Webpages for Research in Mathematics

Links by area

Algebraic Geometry

• The Stacks project collaborative project, currently maintained by Aise Johan de Jong
• COW seminar and mailing list
• Calf Seminar, an algebraic geometry seminar group primarily aimed at PhD students
• EAGER European Algebraic Geometry Research Training Network
• Upcoming conferences in algebraic geometry, by Ravi Vakil
• Nottingham Online Algebraic Geometry Seminar
• Miles Reid's page, contains many algebraic geometry links
• THE RISING SEA, Foundations of Algebraic Geometry, by Ravi Vakil
• Graded Ring Database by Gavin Brown and Alexander Kasprzyk
• Fanography, database of smooth Fano 3-folds, by Pieter Belmans
• Fano Varieties and Extremal Laurent Polynomials, collaborative research blog

Algebraic Topology

• Links to websites related to algebraic topology by Donald M. Davis

Analysis of PDEs

• Calculus of Variation and Geometric Measure Theory collaborative website
• The Kantorovich Initiative - optimal transport
• VisualPDE website with real-time interactive web-based simulations, by Benjamin Walker, Adam Townsend, and Andrew Krause

Applied Mathematics (general)

• IACR International Association for Cryptologic Research
• SIAM Society for Industrial and Applied Mathematicsociety for Industrial and Applied Mathematics

Category Theory

• Logic Matters by Peter Smith
• nLab collaborative project
• The n-Category Cafe A group blog on math, physics and philosophy [Category Theory]

Classical Analysis and ODEs

Combinatorics

• Catalan Numbers by Igor Pak
• Cluster Algebra Portal by Sergey Fomin
• Associahedra and Noncrossing Partitions by Jon McCammond
• Frieze patterns by Anna Felikson
• Combinatorics of polytopes by Anna Felikson
• Encyclopedia of Combinatorial Polytope Sequences..., by Stefan Forcey
• Links to Combinatorial Conferences, by Douglas B. West

Commutative Algebra

• commalg.org, the website for the commutative algebra community

Computational Geometry

• Computational Geometry Pages, by by Jeff Erickson
• Geometry in Action, by David Eppstein

Complex Variables

Differential Geometry & Geometric Analysis

Dynamical Systems

• How to get to grip with (slow) chaos? by Corinna Ulcigrai
• Billiards by Anna Felikson
• Mu-Ency - The Encyclopedia of the Mandelbrot Set by Robert Munafo
• Mandelbrot Sequences and Orbits by Stefan Forcey

Functional Analysis

Geometry & Geometric Topology

• The Geometry Junkyard by David Eppstein
• Geometric Topology page on The Geometry Junkyard by David Eppstein
• Curves on surfaces by Anna Felikson
• Apollonian circle packings by Anna Felikson
• Low Dimensional Topology Conferences Low Dimensional Topology Conferences
• Sketches of topology - visualisations of low dimensional topology by Kenneth Baker
• Geometry conferences, listserv
• Cayley Graph Generator Online group visualiser by Jean-Baptiste Bellynck

Group Theory

• ATLAS of Finite Group Representations
• Atlas of Lie Groups and Representations, by Fokko Du Cloux, Marc van Leeuewn, Jeff Adams, Annegret Paul, David Vogan

Harmonic Analysis

History and Overview

• MacTutor History of Mathematics Archive by Edmund Robertson and John O'Conne
• The Archimedes Palimpsest The Archimedes Palimpsest
• Euclid's Elements illustrated online version by David E. Joyce
• Mathematics History: AMS Books and Resources

Information Theory

K-Theory and Homology

• Resources for homotopy theory and K-theory
• Floer Homology, by Michael Hutchings

Logic

• Directory of links on logic and foundations of mathematics by Sylvain Poirier

Machine learning

• Machine Learning Mastery by Jason Brownlee
• Analytics Vidhya Data Science community

Mathematical Physics

• String Theory Wiki
• Solitons at Work, informal network

Metric Geometry

• Hyperbolic Coxeter Polytopes by Anna Felikson
• Arithmetic Hyperbolic Reflection Groups by Nikolay V. Bogachev
• Geometry by Anna Felikson
• Ptolemy Relation and Friends by Anna Felikson

Number Theory

• Number Theory Web by Keith Matthews
• The L-functions and modular forms database (LMFDB)
• Markov numbers by Anna Felikson
• Continued fractions by Anna Felikson
• Conferences in arithmetic geometry by Kiran Kedlaya
• Conferences in number theory by Johann Birnick
• Motivic stuff Cohomology, homotopy theory, and arithmetic geometry, by Andreas Holmstrom

Numerical Analysis

• Numerical Analysis Digest, a weekly newsletter

Operator Algebras

• Resources for students studying operator algebras by Jesse Peterson
• Operator Algebra Searchable Information Site, OASIS
• Operator Algebra Resources, by N. Christopher Phillips
• Resources for Learning about Graph Algebras, repository

Optimization and Control

Probability

• Almost sure blog on probability and stochastic analysis by George Lowther
• Institute of Mathematical Statistics, the theory and applications of statistics and probability
• Bernoulli Society Mathematical Statistics and Probability

Quantum Algebra

Quantum Computing

• Awesome Quantum Computing, learning and developing resources
• Mini-Library on Quantum Information and Computation, by Xiaodi Wu
• Advice on learning quantum computing, by Aram Harrow

Representation Theory

• FDLIST, website on representation theory of finite dimensional algebras
• Seminars&conferences in Asia and online, by Ryo Kanda

Rings and Algebras

• Database of Ring Theory

Spectral Theory

• Spectral geometry in the clouds, Intergalactic seminar on spectral theory and geometric analysis
• UK Spectral Theory Network

Statistics Theory

• Variable Selection with Knockoffs, maintained by Matteo Sesia

Symplectic Geometry

• Symplectic geometry page on nLab

Theoretical Computer Science

• CS Theory Events, Aggregator for CS theory workshops and schools, by Shachar Lovett and Sasha Kulikov
• dblp computer science bibliography

Topology

• Mathematics Student Resource by Dan Margalit
• A List of Recommended Books in Topology by Allen Hatcher
• The Knot Atlas on wiki
• Knot software, by Lukas Lewark
• Bibliography of Vassiliev Invariants by Dror Bar-Natan and Serhei Duzhin
• Some conferences related to topology, mirror symmetry or symplectic geometry, By Hiro Lee Tanaka
• Topology Atlas founded by Dmitri Shakhmatov and Stephen Watson
• Resources for learning Heegaard Floer homology by Matthew Hedden
• Topology resources by Andy Baker
• Tilings Encyclopedia , nonperiodic substitution tilings, by D. Frettlöh, E. Harriss, F. Gähler