Stanford University

Algebraic Geometry

Research in algebraic geometry uses diverse methods, with input from commutative algebra, PDE, algebraic topology, and complex and arithmetic geometry, among others. At Stanford, faculty in algebraic geometry and related fields use these methods to study 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, as well as many other topics. There is also a great deal of collaboration with geometric representation theory, low-dimensional topology, number theory, and algebraic topology.