# 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, ethics in 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. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories**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