arXiv Mathematics

math.AC | Commutative Algebra | Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics. The area focuses on structure and properties of commutative algebraic objects. Key topics include ideal theory and module theory. |

math.AG | Algebraic Geometry | Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology. The area deals with geometric objects defined by polynomial equations. Key topics include schemes and sheaves. |

math.AP | Analysis of PDEs | Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics. The area studies properties of solutions to partial differential equations. Key topics include elliptic, parabolic, and hyperbolic PDEs. |

math.AT | Algebraic Topology | Homotopy theory, homological algebra, algebraic treatments of manifolds. The area uses algebraic methods to study topological spaces. Key topics include homotopy groups and homology. |

math.CA | Classical Analysis and ODEs | Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics. The area focuses on real analysis and ordinary differential equations. Key topics include asymptotic expansions and special functions. |

math.CO | Combinatorics | Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory. The area deals with counting and discrete structures. Key topics include graphs and combinations. |

math.CT | Category Theory | Enriched categories, topoi, abelian categories, monoidal categories, homological algebra. The area studies mathematical structures and their transformations. Key topics include functors and natural transformations. |

math.CV | Complex Variables | Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves. The area focuses on functions of complex variables. Key topics include Riemann surfaces and several complex variables. |

math.DG | Differential Geometry | Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis. The area studies geometry using differential calculus. Key topics include manifolds and curvature. |

math.DS | Dynamical Systems | Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations. The area studies evolution of systems over time. Key topics include chaos and attractors. |

math.FA | Functional Analysis | Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory. The area studies vector spaces with norms or topologies. Key topics include operator theory and abstract analysis. |

math.GN | General Topology | Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties. The area studies properties of topological spaces. Key topics include compactness and connectedness. |

math.GR | Group Theory | Finite groups, topological groups, representation theory, cohomology, classification and structure. The area studies algebraic structures with group operations. Key topics include group representations and symmetry. |

math.GT | Geometric Topology | Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures. The area studies topology of manifolds and related structures. Key topics include knot theory and 3-manifolds. |

math.HO | History and Overview | Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics, ethics in mathematics. The area covers historical and philosophical aspects of math. Key topics include math education and outreach. |

math.IT | Information Theory | Covers theoretical and experimental aspects of information theory and coding. The area intersects with cs.IT. Key topics include entropy and channel capacity. |

math.KT | K-Theory and Homology | Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras. The area studies invariants of algebraic structures. Key topics include K-groups and homology theories. |

math.LO | Logic | Logic, set theory, point-set topology, formal mathematics. The area studies foundations of mathematics. Key topics include axioms and models. |

math.MG | Metric Geometry | Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces. The area studies geometry with metrics. Key topics include isometries and distances. |

math.MP | Mathematical Physics | 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. The area bridges math and physics. |

math.NA | Numerical Analysis | Numerical algorithms for problems in analysis and algebra, scientific computation. The area studies approximation and discretization. Key topics include error analysis and numerical methods. |

math.NT | Number Theory | Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory. The area studies properties of numbers. Key topics include primes and modular forms. |

math.OA | Operator Algebras | Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry. The area studies algebraic structures of operators. Key topics include functional analysis applications. |

math.OC | Optimization and Control | Operations research, linear programming, control theory, systems theory, optimal control, game theory. The area studies optimization problems. Key topics include linear and nonlinear programming. |

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. The area studies random phenomena. Key topics include stochastic processes and probability distributions. |

math.QA | Quantum Algebra | Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory. The area studies algebraic structures in quantum contexts. Key topics include Hopf algebras and quantum groups. |

math.RA | Rings and Algebras | Non-commutative rings and algebras, modules, ideals and radical theory, structure theory, applications to physics and engineering. The area studies non-commutative algebraic structures. Key topics include associative algebras. |

math.RT | Representation Theory | Representation theory of groups and algebras, Lie algebras, associative algebras, multilinear algebra. The area studies linear representations. Key topics include character theory and module theory. |

math.SG | Symplectic Geometry | Symplectic manifolds, symplectomorphisms, classical Hamiltonian systems, symplectic integration. The area studies geometry preserving volume. Key topics include Hamiltonian dynamics. |

math.SP | Spectral Theory | Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete versions, resonances, eigenvalues, multiplicities, quantum chaos. The area studies spectra of operators. Key topics include eigenvalues and eigenfunctions. |

math.ST | Statistics Theory | 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. The area studies statistical methods. Key topics include inference and estimation. |