Topology of manifolds with almost non-negative curvature and maximal rank and their Gromov--Hausdorff limits

Abstract: There are many characterizations of the torus as a Riemannian manifold. For example, it is the only closed manifold of non-negative Ricci curvature and first Betti number equal to its dimension. In this talk we will discuss two problems:

- When such characterizations are replaced by slightly weaker hypotheses, will we still get a torus or something related?

- If a space X can be approximated by something we know is a torus, is X necessarily a torus?

We will discuss both classical and current results in different contexts. This includes joint work with Xingyu Zhu.

differential geometrygeometric topologymetric geometry

Audience: advanced learners

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, fill the following form: docs.google.com/forms/d/e/1FAIpQLSdKrJ-nivgjr7ZVJmIY0qkN-VbzTl5NHHNyg6nNsCqjhB-4WA/viewform?usp=sf_link.

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