name": "Topology of vector bundles and fiber bundles [See also 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{"id": "B", "name": "Nonlinear incidence geometry", "children": [{"name": "Mobius geometries", "value": 100, "id": "10"}, {"name": "Laguerre geometries", "value": 100, "id": "15"}, {"name": "Lie geometries", "value": 100, "id": "25"}, {"name": "General theory", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Minkowski geometries", "value": 100, "id": "20"}]}, {"id": "E", "name": "Finite geometry and special incidence structures", "children": [{"name": "Buildings and the geometry of diagrams", "value": 100, "id": "24"}, {"name": "Steiner systems", "value": 100, "id": "10"}, {"name": "Other finite linear geometries", "value": 100, "id": "26"}, {"name": "Generalized quadrangles, generalized polygons", "value": 100, "id": "12"}, {"name": "Combinatorial structures in finite projective spaces [See also 05Bxx]", "value": 100, "id": "20"}, {"name": "Finite partial geometries (general), nets, partial spreads", "value": 100, "id": "14"}, {"name": "Linear codes and caps in Galois spaces [See also 94B05]", "value": 100, "id": "22"}, {"name": "General block designs [See also 05B05]", "value": 100, "id": "05"}, {"name": "Spreads and packing problems", "value": 100, "id": "23"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other finite nonlinear geometries", "value": 100, "id": "25"}, {"name": "Other finite incidence structures [See also 05B30]", "value": 100, "id": "30"}, {"name": "Affine and projective planes", "value": 100, "id": "15"}, {"name": "Blocking sets, ovals, $k$-arcs", "value": 100, "id": "21"}]}, {"id": "D", "name": "Geometric closure systems", "children": [{"name": "Abstract geometries with exchange axiom", "value": 100, "id": "10"}, {"name": "Combinatorial geometries [See also 05B25, 05B35]", "value": 100, "id": "20"}, {"name": "Lattices of subspaces [See also 05B35]", "value": 100, "id": "25"}, {"name": "Continuous geometries and related topics [See also 06Cxx]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Abstract geometries with parallelism", "value": 100, "id": "15"}, {"name": "Abstract (Maeda) geometries", "value": 100, "id": "05"}]}, {"id": "G", "name": "Ordered geometries (ordered incidence structures, etc.)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ordered geometries (ordered incidence structures, etc.)", "value": 100, "id": "05"}]}, {"id": "F", "name": "Metric geometry", "children": [{"name": "Absolute spaces", "value": 100, "id": "10"}, {"name": "Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]", "value": 100, "id": "15"}, {"name": "Orthogonal and unitary groups [See also 20H05]", "value": 100, "id": "25"}, {"name": "Absolute planes", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Congruence and orthogonality [See also 20H05]", "value": 100, "id": "20"}]}, {"id": "H", "name": "Topological geometry", "children": [{"name": "Topological linear incidence structures", "value": 100, "id": "10"}, {"name": "Topological geometries on manifolds [See also 57-XX]", "value": 100, "id": "20"}, {"name": "Geometries with differentiable structure [See also 53Cxx, 53C70]", "value": 100, "id": "25"}, {"name": "Geometries with algebraic manifold structure [See also 14-XX]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Topological nonlinear incidence structures", "value": 100, "id": "15"}, {"name": "General theory", "value": 100, "id": "05"}]}, {"id": "K", "name": "Distance geometry", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Synthetic differential geometry", "value": 100, "id": "10"}, {"name": "General theory", "value": 100, "id": "05"}]}, {"id": "J", "name": "Incidence groups", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Projective incidence groups", "value": 100, "id": "10"}, {"name": "General theory", "value": 100, "id": "05"}, {"name": "Kinematic spaces", "value": 100, "id": "15"}, {"name": "Representation by near-fields and near-algebras [See also 12K05, 16Y30]", "value": 100, "id": "20"}]}, {"id": "M", "name": "Real and complex geometry", "children": [{"name": "Hyperbolic and elliptic geometries (general) and generalizations", "value": 100, "id": "10"}, {"name": "Elementary problems in hyperbolic and elliptic geometries", "value": 100, "id": "09"}, {"name": "Geometric constructions", "value": 100, "id": "15"}, {"name": "Elementary problems in Euclidean geometries", "value": 100, "id": "04"}, {"name": "Inequalities and extremum problems {For convex problems, see 52A40}", "value": 100, "id": "16"}, {"name": "Line geometries and their generalizations [See also 53A25]", "value": 100, "id": "30"}, {"name": "Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Length, area and volume [See also 26B15]", "value": 100, "id": "25"}, {"name": "Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]", "value": 100, "id": "20"}, {"name": "Euclidean geometries (general) and generalizations", "value": 100, "id": "05"}]}, {"id": "L", "name": "Geometric order structures [See also 53C75]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Directly differentiable curves", "value": 100, "id": "10"}, {"name": "Geometry of orders of nondifferentiable curves", "value": 100, "id": "05"}, {"name": "$n$-vertex theorems via direct methods", "value": 100, "id": "15"}, {"name": "Geometry of orders of surfaces", "value": 100, "id": "20"}]}, {"id": "N", "name": "Analytic and descriptive geometry", "children": [{"name": "Affine analytic geometry", "value": 100, "id": "10"}, {"name": "Euclidean analytic geometry", "value": 100, "id": "20"}, {"name": "Analytic geometry with other transformation groups", "value": 100, "id": "25"}, {"name": "Geometry of classical groups [See also 20Gxx, 14L35]", "value": 100, "id": "30"}, {"name": "Questions of classical algebraic geometry [See also 14Nxx]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Projective analytic geometry", "value": 100, "id": "15"}, {"name": "Descriptive geometry [See also 65D17, 68U07]", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "P", "name": "Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)", "value": 100, "id": "05"}]}]}, {"id": "53", "name": "Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}", "children": [{"id": "A", "name": "Classical differential geometry", "children": [{"name": "Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]", "value": 100, "id": "10"}, {"name": "Vector and tensor analysis", "value": 100, "id": "45"}, {"name": "Affine differential geometry", "value": 100, "id": "15"}, {"name": "Higher-dimensional and -codimensional surfaces in Euclidean $n$-space", "value": 100, "id": "07"}, {"name": "Kinematics", "value": 100, "id": "17"}, {"name": "Surfaces in Euclidean space", "value": 100, "id": "05"}, {"name": "Differential invariants (local theory), geometric objects", "value": 100, "id": "55"}, {"name": "Conformal differential geometry", "value": 100, "id": "30"}, {"name": "Non-Euclidean differential geometry", "value": 100, "id": "35"}, {"name": "Geometry of webs [See also 14C21, 20N05]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Differential line geometry", "value": 100, "id": "25"}, {"name": "Projective differential geometry", "value": 100, "id": "20"}, {"name": "Other special differential geometries", "value": 100, "id": "40"}, {"name": "Curves in Euclidean space", "value": 100, "id": "04"}]}, {"id": "C", "name": "Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]", "children": [{"name": "Other complex differential geometry [See also 32Cxx]", "value": 100, "id": "56"}, {"name": "Twistor methods [See also 32L25]", "value": 100, "id": "28"}, {"name": "Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]", "value": 100, "id": "30"}, {"name": "Differential geometric aspects of harmonic maps [See also 58E20]", "value": 100, "id": "43"}, {"name": "Finsler spaces and generalizations (areal metrics) [See also 58B20]", "value": 100, "id": "60"}, {"name": "Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]", "value": 100, "id": "65"}, {"name": "Applications to physics", "value": 100, "id": "80"}, {"name": "Rigidity results", "value": 100, "id": "24"}, {"name": "Special Riemannian manifolds (Einstein, Sasakian, etc.)", "value": 100, "id": "25"}, {"name": "Hyper-Kahler and quaternionic Kahler geometry, ``special'' geometry", "value": 100, "id": "26"}, {"name": "Spin and Spin${}^c$ geometry", "value": 100, "id": "27"}, {"name": "Global Riemannian geometry, including pinching [See also 31C12, 58B20]", "value": 100, "id": "20"}, {"name": "Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]", "value": 100, "id": "07"}, {"name": "Geodesics [See also 58E10]", "value": 100, "id": "22"}, {"name": "Connections, general theory", "value": 100, "id": "05"}, {"name": "Gerbes, differential characters: differential geometric aspects", "value": 100, "id": "08"}, {"name": "Global surface theory (convex surfaces a la A. D. Aleksandrov)", "value": 100, "id": "45"}, {"name": "Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]", "value": 100, "id": "42"}, {"name": "Issues of holonomy", "value": 100, "id": "29"}, {"name": "Global submanifolds [See also 53B25]", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Geometric orders, order geometry [See also 51Lxx]", "value": 100, "id": "75"}, {"name": "Calibrations and calibrated geometries", "value": 100, "id": "38"}, {"name": "Direct methods ($G$-spaces of Busemann, etc.)", "value": 100, "id": "70"}, {"name": "Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]", "value": 100, "id": "21"}, {"name": "$G$-structures", "value": 100, "id": "10"}, {"name": "Foliations (differential geometric aspects) [See also 57R30, 57R32]", "value": 100, "id": "12"}, {"name": "General geometric structures on manifolds (almost complex, almost product structures, etc.)", "value": 100, "id": "15"}, {"name": "Sub-Riemannian geometry", "value": 100, "id": "17"}, {"name": "Hermitian and Kahlerian manifolds [See also 32Cxx]", "value": 100, "id": "55"}, {"name": "Global geometric and topological methods (a la Gromov); differential geometric analysis on metric spaces", "value": 100, "id": "23"}, {"name": "Lorentz manifolds, manifolds with indefinite metrics", "value": 100, "id": "50"}, {"name": "Symmetric spaces [See also 32M15, 57T15]", "value": 100, "id": "35"}, {"name": "Geometric evolution equations (mean curvature flow, Ricci flow, etc.)", "value": 100, "id": "44"}]}, {"id": "B", "name": "Local differential geometry", "children": [{"name": "Projective connections", "value": 100, "id": "10"}, {"name": "Local Riemannian geometry", "value": 100, "id": "20"}, {"name": "Methods of Riemannian geometry", "value": 100, "id": "21"}, {"name": "Linear and affine connections", "value": 100, "id": "05"}, {"name": "Lorentz metrics, indefinite metrics", "value": 100, "id": "30"}, {"name": "Applications to physics", "value": 100, "id": "50"}, {"name": "Hermitian and Kahlerian structures [See also 32Cxx]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Local submanifolds [See also 53C40]", "value": 100, "id": "25"}, {"name": "Other connections", "value": 100, "id": "15"}, {"name": "Finsler spaces and generalizations (areal metrics)", "value": 100, "id": "40"}]}, {"id": "D", "name": "Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]", "children": [{"name": "Contact manifolds, general", "value": 100, "id": "10"}, {"name": "Lagrangian submanifolds; Maslov index", "value": 100, "id": "12"}, {"name": "Almost contact and almost symplectic manifolds", "value": 100, "id": "15"}, {"name": "Canonical transformations", "value": 100, "id": "22"}, {"name": "Poisson manifolds; Poisson groupoids and algebroids", "value": 100, "id": "17"}, {"name": "Symplectic manifolds, general", "value": 100, "id": "05"}, {"name": "Deformation quantization, star products", "value": 100, "id": "55"}, {"name": "Generalized geometries (a la Hitchin)", "value": 100, "id": "18"}, {"name": "Symplectic structures of moduli spaces", "value": 100, "id": "30"}, {"name": "Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]", "value": 100, "id": "37"}, {"name": "Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]", "value": 100, "id": "45"}, {"name": "Global theory of symplectic and contact manifolds [See also 57Rxx]", "value": 100, "id": "35"}, {"name": "Symplectic field theory; contact homology", "value": 100, "id": "42"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Geodesic flows", "value": 100, "id": "25"}, {"name": "Momentum maps; symplectic reduction", "value": 100, "id": "20"}, {"name": "Floer homology and cohomology, symplectic aspects", "value": 100, "id": "40"}, {"name": "Geometric quantization", "value": 100, "id": "50"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "Z", "name": "Applications to physics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications to physics", "value": 100, "id": "05"}]}]}, {"id": "52", "name": "Convex and discrete geometry", "children": [{"id": "A", "name": "General convexity", "children": [{"name": "Convex sets in $2$ dimensions (including convex curves) [See also 53A04]", "value": 100, "id": "10"}, {"name": "Mixed volumes and related topics", "value": 100, "id": "39"}, {"name": "Axiomatic and generalized convexity", "value": 100, "id": "01"}, {"name": "Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]", "value": 100, "id": "20"}, {"name": "Convex sets in topological vector spaces [See also 46A55]", "value": 100, "id": "07"}, {"name": "Random convex sets and integral geometry [See also 53C65, 60D05]", "value": 100, "id": "22"}, {"name": "Convex sets without dimension restrictions", "value": 100, "id": "05"}, {"name": "Spherical and hyperbolic convexity", "value": 100, "id": "55"}, {"name": "Asymptotic theory of convex bodies [See also 46B06]", "value": 100, "id": "23"}, {"name": "Other problems of combinatorial convexity", "value": 100, "id": "37"}, {"name": "Helly-type theorems and geometric transversal theory", "value": 100, "id": "35"}, {"name": "Convex functions and convex programs [See also 26B25, 90C25]", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Approximation by convex sets", "value": 100, "id": "27"}, {"name": "Inequalities and extremum problems", "value": 100, "id": "40"}, {"name": "Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)", "value": 100, "id": "30"}, {"name": "Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45]", "value": 100, "id": "15"}, {"name": "Length, area, volume [See also 26B15, 28A75, 49Q20]", "value": 100, "id": "38"}, {"name": "Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]", "value": 100, "id": "21"}]}, {"id": "C", "name": "Discrete geometry", "children": [{"name": "Erdoos problems and related topics of discrete geometry [See also 11Hxx]", "value": 100, "id": "10"}, {"name": "Circle packings and discrete conformal geometry", "value": 100, "id": "26"}, {"name": "Planar arrangements of lines and pseudolines", "value": 100, "id": "30"}, {"name": "Tilings in $2$ dimensions [See also 05B45, 51M20]", "value": 100, "id": "20"}, {"name": "Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]", "value": 100, "id": "07"}, {"name": "Packing