Algebraic Geometry Seminar

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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.