Mathematics

<!DOCTYPE html> <html lang="en"> <head><title>Mathematics</title> <meta name="viewport" content="width=device-width, initial-scale=1"> <link rel="apple-touch-icon" sizes="180x180" href="/static/browse/0.3.4/images/icons/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="/static/browse/0.3.4/images/icons/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="/static/browse/0.3.4/images/icons/favicon-16x16.png"> <link rel="manifest" href="/static/browse/0.3.4/images/icons/site.webmanifest"> <link rel="mask-icon" href="/static/browse/0.3.4/images/icons/safari-pinned-tab.svg" color="#5bbad5"> <meta name="msapplication-TileColor" content="#da532c"> <meta name="theme-color" content="#ffffff"> <link rel="stylesheet" type="text/css" media="screen" href="/static/browse/0.3.4/css/arXiv.css?v=20241206" /> <link rel="stylesheet" type="text/css" media="print" href="/static/browse/0.3.4/css/arXiv-print.css?v=20200611" /> <link rel="stylesheet" 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for="catchup_category">Categories:</label> <select name="catchup_category" id="catchup_category"> <option value="" selected>All</option> <option value="math.AC"> Commutative Algebra </option> <option value="math.AG"> Algebraic Geometry </option> <option value="math.AP"> Analysis of PDEs </option> <option value="math.AT"> Algebraic Topology </option> <option value="math.CA"> Classical Analysis and ODEs </option> <option value="math.CO"> Combinatorics </option> <option value="math.CT"> Category Theory </option> <option value="math.CV"> Complex Variables </option> <option value="math.DG"> Differential Geometry </option> <option value="math.DS"> Dynamical Systems </option> <option value="math.FA"> Functional Analysis </option> <option value="math.GM"> General Mathematics </option> <option value="math.GN"> General Topology </option> <option value="math.GR"> Group Theory </option> <option value="math.GT"> Geometric Topology </option> <option value="math.HO"> History and Overview </option> <option value="math.IT"> Information Theory </option> <option value="math.KT"> K-Theory and Homology </option> <option value="math.LO"> Logic </option> <option value="math.MG"> Metric Geometry </option> <option value="math.MP"> Mathematical Physics </option> <option value="math.NA"> Numerical Analysis </option> <option value="math.NT"> Number Theory </option> <option value="math.OA"> Operator Algebras </option> <option value="math.OC"> Optimization and Control </option> <option value="math.PR"> Probability </option> <option value="math.QA"> Quantum Algebra </option> <option value="math.RA"> Rings and Algebras </option> <option value="math.RT"> Representation Theory </option> <option value="math.SG"> Symplectic Geometry </option> <option value="math.SP"> Spectral Theory </option> <option value="math.ST"> Statistics Theory </option> </select> <br> Changes since: <select id="catchup_day"> <option value="01">01</option> <option value="02">02</option> <option value="03">03</option> <option 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selected>03 (Mar)</option> <option value="04" >04 (Apr)</option> <option value="05" >05 (May)</option> <option value="06" >06 (Jun)</option> <option value="07" >07 (Jul)</option> <option value="08" >08 (Aug)</option> <option value="09" >09 (Sep)</option> <option value="10" >10 (Oct)</option> <option value="11" >11 (Nov)</option> <option value="12" >12 (Dec)</option> </select> <select id="catchup_year"> <option value="2025">2025</option> <option value="2024">2024</option> </select> <input type="hidden" id="date" name="date" /> , view results <select name="include_abs"> <option value="False" selected> without </option> <option value="True" > with </option> </select> abstracts <input type="submit" value="Go"/> </form> </li> <li><b>Search</b> within the <a href="https://arxiv.org/search/math">math archive</a></li> <li>Article statistics by year:<br> <a href="/year/math/2025">2025</a> <a href="/year/math/2024">2024</a> <a href="/year/math/2023">2023</a> <a href="/year/math/2022">2022</a> <a href="/year/math/2021">2021</a> <a href="/year/math/2020">2020</a> <a href="/year/math/2019">2019</a> <a href="/year/math/2018">2018</a> <a href="/year/math/2017">2017</a> <a href="/year/math/2016">2016</a> <a href="/year/math/2015">2015</a> <a href="/year/math/2014">2014</a> <a href="/year/math/2013">2013</a> <a href="/year/math/2012">2012</a> <a href="/year/math/2011">2011</a> <a href="/year/math/2010">2010</a> <a href="/year/math/2009">2009</a> <a href="/year/math/2008">2008</a> <a href="/year/math/2007">2007</a> <a href="/year/math/2006">2006</a> <a href="/year/math/2005">2005</a> <a href="/year/math/2004">2004</a> <a href="/year/math/2003">2003</a> <a href="/year/math/2002">2002</a> <a href="/year/math/2001">2001</a> <a