and covering in $n$ dimensions [See also 05B40, 11H31]", "value": 100, "id": "17"}, {"name": "Lattices and convex bodies in $2$ dimensions [See also 11H06, 11H31, 11P21]", "value": 100, "id": "05"}, {"name": "Quasicrystals, aperiodic tilings", "value": 100, "id": "23"}, {"name": "Combinatorial complexity of geometric structures [See also 68U05]", "value": 100, "id": "45"}, {"name": "Tilings in $n$ dimensions [See also 05B45, 51M20]", "value": 100, "id": "22"}, {"name": "Arrangements of points, flats, hyperplanes [See also 32S22]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Rigidity and flexibility of structures [See also 70B15]", "value": 100, "id": "25"}, {"name": "Packing and covering in $2$ dimensions [See also 05B40, 11H31]", "value": 100, "id": "15"}, {"name": "Oriented matroids", "value": 100, "id": "40"}]}, {"id": "B", "name": "Polytopes and polyhedra", "children": [{"name": "$n$-dimensional polytopes", "value": 100, "id": "11"}, {"name": "Three-dimensional polytopes", "value": 100, "id": "10"}, {"name": "Special polytopes (linear programming, centrally symmetric, etc.)", "value": 100, "id": "12"}, {"name": "Symmetry properties of polytopes", "value": 100, "id": "15"}, {"name": "Shellability", "value": 100, "id": "22"}, {"name": "Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]", "value": 100, "id": "05"}, {"name": "Computational aspects related to convexity {For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx]", "value": 100, "id": "55"}, {"name": "Dissections and valuations (Hilbert's third problem, etc.)", "value": 100, "id": "45"}, {"name": "Gale and other diagrams", "value": 100, "id": "35"}, {"name": "Isoperimetric problems for polytopes", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]", "value": 100, "id": "40"}, {"name": "Polyhedral manifolds", "value": 100, "id": "70"}, {"name": "Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]", "value": 100, "id": "20"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}]}, {"id": "ALG", "name": "Algebraic Mathematics", "children": [{"id": "11", "name": "Number theory", "children": [{"id": "A", "name": "Elementary number theory {For analogues in number fields, see 11R04}", "children": [{"name": "Arithmetic functions; related numbers; inversion formulas", "value": 100, "id": "25"}, {"name": "Power residues, reciprocity", "value": 100, "id": "15"}, {"name": "Congruences; primitive roots; residue systems", "value": 100, "id": "07"}, {"name": "Multiplicative structure; Euclidean algorithm; greatest common divisors", "value": 100, "id": "05"}, {"name": "Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]", "value": 100, "id": "55"}, {"name": "Factorization; primality", "value": 100, "id": "51"}, {"name": "Primes", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Radix representation; digital problems {For metric results, see 11K16}", "value": 100, "id": "63"}, {"name": "Other representations", "value": 100, "id": "67"}]}, {"id": "C", "name": "Polynomials and matrices", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Polynomials [See also 13F20]", "value": 100, "id": "08"}, {"name": "Matrices, determinants [See also 15B36]", "value": 100, "id": "20"}]}, {"id": "B", "name": "Sequences and sets", "children": [{"name": "Arithmetic progressions [See also 11N13]", "value": 100, "id": "25"}, {"name": "Additive bases, including sumsets [See also 05B10]", "value": 100, "id": "13"}, {"name": "Density, gaps, topology", "value": 100, "id": "05"}, {"name": "Farey sequences; the sequences ${1^k, 2^k, \\cdots}$", "value": 100, "id": "57"}, {"name": "Arithmetic combinatorics; higher degree uniformity", "value": 100, "id": "30"}, {"name": "Recurrences {For applications to special functions, see 33-XX}", "value": 100, "id": "37"}, {"name": "Fibonacci and Lucas numbers and polynomials and generalizations", "value": 100, "id": "39"}, {"name": "Representation functions", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other combinatorial number theory", "value": 100, "id": "75"}, {"name": "Bell and Stirling numbers", "value": 100, "id": "73"}, {"name": "Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]", "value": 100, "id": "65"}, {"name": "Bernoulli and Euler numbers and polynomials", "value": 100, "id": "68"}, {"name": "Special sequences and polynomials", "value": 100, "id": "83"}, {"name": "Automata sequences", "value": 100, "id": "85"}, {"name": "Sequences (mod $m$)", "value": 100, "id": "50"}]}, {"id": "E", "name": "Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}", "children": [{"name": "Forms over real fields", "value": 100, "id": "10"}, {"name": "Bilinear and Hermitian forms", "value": 100, "id": "39"}, {"name": "Quadratic forms over global rings and fields", "value": 100, "id": "12"}, {"name": "General ternary and quaternary quadratic forms; forms of more than two variables", "value": 100, "id": "20"}, {"name": "Quadratic forms over general fields", "value": 100, "id": "04"}, {"name": "General binary quadratic forms", "value": 100, "id": "16"}, {"name": "Quadratic forms over local rings and fields", "value": 100, "id": "08"}, {"name": "Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)", "value": 100, "id": "45"}, {"name": "Class numbers of quadratic and Hermitian forms", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Forms of degree higher than two", "value": 100, "id": "76"}, {"name": "Quadratic spaces; Clifford algebras [See also 15A63, 15A66]", "value": 100, "id": "88"}, {"name": "Sums of squares and representations by other particular quadratic forms", "value": 100, "id": "25"}, {"name": "$K$-theory of quadratic and Hermitian forms", "value": 100, "id": "70"}, {"name": "Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]", "value": 100, "id": "81"}, {"name": "$p$-adic theory", "value": 100, "id": "95"}, {"name": "Classical groups [See also 14Lxx, 20Gxx]", "value": 100, "id": "57"}, {"name": "Galois cohomology of linear algebraic groups [See also 20G10]", "value": 100, "id": "72"}]}, {"id": "D", "name": "Diophantine equations [See also 11Gxx, 14Gxx]", "children": [{"name": "Cubic and quartic equations", "value": 100, "id": "25"}, {"name": "Quadratic and bilinear equations", "value": 100, "id": "09"}, {"name": "Thue-Mahler equations", "value": 100, "id": "59"}, {"name": "The Frobenius problem", "value": 100, "id": "07"}, {"name": "Linear equations", "value": 100, "id": "04"}, {"name": "Multiplicative and norm form equations", "value": 100, "id": "57"}, {"name": "Counting solutions of Diophantine equations", "value": 100, "id": "45"}, {"name": "$p$-adic and power series fields", "value": 100, "id": "88"}, {"name": "Higher degree equations; Fermat's equation", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Exponential equations", "value": 100, "id": "61"}, {"name": "Diophantine inequalities [See also 11J25]", "value": 100, "id": "75"}, {"name": "Equations in many variables [See also 11P55]", "value": 100, "id": "72"}, {"name": "Rational numbers as sums of fractions", "value": 100, "id": "68"}, {"name": "Congruences in many variables", "value": 100, "id": "79"}, {"name": "Representation problems [See also 11P55]", "value": 100, "id": "85"}]}, {"id": "G", "name": "Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]", "children": [{"name": "Abelian varieties of dimension $> 1$ [See also 14Kxx]", "value": 100, "id": "10"}, {"name": "Curves of arbitrary genus or genus $", "value": 100, "id": "30"}, {"name": "Complex multiplication and moduli of abelian varieties [See also 14K22]", "value": 100, "id": "15"}, {"name": "Elliptic curves over local fields [See also 14G20, 14H52]", "value": 100, "id": "07"}, {"name": "Elliptic and modular units [See also 11R27]", "value": 100, "id": "16"}, {"name": "Polylogarithms and relations with $K$-theory", "value": 100, "id": "55"}, {"name": "Arithmetic aspects of modular and Shimura varieties [See also 14G35]", "value": 100, "id": "18"}, {"name": "Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05]", "value": 100, "id": "09"}, {"name": "Arithmetic mirror symmetry [See also 14J33]", "value": 100, "id": "42"}, {"name": "Geometric class field theory [See also 11R37, 14C35, 19F05]", "value": 100, "id": "45"}, {"name": "Varieties over global fields [See also 14G25]", "value": 100, "id": "35"}, {"name": "Heights [See also 14G40, 37P30]", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Varieties over finite and local fields [See also 14G15, 14G20]", "value": 100, "id": "25"}, {"name": "Dessins d'enfants, Belyii theory", "value": 100, "id": "32"}, {"name": "Curves over finite and local fields [See also 14H25]", "value": 100, "id": "20"}, {"name": "$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]", "value": 100, "id": "40"}, {"name": "Elliptic curves over global fields [See also 14H52]", "value": 100, "id": "05"}]}, {"id": "F", "name": "Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}", "children": [{"name": "Hecke-Petersson operators, differential operators (several variables)", "value": 100, "id": "60"}, {"name": "Langlands $L$-functions; one variable Dirichlet series and functional equations", "value": 100, "id": "66"}, {"name": "Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols", "value": 100, "id": "67"}, {"name": "Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series", "value": 100, "id": "68"}, {"name": "Galois representations", "value": 100, "id": "80"}, {"name": "$p$-adic theory, local fields [See also 14G20, 22E50]", "value": 100, "id": "85"}, {"name": "Modular and automorphic functions", "value": 100, "id": "03"}, {"name": "Theta series; Weil representation; theta correspondences", "value": 100, "id": "27"}, {"name": "Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]", "value": 100, "id": "06"}, {"name": "Relationship to Lie algebras and finite simple groups", "value": 100, "id": "22"}, {"name": "Relations with algebraic geometry and topology", "value": 100, "id": "23"}, {"name": "Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms", "value": 100, "id": "46"}, {"name": "Automorphic forms on ${\\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]", "value": 100, "id": "41"}, {"name": "Hecke-Petersson operators, differential operators (one variable)", "value": 100, "id": "25"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Cohomology of arithmetic groups", "value": 100, "id": "75"}, {"name": "Spectral theory; Selberg trace formula", "value": 100, "id": "72"}, {"name": "Representation-theoretic methods; automorphic representations over local and global fields", "value": 100, "id": "70"}, {"name": "Dedekind eta function, Dedekind sums", "value": 100, "id": "20"}, {"name": "Holomorphic modular forms of integral weight", "value": 100, "id": "11"}, {"name": "Automorphic forms, one variable", "value": 100, "id": "12"}, {"name": "Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]", "value": 100, "id": "33"}, {"name": "Modular correspondences, etc.", "value": 100, "id": "32"}, {"name": "Fourier coefficients of automorphic forms", "value": 100, "id": "30"}, {"name": "Forms of half-integer weight; nonholomorphic modular forms", "value": 100, "id": "37"}, {"name": "Jacobi forms", "value": 100, "id": "50"}, {"name": "Modular forms associated to Drinfel'd modules", "value": 100, "id": "52"}, {"name": "Other groups and their modular and automorphic forms (several variables)", "value": 100, "id": "55"}]}, {"id": "H", "name": "Geometry of numbers {For applications in coding theory, see 94B75}", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Lattices and convex bodies [See also 11P21, 52C05, 52C07]", "value": 100, "id": "06"}, {"name": "Nonconvex bodies", "value": 100, "id": "16"}, {"name": "Products of linear forms", "value": 100, "id": "46"}, {"name": "Lattice packing and covering [See also 05B40, 52C15, 52C17]", "value": 100, "id": "31"}, {"name": "Automorphism groups of lattices", "value": 100, "id": "56"}, {"name": "Minima of forms", "value": 100, "id": "50"}, {"name": "Mean value and transfer theorems", "value": 100, "id": "60"}, {"name": "Quadratic forms (reduction theory, extreme forms, etc.)", "value": 100, "id": "55"}, {"name": "Relations with coding theory", "value": 100, "id": "71"}]}, {"id": "K", "name": "Probabilistic theory: distribution modulo $1$; metric theory of algorithms", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Irregularities of distribution, discrepancy [See also 11Nxx]", "value": 100, "id": "38"}, {"name": "General theory of distribution modulo $1$ [See also 11J71]", "value": 100, "id": "06"}, {"name": "Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]", "value": 100, "id": "16"}, {"name": "Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]", "value": 100, "id": "55"}, {"name": "Special sequences", "value": 100, "id": "31"}, {"name": "Pseudo-random numbers; Monte Carlo methods", "value": 100, "id": "45"}, {"name": "Well-distributed sequences and other variations", "value": 100, "id": "36"}, {"name": "Continuous, $p$-adic and abstract analogues", "value": 100, "id": "41"}, {"name": "Diophantine approximation [See also 11Jxx]", "value": 100, "id": "60"}, {"name": "Arithmetic functions [See also 11Nxx]", "value": 100, "id": "65"}, {"name": "Harmonic analysis and almost periodicity", "value": 100, "id": "70"}, {"name": "Metric theory of continued fractions [See also 11A55, 11J70]", "value": 100, "id": "50"}]}, {"id": "J", "name": "Diophantine approximation, transcendental number theory [See also 11K60]", "children": [{"name": "Approximation in non-Archimedean valuations", "value": 100, "id": "61"}, {"name": "Transcendence theory of elliptic and abelian functions", "value": 100, "id": "89"}, {"name": "Measures of irrationality and of transcendence", "value": 100, "id": "82"}, {"name": "Metric theory", "value": 100, "id": "83"}, {"name": "Transcendence (general theory)", "value": 100, "id": "81"}, {"name": "Linear forms in logarithms; Baker's method", "value": 100, "id": "86"}, {"name": "Schmidt Subspace Theorem and applications", "value": 100, "id": "87"}, {"name": "Algebraic independence; Gel'fond's method", "value": 100, "id": "85"}, {"name": "Diophantine inequalities [See also 11D75]", "value": 100, "id": "25"}, {"name": "Markov and Lagrange spectra and generalizations", "value": 100, "id": "06"}, {"name": "Homogeneous approximation to one number", "value": 100, "id": "04"}, {"name": "Approximation to algebraic numbers", "value": 100, "id": "68"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Irrationality; linear independence over a field", "value": 100, "id": "72"}, {"name": "Distribution modulo one [See also 11K06]", "value": 100, "id": "71"}, {"name": "Continued fractions and generalizations [See also 11A55, 11K50]", "value": 100, "id": "70"}, {"name": "Transcendence theory of other special functions", "value": 100, "id": "91"}, {"name": "Inhomogeneous linear forms", "value": 100, "id": "20"}, {"name": "Transcendence theory of Drinfel'd and $t$-modules", "value": 100, "id": "93"}, {"name": "Results involving abelian varieties", "value": 100, "id": "95"}, {"name": "Analogues of methods in Nevanlinna