EVENT DETAILS AND ABSTRACT

Title: Noether-Lefschetz theory and Gromov-Witten theory
Speaker: Davesh Maulik
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

In this lecture, we discuss two theories concerning families of K3 surfaces (a special class of algebraic surface with trivial canonical bundle). Noether-Lefschetz theory arises 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. I will introduce these circles of ideas and explain the quantitative relationship between them along with applications to each side. As time permits, I will discuss some recent attempts to study these questions for other surfaces.