Abstract

I will discuss a conjecture relating the topology of a manifold’s universal cover with the existence of metrics of positive intermediate curvature.  This conjecture simultaneously generalizes Gromov and Schoen-Yau's K(pi,1) conjecture and Brendle-Hirsch-Johne's generalized Geroch conjecture.  We prove the conjecture in almost all cases for manifolds of dimension up to 6.  As an application, we show that a closed, aspherical 6-manifold does not admit a metric of positive 4-intermediate curvature.  This is joint work with Tongrui Wang and Xuan Yao.

Biography

Liam Mazurowski is a postdoctoral researcher at Lehigh University. Before that, he was a postdoctoral researcher at Cornell University mentored by Xin Zhou. He received his Ph.D. from the University of Chicago in 2021 under the supervision of Andre Neves. His research specialties are differential geometry and geometric analysis.

Zoom meeting

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