Taxonomy: Mathematics

Computing Research Repository (CoRR) style

math.AG - Algebraic Geometry

• Algebraic varieties

• stacks

• sheaves

• schemes

• moduli spaces

• complex geometry

• quantum cohomology (subsumes alg-geom)

math.AT - Algebraic Topology

• Homotopy theory

• homological algebra

• algebraic treatments of manifolds

math.AP - Analysis of Partial Differential Equations (PDE)

• Existence and uniqueness

• boundary conditions

• linear and non-linear operators

• stability

• soliton theory

• integrable PDE's

• conservation laws

• qualitative dynamics

math.CT - Category Theory

• Enriched categories

• topoi

• abelian categories

• monoidal categories

• homological algebra

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.AC - Commutative Algebra

• Commutative rings

• modules

• ideals

• homological algebra

• computational aspects

• invariant theory

• connections to algebraic geometry and combinatorics

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 (subsumes dg-ga)

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 (subsumes funct-an)

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.GT - Geometric Topology

• Manifolds

• orbifolds

• polyhedra

• cell complexes

• foliations

• geometric structures

math.GR - Group Theory

• Finite groups

• topological groups

• representation theory

• cohomology

• classification and structure

math.HO - History and Overview

• Biographies

• philosophy of mathematics

• mathematics education

• recreational mathematics

• communication of mathematics

math.IT - Information Theory math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.

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.MP - Mathematical Physics

• Mathematical methods in quantum field theory

• quantum mechanics

• statistical mechanics

• condensed matter

• nuclear and atomic physics

math.MG - Metric Geometry

• Euclidean

• hyperbolic

• discrete

• convex

• coarse geometry

• comparisons in Riemannian geometry

• symmetric spaces

math.NT - Number Theory

• Prime numbers

• Diophantine equations

• Analytic number theory

• Algebraic number theory

• Arithmetic geometry

• Galois theory

math.NA - Numerical Analysis

• Numerical algorithms for problems in analysis and algebra

• Scientific computation

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 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

• Quantum groups

• skein theories

• operadic and diagrammatic algebra

• quantum field theory (subsumes q-alg)

math.RT - Representation Theory

• Linear representations of algebras and groups

• Lie theory

• associative algebras

• multilinear algebra

math.RA - Rings and Algebras

• Non-commutative rings and algebras

• non-associative algebras

• universal algebra and lattice theory

• linear algebra

• semigroups

math.SP - Spectral Theory

• 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 math.ST is an alias for stat.TH

• 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

• Hamiltonian systems

• symplectic flows

• classical integrable systems