Mathematics Department Colloquium: Geometry and dynamics of K3 surfaces

Colloquium | November 14 | 4:10-5 p.m. | 60 Evans Hall

 Simion Filip, Institute for Advanced Study and Clay Mathematics Institute

 Department of Mathematics

In the classification of compact complex surfaces, K3s are the intermediate case between the positively and negatively curved ones. Alternatively, one can think of K3s as holomorphically symplectic surfaces. Their geometry is rich: K3s admit Ricci-flat metrics and have homogeneous parameter spaces, analogous to Teichmuller and moduli spaces of Riemann surfaces. Additionally, K3s often admit dynamically interesting automorphisms about which many questions remain open. I will first provide the necessary background, including some concrete examples. Then I will discuss results regarding the interaction of automorphisms and Ricci-flat metrics on K3s. Joint work with Valentino Tosatti.