Here are the categories and category groups in the mathematics arXiv listed with sample topics. Please use restraint when cross-listing new submissions.

The moderators for each category are listed in parentheses.

math.** All Mathematics

math.AC Commutative Algebra (Irena Swanson, Anurag Singh, David R. Morrison)

commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics

math.AG Algebraic Geometry (David R. Morrison, Irena Swanson, Anurag Singh, Bill McCallum)

Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology

math.AP Analysis of PDEs (Christopher Sogge)

Existence and uniquness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics

math.AT Algebraic Topology (Mark Hovey, Mark Steinberger)

Homotopy theory, homological algebra, algebraic treatments of manifolds

math.CA Classical Analysis and ODEs (Terence Tao)

Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics

math.CO Combinatorics (Greg Kuperberg)

Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory

math.CT Category Theory (James D. Stasheff)

Enriched categories, topoi, abelian categories, monoidal categories, homological algebra

math.CV Complex Variables (Harold P. Boas)

Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves

math.DG Differential Geometry (Robert Bryant, Raffe Mazzeo)

Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis

math.DS Dynamical Systems (Krystyna Kuperberg)

Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations

math.FA Functional Analysis (Dale E. Alspach, Marc A. Rieffel)

Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory

math.GM General Mathematics (The Math Advisory Committee (collectively))

Mathematical material of general interest, topics not covered elsewhere

math.GN General Topology (Krystyna Kuperberg, Dmitri Shakhmatov)

Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties

math.GR Group Theory (Robert Guralnick)

Finite groups, topological groups, representation theory, cohomology, classification and structure

math.GT Geometric Topology (Greg Kuperberg, Mark Steinberger)

Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures

math.HO History and Overview (The math advisory committee)

Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics

math.IT Information Theory (Madhu Sudan, Joachim Rosenthal)

Shannon's theory of information, error-correcting codes, data compression.

math.KT K-Theory and Homology (David R. Morrison)

Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

math.LO Logic (William Mitchell)

Logic, set theory, point-set topology, formal mathematics

math.MG Metric Geometry (Andras Bezdek)

Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces

math.MP Mathematical Physics (Paul Fendley, Bruno Nachtergaele)

Mathematical methods in quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics

math.NA Numerical Analysis (Douglas Arnold)

Numerical algorithms for problems in analysis and algebra, scientific computation

math.NT Number Theory (Paul Gunnells, Bill McCallum, David R. Morrison)

Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory

math.OA Operator Algebras (Marc A. Rieffel)

Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry

math.OC Optimization and Control (Yuan Wang)

Operations research, linear programming, control theory, systems theory, optimal control, game theory

math.PR Probability Theory (Chris Burdzy)

Stochastic processes, large deviations, martingale theory, measure theory, mathematical statistics

math.QA Quantum Algebra (Alexander Kirillov Jr.)

Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory

math.RA Rings and Algebras (Joseph Brennan)

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups

math.RT Representation Theory (Bill Casselman)

Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra

math.SG Symplectic Geometry (Richard S. Palais)

Hamiltonian systems, symplectic flows, classical integrable systems

math.SP Spectral Theory (Malcolm Brown)

Schr\"odinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators and matrices

math.ST Statistics (Chris Burdzy, Rob Strawderman)

asymptotics, Bayesian inference, decision theory, estimation, foundations, inference, testing

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