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Mathematics Colloquium

Tuesday, January 5, 2021
12:00pm to 1:00pm
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Online Event
The geometry and topology of scalar curvature
Chao Li, Department of Mathematics, Princeton University,

Scalar curvature is a simple curvature invariant of a Riemannian manifold. Understanding its effects on the geometry and topology of a manifold has been a challenge for geometers. I will present some recent progress in this direction, including polyhedron comparison theorems of scalar curvature lower bounds, as well as non-existence of positive scalar curvature metrics on aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov). The solutions to these problems are based on constructing minimal surfaces and surfaces of prescribed mean curvature by calculus of variations. I will discuss a regularity question that naturally arises in the strategy.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].