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Mathematics Colloquium

Eknath Ghate

Title: Mod p representations
Date: Friday, January 29, 2021
Place and Time: Zoom, 3:05-3:55 pm

Abstract. We survey several results about mod p representations of the general linear group with entries in a) the finite field with p elements and b) the field of p-adic numbers. We then discuss the link to representations of the Galois group of the field of p-adic numbers via Langlands correspondences. As an application, we discuss our study of the reductions of such local Galois representations. We also briefly touch upon some new phenomena that arise when one replaces the above mentioned fields by finite extensions. This talk is based on joint work with several coauthors, but focusses on recent work with Ravitheja Vangala, Vivek Rai and Mihir Sheth.