Geometry

Modern geometry takes many different guises, ranging from geometric topology and algebraic geometry and symplectic geometry to geometric analysis (which has a significant overlap with PDE and geometric measure theory) to dynamical problems. Stanford has long been one of the key centers in all these aspects of geometry.  Prominent areas of current research among faculty who work in geometry include algebraic geometry, Ricci and mean curvature flows and other curvature equations, minimal surfaces and geometric measure theory, mathematical relativity, spectral geometry, geometric scattering theory, and the geometry and dynamics of the Riemann & Teichmüller moduli spaces.