# Hyperdiscriminant polytopes, Chow Polytopes, and K-energy asymptotics

Friday, February 6, 2009 -

4:00pm to 6:00pm

Let (X,L) be a polarized algebraic manifold. I have recently proved that the Mabuchi energy of (X,L) is bounded from below along any degeneration if and only if the Hyperdiscriminant polytope contains the Chow polytope (with respect to the various Kodaira embeddings). This completes the analysis initiated by Ding and Tian in their 1992 Inventiones paper "Kahler Einstein metrics and the Generalized Futaki Invariant," and therefore gives the final form to Tian's concept of K-semistability.

Speaker:

Sean Paul

University of Wisconsin

Event Location:

Fine Hall 314