Schwartz Spaces Associated with the Stack of Rank 2 Bundles on a Curve over a Local Field

Explore a 53-minute mathematics lecture examining Schwartz spaces associated with the stack of rank 2 bundles on a curve over a local field, presented by Alexander Polishchuk from the University of Oregon. Delve into collaborative research with Alexander Braverman and David Kazhdan that advances the Analytic Langlands program, investigating natural Schwartz space of half-densities in relation to rank 2 bundle stacks. Learn about the key findings demonstrating how Schwartz half-density on the stack of rank 2 bundles creates smooth half-density on very stable bundles' open subscheme, and examine proposed algebro-geometric conjectures suggesting boundedness of these half-densities near stable bundles, with particular attention to low genus cases.