theory (work of Vojta et al.)", "value": 100, "id": "97"}, {"name": "Simultaneous homogeneous approximation, linear forms", "value": 100, "id": "13"}, {"name": "Approximation by numbers from a fixed field", "value": 100, "id": "17"}, {"name": "Small fractional parts of polynomials and generalizations", "value": 100, "id": "54"}]}, {"id": "M", "name": "Zeta and $L$-functions: analytic theory", "children": [{"name": "Nonreal zeros of $\\zeta (s)$ and $L(s, \\chi)$; Riemann and other hypotheses", "value": 100, "id": "26"}, {"name": "Zeta and $L$-functions in characteristic $p$", "value": 100, "id": "38"}, {"name": "Real zeros of $L(s, \\chi)$; results on $L(1, \\chi)$", "value": 100, "id": "20"}, {"name": "Relations with noncommutative geometry", "value": 100, "id": "55"}, {"name": "Multiple Dirichlet series and zeta functions and multizeta values", "value": 100, "id": "32"}, {"name": "Tauberian theorems [See also 40E05]", "value": 100, "id": "45"}, {"name": "Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas", "value": 100, "id": "36"}, {"name": "Hurwitz and Lerch zeta functions", "value": 100, "id": "35"}, {"name": "Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 1", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$\\zeta (s)$ and $L(s, \\chi)$", "value": 100, "id": "06"}, {"name": "Relations with random matrices", "value": 100, "id": "50"}]}, {"id": "L", "name": "Exponential sums and character sums {For finite fields, see 11Txx}", "children": [{"name": "Trigonometric and exponential sums, general", "value": 100, "id": "03"}, {"name": "Sums over arbitrary intervals", "value": 100, "id": "26"}, {"name": "Sums over primes", "value": 100, "id": "20"}, {"name": "Estimates on exponential sums", "value": 100, "id": "07"}, {"name": "Gauss and Kloosterman sums; generalizations", "value": 100, "id": "05"}, {"name": "Estimates on character sums", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Weyl sums", "value": 100, "id": "15"}, {"name": "Jacobsthal and Brewer sums; other complete character sums", "value": 100, "id": "10"}]}, {"id": "N", "name": "Multiplicative number theory", "children": [{"name": "Distribution of integers with specified multiplicative constraints", "value": 100, "id": "25"}, {"name": "Primes in progressions [See also 11B25]", "value": 100, "id": "13"}, {"name": "Asymptotic results on counting functions for algebraic and topological structures", "value": 100, "id": "45"}, {"name": "Distribution of primes", "value": 100, "id": "05"}, {"name": "Primes represented by polynomials; other multiplicative structure of polynomial values", "value": 100, "id": "32"}, {"name": "Turan theory [See also 30Bxx]", "value": 100, "id": "30"}, {"name": "Asymptotic results on arithmetic functions", "value": 100, "id": "37"}, {"name": "Applications of sieve methods", "value": 100, "id": "36"}, {"name": "Sieves", "value": 100, "id": "35"}, {"name": "Distribution functions associated with additive and positive multiplicative functions", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]", "value": 100, "id": "75"}, {"name": "Other results on the distribution of values or the characterization of arithmetic functions", "value": 100, "id": "64"}, {"name": "Distribution of integers in special residue classes", "value": 100, "id": "69"}, {"name": "Generalized primes and integers", "value": 100, "id": "80"}, {"name": "Rate of growth of arithmetic functions", "value": 100, "id": "56"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "P", "name": "Additive number theory; partitions", "children": [{"name": "Lattice points in specified regions", "value": 100, "id": "21"}, {"name": "Waring's problem and variants", "value": 100, "id": "05"}, {"name": "Applications of the Hardy-Littlewood method [See also 11D85]", "value": 100, "id": "55"}, {"name": "Goldbach-type theorems; other additive questions involving primes", "value": 100, "id": "32"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inverse problems of additive number theory, including sumsets", "value": 100, "id": "70"}, {"name": "Analytic theory of partitions", "value": 100, "id": "82"}, {"name": "Partitions; congruences and congruential restrictions", "value": 100, "id": "83"}, {"name": "Elementary theory of partitions [See also 05A17]", "value": 100, "id": "81"}, {"name": "Partition identities; identities of Rogers-Ramanujan type", "value": 100, "id": "84"}]}, {"id": "S", "name": "Algebraic number theory: local and $p$-adic fields", "children": [{"name": "Galois cohomology [See also 12Gxx, 16H05]", "value": 100, "id": "25"}, {"name": "Galois theory", "value": 100, "id": "20"}, {"name": "Integral representations", "value": 100, "id": "23"}, {"name": "Class field theory; $p$-adic formal groups [See also 14L05]", "value": 100, "id": "31"}, {"name": "Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx]", "value": 100, "id": "45"}, {"name": "Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]", "value": 100, "id": "37"}, {"name": "Zeta functions and $L$-functions [See also 11M41, 19F27]", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$K$-theory of local fields [See also 19Fxx]", "value": 100, "id": "70"}, {"name": "Non-Archimedean dynamical systems [See mainly 37Pxx]", "value": 100, "id": "82"}, {"name": "Ramification and extension theory", "value": 100, "id": "15"}, {"name": "Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)", "value": 100, "id": "80"}, {"name": "Polynomials", "value": 100, "id": "05"}, {"name": "Prehomogeneous vector spaces", "value": 100, "id": "90"}, {"name": "Other nonanalytic theory", "value": 100, "id": "85"}]}, {"id": "R", "name": "Algebraic number theory: global fields {For complex multiplication, see 11G15}", "children": [{"name": "Density theorems", "value": 100, "id": "45"}, {"name": "Cyclotomic function fields (class groups, Bernoulli objects, etc.)", "value": 100, "id": "60"}, {"name": "Class groups and Picard groups of orders", "value": 100, "id": "65"}, {"name": "Totally real fields [See also 12J15]", "value": 100, "id": "80"}, {"name": "Quaternion and other division algebras: arithmetic, zeta functions", "value": 100, "id": "52"}, {"name": "Units and factorization", "value": 100, "id": "27"}, {"name": "PV-numbers and generalizations; other special algebraic numbers; Mahler measure", "value": 100, "id": "06"}, {"name": "Other number fields", "value": 100, "id": "21"}, {"name": "Algebraic numbers; rings of algebraic integers", "value": 100, "id": "04"}, {"name": "Iwasawa theory", "value": 100, "id": "23"}, {"name": "Other analytic theory [See also 11Nxx]", "value": 100, "id": "47"}, {"name": "Distribution of prime ideals [See also 11N05]", "value": 100, "id": "44"}, {"name": "Polynomials (irreducibility, etc.)", "value": 100, "id": "09"}, {"name": "Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]", "value": 100, "id": "42"}, {"name": "Class numbers, class groups, discriminants", "value": 100, "id": "29"}, {"name": "Cyclotomic extensions", "value": 100, "id": "18"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$K$-theory of global fields [See also 19Fxx]", "value": 100, "id": "70"}, {"name": "Other abelian and metabelian extensions", "value": 100, "id": "20"}, {"name": "Quadratic extensions", "value": 100, "id": "11"}, {"name": "Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]", "value": 100, "id": "39"}, {"name": "Arithmetic theory of algebraic function fields [See also 14-XX]", "value": 100, "id": "58"}, {"name": "Cubic and quartic extensions", "value": 100, "id": "16"}, {"name": "Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]", "value": 100, "id": "33"}, {"name": "Galois theory", "value": 100, "id": "32"}, {"name": "Adele rings and groups", "value": 100, "id": "56"}, {"name": "Class field theory", "value": 100, "id": "37"}, {"name": "Galois cohomology [See also 12Gxx, 19A31]", "value": 100, "id": "34"}, {"name": "Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16Hxx, 16Kxx]", "value": 100, "id": "54"}]}, {"id": "U", "name": "Connections with logic", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nonstandard arithmetic [See also 03H15]", "value": 100, "id": "10"}, {"name": "Model theory [See also 03Cxx]", "value": 100, "id": "09"}, {"name": "Ultraproducts [See also 03C20]", "value": 100, "id": "07"}, {"name": "Decidability [See also 03B25]", "value": 100, "id": "05"}]}, {"id": "T", "name": "Finite fields and commutative rings (number-theoretic aspects)", "children": [{"name": "Other character sums and Gauss sums", "value": 100, "id": "24"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Polynomials", "value": 100, "id": "06"}, {"name": "Cyclotomy", "value": 100, "id": "22"}, {"name": "Exponential sums", "value": 100, "id": "23"}, {"name": "Arithmetic theory of polynomial rings over finite fields", "value": 100, "id": "55"}, {"name": "Structure theory", "value": 100, "id": "30"}, {"name": "Finite upper half-planes", "value": 100, "id": "60"}, {"name": "Algebraic coding theory; cryptography", "value": 100, "id": "71"}]}, {"id": "Y", "name": "Computational number theory [See also 11-04]", "children": [{"name": "Primality", "value": 100, "id": "11"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Algorithms; complexity [See also 68Q25]", "value": 100, "id": "16"}, {"name": "Calculation of integer sequences", "value": 100, "id": "55"}, {"name": "Factorization", "value": 100, "id": "05"}, {"name": "Computer solution of Diophantine equations", "value": 100, "id": "50"}, {"name": "Algebraic number theory computations", "value": 100, "id": "40"}, {"name": "Evaluation of constants", "value": 100, "id": "60"}, {"name": "Analytic computations", "value": 100, "id": "35"}, {"name": "Values of arithmetic functions; tables", "value": 100, "id": "70"}, {"name": "Continued fraction calculations", "value": 100, "id": "65"}]}, {"id": "Z", "name": "Miscellaneous applications of number theory", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Miscellaneous applications of number theory", "value": 100, "id": "05"}]}]}, {"id": "13", "name": "Commutative algebra", "children": [{"id": "A", "name": "General commutative ring theory", "children": [{"name": "Graded rings [See also 16W50]", "value": 100, "id": "02"}, {"name": "Ideals; multiplicative ideal theory", "value": 100, "id": "15"}, {"name": "Divisibility; factorizations [See also 13F15]", "value": 100, "id": "05"}, {"name": "Valuations and their generalizations [See also 12J20]", "value": 100, "id": "18"}, {"name": "Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics", "value": 100, "id": "30"}, {"name": "Actions of groups on commutative rings; invariant theory [See also 14L24]", "value": 100, "id": "50"}, {"name": "Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also 13B22]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "C", "name": "Theory of modules and ideals", "children": [{"name": "Injective and flat modules and ideals", "value": 100, "id": "11"}, {"name": "Projective and free modules and ideals [See also 19A13]", "value": 100, "id": "10"}, {"name": "Other special types", "value": 100, "id": "13"}, {"name": "Torsion modules and ideals", "value": 100, "id": "12"}, {"name": "Dimension theory, depth, related rings (catenary, etc.)", "value": 100, "id": "15"}, {"name": "Cohen-Macaulay modules [See also 13H10]", "value": 100, "id": "14"}, {"name": "Structure, classification theorems", "value": 100, "id": "05"}, {"name": "Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]", "value": 100, "id": "40"}, {"name": "Module categories", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Class groups [See also 11R29]", "value": 100, "id": "20"}]}, {"id": "B", "name": "Ring extensions and related topics", "children": [{"name": "Extension theory", "value": 100, "id": "02"}, {"name": "Morphisms", "value": 100, "id": "10"}, {"name": "Integral dependence; going up, going down", "value": 100, "id": "21"}, {"name": "Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)", "value": 100, "id": "22"}, {"name": "Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]", "value": 100, "id": "25"}, {"name": "Rings of fractions and localization [See also 16S85]", "value": 100, "id": "30"}, {"name": "Completion [See also 13J10]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Etale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]", "value": 100, "id": "40"}, {"name": "Galois theory", "value": 100, "id": "05"}]}, {"id": "E", "name": "Chain conditions, finiteness conditions", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Artinian rings and modules, finite-dimensional algebras", "value": 100, "id": "10"}, {"name": "Rings and modules of finite generation or presentation; number of generators", "value": 100, "id": "15"}, {"name": "Noetherian rings and modules", "value": 100, "id": "05"}]}, {"id": "D", "name": "Homological methods {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}", "children": [{"name": "Syzygies, resolutions, complexes", "value": 100, "id": "02"}, {"name": "(Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.)", "value": 100, "id": "03"}, {"name": "Torsion theory [See also 13C12, 18E40]", "value": 100, "id": "30"}, {"name": "Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]", "value": 100, "id": "15"}, {"name": "Homological functors on modules (Tor, Ext, etc.)", "value": 100, "id": "07"}, {"name": "Homological conjectures (intersection theorems)", "value": 100, "id": "22"}, {"name": "Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]", "value": 100, "id": "10"}, {"name": "Derived categories", "value": 100, "id": "09"}, {"name": "Local cohomology [See also 14B15]", "value": 100, "id": "45"}, {"name": "Hilbert-Samuel and Hilbert-Kunz functions; Poincare series", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Homological dimension", "value": 100, "id": "05"}]}, {"id": "G", "name": "Integral domains", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Integral domains", "value": 100, "id": "05"}]}, {"id": "F", "name": "Arithmetic rings and other special rings", "children": [{"name": "Principal ideal rings", "value": 100, "id": "10"}, {"name": "Valuation rings [See also 13A18]", "value": 100, "id": "30"}, {"name": "Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]", "value": 100, "id": "20"}, {"name": "Euclidean rings and generalizations", "value": 100, "id": "07"}, {"name": "Formal power series rings [See also 13J05]", "value": 100, "id": "25"}, {"name": "Stanley-Reisner face rings; simplicial complexes [See also 55U10]", "value": 100, "id": "55"}, {"name": "Seminormal rings", "value": 100, "id": "45"}, {"name": "Rings with straightening laws, Hodge algebras", "value": 100, "id": "50"}, {"name": "Witt vectors and related rings", "value": 100, "id": "35"}, {"name": "Cluster algebras", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Excellent rings", "value": 100, "id": "40"}, {"name": "Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]", "value": 100, "id": "15"}, {"name": "Dedekind, Prufer, Krull and Mori rings and their generalizations", "value": 100, "id": "05"}]}, {"id": "H", "name": "Local rings and semilocal