href="/year/math/2000">2000</a> <a href="/year/math/1999">1999</a> <a href="/year/math/1998">1998</a> <a href="/year/math/1997">1997</a> <a href="/year/math/1996">1996</a> <a href="/year/math/1995">1995</a> <a href="/year/math/1994">1994</a> <a href="/year/math/1993">1993</a> <a href="/year/math/1992">1992</a> </li> </ul> <h2>Categories within Mathematics</h2> <ul> <li><b>math.AC - Commutative Algebra</b> (<a href="/list/math.AC/new">new</a>, <a href="/list/math.AC/recent">recent</a>, <a href="/list/math.AC/current">current month</a>) <div class="description">Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics</div> </li> <li><b>math.AG - Algebraic Geometry</b> (<a href="/list/math.AG/new">new</a>, <a href="/list/math.AG/recent">recent</a>, <a href="/list/math.AG/current">current month</a>) <div class="description">Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology</div> </li> <li><b>math.AP - Analysis of PDEs</b> (<a href="/list/math.AP/new">new</a>, <a href="/list/math.AP/recent">recent</a>, <a href="/list/math.AP/current">current month</a>) <div class="description">Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics</div> </li> <li><b>math.AT - Algebraic Topology</b> (<a href="/list/math.AT/new">new</a>, <a href="/list/math.AT/recent">recent</a>, <a href="/list/math.AT/current">current month</a>) <div class="description">Homotopy theory, homological algebra, algebraic treatments of manifolds</div> </li> <li><b>math.CA - Classical Analysis and ODEs</b> (<a href="/list/math.CA/new">new</a>, <a href="/list/math.CA/recent">recent</a>, <a href="/list/math.CA/current">current month</a>) <div class="description">Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics</div> </li> <li><b>math.CO - Combinatorics</b> (<a href="/list/math.CO/new">new</a>, <a href="/list/math.CO/recent">recent</a>, <a href="/list/math.CO/current">current month</a>) <div class="description">Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory</div> </li> <li><b>math.CT - Category Theory</b> (<a href="/list/math.CT/new">new</a>, <a href="/list/math.CT/recent">recent</a>, <a href="/list/math.CT/current">current month</a>) <div class="description">Enriched categories, topoi, abelian categories, monoidal categories, homological algebra</div> </li> <li><b>math.CV - Complex Variables</b> (<a href="/list/math.CV/new">new</a>, <a href="/list/math.CV/recent">recent</a>, <a href="/list/math.CV/current">current month</a>) <div class="description">Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves</div> </li> <li><b>math.DG - Differential Geometry</b> (<a href="/list/math.DG/new">new</a>, <a href="/list/math.DG/recent">recent</a>, <a href="/list/math.DG/current">current month</a>) <div class="description">Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis</div> </li> <li><b>math.DS - Dynamical Systems</b> (<a href="/list/math.DS/new">new</a>, <a href="/list/math.DS/recent">recent</a>, <a href="/list/math.DS/current">current month</a>) <div class="description">Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations</div> </li> <li><b>math.FA - Functional Analysis</b> (<a href="/list/math.FA/new">new</a>, <a href="/list/math.FA/recent">recent</a>, <a href="/list/math.FA/current">current month</a>) <div class="description">Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory</div> </li> <li><b>math.GM - General Mathematics</b> (<a href="/list/math.GM/new">new</a>, <a href="/list/math.GM/recent">recent</a>, <a href="/list/math.GM/current">current month</a>) <div class="description">Mathematical material of general interest, topics not covered elsewhere</div> </li> <li><b>math.GN - General Topology</b> (<a href="/list/math.GN/new">new</a>, <a href="/list/math.GN/recent">recent</a>, <a href="/list/math.GN/current">current month</a>) <div class="description">Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties</div> </li> <li><b>math.GR - Group Theory</b> (<a href="/list/math.GR/new">new</a>, <a href="/list/math.GR/recent">recent</a>, <a href="/list/math.GR/current">current month</a>) <div class="description">Finite groups, topological groups, representation theory, cohomology, classification and structure</div> </li> <li><b>math.GT - Geometric Topology</b> (<a href="/list/math.GT/new">new</a>, <a href="/list/math.GT/recent">recent</a>, <a href="/list/math.GT/current">current month</a>) <div class="description">Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures</div> </li> <li><b>math.HO - History and Overview</b> (<a href="/list/math.HO/new">new</a>, <a href="/list/math.HO/recent">recent</a>, <a href="/list/math.HO/current">current month</a>) <div class="description">Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics, ethics in mathematics</div> </li> <li><b>math.IT - Information Theory</b> (<a href="/list/math.IT/new">new</a>, <a href="/list/math.IT/recent">recent</a>, <a href="/list/math.IT/current">current month</a>) <div class="description">math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.