Program

3:00-3:50pm  APM 7421 

Ovidiu Munteanu (Univ. of Connecticut)  ``Poisson equation on complete manifolds''

Abstract: I will discuss sharp estimates for the Green's function on
complete manifolds and their applications to solving the Poisson
equation. I will mention new sharp results about existence of
solutions and their asymptotic behavior. Some new results
about gradient Ricci solitons will be presented as application.

4:00-4:50pm  APM 2402  

Jacob Bernstein (Johns Hopkins)  ``Surfaces of Low Entropy''

Abstract: Following Colding and Minicozzi, we consider the entropy of
(hyper)-surfaces in Euclidean space.  This is a numerical measure of
the geometric complexity of the surface.  In addition, this quantity
is intimately tied to to the singularity formation of the mean
curvature flow which is a natural geometric heat flow of
submanifolds.  In the talk, I will discuss several results that show
that closed surfaces for which the entropy is small are simple in
various senses.  This is all joint work with L. Wang.