## JOINT MATHEMATICS COLLOQUIUM

 The Kahler-Ricci flow and stability

# Duong Hong Phong

Columbia University

### Harvard University

#### Tea at 4:00 p.m. in the Math Lounge

 Abstract:   The Kahler-Ricci flow is a parabolic flow of metrics, whose fixed points are Kahler-Einstein metrics. According to a well- known conjecture of Yau, the existence of such metrics, and hence the convergence of the flow, should be equivalent to the stability of the underlying manifold in the sense of geometric invariant theory. We discuss recent progresses in this direction, including conditions for the convergence of the flow in terms of orbits of almost-complex structure under the diffeomorphism group, and lower bounds for the $\bar\partial$-operator on vector fields.

 Web page:  Alexandru I. Suciu Comments to:  alexsuciu@neu.edu Posted: September 28, 2007 URL: http://www.math.neu.edu/bhmn/phong07.html