</div> </li> <li><b>math.KT - K-Theory and Homology</b> (<a href="/list/math.KT/new">new</a>, <a href="/list/math.KT/recent">recent</a>, <a href="/list/math.KT/current">current month</a>) <div class="description">Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras</div> </li> <li><b>math.LO - Logic</b> (<a href="/list/math.LO/new">new</a>, <a href="/list/math.LO/recent">recent</a>, <a href="/list/math.LO/current">current month</a>) <div class="description">Logic, set theory, point-set topology, formal mathematics</div> </li> <li><b>math.MG - Metric Geometry</b> (<a href="/list/math.MG/new">new</a>, <a href="/list/math.MG/recent">recent</a>, <a href="/list/math.MG/current">current month</a>) <div class="description">Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces</div> </li> <li><b>math.MP - Mathematical Physics</b> (<a href="/list/math.MP/new">new</a>, <a href="/list/math.MP/recent">recent</a>, <a href="/list/math.MP/current">current month</a>) <div class="description">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</div> </li> <li><b>math.NA - Numerical Analysis</b> (<a href="/list/math.NA/new">new</a>, <a href="/list/math.NA/recent">recent</a>, <a href="/list/math.NA/current">current month</a>) <div class="description">Numerical algorithms for problems in analysis and algebra, scientific computation</div> </li> <li><b>math.NT - Number Theory</b> (<a href="/list/math.NT/new">new</a>, <a href="/list/math.NT/recent">recent</a>, <a href="/list/math.NT/current">current month</a>) <div class="description">Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory</div> </li> <li><b>math.OA - Operator Algebras</b> (<a href="/list/math.OA/new">new</a>, <a href="/list/math.OA/recent">recent</a>, <a href="/list/math.OA/current">current month</a>) <div class="description">Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry</div> </li> <li><b>math.OC - Optimization and Control</b> (<a href="/list/math.OC/new">new</a>, <a href="/list/math.OC/recent">recent</a>, <a href="/list/math.OC/current">current month</a>) <div class="description">Operations research, linear programming, control theory, systems theory, optimal control, game theory</div> </li> <li><b>math.PR - Probability</b> (<a href="/list/math.PR/new">new</a>, <a href="/list/math.PR/recent">recent</a>, <a href="/list/math.PR/current">current month</a>) <div class="description">Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory</div> </li> <li><b>math.QA - Quantum Algebra</b> (<a href="/list/math.QA/new">new</a>, <a href="/list/math.QA/recent">recent</a>, <a href="/list/math.QA/current">current month</a>) <div class="description">Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory</div> </li> <li><b>math.RA - Rings and Algebras</b> (<a href="/list/math.RA/new">new</a>, <a href="/list/math.RA/recent">recent</a>, <a href="/list/math.RA/current">current month</a>) <div class="description">Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups</div> </li> <li><b>math.RT - Representation Theory</b> (<a href="/list/math.RT/new">new</a>, <a href="/list/math.RT/recent">recent</a>, <a href="/list/math.RT/current">current month</a>) <div class="description">Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra</div> </li> <li><b>math.SG - Symplectic Geometry</b> (<a href="/list/math.SG/new">new</a>, <a href="/list/math.SG/recent">recent</a>, <a href="/list/math.SG/current">current month</a>) <div class="description">Hamiltonian systems, symplectic flows, classical integrable systems</div> </li> <li><b>math.SP - Spectral Theory</b> (<a href="/list/math.SP/new">new</a>, <a href="/list/math.SP/recent">recent</a>, <a href="/list/math.SP/current">current month</a>) <div class="description">Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices</div> </li> <li><b>math.ST - Statistics Theory</b> (<a href="/list/math.ST/new">new</a>, <a href="/list/math.ST/recent">recent</a>, <a href="/list/math.ST/current">current month</a>) <div class="description">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</div> </li> </ul> <script> function catchupParamSelection(archive) { var day = document.getElementById('catchup_day').value.padStart(2, '0'); var month = document.getElementById('catchup_month').value.padStart(2, '0'); var year = document.getElementById('catchup_year').value; var combinedDate = `${year}-${month}-${day}`; document.getElementById('date').value = combinedDate; var categoryElement = document.getElementById('catchup_category'); var category = categoryElement ? 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