skip to main content
Caltech

Geometry and Topology Seminar

Friday, January 12, 2024
4:00pm to 5:00pm
Add to Cal
Linde Hall 187
On a generalization of Geroch's conjecture
Sven Hirsch, Mathematics, Institute for Advanced Study,

The theorem of Bonnet-Myers implies that manifolds with topology $M^{n-1}\times S^1$ do not admit a metric of positive Ricci curvature, while the resolution of Geroch's conjecture shows that the torus $T^n$ does not admit a metric of positive scalar curvature. In this talk, I will introduce a new notion of curvature which interpolates between Ricci and scalar curvature (so-called $m$-intermediate curvature) and use stable weighted slicings to show that for $n\le7$ the manifolds $M^{n-m}\times T^m$ do not admit a metric of positive $m$-intermediate curvature. This is joint work with Simon Brendle and Florian Johne.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://sites.google.com/site/caltechgtseminar/home.