Speaker: Benjamin Bakker (New York University)

Time: Nov 27 (2-4pm), 29 (10-12am), Dec (10-12am)

Classroom: Quan 09

Abstract: Since Yau's resolution of the Calabi conjecture, compact Ricci-flat manifolds have played a prominent role in mathematics. Bogomolov's decomposition theorem implies that they only come in three flavors: complex tori, strict Calabi-Yau manifolds, and holomorphic symplectic manifolds, which are the natural higher-dimensional analogs of K3 surfaces. The geometry of holomorphic symplectic manifolds inherits their richness, and in these lectures we develop some aspects of the algebraic theory. We will start with the basic properties of such varieties, and continue with topics including moduli spaces of sheaves on K3 surfaces, some recent advances in the birational geometry of holomorphic symplectic varieties, the Torelli theorem, and some applications.