Event Type:

Department Colloquium

Date/Time:

Monday, May 2, 2022 - 16:00 to 16:50

Location:

Pharmacy Building 305 and Zoom

Guest Speaker:

Institution:

University of California, Berkeley

Abstract:

Riemannian geometry has several notions of positive curvature- such as scalar, Ricci, and sectional curvature- each generalizing the curvature of the standard sphere. Much work has gone in to finding examples of positively curved spaces and topological properties such a space must have. In this talk, I will discuss the following question: given two spaces of positive (scalar, Ricci, or sectional) curvature with the same underlying manifold, can we deform one to the other, maintaining positive curvature along the way? In other words, I will discuss the topological properties of "moduli spaces" of positively curved metrics, focusing on connectedness. I will discuss the history of these investigations in various dimensions, which use diverse techniques such as uniformization, Ricci flow, surgery, and index theory. Finally I will describe recent results about moduli spaces of nonnegative sectional curvature on exotic seven spheres.

Host: