Scalar curvature on aspherical manifolds

Abstract: It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. I will first review some history of this question, and present some recent progress, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov). I will also discuss some related questions including the Urysohn width inequalities on manifolds with scalar curvature lower bounds. This talk is based on joint work with Otis Chodosh.

differential geometry

Audience: researchers in the topic

B.O.W.L Geometry Seminar