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K3 surfaces: dynamics and moduli spaces

Holomorphic Differentials in Mathematics and Physics November 18, 2019 - November 22, 2019

November 19, 2019 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Simion Filip (University of Chicago)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • K3 surfaces

  • Ricci-flat metrics

  • Holomorphic dynamics

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Abstract

A compact complex surface that has a nowhere vanishing holomorphic 2-form, and which is simply-connected, is called a K3 surface. The geometry and dynamics of K3s is rich: they admit Ricci-flat metrics and have homogeneous parameter spaces, analogous to Teichmuller and moduli spaces of Riemann surfaces. Additionally, K3s often admit interesting automorphisms about which many questions remain open. I will first provide the necessary background, following an analogy with Riemann surface equipped with a holomorphic 1-form. Then I will discuss some results regarding the interaction of automorphisms and Ricci-flat metrics on K3s. Joint work with Valentino Tosatti.

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