EVENT DETAILS AND ABSTRACT

Title: Rank rigidity via ergodic 2-frame flow
Speaker: Dave Constantine
Speaker Info: Michigan
Brief Description:
Special Note:
Abstract:

The rank rigidity theorem of Ballmann and Burns-Spatzier states that a non-positively curved space with higher rank is locally symmetric. Analogous notions of higher rank in strict negative and positive curvature have been developed and similar theorems proven in those curvature settings. In this talk I'll present a recent result in this vein for negatively curved spaces, namely if a compact, negatively curved manifold has what's called higher hyperbolic rank then (subject to a curvature pinching condition in even dimension) it has constant curvature. This provides a new proof of Hammenstadt's hyperbolic rank rigidity theorem (subject to the pinching condition) and also adresses some previously untouched curvature settings. The proof uses a nice geometric description of the dynamics of the frame flow given by Brin.