Calendar

Abstract:

TBA

Joint with Moritz Kerz. We show a structure theorem on those loci which enables us to deduce several consequences, one of which being Hard Lefschetz in rank one in positive characteristic.

The Gauss curvature flow was introduced to model the shape of worn stones. It is a parabolic Monge-Ampere type flow for convex hypersurfaces, involving regularity issues for fully nonlinear equations and free boundary problems, and involving several entropy. In this talk, we will discuss the free boundary problem concerning worn stone with flat sides, and the optimal regularity of non-concave fully nonlinear equations. When time permits, we also talk about the singularity analysis, especially about the relations to the affine geometry at the critical case, to fully nonlinear equations at the super-critical case, and to convex geometry and spectral analysis at the sub-critical case.

After reviewing the definition of intrinsic flat convergence, I will present open problems on the almost rigidity or stability of classic rigidity theorems for manifolds with scalar curvature bounds and survey partial results towards these conjectures.

The absolute cohomological purity for étale cohomology of Gabber–Thomasson implies that an étale cohomology class on a regular scheme extends uniquely over a closed subscheme of large codimension. I will discuss the corresponding phenomenon for flat cohomology. The talk is based on joint work with Peter Scholze.