Oliver Club

Daniel RubinCornell University
When does a Kähler manifold admit a metric of constant scalar curvature?

Thursday, September 7, 2017 - 4:00pm
Malott 532

I will describe the problem of existence of canonical metrics in Kähler geometry. From the PDE point of view, it amounts to solving certain complex Monge-Ampère equations. Picking out a canonical metric in a Kähler class amounts to understanding the moduli space of such classes, and there is an obstruction to the existence of a smooth solution in terms of an algebraic stability condition (as described in Dan Halpern-Leister's Oliver Club talk from last week). I will show how to tell whether a manifold is K-stable and identify destabilizing degenerations by taking a variational approach and computing the asymptotics of certain singular rational integrals.

Refreshments will be served at 3:30 PM.