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This is an index of all the directories that are relatively esoteric,
taken with a grain of salt.
CoRR (Computing Research Repository)
all my source code resides here
math.AC (Commutative Algebra)
commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
math.AG (Algebraic Geometry)
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
math.AP (Analysis of PDEs)
Existence and uniquness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
math.AT (Algebraic Topology)
Homotopy theory, homological algebra, algebraic treatments of manifolds
math.CA (Classical Analysis and ODEs)
Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
math.CO (Combinatorics)
Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
math.CT (Category Theory)
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
math.CV (Complex Variables)
Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
math.DG (Differential Geometry)
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
math.DS (Dynamical Systems)
Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
math.FA (Functional Analysis)
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
math.GM (General Mathematics)
Mathematical material of general interest, topics not covered elsewhere
math.GN (General Topology)
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
math.GR (Group Theory)
Finite groups, topological groups, representation theory, cohomology, classification and structure
math.GT (Geometric Topology)
Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
math.HO (History and Overview)
Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics
math.IT (Information Theory)
Shannon's theory of information, error-correcting codes, data compression.
math.KT (K-Theory and Homology)
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
math.LO (Logic)
Logic, set theory, point-set topology, formal mathematics
math.MG (Metric Geometry)
Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces
math.MP (Mathematical Physics)
Mathematical methods in quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics
math.NA (Numerical Analysis)
Numerical algorithms for problems in analysis and algebra, scientific computation
math.NT (Number Theory)
Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
math.OA (Operator Algebras)
Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry
math.OC (Optimization and Control)
Operations research, linear programming, control theory, systems theory, optimal control, game theory
math.PR (Probability Theory)
Stochastic processes, large deviations, martingale theory, measure theory, mathematical statistics
math.QA (Quantum Algebra)
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
math.RA (Rings and Algebras)
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
math.RT (Representation Theory)
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
math.SG (Symplectic Geometry)
Hamiltonian systems, symplectic flows, classical integrable systems
math.SP (Spectral Theory)
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)
asymptotics, Bayesian inference, decision theory, estimation, foundations, inference, testing