rings", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]", "value": 100, "id": "10"}, {"name": "Multiplicity theory and related topics [See also 14C17]", "value": 100, "id": "15"}, {"name": "Regular local rings", "value": 100, "id": "05"}]}, {"id": "J", "name": "Topological rings and modules [See also 16W60, 16W80]", "children": [{"name": "Complete rings, completion [See also 13B35]", "value": 100, "id": "10"}, {"name": "Global topological rings", "value": 100, "id": "20"}, {"name": "Analytical algebras and rings [See also 32B05]", "value": 100, "id": "07"}, {"name": "Power series rings [See also 13F25]", "value": 100, "id": "05"}, {"name": "Real algebra [See also 12D15, 14Pxx]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ordered rings [See also 06F25]", "value": 100, "id": "25"}, {"name": "Henselian rings [See also 13B40]", "value": 100, "id": "15"}]}, {"id": "M", "name": "Finite commutative rings {For number-theoretic aspects, see 11Txx}", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Polynomials", "value": 100, "id": "10"}, {"name": "Structure", "value": 100, "id": "05"}]}, {"id": "L", "name": "Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]", "value": 100, "id": "05"}]}, {"id": "N", "name": "Differential algebra [See also 12H05, 14F10]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Rings of differential operators and their modules [See also 16S32, 32C38]", "value": 100, "id": "10"}, {"name": "Derivations", "value": 100, "id": "15"}, {"name": "Modules of differentials", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "P", "name": "Computational aspects and applications [See also 14Qxx, 68W30]", "children": [{"name": "Grobner bases; other bases for ideals and modules (e.g., Janet and border bases)", "value": 100, "id": "10"}, {"name": "Solving polynomial systems; resultants", "value": 100, "id": "15"}, {"name": "Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)", "value": 100, "id": "25"}, {"name": "Polynomials, factorization [See also 12Y05]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Computational homological algebra [See also 13Dxx]", "value": 100, "id": "20"}]}]}, {"id": "12", "name": "Field theory and polynomials", "children": [{"id": "E", "name": "General field theory", "children": [{"name": "Special polynomials", "value": 100, "id": "10"}, {"name": "Equations", "value": 100, "id": "12"}, {"name": "Finite fields (field-theoretic aspects)", "value": 100, "id": "20"}, {"name": "Polynomials (irreducibility, etc.)", "value": 100, "id": "05"}, {"name": "Field arithmetic", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Hilbertian fields; Hilbert's irreducibility theorem", "value": 100, "id": "25"}, {"name": "Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]", "value": 100, "id": "15"}]}, {"id": "D", "name": "Real and complex fields", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}", "value": 100, "id": "10"}, {"name": "Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]", "value": 100, "id": "15"}, {"name": "Polynomials: factorization", "value": 100, "id": "05"}]}, {"id": "G", "name": "Homological methods (field theory)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Cohomological dimension", "value": 100, "id": "10"}, {"name": "Galois cohomology [See also 14F22, 16Hxx, 16K50]", "value": 100, "id": "05"}]}, {"id": "F", "name": "Field extensions", "children": [{"name": "Separable extensions, Galois theory", "value": 100, "id": "10"}, {"name": "Inverse Galois theory", "value": 100, "id": "12"}, {"name": "Transcendental extensions", "value": 100, "id": "20"}, {"name": "Algebraic extensions", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Inseparable extensions", "value": 100, "id": "15"}]}, {"id": "H", "name": "Differential and difference algebra", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Difference algebra [See also 39Axx]", "value": 100, "id": "10"}, {"name": "Abstract differential equations [See also 34Mxx]", "value": 100, "id": "20"}, {"name": "$p$-adic differential equations [See also 11S80, 14G20]", "value": 100, "id": "25"}, {"name": "Differential algebra [See also 13Nxx]", "value": 100, "id": "05"}]}, {"id": "K", "name": "Generalizations of fields", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Semifields [See also 16Y60]", "value": 100, "id": "10"}, {"name": "Near-fields [See also 16Y30]", "value": 100, "id": "05"}]}, {"id": "J", "name": "Topological fields", "children": [{"name": "Valued fields", "value": 100, "id": "10"}, {"name": "Formally $p$-adic fields", "value": 100, "id": "12"}, {"name": "General valuation theory [See also 13A18]", "value": 100, "id": "20"}, {"name": "Topological semifields", "value": 100, "id": "17"}, {"name": "Normed fields", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]", "value": 100, "id": "27"}, {"name": "Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]", "value": 100, "id": "25"}, {"name": "Ordered fields", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "L", "name": "Connections with logic", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ultraproducts [See also 03C20]", "value": 100, "id": "10"}, {"name": "Model theory [See also 03C60]", "value": 100, "id": "12"}, {"name": "Nonstandard arithmetic [See also 03H15]", "value": 100, "id": "15"}, {"name": "Decidability [See also 03B25]", "value": 100, "id": "05"}]}, {"id": "Y", "name": "Computational aspects of field theory and polynomials", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Computational aspects of field theory and polynomials", "value": 100, "id": "05"}]}]}, {"id": "20", "name": "Group theory and generalizations", "children": [{"id": "A", "name": "Foundations", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Metamathematical considerations {For word problems, see 20F10}", "value": 100, "id": "10"}, {"name": "Applications of logic to group theory", "value": 100, "id": "15"}, {"name": "Axiomatics and elementary properties", "value": 100, "id": "05"}]}, {"id": "C", "name": "Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]", "children": [{"name": "$p$-adic representations of finite groups", "value": 100, "id": "11"}, {"name": "Integral representations of finite groups", "value": 100, "id": "10"}, {"name": "Integral representations of infinite groups", "value": 100, "id": "12"}, {"name": "Ordinary representations and characters", "value": 100, "id": "15"}, {"name": "Group rings of infinite groups and their modules [See also 16S34]", "value": 100, "id": "07"}, {"name": "Group rings of finite groups and their modules [See also 16S34]", "value": 100, "id": "05"}, {"name": "Representations of finite groups of Lie type", "value": 100, "id": "33"}, {"name": "Representations of infinite symmetric groups", "value": 100, "id": "32"}, {"name": "Hecke algebras and their representations", "value": 100, "id": "08"}, {"name": "Representations of finite symmetric groups", "value": 100, "id": "30"}, {"name": "Applications of group representations to physics", "value": 100, "id": "35"}, {"name": "Representations of sporadic groups", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Projective representations and multipliers", "value": 100, "id": "25"}, {"name": "Modular representations and characters", "value": 100, "id": "20"}, {"name": "Computational methods", "value": 100, "id": "40"}]}, {"id": "B", "name": "Permutation groups", "children": [{"name": "Characterization theorems", "value": 100, "id": "10"}, {"name": "Infinite automorphism groups [See also 12F10]", "value": 100, "id": "27"}, {"name": "Multiply transitive finite groups", "value": 100, "id": "20"}, {"name": "General theory for infinite groups", "value": 100, "id": "07"}, {"name": "Multiply transitive infinite groups", "value": 100, "id": "22"}, {"name": "General theory for finite groups", "value": 100, "id": "05"}, {"name": "Symmetric groups", "value": 100, "id": "30"}, {"name": "Subgroups of symmetric groups", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]", "value": 100, "id": "25"}, {"name": "Primitive groups", "value": 100, "id": "15"}, {"name": "Computational methods", "value": 100, "id": "40"}]}, {"id": "E", "name": "Structure and classification of infinite or finite groups", "children": [{"name": "Quasivarieties and varieties of groups", "value": 100, "id": "10"}, {"name": "Residual properties and generalizations; residually finite groups", "value": 100, "id": "26"}, {"name": "Chains and lattices of subgroups, subnormal subgroups [See also 20F22]", "value": 100, "id": "15"}, {"name": "Subgroup theorems; subgroup growth", "value": 100, "id": "07"}, {"name": "Extensions, wreath products, and other compositions [See also 20J05]", "value": 100, "id": "22"}, {"name": "Free nonabelian groups", "value": 100, "id": "05"}, {"name": "Limits, profinite groups", "value": 100, "id": "18"}, {"name": "Groups acting on trees [See also 20F65]", "value": 100, "id": "08"}, {"name": "Conjugacy classes", "value": 100, "id": "45"}, {"name": "Groups with a $BN$-pair; buildings [See also 51E24]", "value": 100, "id": "42"}, {"name": "Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]", "value": 100, "id": "36"}, {"name": "General structure theorems", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Local properties", "value": 100, "id": "25"}, {"name": "Simple groups [See also 20D05]", "value": 100, "id": "32"}, {"name": "Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations", "value": 100, "id": "06"}, {"name": "Maximal subgroups", "value": 100, "id": "28"}]}, {"id": "D", "name": "Abstract finite groups", "children": [{"name": "Solvable groups, theory of formations, Schunck classes, Fitting classes, $\\pi$-length, ranks [See also 20F17]", "value": 100, "id": "10"}, {"name": "Series and lattices of subgroups", "value": 100, "id": "30"}, {"name": "Nilpotent groups, $p$-groups", "value": 100, "id": "15"}, {"name": "Finite simple groups and their classification", "value": 100, "id": "05"}, {"name": "Simple groups: alternating groups and groups of Lie type [See also 20Gxx]", "value": 100, "id": "06"}, {"name": "Simple groups: sporadic groups", "value": 100, "id": "08"}, {"name": "Automorphisms", "value": 100, "id": "45"}, {"name": "Subnormal subgroups", "value": 100, "id": "35"}, {"name": "Arithmetic and combinatorial problems", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Special subgroups (Frattini, Fitting, etc.)", "value": 100, "id": "25"}, {"name": "Sylow subgroups, Sylow properties, $\\pi$-groups, $\\pi$-structure", "value": 100, "id": "20"}, {"name": "Products of subgroups", "value": 100, "id": "40"}]}, {"id": "G", "name": "Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation th", "children": [{"name": "Cohomology theory", "value": 100, "id": "10"}, {"name": "Linear algebraic groups over global fields and their integers", "value": 100, "id": "30"}, {"name": "Linear algebraic groups over the reals, the complexes, the quaternions", "value": 100, "id": "20"}, {"name": "Structure theory", "value": 100, "id": "07"}, {"name": "Linear algebraic groups over local fields and their integers", "value": 100, "id": "25"}, {"name": "Kac-Moody groups", "value": 100, "id": "44"}, {"name": "Applications to physics", "value": 100, "id": "45"}, {"name": "Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]", "value": 100, "id": "42"}, {"name": "Schur and $q$-Schur algebras", "value": 100, "id": "43"}, {"name": "Linear algebraic groups over adeles and other rings and schemes", "value": 100, "id": "35"}, {"name": "Exceptional groups", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Linear algebraic groups over finite fields", "value": 100, "id": "40"}, {"name": "Linear algebraic groups over arbitrary fields", "value": 100, "id": "15"}, {"name": "Representation theory", "value": 100, "id": "05"}]}, {"id": "F", "name": "Special aspects of infinite or finite groups", "children": [{"name": "Periodic groups; locally finite groups", "value": 100, "id": "50"}, {"name": "Ordered groups [See mainly 06F15]", "value": 100, "id": "60"}, {"name": "Geometric group theory [See also 05C25, 20E08, 57Mxx]", "value": 100, "id": "65"}, {"name": "Hyperbolic groups and nonpositively curved groups", "value": 100, "id": "67"}, {"name": "Asymptotic properties of groups", "value": 100, "id": "69"}, {"name": "FC-groups and their generalizations", "value": 100, "id": "24"}, {"name": "Cancellation theory; application of van Kampen diagrams [See also 57M05]", "value": 100, "id": "06"}, {"name": "Other classes of groups defined by subgroup chains", "value": 100, "id": "22"}, {"name": "Generators, relations, and presentations", "value": 100, "id": "05"}, {"name": "Engel conditions", "value": 100, "id": "45"}, {"name": "Automorphism groups of groups [See also 20E36]", "value": 100, "id": "28"}, {"name": "Representations of groups as automorphism groups of algebraic systems", "value": 100, "id": "29"}, {"name": "Associated Lie structures", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other groups related to topology or analysis", "value": 100, "id": "38"}, {"name": "Algebraic geometry over groups; equations over groups", "value": 100, "id": "70"}, {"name": "Groups of finite Morley rank [See also 03C45, 03C60]", "value": 100, "id": "11"}, {"name": "Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]", "value": 100, "id": "10"}, {"name": "Commutator calculus", "value": 100, "id": "12"}, {"name": "Derived series, central series, and generalizations", "value": 100, "id": "14"}, {"name": "Formations of groups, Fitting classes [See also 20D10]", "value": 100, "id": "17"}, {"name": "Solvable groups, supersolvable groups [See also 20D10]", "value": 100, "id": "16"}, {"name": "Generalizations of solvable and nilpotent groups", "value": 100, "id": "19"}, {"name": "Nilpotent groups [See also 20D15]", "value": 100, "id": "18"}, {"name": "Braid groups; Artin groups", "value": 100, "id": "36"}, {"name": "Fundamental groups and their automorphisms [See also 57M05, 57Sxx]", "value": 100, "id": "34"}, {"name": "Reflection and Coxeter groups [See also 22E40, 51F15]", "value": 100, "id": "55"}]}, {"id": "H", "name": "Other groups of matrices [See also 15A30]", "children": [{"name": "Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]", "value": 100, "id": "10"}, {"name": "Other matrix groups over fields", "value": 100, "id": "20"}, {"name": "Other matrix groups over rings", "value": 100, "id": "25"}, {"name": "Other matrix groups over finite fields", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]", "value": 100, "id": "15"}, {"name": "Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]", "value": 100, "id": "05"}]}, {"id": "K", "name": "Abelian groups", "children": [{"name": "Torsion groups, primary groups and generalized primary groups", "value": 100, "id": "10"}, {"name": "Finite abelian groups [For sumsets, see 11B13 and 11P70]", "value": 100, "id": "01"}, {"name": "Torsion-free groups, finite rank", "value": 100, "id": "15"}, {"name": "Mixed groups", "value": 100, "id": "21"}, {"name": "Direct sums, direct products, etc.", "value": 100, "id": "25"}, {"name": "Automorphisms, homomorphisms, endomorphisms, etc.", "value": 