Events for 11/06/2024 from all calendars

Departmental Colloquia

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Robert Cass, University of Michigan

Title: Geometrization in the Langlands program

Abstract: The Langlands program has been a guiding force in number theory since its inception over 50 years ago. At its core the Langlands program seeks to parametrize the Galois extensions of a number field, often revealing surprising connections between representation theory, geometry, and arithmetic. Many variants of the Langlands program have emerged, for example by replacing number fields with algebraic curves, or by enlarging the classes of representations under consideration. Geometric methods have been spectacularly successful in the Langlands program, such as in the works of V. Lafforgue and Fargues-Scholze. I will describe my ongoing projects aimed at introducing geometric methods into other variants of the Langlands program. This includes versions of the geometric Satake equivalence for integral motives and for mod p sheaves, which can be viewed as unramified geometric Langlands correspondences on which to base future directions. Along the way I will describe new results about the F-singularities of affine Schubert varieties, generalizing classical results of Mehta-Ramanathan on Frobenius splittings.