Harvard–MIT Algebraic Geometry Seminar: Mirror symmetry, stability conditions, and geometric invariant theory

SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY

Speaker:

Tristan Collins - MIT

Bridgeland stability conditions were originally motivated by the concept of Pi stability in theoretical physics, as introduced in work of M. Douglas. Pi stability is an attempt to describe BPS states in string theory compactifications. Alternatively, BPS states in string theory can often be described by solutions of certain nonlinear partial differential equations. In this talk I will explain how, starting from nonlinear PDEs, ideas in GIT lead to a version of algebraic stability which is similar to Bridgeland stability. In particular, I will explain how in several examples in dimension 2, GIT stability for line bundles implies Bridgeland stability, but not conversely. In particular, this yields effective tests for Bridgeland stability in many examples.