100, "id": "30"}, {"name": "Topological methods [See also 22A05, 22B05]", "value": 100, "id": "45"}, {"name": "Extensions", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Subgroups", "value": 100, "id": "27"}, {"name": "Homological and categorical methods", "value": 100, "id": "40"}, {"name": "Torsion-free groups, infinite rank", "value": 100, "id": "20"}]}, {"id": "J", "name": "Connections with homological algebra and category theory", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Category of groups", "value": 100, "id": "15"}, {"name": "Cohomology of groups", "value": 100, "id": "06"}, {"name": "Homological methods in group theory", "value": 100, "id": "05"}]}, {"id": "M", "name": "Semigroups", "children": [{"name": "Radical theory", "value": 100, "id": "11"}, {"name": "General structure theory", "value": 100, "id": "10"}, {"name": "Arithmetic theory of monoids", "value": 100, "id": "13"}, {"name": "Ideal theory", "value": 100, "id": "12"}, {"name": "Mappings of semigroups", "value": 100, "id": "15"}, {"name": "Varieties and pseudovarieties of semigroups", "value": 100, "id": "07"}, {"name": "Regular semigroups", "value": 100, "id": "17"}, {"name": "Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]", "value": 100, "id": "05"}, {"name": "Orthodox semigroups", "value": 100, "id": "19"}, {"name": "Inverse semigroups", "value": 100, "id": "18"}, {"name": "Representation of semigroups; actions of semigroups on sets", "value": 100, "id": "30"}, {"name": "Connections of semigroups with homological algebra and category theory", "value": 100, "id": "50"}, {"name": "Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]", "value": 100, "id": "25"}, {"name": "Algebraic monoids", "value": 100, "id": "32"}, {"name": "Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]", "value": 100, "id": "20"}, {"name": "Commutative semigroups", "value": 100, "id": "14"}]}, {"id": "L", "name": "Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22", "value": 100, "id": "05"}]}, {"id": "N", "name": "Other generalizations of groups", "children": [{"name": "Sets with a single binary operation (groupoids)", "value": 100, "id": "02"}, {"name": "Ternary systems (heaps, semiheaps, heapoids, etc.)", "value": 100, "id": "10"}, {"name": "Hypergroups", "value": 100, "id": "20"}, {"name": "Fuzzy groups [See also 03E72]", "value": 100, "id": "25"}, {"name": "Loops, quasigroups [See also 05Bxx]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$n$-ary systems $(n\\ge 3)$", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "P", "name": "Probabilistic methods in group theory [See also 60Bxx]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Probabilistic methods in group theory [See also 60Bxx]", "value": 100, "id": "05"}]}]}, {"id": "17", "name": "Nonassociative rings and algebras", "children": [{"id": "A", "name": "General nonassociative rings", "children": [{"name": "Structure theory", "value": 100, "id": "60"}, {"name": "Quadratic algebras (but not quadratic Jordan algebras)", "value": 100, "id": "45"}, {"name": "General theory", "value": 100, "id": "01"}, {"name": "Flexible algebras", "value": 100, "id": "20"}, {"name": "Power-associative rings", "value": 100, "id": "05"}, {"name": "Leibniz algebras", "value": 100, "id": "32"}, {"name": "Algebras satisfying other identities", "value": 100, "id": "30"}, {"name": "Other $n$-ary compositions $(n \\ge 3)$", "value": 100, "id": "42"}, {"name": "Automorphisms, derivations, other operators", "value": 100, "id": "36"}, {"name": "Division algebras", "value": 100, "id": "35"}, {"name": "Free algebras", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Composition algebras", "value": 100, "id": "75"}, {"name": "Ternary compositions", "value": 100, "id": "40"}, {"name": "Superalgebras", "value": 100, "id": "70"}, {"name": "Noncommutative Jordan algebras", "value": 100, "id": "15"}, {"name": "Valued algebras", "value": 100, "id": "80"}, {"name": "Radical theory", "value": 100, "id": "65"}]}, {"id": "C", "name": "Jordan algebras (algebras, triples and pairs)", "children": [{"name": "Structure theory", "value": 100, "id": "10"}, {"name": "Idempotents, Peirce decompositions", "value": 100, "id": "27"}, {"name": "Simple, semisimple algebras", "value": 100, "id": "20"}, {"name": "Radicals", "value": 100, "id": "17"}, {"name": "Identities and free Jordan structures", "value": 100, "id": "05"}, {"name": "Finite-dimensional structures", "value": 100, "id": "55"}, {"name": "Associated groups, automorphisms", "value": 100, "id": "30"}, {"name": "Associated geometries", "value": 100, "id": "37"}, {"name": "Associated manifolds", "value": 100, "id": "36"}, {"name": "Exceptional Jordan structures", "value": 100, "id": "40"}, {"name": "Jordan structures associated with other structures [See also 16W10]", "value": 100, "id": "50"}, {"name": "Division algebras", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]", "value": 100, "id": "65"}, {"name": "Super structures", "value": 100, "id": "70"}, {"name": "Applications to physics", "value": 100, "id": "90"}]}, {"id": "B", "name": "Lie algebras and Lie superalgebras {For Lie groups, see 22Exx}", "children": [{"name": "Solvable, nilpotent (super)algebras", "value": 100, "id": "30"}, {"name": "Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]", "value": 100, "id": "60"}, {"name": "Lie bialgebras; Lie coalgebras", "value": 100, "id": "62"}, {"name": "Poisson algebras", "value": 100, "id": "63"}, {"name": "Infinite-dimensional Lie (super)algebras [See also 22E65]", "value": 100, "id": "65"}, {"name": "Lie algebras of vector fields and related (super) algebras", "value": 100, "id": "66"}, {"name": "Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras", "value": 100, "id": "67"}, {"name": "Virasoro and related algebras", "value": 100, "id": "68"}, {"name": "Vertex operators; vertex operator algebras and related structures", "value": 100, "id": "69"}, {"name": "Applications to integrable systems", "value": 100, "id": "80"}, {"name": "Applications to physics", "value": 100, "id": "81"}, {"name": "Exceptional (super)algebras", "value": 100, "id": "25"}, {"name": "Identities, free Lie (super)algebras", "value": 100, "id": "01"}, {"name": "Simple, semisimple, reductive (super)algebras", "value": 100, "id": "20"}, {"name": "Root systems", "value": 100, "id": "22"}, {"name": "Structure theory", "value": 100, "id": "05"}, {"name": "Coadjoint orbits; nilpotent varieties", "value": 100, "id": "08"}, {"name": "Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]", "value": 100, "id": "45"}, {"name": "Automorphisms, derivations, other operators", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Color Lie (super)algebras", "value": 100, "id": "75"}, {"name": "Graded Lie (super)algebras", "value": 100, "id": "70"}, {"name": "Representations, algebraic theory (weights)", "value": 100, "id": "10"}, {"name": "Representations, analytic theory", "value": 100, "id": "15"}, {"name": "Homological methods in Lie (super)algebras", "value": 100, "id": "55"}, {"name": "Cohomology of Lie (super)algebras", "value": 100, "id": "56"}, {"name": "Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]", "value": 100, "id": "37"}, {"name": "Modular Lie (super)algebras", "value": 100, "id": "50"}, {"name": "Universal enveloping (super)algebras [See also 16S30]", "value": 100, "id": "35"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}, {"name": "Computational methods", "value": 100, "id": "08"}]}, {"id": "D", "name": "Other nonassociative rings and algebras", "children": [{"name": "Mal'cev (Mal'tsev) rings and algebras", "value": 100, "id": "10"}, {"name": "Right alternative rings", "value": 100, "id": "15"}, {"name": "Lie-admissible algebras", "value": 100, "id": "25"}, {"name": "Alternative rings", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$(\\gamma, \\delta)$-rings, including $(1,-1)$-rings", "value": 100, "id": "20"}, {"name": "Genetic algebras", "value": 100, "id": "92"}]}]}, {"id": "22", "name": "Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. 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groups", "value": 100, "id": "05"}]}, {"id": "C", "name": "Compact groups", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Compact groups", "value": 100, "id": "05"}]}, {"id": "B", "name": "Locally compact abelian groups (LCA groups)", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Structure of group algebras of LCA groups", "value": 100, "id": "10"}, {"name": "General properties and structure of LCA groups", "value": 100, "id": "05"}]}, {"id": "E", "name": "Lie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90}", "children": [{"name": "Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx}", "value": 100, "id": "60"}, {"name": "Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05]", "value": 100, "id": "65"}, {"name": "Analysis on and representations of infinite-dimensional Lie groups", "value": 100, "id": "66"}, {"name": "Loop groups and related constructions, group-theoretic treatment [See also 58D05]", "value": 100, "id": "67"}, {"name": "Nilpotent and solvable Lie groups", "value": 100, "id": "25"}, {"name": "Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)", "value": 100, "id": "27"}, {"name": "General properties and structure of other Lie groups", "value": 100, "id": "20"}, {"name": "Local Lie groups [See also 34-XX, 35-XX, 58H05]", "value": 100, "id": "05"}, {"name": "Semisimple Lie groups and their representations", "value": 100, "id": "46"}, {"name": "Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]", "value": 100, "id": "47"}, {"name": "Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}", "value": 100, "id": "45"}, {"name": "Structure and representation of the Lorentz group", "value": 100, "id": "43"}, {"name": "Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]", "value": 100, "id": "40"}, {"name": "Continuous cohomology [See also 57R32, 57Txx, 58H10]", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]", "value": 100, "id": "70"}, {"name": "General properties and structure of complex Lie groups [See also 32M05]", "value": 100, "id": "10"}, {"name": "General properties and structure of real Lie groups", "value": 100, "id": "15"}, {"name": "Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05]", "value": 100, "id": "55"}, {"name": "Geometric Langlands program: representation-theoretic aspects [See also 14D24]", "value": 100, "id": "57"}, {"name": "Analysis on real and complex Lie groups [See also 33C80, 43-XX]", "value": 100, "id": "30"}, {"name": "Representations of Lie and linear algebraic groups over local fields [See also 20G05]", "value": 100, "id": "50"}, {"name": "Analysis on $p$-adic Lie groups", "value": 100, "id": "35"}]}, {"id": "D", "name": "Locally compact groups and their algebras", "children": [{"name": "Unitary representations of locally compact groups", "value": 100, "id": "10"}, {"name": "Other representations of locally compact groups", "value": 100, "id": "12"}, {"name": "Representations of group algebras", "value": 100, "id": "20"}, {"name": "General properties and structure of locally compact groups", "value": 100, "id": "05"}, {"name": "Automorphism groups of locally compact groups", "value": 100, "id": "45"}, {"name": "Duality theorems", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "$C^*$-algebras and $W^*$-algebras in relation to group representations 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[{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "16", "name": "Associative rings and algebras {For the commutative case, see 13-XX}", "children": [{"id": "B", "name": "General and miscellaneous", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Category-theoretic methods and results (except as in 16D90) [See also 18-XX]", "value": 100, "id": "50"}, {"name": "Applications of logic [See also 03Cxx]", "value": 100, "id": "70"}]}, {"id": "E", "name": "Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}", "children": [{"name": "Homological dimension", "value": 100, "id": "10"}, {"name": "Differential graded algebras and applications", "value": 100, "id": "45"}, {"name": "Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50]", "value": 100, "id": "20"}, {"name": "Syzygies, resolutions, complexes", "value": 100, "id": "05"}, {"name": "Homological functors on modules (Tor, Ext, etc.)", "value": 100, "id": "30"}, {"name": "von Neumann regular rings and generalizations", "value": 100, "id": "50"}, {"name": "(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)", "value": 100, "id": "40"}, {"name": "Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Derived categories", "value": 100, "id": "35"}, {"name": "Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)", "value": 100, "id": "65"}]}, {"id": "D", "name": "Modules, bimodules and ideals", "children": [{"name": "General module theory", "value": 100, "id": "10"}, {"name": "Bimodules", "value": 100, "id": "20"}, {"name": "Ideals", "value": 100, "id": "25"}, {"name": "Infinite-dimensional simple rings (except as in 16Kxx)", "value": 100, "id": "30"}, {"name": "Injective modules, self-injective rings [See also 16L60]", "value": 100, "id": "50"}, {"name": "Free, projective, and flat modules and ideals [See also 19A13]", "value": 100, "id": "40"}, {"name": "Simple and semisimple modules, primitive rings and ideals", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation", "value": 100, "id": "70"}, {"name": "Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality", "value": 100, "id": "90"}, {"name": "Other classes of modules and ideals [See also 16G50]", "value": 100, "id": "80"}]}, {"id": "G", "name": "Representation theory of rings and algebras", "children": [{"name": "Representations of Artinian rings", "value": 100, "id": "10"}, {"name": "Representations of quivers and partially ordered sets", "value": 100, "id": "20"}, {"name": "Representations of orders, lattices, algebras over commutative rings [See also 16Hxx]", "value": 100, "id": "30"}, {"name": "Cohen-Macaulay modules", "value": 100, "id": "50"}, {"name": "Representation type (finite, tame, wild, etc.)", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers", "value": 100, "id": "70"}]}, {"id": "H", "name": "Algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30}", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Orders in separable algebras", "value": 100, "id": "10"}, {"name": "Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)", "value": 100, "id": "05"}, {"name": "Commutative orders", "value": 100, "id": "15"}, {"name": "Lattices over orders", "value": 100, "id": "20"}]}, {"id": "K", "name": "Division rings and semisimple Artin rings [See also 12E15, 15A30]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Finite-dimensional {For crossed products, see 16S35}", "value": 100, "id": "20"}, {"name": "Brauer groups [See also 12G05, 14F22]", "value": 100, "id": "50"}, {"name": "Infinite-dimensional and general", "value": 100, "id": "40"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "L", "name": "Local rings and generalizations", "children": [{"name": "Quasi-Frobenius