Wednesday, March 2, 2011 - 11:00 , Location: Skiles 006 , Eric Choi , Emory , Organizer:
The soul of a complete, noncompact, connected Riemannian manifold (M; g) of nonnegative sectional curvature is a compact, totally convex, totally geodesic submanifold such that M is dieomorphic to the normal bundle of the soul. Hence, understanding of the souls of M can reduce the study of M to the study of a compact set. Also, souls are metric invariants, so understanding how they behave under deformations of the metric is useful to analyzing the space of metrics on M. In particular, little is understood about the case when M = R2 . Convex surfaces of revolution in R3 are one class of two-dimensional Riemannian manifolds of nonnegative sectional curvature, and I will discuss some results regarding the sets of souls for some of such convex surfaces.
Wednesday, February 23, 2011 - 11:00 , Location: Skiles 006 , Becca Winarski , Georgia Tech , Organizer:
Wednesday, February 16, 2011 - 11:00 , Location: Skiles 006 , Meredith Casey , Georgia Tech , Organizer:
Wednesday, February 9, 2011 - 11:00 , Location: Skiles 006 , Bulent Tosun , Georgia Tech , Organizer:
This will be a continuation of last week's talk on exotic four manifolds. We will recall the rational blow down operation and give a quick exotic example.