# Mathematics (since February 1992)

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## Categories within Mathematics

**math.AG - Algebraic Geometry**(new, recent, current month)Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology**math.AT - Algebraic Topology**(new, recent, current month)Homotopy theory, homological algebra, algebraic treatments of manifolds**math.AP - Analysis of PDEs**(new, recent, current month)Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics**math.CT - Category Theory**(new, recent, current month)Enriched categories, topoi, abelian categories, monoidal categories, homological algebra**math.CA - Classical Analysis and ODEs**(new, recent, current month)Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics**math.CO - Combinatorics**(new, recent, current month)Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory**math.AC - Commutative Algebra**(new, recent, current month)Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics**math.CV - Complex Variables**(new, recent, current month)Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves**math.DG - Differential Geometry**(new, recent, current month)Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis**math.DS - Dynamical Systems**(new, recent, current month)Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations**math.FA - Functional Analysis**(new, recent, current month)Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory**math.GM - General Mathematics**(new, recent, current month)Mathematical material of general interest, topics not covered elsewhere**math.GN - General Topology**(new, recent, current month)Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties**math.GT - Geometric Topology**(new, recent, current month)Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures**math.GR - Group Theory**(new, recent, current month)Finite groups, topological groups, representation theory, cohomology, classification and structure**math.HO - History and Overview**(new, recent, current month)Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics**math.IT - Information Theory**(new, recent, current month)math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.**math.KT - K-Theory and Homology**(new, recent, current month)Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras**math.LO - Logic**(new, recent, current month)Logic, set theory, point-set topology, formal mathematics**math.MP - Mathematical Physics**(new, recent, current month)math.MP is an alias for math-ph. Mathematical methods in quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.**math.MG - Metric Geometry**(new, recent, current month)Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces**math.NT - Number Theory**(new, recent, current month)Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory**math.NA - Numerical Analysis**(new, recent, current month)Numerical algorithms for problems in analysis and algebra, scientific computation**math.OA - Operator Algebras**(new, recent, current month)Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry**math.OC - Optimization and Control**(new, recent, current month)Operations research, linear programming, control theory, systems theory, optimal control, game theory**math.PR - Probability**(new, recent, current month)Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory**math.QA - Quantum Algebra**(new, recent, current month)Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory**math.RT - Representation Theory**(new, recent, current month)Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra**math.RA - Rings and Algebras**(new, recent, current month)Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups**math.SP - Spectral Theory**(new, recent, current month)Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices**math.ST - Statistics Theory**(new, recent, current month)Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies**math.SG - Symplectic Geometry**(new, recent, current month)Hamiltonian systems, symplectic flows, classical integrable systems