rings [See also 16D50]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Noncommutative local and semilocal rings, perfect rings", "value": 100, "id": "30"}]}, {"id": "N", "name": "Radicals and radical properties of rings", "children": [{"name": "Prime and semiprime rings [See also 16D60, 16U10]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "General radicals and rings {For radicals in module categories, see 16S90}", "value": 100, "id": "80"}, {"name": "Jacobson radical, quasimultiplication", "value": 100, "id": "20"}, {"name": "Nil and nilpotent radicals, sets, ideals, rings", "value": 100, "id": "40"}]}, {"id": "P", "name": "Chain conditions, growth conditions, and other forms of finiteness", "children": [{"name": "Finite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx}", "value": 100, "id": "10"}, {"name": "Artinian rings and modules", "value": 100, "id": "20"}, {"name": "Localization and Noetherian rings [See also 16U20]", "value": 100, "id": "50"}, {"name": "Noetherian rings and modules", "value": 100, "id": "40"}, {"name": "Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence", "value": 100, "id": "70"}, {"name": "Growth rate, Gelfand-Kirillov dimension", "value": 100, "id": "90"}]}, {"id": "S", "name": "Rings and algebras arising under various constructions", "children": [{"name": "Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)", "value": 100, "id": "10"}, {"name": "Rings arising from non-commutative algebraic geometry [See also 14A22]", "value": 100, "id": "38"}, {"name": "Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)", "value": 100, "id": "15"}, {"name": "Rings of differential operators [See also 13N10, 32C38]", "value": 100, "id": "32"}, {"name": "Universal enveloping algebras of Lie algebras [See mainly 17B35]", "value": 100, "id": "30"}, {"name": "Quadratic and Koszul algebras", "value": 100, "id": "37"}, {"name": "Ordinary and skew polynomial rings and semigroup rings [See also 20M25]", "value": 100, "id": "36"}, {"name": "Twisted and skew group rings, crossed products", "value": 100, "id": "35"}, {"name": "Group rings [See also 20C05, 20C07], Laurent polynomial rings", "value": 100, "id": "34"}, {"name": "Rings of functions, subdirect products, sheaves of rings", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Smash products of general Hopf actions [See also 16T05]", "value": 100, "id": "40"}, {"name": "Extensions of rings by ideals", "value": 100, "id": "70"}, {"name": "Centralizing and normalizing extensions", "value": 100, "id": "20"}, {"name": "Deformations of rings [See also 13D10, 14D15]", "value": 100, "id": "80"}, {"name": "Rings of fractions and localizations [See also 13B30]", "value": 100, "id": "85"}, {"name": "Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}", "value": 100, "id": "90"}, {"name": "Endomorphism rings; matrix rings [See also 15-XX]", "value": 100, "id": "50"}]}, {"id": "R", "name": "Rings with polynomial identity", "children": [{"name": "$T$-ideals, identities, varieties of rings and algebras", "value": 100, "id": "10"}, {"name": "Semiprime p.i. rings, rings embeddable in matrices over commutative rings", "value": 100, "id": "20"}, {"name": "Trace rings and invariant theory", "value": 100, "id": "30"}, {"name": "Other kinds of identities (generalized polynomial, rational, involution)", "value": 100, "id": "50"}, {"name": "Identities other than those of matrices over commutative rings", "value": 100, "id": "40"}, {"name": "Functional identities", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "U", "name": "Conditions on elements", "children": [{"name": "Integral domains", "value": 100, "id": "10"}, {"name": "Ore rings, multiplicative sets, Ore localization", "value": 100, "id": "20"}, {"name": "Divisibility, noncommutative UFDs", "value": 100, "id": "30"}, {"name": "Units, groups of units", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Center, normalizer (invariant elements)", "value": 100, "id": "70"}, {"name": "Generalizations of commutativity", "value": 100, "id": "80"}]}, {"id": "T", "name": "Hopf algebras, quantum groups and related topics", "children": [{"name": "Bialgebras", "value": 100, "id": "10"}, {"name": "Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]", "value": 100, "id": "20"}, {"name": "Yang-Baxter equations", "value": 100, "id": "25"}, {"name": "Connections with combinatorics", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Coalgebras and comodules; corings", "value": 100, "id": "15"}, {"name": "Hopf algebras and their applications [See also 16S40, 57T05]", "value": 100, "id": "05"}]}, {"id": "W", "name": "Rings and algebras with additional structure", "children": [{"name": "Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]", "value": 100, "id": "10"}, {"name": "Automorphisms and endomorphisms", "value": 100, "id": "20"}, {"name": "Actions of groups and semigroups; invariant theory", "value": 100, "id": "22"}, {"name": "Derivations, actions of Lie algebras", "value": 100, "id": "25"}, {"name": "``Super'' (or ``skew'') structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66}", "value": 100, "id": "55"}, {"name": "Graded rings and modules", "value": 100, "id": "50"}, {"name": "Valuations, completions, formal power series and related constructions [See also 13Jxx]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Filtered rings; filtrational and graded techniques", "value": 100, "id": "70"}, {"name": "Topological and ordered rings and modules [See also 06F25, 13Jxx]", "value": 100, "id": "80"}]}, {"id": "Y", "name": "Generalizations {For nonassociative rings, see 17-XX}", "children": [{"name": "Semirings [See also 12K10]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Near-rings [See also 12K05]", "value": 100, "id": "30"}]}, {"id": "Z", "name": "Computational aspects of associative rings", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Computational aspects of associative rings [See also 68W30]", "value": 100, "id": "05"}]}]}, {"id": "19", "name": "$K$-theory [See also 16E20, 18F25]", "children": [{"id": "A", "name": "Grothendieck groups and $K_0$ [See also 13D15, 18F30]", "children": [{"name": "Stability for projective modules [See also 13C10]", "value": 100, "id": "13"}, {"name": "Efficient generation", "value": 100, "id": "15"}, {"name": "Frobenius induction, Burnside and representation rings", "value": 100, "id": "22"}, {"name": "$K_0$ of other rings", "value": 100, "id": "49"}, {"name": "$K_0$ of group rings and orders", "value": 100, "id": "31"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "C", "name": "Steinberg groups and $K_2$", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Central extensions and Schur multipliers", "value": 100, "id": "09"}, {"name": "Symbols, presentations and stability of $K_2$", "value": 100, "id": "20"}, {"name": "Excision for $K_2$", "value": 100, "id": "40"}, {"name": "$K_2$ and the Brauer group", "value": 100, "id": "30"}]}, {"id": "B", "name": "Whitehead groups and $K_1$", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Stable range conditions", "value": 100, "id": "10"}, {"name": "Congruence subgroup problems [See also 20H05]", "value": 100, "id": "37"}, {"name": "Stability for linear groups", "value": 100, "id": "14"}, {"name": "$K_1$ of group rings and orders [See also 57Q10]", "value": 100, "id": "28"}]}, {"id": "E", "name": "$K$-theory in geometry", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Relations with cohomology theories [See also 14Fxx]", "value": 100, "id": "20"}, {"name": "$K$-theory of schemes [See also 14C35]", "value": 100, "id": "08"}, {"name": "Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42]", "value": 100, "id": "15"}]}, {"id": "D", "name": "Higher algebraic $K$-theory", "children": [{"name": "Algebraic $K$-theory of spaces", "value": 100, "id": "10"}, {"name": "$Q$- and plus-constructions", "value": 100, "id": "06"}, {"name": "Symmetric monoidal categories [See also 18D10]", "value": 100, "id": "23"}, {"name": "$K$-theory and homology; cyclic homology and cohomology [See also 18G60]", "value": 100, "id": "55"}, {"name": "Higher symbols, Milnor $K$-theory", "value": 100, "id": "45"}, {"name": "Computations of higher $K$-theory of rings [See also 13D15, 16E20]", "value": 100, "id": "50"}, {"name": "Negative $K$-theory, NK and Nil", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Karoubi-Villamayor-Gersten $K$-theory", "value": 100, "id": "25"}]}, {"id": "G", "name": "$K$-theory of forms [See also 11Exx]", "children": [{"name": "$L$-theory of group rings [See also 11E81]", "value": 100, "id": "24"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Witt groups of rings [See also 11E81]", "value": 100, "id": "12"}, {"name": "Stability for quadratic modules", "value": 100, "id": "05"}, {"name": "Hermitian $K$-theory, relations with $K$-theory of rings", "value": 100, "id": "38"}]}, {"id": "F", "name": "$K$-theory in number theory [See also 11R70, 11S70]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Etale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]", "value": 100, "id": "27"}, {"name": "Symbols and arithmetic [See also 11R37]", "value": 100, "id": "15"}, {"name": "Generalized class field theory [See also 11G45]", "value": 100, "id": "05"}]}, {"id": "M", "name": "Miscellaneous applications of $K$-theory", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Miscellaneous applications of $K$-theory", "value": 100, "id": "05"}]}, {"id": "K", "name": "$K$-theory and operator algebras [See mainly 46L80, and also 46M20]", "children": [{"name": "EXT and $K$-homology [See also 55N22]", "value": 100, "id": "33"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Index theory [See also 58J20, 58J22]", "value": 100, "id": "56"}, {"name": "$K_0$ as an ordered group, traces", "value": 100, "id": "14"}, {"name": "Kasparov theory ($KK$-theory) [See also 58J22]", "value": 100, "id": "35"}]}, {"id": "J", "name": "Obstructions from topology", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Whitehead (and related) torsion", "value": 100, "id": "10"}, {"name": "Surgery obstructions [See also 57R67]", "value": 100, "id": "25"}, {"name": "Obstructions to group actions", "value": 100, "id": "35"}, {"name": "Finiteness and other obstructions in $K_0$", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}, {"id": "L", "name": "Topological $K$-theory [See also 55N15, 55R50, 55S25]", "children": [{"name": "Riemann-Roch theorems, Chern characters", "value": 100, "id": "10"}, {"name": "$J$-homomorphism, Adams operations [See also 55Q50]", "value": 100, "id": "20"}, {"name": "Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]", "value": 100, "id": "47"}, {"name": "Twisted $K$-theory; differential $K$-theory", "value": 100, "id": "50"}, {"name": "Connective $K$-theory, cobordism [See also 55N22]", "value": 100, "id": "41"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Computations, geometric applications", "value": 100, "id": "64"}]}]}, {"id": "18", "name": "Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures", "children": [{"id": "A", "name": "General theory of categories and functors", "children": [{"name": "Graphs, diagram schemes, precategories [See especially 20L05]", "value": 100, "id": "10"}, {"name": "Epimorphisms, monomorphisms, special classes of morphisms, null morphisms", "value": 100, "id": "20"}, {"name": "Special properties of functors (faithful, full, etc.)", "value": 100, "id": "22"}, {"name": "Natural morphisms, dinatural morphisms", "value": 100, "id": "23"}, {"name": "Factorization of morphisms, substructures, quotient structures, congruences, amalgams", "value": 100, "id": "32"}, {"name": "Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)", "value": 100, "id": "30"}, {"name": "Categories admitting limits (complete categories), functors preserving limits, completions", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Functor categories, comma categories", "value": 100, "id": "25"}, {"name": "Foundations, relations to logic and deductive systems [See also 03-XX]", "value": 100, "id": "15"}, {"name": "Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)", "value": 100, "id": "40"}, {"name": "Definitions, generalizations", "value": 100, "id": "05"}]}, {"id": "C", "name": "Categories and theories", "children": [{"name": "Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]", "value": 100, "id": "10"}, {"name": "Algebras and Kleisli categories associated with monads", "value": 100, "id": "20"}, {"name": "Equational categories [See also 03C05, 08C05]", "value": 100, "id": "05"}, {"name": "Sketches and generalizations", "value": 100, "id": "30"}, {"name": "Categorical semantics of formal languages [See also 68Q55, 68Q65]", "value": 100, "id": "50"}, {"name": "Accessible and locally presentable categories", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]", "value": 100, "id": "15"}]}, {"id": "B", "name": "Special categories", "children": [{"name": "Category of relations, additive relations", "value": 100, "id": "10"}, {"name": "Categories of machines, automata, operative categories [See also 03D05, 68Qxx]", "value": 100, "id": "20"}, {"name": "Topoi [See also 03G30]", "value": 100, "id": "25"}, {"name": "Categories of topological spaces and continuous mappings [See also 54-XX]", "value": 100, "id": "30"}, {"name": "Preorders, orders and lattices (viewed as categories) [See also 06-XX]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]", "value": 100, "id": "40"}, {"name": "Embedding theorems, universal categories [See also 18E20]", "value": 100, "id": "15"}, {"name": "Category of sets, characterizations [See also 03-XX]", "value": 100, "id": "05"}]}, {"id": "E", "name": "Abelian categories", "children": [{"name": "Exact categories, abelian categories", "value": 100, "id": "10"}, {"name": "Embedding theorems [See also 18B15]", "value": 100, "id": "20"}, {"name": "Derived functors and satellites", "value": 100, "id": "25"}, {"name": "Derived categories, triangulated categories", "value": 100, "id": "30"}, {"name": "Localization of categories", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Torsion theories, radicals [See also 13D30, 16S90]", "value": 100, "id": "40"}, {"name": "Grothendieck categories", "value": 100, "id": "15"}, {"name": "Preadditive, additive categories", "value": 100, "id": "05"}]}, {"id": "D", "name": "Categories with structure", "children": [{"name": "Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]", "value": 100, "id": "10"}, {"name": "Enriched categories (over closed or monoidal categories)", "value": 100, "id": "20"}, {"name": "Strong functors, strong adjunctions", "value": 100, "id": "25"}, {"name": "Fibered categories", "value": 100, "id": "30"}, {"name": "Operads [See also 55P48]", "value": 100, "id": "50"}, {"name": "Structured objects in a category (group objects, etc.)", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Closed categories (closed monoidal and Cartesian closed categories, etc.)", "value": 100, "id": "15"}, {"name": "Double categories, $2$-categories, bicategories and generalizations", "value": 