Abstracts

Friday, September 22:

2:15 PM
Speaker: Detlef Gromoll
Title: Metric fibrations and nonnegative curvature
Abstract: We discuss some old and new questions on Riemannian submersions in nonnegatively curved spaces and a remarkable interplay.

3:45 PM
Speaker: Steve Halperin
Title: Exponential growth: some new results in topology and some old questions in geometry
Abstract: This talk will describe a new theorem that provides strong estimates for the growth of homotopy groups of a finite CW complex, and ask if this might contribute to the solution of some old questions about the implications of positive curvature.

Saturday, September 23:

9:00 AM
Speaker: Peter Petersen
Title: Perturbing from nonnegative to positive curvature
Abstract: I'll report on joint work with F. Wilhelm. Our current work has focused on trying to perturb metrics of nonnegative curvature on the Gromoll-Meyer sphere to metrics with positive curvature. The main
technical difficulty lies in dealing with totally geodesic tori. I'll report on a new approach for how this might be accomplished.

Sunday, September 24:

10:00 AM
Speaker: Chris Croke
Title: Some questions of sharp isoperimetric type and rigidity
Abstract: In this talk we will discuss some open questions and some recent results of sharp isoperimetric type. The rigidity and stability statements and their consequences are perhaps more interesting than the
inequalities themselves. One particular rigidity result is that the only compact Riemannian surfaces with boundary where almost every pair of geodesics intersect exactly once are the round hemispheres.