Colloquium
12:30 p.m., Tuesday (January 9, 2007)
MATH 104
Dan Knopf
University of Texas at Austin
Local singularities of Ricci flow
In applications of Ricci flow, one evolves a Riemannian metric
g(t) on a manifold M to improve its geometry. This evolution often
forces changes in topology, changes that are triggered by singularity
formation. The most interesting are local singularities, in which the
metric remains regular on an open subset of the manifold. In these
cases, an adequate understanding of the geometry in a spacetime
neighborhood of the singularity enables one to perform
topologicalgeometric surgeries. I will introduce the subject and
describe aspects of a program with Sigurd Angenent in which we obtain
precise asymptotic expansions for local singularities. The talk will be
suitable for a general audience.
Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge).