100, "id": "05"}]}, {"id": "G", "name": "Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]", "children": [{"name": "Resolutions; derived functors [See also 13D02, 16E05, 18E25]", "value": 100, "id": "10"}, {"name": "Homological dimension [See also 13D05, 16E10]", "value": 100, "id": "20"}, {"name": "Relative homological algebra, projective classes", "value": 100, "id": "25"}, {"name": "Homotopical algebra", "value": 100, "id": "55"}, {"name": "Simplicial sets, simplicial objects (in a category) [See also 55U10]", "value": 100, "id": "30"}, {"name": "Nonabelian homological algebra", "value": 100, "id": "50"}, {"name": "Chain complexes [See also 18E30, 55U15]", "value": 100, "id": "35"}, {"name": "Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Spectral sequences, hypercohomology [See also 55Txx]", "value": 100, "id": "40"}, {"name": "Ext and Tor, generalizations, Kunneth formula [See also 55U25]", "value": 100, "id": "15"}, {"name": "Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]", "value": 100, "id": "05"}]}, {"id": "F", "name": "Categories and geometry", "children": [{"name": "Grothendieck topologies [See also 14F20]", "value": 100, "id": "10"}, {"name": "Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]", "value": 100, "id": "20"}, {"name": "Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]", "value": 100, "id": "25"}, {"name": "Grothendieck groups [See also 13D15, 16E20, 19Axx]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]", "value": 100, "id": "15"}, {"name": "Local categories and functors", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "08", "name": "General algebraic systems", "children": [{"id": "A", "name": "Algebraic structures [See also 03C05]", "children": [{"name": "Relational systems, laws of composition", "value": 100, "id": "02"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Subalgebras, congruence relations", "value": 100, "id": "30"}, {"name": "Structure theory", "value": 100, "id": "05"}, {"name": "Partial algebras", "value": 100, "id": "55"}, {"name": "Equational compactness", "value": 100, "id": "45"}, {"name": "Word problems [See also 03D40, 06B25, 20F10, 68R15]", "value": 100, "id": "50"}, {"name": "Operations, polynomials, primal algebras", "value": 100, "id": "40"}, {"name": "Unary algebras", "value": 100, "id": "60"}, {"name": "Automorphisms, endomorphisms", "value": 100, "id": "35"}, {"name": "Finitary algebras", "value": 100, "id": "62"}, {"name": "Infinitary algebras", "value": 100, "id": "65"}, {"name": "Applications of universal algebra in computer science", "value": 100, "id": "70"}, {"name": "Heterogeneous algebras", "value": 100, "id": "68"}, {"name": "Fuzzy algebraic structures", "value": 100, "id": "72"}]}, {"id": "C", "name": "Other classes of algebras", "children": [{"name": "None of the above, but in this 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"children": [{"name": "Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)", "value": 100, "id": "60"}, {"name": "Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10}", "value": 100, "id": "62"}, {"name": "Infinite graphs", "value": 100, "id": "63"}, {"name": "Hypergraphs", "value": 100, "id": "65"}, {"name": "Graph minors", "value": 100, "id": "83"}, {"name": "Small world graphs, complex networks [See also 90Bxx, 91D30]", "value": 100, "id": "82"}, {"name": "Dominating sets, independent sets, cliques", "value": 100, "id": "69"}, {"name": "Random graphs [See also 60B20]", "value": 100, "id": "80"}, {"name": "Random walks on graphs", "value": 100, "id": "81"}, {"name": "Graph algorithms [See also 68R10, 68W05]", "value": 100, "id": "85"}, {"name": "Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]", "value": 100, "id": "25"}, {"name": "Directed graphs (digraphs), tournaments", "value": 100, "id": "20"}, {"name": "Vertex degrees [See also 05E30]", "value": 100, "id": "07"}, {"name": "Signed and weighted graphs", "value": 100, "id": "22"}, {"name": "Trees", "value": 100, "id": "05"}, {"name": "Eulerian and Hamiltonian graphs", "value": 100, "id": "45"}, {"name": "Density (toughness, etc.)", "value": 100, "id": "42"}, {"name": "Connectivity", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Graph operations (line graphs, products, etc.)", "value": 100, "id": "76"}, {"name": "Structural characterization of families of graphs", "value": 100, "id": "75"}, {"name": "Paths and cycles [See also 90B10]", "value": 100, "id": "38"}, {"name": "Fractional graph theory, fuzzy graph theory", "value": 100, "id": "72"}, {"name": "Factorization, matching, partitioning, covering and packing", "value": 100, "id": "70"}, {"name": "Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]", "value": 100, "id": "90"}, {"name": "Graph labelling (graceful graphs, bandwidth, etc.)", "value": 100, "id": "78"}, {"name": "Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]", "value": 100, "id": "10"}, {"name": "Distance in graphs", "value": 100, "id": "12"}, {"name": "Coloring of graphs and hypergraphs", "value": 100, "id": "15"}, {"name": "Perfect graphs", "value": 100, "id": "17"}, {"name": "Generalized Ramsey theory [See also 05D10]", "value": 100, "id": "55"}, {"name": "Graph polynomials", "value": 100, "id": "31"}, {"name": "Enumeration in graph theory", "value": 100, "id": "30"}, {"name": "Graph designs and isomomorphic decomposition [See also 05B30]", "value": 100, "id": "51"}, {"name": "Graphs and linear algebra (matrices, eigenvalues, etc.)", "value": 100, "id": "50"}, {"name": "Extremal problems [See also 90C35]", "value": 100, "id": "35"}, {"name": "Flows in graphs", "value": 100, "id": "21"}, {"name": "Games on graphs [See also 91A43, 91A46]", "value": 100, "id": "57"}]}, {"id": "B", "name": "Designs and configurations {For applications of design theory, see 94C30}", "children": [{"name": "Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]", "value": 100, "id": "10"}, {"name": "Tessellation and tiling problems [See also 52C20, 52C22]", "value": 100, "id": "45"}, {"name": "Matrices (incidence, Hadamard, etc.)", "value": 100, "id": "20"}, {"name": "Triple systems", "value": 100, "id": "07"}, {"name": "Block designs [See also 51E05, 62K10]", "value": 100, "id": "05"}, {"name": "Other designs, configurations [See also 51E30]", "value": 100, "id": "30"}, {"name": "Polyominoes", "value": 100, "id": "50"}, {"name": "Matroids, geometric lattices [See also 52B40, 90C27]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Finite geometries [See also 51D20, 51Exx]", "value": 100, "id": "25"}, {"name": "Orthogonal arrays, Latin squares, Room squares", "value": 100, "id": "15"}, {"name": "Packing and covering [See also 11H31, 52C15, 52C17]", "value": 100, "id": "40"}]}, {"id": "E", "name": "Algebraic combinatorics", "children": [{"name": "Combinatorial aspects of representation theory [See also 20C30]", "value": 100, "id": "10"}, {"name": "Combinatorial aspects of simplicial complexes", "value": 100, "id": "45"}, {"name": "Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]", "value": 100, "id": "15"}, {"name": "Symmetric functions and generalizations", "value": 100, "id": "05"}, {"name": "Group actions on combinatorial structures", "value": 100, "id": "18"}, {"name": "Association schemes, strongly regular graphs", "value": 100, "id": "30"}, {"name": "Combinatorial aspects of commutative algebra", "value": 100, "id": "40"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}]}, {"id": "D", "name": "Extremal combinatorics", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ramsey theory [See also 05C55]", "value": 100, "id": "10"}, {"name": "Transversal (matching) theory", "value": 100, "id": "15"}, {"name": "Probabilistic methods", "value": 100, "id": "40"}, {"name": "Extremal set theory", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "15", "name": "Linear and multilinear algebra; matrix theory", "children": [{"id": "A", "name": "Basic linear algebra", "children": [{"name": "Miscellaneous inequalities involving matrices", "value": 100, "id": "45"}, {"name": "Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]", "value": 100, "id": "60"}, {"name": "Quadratic and bilinear forms, inner products [See mainly 11Exx]", "value": 100, "id": "63"}, {"name": "Clifford algebras, spinors", "value": 100, "id": "66"}, {"name": "Matrix completion problems", "value": 100, "id": "83"}, {"name": "Multilinear algebra, tensor products", "value": 100, "id": "69"}, {"name": "Max-plus and related algebras", "value": 100, "id": "80"}, {"name": "Linear preserver problems", "value": 100, "id": "86"}, {"name": "Matrix equations and identities", "value": 100, "id": "24"}, {"name": "Vector spaces, linear dependence, rank", "value": 100, "id": "03"}, {"name": "Commutativity", "value": 100, "id": "27"}, {"name": "Linear equations", "value": 100, "id": "06"}, {"name": "Canonical forms, reductions, classification", "value": 100, "id": "21"}, {"name": "Linear transformations, semilinear transformations", "value": 100, "id": "04"}, {"name": "Factorization of matrices", "value": 100, "id": "23"}, {"name": "Matrix inversion, generalized inverses", "value": 100, "id": "09"}, {"name": "Inequalities involving eigenvalues and eigenvectors", "value": 100, "id": "42"}, {"name": "Inverse problems", "value": 100, "id": "29"}, {"name": "Miscellaneous topics", "value": 100, "id": "99"}, {"name": "Exterior algebra, Grassmann algebras", "value": 100, "id": "75"}, {"name": "Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]", "value": 100, "id": "72"}, {"name": "Other algebras built from modules", "value": 100, "id": "78"}, {"name": "Linear inequalities", "value": 100, "id": "39"}, {"name": "Conditioning of matrices [See also 65F35]", "value": 100, "id": "12"}, {"name": "Determinants, permanents, other special matrix functions [See also 19B10, 19B14]", "value": 100, "id": "15"}, {"name": "Matrix pencils [See also 47A56]", "value": 100, "id": "22"}, {"name": "Matrix exponential and similar functions of matrices", "value": 100, "id": "16"}, {"name": "Eigenvalues, singular values, and eigenvectors", "value": 100, "id": "18"}, {"name": "Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]", "value": 100, "id": "30"}, {"name": "Matrices over function rings in one or more variables", "value": 100, "id": "54"}]}, {"id": "B", "name": "Special matrices", "children": [{"name": "Orthogonal matrices", "value": 100, "id": "10"}, {"name": "Fuzzy matrices", "value": 100, "id": "15"}, {"name": "Positive matrices and their generalizations; cones of matrices", "value": 100, "id": "48"}, {"name": "Toeplitz, Cauchy, and related matrices", "value": 100, "id": "05"}, {"name": "Matrices over special rings (quaternions, finite fields, etc.)", "value": 100, "id": "33"}, {"name": "Hermitian, skew-Hermitian, and related matrices", "value": 100, "id": "57"}, {"name": "Stochastic matrices", "value": 100, "id": "51"}, {"name": "Matrices of integers [See also 11C20]", "value": 100, "id": "36"}, {"name": "Sign pattern matrices", "value": 100, "id": "35"}, {"name": "Boolean and Hadamard matrices", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Random matrices", "value": 100, "id": "52"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "06", "name": "Order, lattices, ordered algebraic structures [See also 18B35]", "children": [{"id": "A", "name": "Ordered sets", "children": [{"name": "Algebraic aspects of posets", "value": 100, "id": "11"}, {"name": "Semilattices [See also 20M10; for topological semilattices see 22A26]", "value": 100, "id": "12"}, {"name": "Galois correspondences, closure operators", "value": 100, "id": "15"}, {"name": "Combinatorics of partially ordered sets", "value": 100, "id": "07"}, {"name": "Total order", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Generalizations of ordered sets", "value": 100, "id": "75"}, {"name": "Partial order, general", "value": 100, "id": "06"}]}, {"id": "C", "name": "Modular lattices, complemented lattices", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Semimodular lattices, geometric lattices", "value": 100, "id": "10"}, {"name": "Modular lattices, Desarguesian lattices", "value": 100, "id": "05"}, {"name": "Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]", "value": 100, "id": "15"}, {"name": "Complemented modular lattices, continuous geometries", "value": 100, "id": "20"}]}, {"id": "B", "name": "Lattices [See also 03G10]", "children": [{"name": "Ideals, congruence relations", "value": 100, "id": "10"}, {"name": "Varieties of lattices", "value": 100, "id": "20"}, {"name": "Complete lattices, completions", "value": 100, "id": "23"}, {"name": "Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]", "value": 100, "id": "30"}, {"name": "Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Generalizations of lattices", "value": 100, "id": "75"}, {"name": "Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]", "value": 100, "id": "25"}, {"name": "Representation theory", "value": 100, "id": "15"}, {"name": "Structure theory", "value": 100, "id": "05"}]}, {"id": "E", "name": "Boolean algebras (Boolean rings) [See also 03G05]", "children": [{"name": "Chain conditions, complete algebras", "value": 100, "id": "10"}, {"name": "Ring-theoretic properties [See also 16E50, 16G30]", "value": 100, "id": "20"}, {"name": "Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]", "value": 100, "id": "25"}, {"name": "Boolean functions [See also 94C10]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Generalizations of Boolean algebras", "value": 100, "id": "75"}, {"name": "Stone spaces (Boolean spaces) and related structures", "value": 100, "id": "15"}, {"name": "Structure theory", "value": 100, "id": "05"}]}, {"id": "D", "name": "Distributive lattices", "children": [{"name": "Complete distributivity", "value": 100, "id": "10"}, {"name": "Heyting algebras [See also 03G25]", "value": 100, "id": "20"}, {"name": "Frames, locales {For topological questions see 54-XX}", "value": 100, "id": "22"}, {"name": "Structure and representation theory", "value": 100, "id": "05"}, {"name": "De Morgan algebras, Lukasiewicz algebras [See also 03G20]", "value": 100, "id": "30"}, {"name": "Lattices and duality", "value": 100, "id": "50"}, {"name": "MV-algebras", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other generalizations of distributive lattices", "value": 100, "id": "75"}, {"name": "Post algebras [See also 03G20]", "value": 100, "id": "25"}, {"name": "Pseudocomplemented lattices", "value": 100, "id": "15"}, {"name": "Fuzzy lattices (soft algebras) and related topics", "value": 100, "id": "72"}]}, {"id": "F", "name": "Ordered structures", "children": [{"name": "Noether lattices", "value": 100, "id": "10"}, {"name": "Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]", "value": 100, "id": "20"}, {"name": "Quantales", "value": 100, "id": "07"}, {"name": "Ordered semigroups and monoids [See also 20Mxx]", "value": 100, "id": "05"}, {"name": "Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]", "value": 100, "id": "30"}, {"name": "BCK-algebras, BCI-algebras [See also 03G25]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Ordered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80}", "value": 