Hodge Theory in Nonsmooth Settings I

Abstract: There has been a considerable amount of interest in the study of non-smooth geometries in the recent past. Taking motivation from the smooth settings with boundary, where even nice operators can behave badly but where techniques have been developed to understand these operators, it is likely possible to consider operators in these non-smooth settings. This series will focus on a particular operator - Hodge-Dirac type operators in the presence of measurable-coefficient Riemannian metrics on smooth manifolds. Hilbert space Hodge theory will be covered which can then be used to prove a Hodge-type theorem even when the underlying manifold is non-compact.

Venue: meet.google.com/wha-yopd-trc

Mathematics

Audience: researchers in the topic

Geometric Analysis and Related Fields