Filip Simion

Among complex 2-dimensional manifolds, K3 surfaces have some of the richest geometry. I will discuss two questions about families of K3 surfaces with origin in the theory of flat (or translation) surfaces. The first is concerned with a family of K3s over a hyperbolic Riemann surface. I will explain an analogue of the Eskin-Kontsevich-Zorich formula for the sum of Lyapunov exponents. The second question concerns an analogue for K3s of counting flat cylinders on a translation surface. I will provide the necessary background from dynamics and from the theory of K3 surfaces.