Noncommutative Geometry Seminar

Date: March 2, 2023

Time: 10:45AM - 11:45AM

Location: ZOOM

Speaker: Florian Johne, Columbia

Title: Intermediate curvature and a generalization of Geroch's conjecture

Abstract: In this talk we explain a non-existence result for metrics of positive m-intermediate curvature (a notion of curvature reducing to positive Ricci curvature for m=1, and positive scalar curvature for m=n−1) on closed orientable manifolds with topology Nn=Mn−m×Tm for n≤7. Our proof uses a slicing constructed by minimization of weighted areas, the associated stability inequality, and estimates on the gradients of the weights and the second fundamental form of the slices. This is joint work with Simon Brendle and Sven Hirsch.