Classification Search Result

Mathematics Subject Classification – MSC2020

Differential geometry {For differential topology, see 57Rxx; for foundational questions of differentiable manifolds, see 58Axx}

135608

53Dxx

Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]

17494

53D05

Symplectic manifolds (general theory)

2133

53D10

Contact manifolds (general theory)

1890

53D12

Lagrangian submanifolds; Maslov index

1591

53D15

Almost contact and almost symplectic manifolds

1084

53D17

Poisson manifolds; Poisson groupoids and algebroids

2217

53D18

Generalized geometries (à la Hitchin)

234

53D20

Momentum maps; symplectic reduction

1440

53D22

Canonical transformations in symplectic and contact geometry

173

53D25

Geodesic flows in symplectic geometry and contact geometry

1354

53D30

Symplectic structures of moduli spaces

357

53D35

Global theory of symplectic and contact manifolds [See also 57Rxx]

1321

53D37

Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category [See also 14J33]

467

53D40

Symplectic aspects of Floer homology and cohomology

920

53D42

Symplectic field theory; contact homology

241

53D45

Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

1183

53D50

Geometric quantization

2462

53D55

Deformation quantization, star products

1563

53D99

None of the above, but in this section

167

Overview

General and overarching topics; collections

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory; homological algebra

\(K\)-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximations and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

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Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, finance, and other social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication theory, circuits

Mathematics education

any	anywhere
cc	classification code
ct	classification text

a & b	logical and
abc*	right wildcard
a \| b	logical or
"ab c"	phrase
!ab	logical not
(ab c)	parentheses

Examples

Fields

Operators

Mathematics Subject Classification – MSC2020

Overview