# Algebraic Geometry Seminar

#### Asymptotic Properties of Families of K3 Surfaces

**Speaker:**
Simion Filip, University of Chicago

**Location:**
Warren Weaver Hall 201

**Date:**
Tuesday, March 31, 2015, 3:30 p.m.

**Synopsis:**

I will address two questions about families of K3 surfaces that have their origin in the theory of flat surfaces (i.e. Riemann surfaces with a holomorphic 1-form). The first one is about families over a hyperbolic base and associated dynamical invariants, called Lyapunov exponents. I will describe a formula analogous to the Eskin-Kontsevich-Zorich formula, but in the context of K3 surfaces. The second question is about twistor families of K3 surfaces, and a count of special Lagrangian (equivalently, elliptic) fibrations. This question involves dynamics and point counts on various homogeneous spaces. I will provide the necessary background from dynamics and from the theory of K3 surfaces.