## Oliver Club

Laurent Saloff-CosteCornell University
The geometries of $SU(2)$ and other compact Lie groups
Thursday, October 12, 2017 - 4:00pm
Malott 532

A typical example of a "spectral geometry result" states that the lowest non-zero positive eigenvalue of the Laplacian on a Riemannian manifold multiplied by the square of the diameter is bounded away from $0$ and infinity, uniformly for all manifolds of nonnegative Ricci curvature of a fixed dimension (S. Cheng, P. Li and S.-T. Yau).

I will explain a conjecture in this spirit which concerns all left-invariant geometries (Riemannian or sub-Riemannian) on any given compact Lie group. This conjecture is true for $SU(2)$.

Refreshments will be served at 3:30 PM.