|Date: Tuesday, October 12, 2010
Title: Enumerative geometry of K3 surfaces
Abstract: In this lecture, we discuss enumerative invariants for families of K3 surfaces (a special class of algebraic surface with trivial canonical bundle). The first example - Noether-Lefschetz invariants - arise from classical geometric questions about holomorphic line bundles on these surfaces and how they vary in families. Gromov-Witten theory, on the other hand, involves counting pseudoholomorphic curves on a symplectic manifold and is closely related to ideas from mirror symmetry and hypergeometric series. In this talk, I will try to introduce these circles of ideas and how they're related. If time permits, I'll discuss conjectural generalizations to other types of surfaces.
Speaker: Davesh Maulik
Institution: Clay Fellow