Stanford University

Research Areas

  • Faculty in algebraic geometry study a diverse set of topics including the cohomology and geometry of the moduli space of curves, the foundations of Gromov-Witten theory, the geometry of algebraic cycles, and problems of enumerative geometry

  • Analysis and PDE are a major strength of Stanford’s Department of Mathematics, with strong connections to geometry and applied mathematics (since PDE describe fundamental aspects...

  • Applied mathematics at the Stanford Department of Mathematics focuses, very broadly, on the areas of scientific computing, stochastic modeling, and applied analysis. Some of the more specific...

  • Combinatorics concerns the study of discrete objects. It has applications to diverse areas of mathematics and science, and has played a particularly important role in...

  • Currently research in financial mathematics at Stanford is in two broad areas. One is on mathematical problems arising from the analysis of financial data; it involves...

  • Modern geometry takes many different guises, ranging from geometric topology and symplectic geometry to geometric analysis (which has a significant overlap with PDE and geometric measure...

  • Contemporary number theory is developing rapidly through its interactions with many other areas of mathematics. Insights from ergodic theory have led to dramatic progress in...

  • The probability group at Stanford is engaged in numerous research activities, including problems from statistical mechanics, analysis of Markov chains, mathematical finance, problems at the...

  • Representation theory is fundamental in the study of objects with symmetry. It arises in contexts as diverse as card shuffling and quantum mechanics. An early...

  • Symplectic topology is at the crossroads of several mathematical disciplines such as low-dimensional topology, algebraic geometry, representation theory, Hamiltonian dynamics, integrable systems, mirror symmetry, and string theory. It...

  • Topology studies properties of spaces that are invariant under deformations. A special role is played by manifolds, whose properties closely resemble those of the physical universe. Stanford...