Hodge theory and derived categories of cubic fourfolds

Topology of Algebraic Varieties
Topic:Hodge theory and derived categories of cubic fourfolds
Speaker:Richard Thomas
Affiliation:Imperial College London
Date:Tuesday, September 16
Time/Room:2:00pm - 3:00pm/S-101
Video Link:http://video.ias.edu/tav/2014/0916-RichardThomas

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. I will explain all this via some pretty explicit examples, and then I will explain joint work with Addington showing that these 2 notions of having an associated K3 surface coincide generically.