Analysis and Mathematical Physics

Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properties determined by spectral properties of Dirac operators. For instance, a fundamental result of Llarull states that there is no smooth Riemannian metric on...

I will discuss how to use mean curvature flow to give nearly optimal lower bounds on the density of topologically non-trivial minimal hypercones in low dimensions. This compliments work of Ilmanen-White who gave analogous bounds for topologically...

There is a celebrated connection between minimal (or constant mean curvature) hypersurfaces and Ricci curvature in Riemannian Geometry, often boiling down to the presence of a Ricci term in the second variation formula for the area. The first goal...