100, "id": "25"}, {"name": "Ordered groups [See also 20F60]", "value": 100, "id": "15"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}, {"id": "14", "name": "Algebraic geometry", "children": [{"id": "A", "name": "Foundations", "children": [{"name": "Varieties and morphisms", "value": 100, "id": "10"}, {"name": "Generalizations (algebraic spaces, stacks)", "value": 100, "id": "20"}, {"name": "Noncommutative algebraic geometry [See also 16S38]", "value": 100, "id": "22"}, {"name": "Elementary questions", "value": 100, "id": "25"}, {"name": "Relevant commutative algebra [See also 13-XX]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Schemes and morphisms", "value": 100, "id": "15"}]}, {"id": "C", "name": "Cycles and subschemes", "children": [{"name": "Algebraic cycles", "value": 100, "id": "25"}, {"name": "Divisors, linear systems, invertible sheaves", "value": 100, "id": "20"}, {"name": "Pencils, nets, webs [See also 53A60]", "value": 100, "id": "21"}, {"name": "Picard groups", "value": 100, "id": "22"}, {"name": "Parametrization (Chow and Hilbert schemes)", "value": 100, "id": "05"}, {"name": "Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture", "value": 100, "id": "30"}, {"name": "Applications of methods of algebraic $K$-theory [See also 19Exx]", "value": 100, "id": "35"}, {"name": "Torelli problem [See also 32G20]", "value": 100, "id": "34"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]", "value": 100, "id": "17"}, {"name": "(Equivariant) Chow groups and rings; motives", "value": 100, "id": "15"}, {"name": "Riemann-Roch theorems [See also 19E20, 19L10]", "value": 100, "id": "40"}]}, {"id": "B", "name": "Local theory", "children": [{"name": "Infinitesimal methods [See also 13D10]", "value": 100, "id": "10"}, {"name": "Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]", "value": 100, "id": "12"}, {"name": "Formal neighborhoods", "value": 100, "id": "20"}, {"name": "Deformations of singularities [See also 14D15, 32S30]", "value": 100, "id": "07"}, {"name": "Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Local structure of morphisms: etale, flat, etc. [See also 13B40]", "value": 100, "id": "25"}, {"name": "Local cohomology [See also 13D45, 32C36]", "value": 100, "id": "15"}]}, {"id": "E", "name": "Birational geometry", "children": [{"name": "Embeddings", "value": 100, "id": "25"}, {"name": "Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]", "value": 100, "id": "15"}, {"name": "Birational automorphisms, Cremona group and generalizations", "value": 100, "id": "07"}, {"name": "Ramification problems [See also 11S15]", "value": 100, "id": "22"}, {"name": "McKay correspondence", "value": 100, "id": "16"}, {"name": "Arcs and motivic integration", "value": 100, "id": "18"}, {"name": "Rationality questions [See also 14M20]", "value": 100, "id": "08"}, {"name": "Minimal model program (Mori theory, extremal rays)", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Coverings [See also 14H30]", "value": 100, "id": "20"}, {"name": "Rational and birational maps", "value": 100, "id": "05"}]}, {"id": "D", "name": "Families, fibrations", "children": [{"name": "Geometric Langlands program: algebro-geometric aspects [See also 22E57]", "value": 100, "id": "24"}, {"name": "Arithmetic ground fields (finite, local, global)", "value": 100, "id": "10"}, {"name": "Fibrations, degenerations", "value": 100, "id": "06"}, {"name": "Variation of Hodge structures [See also 32G20]", "value": 100, "id": "07"}, {"name": "Fine and coarse moduli spaces", "value": 100, "id": "22"}, {"name": "Structure of families (Picard-Lefschetz, monodromy, etc.)", "value": 100, "id": "05"}, {"name": "Stacks and moduli problems", "value": 100, "id": "23"}, {"name": "Formal methods; deformations [See also 13D10, 14B07, 32Gxx]", "value": 100, "id": "15"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}", "value": 100, "id": "20"}, {"name": "Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx]", "value": 100, "id": "21"}]}, {"id": "G", "name": "Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]", "children": [{"name": "Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)", "value": 100, "id": "10"}, {"name": "Other nonalgebraically closed ground fields", "value": 100, "id": "27"}, {"name": "Local ground fields", "value": 100, "id": "20"}, {"name": "Positive characteristic ground fields", "value": 100, "id": "17"}, {"name": "Rigid analytic geometry", "value": 100, "id": "22"}, {"name": "Rational points", "value": 100, "id": "05"}, {"name": "Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)", "value": 100, "id": "32"}, {"name": "Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]", "value": 100, "id": "50"}, {"name": "Modular and Shimura varieties [See also 11F41, 11F46, 11G18]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Global ground fields", "value": 100, "id": "25"}, {"name": "Finite ground fields", "value": 100, "id": "15"}, {"name": "Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]", "value": 100, "id": "40"}]}, {"id": "F", "name": "(Co)homology theory [See also 13Dxx]", "children": [{"name": "Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]", "value": 100, "id": "10"}, {"name": "Topological properties", "value": 100, "id": "45"}, {"name": "Etale and other Grothendieck topologies and (co)homologies", "value": 100, "id": "20"}, {"name": "Vanishing theorems [See also 32L20]", "value": 100, "id": "17"}, {"name": "Brauer groups of schemes [See also 12G05, 16K50]", "value": 100, "id": "22"}, {"name": "Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]", "value": 100, "id": "05"}, {"name": "Multiplier ideals", "value": 100, "id": "18"}, {"name": "$p$-adic cohomology, crystalline cohomology", "value": 100, "id": "30"}, {"name": "Motivic cohomology; motivic homotopy theory [See also 19E15]", "value": 100, "id": "42"}, {"name": "Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)", "value": 100, "id": "43"}, {"name": "Homotopy theory; fundamental groups [See also 14H30]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Classical real and complex (co)homology", "value": 100, "id": "25"}, {"name": "de Rham cohomology [See also 14C30, 32C35, 32L10]", "value": 100, "id": "40"}]}, {"id": "H", "name": "Curves", "children": [{"name": "Families, moduli (algebraic)", "value": 100, "id": "10"}, {"name": "Special curves and curves of low genus", "value": 100, "id": "45"}, {"name": "Singularities, local rings [See also 13Hxx, 14B05]", "value": 100, "id": "20"}, {"name": "Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]", "value": 100, "id": "25"}, {"name": "Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]", "value": 100, "id": "55"}, {"name": "Theta functions; Schottky problem [See also 14K25, 32G20]", "value": 100, "id": "42"}, {"name": "Dessins d'enfants theory {For arithmetic aspects, see 11G32}", "value": 100, "id": "57"}, {"name": "Coverings, fundamental group [See also 14E20, 14F35]", "value": 100, "id": "30"}, {"name": "Automorphisms", "value": 100, "id": "37"}, {"name": "Plane and space curves", "value": 100, "id": "50"}, {"name": "Jacobians, Prym varieties [See also 32G20]", "value": 100, "id": "40"}, {"name": "Elliptic curves [See also 11G05, 11G07, 14Kxx]", "value": 100, "id": "52"}, {"name": "Vector bundles on curves and their moduli [See also 14D20, 14F05]", "value": 100, "id": "60"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Relationships with integrable systems", "value": 100, "id": "70"}, {"name": "Families, moduli (analytic) [See also 30F10, 32G15]", "value": 100, "id": "15"}, {"name": "Relationships with physics", "value": 100, "id": "81"}, {"name": "Algebraic functions; function fields [See also 11R58]", "value": 100, "id": "05"}, {"name": "Special divisors (gonality, Brill-Noether theory)", "value": 100, "id": "51"}]}, {"id": "K", "name": "Abelian varieties and schemes", "children": [{"name": "Isogeny", "value": 100, "id": "02"}, {"name": "Algebraic moduli, classification [See also 11G15]", "value": 100, "id": "10"}, {"name": "Subvarieties", "value": 100, "id": "12"}, {"name": "Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]", "value": 100, "id": "15"}, {"name": "Complex multiplication [See also 11G15]", "value": 100, "id": "22"}, {"name": "Algebraic theory", "value": 100, "id": "05"}, {"name": "Picard schemes, higher Jacobians [See also 14H40, 32G20]", "value": 100, "id": "30"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Theta functions [See also 14H42]", "value": 100, "id": "25"}, {"name": "Analytic theory; abelian integrals and differentials", "value": 100, "id": "20"}]}, {"id": "J", "name": "Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}", "children": [{"name": "Families, moduli, classification: algebraic theory", "value": 100, "id": "10"}, {"name": "Rational and ruled surfaces", "value": 100, "id": "26"}, {"name": "Elliptic surfaces", "value": 100, "id": "27"}, {"name": "Moduli, classification: analytic theory; relations with modular forms [See also 32G13]", "value": 100, "id": "15"}, {"name": "Singularities [See also 14B05, 14E15]", "value": 100, "id": "17"}, {"name": "Special surfaces {For Hilbert modular surfaces, see 14G35}", "value": 100, "id": "25"}, {"name": "Mirror symmetry [See also 11G42, 53D37]", "value": 100, "id": "33"}, {"name": "Calabi-Yau manifolds", "value": 100, "id": "32"}, {"name": "$3$-folds [See also 32Q25]", "value": 100, "id": "30"}, {"name": "$K3$ surfaces and Enriques surfaces", "value": 100, "id": "28"}, {"name": "Surfaces of general type", "value": 100, "id": "29"}, {"name": "$4$-folds", "value": 100, "id": "35"}, {"name": "Automorphisms of surfaces and higher-dimensional varieties", "value": 100, "id": "50"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Fano varieties", "value": 100, "id": "45"}, {"name": "$n$-folds ($n>4$)", "value": 100, "id": "40"}, {"name": "Hypersurfaces", "value": 100, "id": "70"}, {"name": "Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]", "value": 100, "id": "20"}, {"name": "Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)", "value": 100, "id": "80"}, {"name": "Relationships with physics", "value": 100, "id": "81"}, {"name": "Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]", "value": 100, "id": "60"}]}, {"id": "M", "name": "Special varieties", "children": [{"name": "Complete intersections [See also 13C40]", "value": 100, "id": "10"}, {"name": "Determinantal varieties [See also 13C40]", "value": 100, "id": "12"}, {"name": "Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]", "value": 100, "id": "15"}, {"name": "Low codimension problems", "value": 100, "id": "07"}, {"name": "Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]", "value": 100, "id": "17"}, {"name": "Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]", "value": 100, "id": "05"}, {"name": "Rationally connected varieties", "value": 100, "id": "22"}, {"name": "Rational and unirational varieties [See also 14E08]", "value": 100, "id": "20"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Compactifications; symmetric and spherical varieties", "value": 100, "id": "27"}, {"name": "Toric varieties, Newton polyhedra [See also 52B20]", "value": 100, "id": "25"}, {"name": "Supervarieties [See also 32C11, 58A50]", "value": 100, "id": "30"}, {"name": "Linkage [See also 13C40]", "value": 100, "id": "06"}]}, {"id": "L", "name": "Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}", "children": [{"name": "Geometric invariant theory [See also 13A50]", "value": 100, "id": "24"}, {"name": "Group varieties", "value": 100, "id": "10"}, {"name": "Group schemes", "value": 100, "id": "15"}, {"name": "Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]", "value": 100, "id": "17"}, {"name": "Formal groups, $p$-divisible groups [See also 55N22]", "value": 100, "id": "05"}, {"name": "Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]", "value": 100, "id": "30"}, {"name": "Classical groups (geometric aspects) [See also 20Gxx, 51N30]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Other algebraic groups (geometric aspects)", "value": 100, "id": "40"}]}, {"id": "N", "name": "Projective and enumerative geometry [See also 51-XX]", "children": [{"name": "Enumerative problems (combinatorial problems)", "value": 100, "id": "10"}, {"name": "Configurations and arrangements of linear subspaces", "value": 100, "id": "20"}, {"name": "Varieties of low degree", "value": 100, "id": "25"}, {"name": "Adjunction problems", "value": 100, "id": "30"}, {"name": "Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]", "value": 100, "id": "35"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Classical problems, Schubert calculus", "value": 100, "id": "15"}, {"name": "Projective techniques [See also 51N35]", "value": 100, "id": "05"}]}, {"id": "Q", "name": "Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Surfaces, hypersurfaces", "value": 100, "id": "10"}, {"name": "Curves", "value": 100, "id": "05"}, {"name": "Higher-dimensional varieties", "value": 100, "id": "15"}, {"name": "Effectivity, complexity", "value": 100, "id": "20"}]}, {"id": "P", "name": "Real algebraic and real analytic geometry", "children": [{"name": "Semialgebraic sets and related spaces", "value": 100, "id": "10"}, {"name": "Real analytic and semianalytic sets [See also 32B20, 32C05]", "value": 100, "id": "15"}, {"name": "Topology of real algebraic varieties", "value": 100, "id": "25"}, {"name": "Real algebraic sets [See also 12D15, 13J30]", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Nash functions and manifolds [See also 32C07, 58A07]", "value": 100, "id": "20"}]}, {"id": "R", "name": "Affine geometry", "children": [{"name": "Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)", "value": 100, "id": "10"}, {"name": "Jacobian problem [See also 13F20]", "value": 100, "id": "15"}, {"name": "Affine fibrations [See also 14D06]", "value": 100, "id": "25"}, {"name": "Classification of affine varieties", "value": 100, "id": "05"}, {"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Group actions on affine varieties [See also 13A50, 14L30]", "value": 100, "id": "20"}]}, {"id": "T", "name": "Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]", "children": [{"name": "None of the above, but in this section", "value": 100, "id": "99"}, {"name": "Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]", "value": 100, "id": "05"}]}, {"id": "-", "name": "Unlabeled", "children": [{"name": "Research exposition (monographs, survey articles)", "value": 100, "id": "02"}, {"name": "Historical (must also be assigned at least one classification number from Section 01)", "value": 100, "id": "03"}, {"name": "General reference works (handbooks, dictionaries, bibliographies, etc.)", "value": 100, "id": "00"}, {"name": "Instructional exposition (textbooks, tutorial papers, etc.)", "value": 100, "id": "01"}, {"name": "Proceedings, conferences, collections, etc.", "value": 100, "id": "06"}, {"name": "Explicit machine computation and programs (not the theory of computation or programming)", "value": 100, "id": "04"}]}]}]}], "name": "Mathematics"};