Abstract

In this seminar I will explain some recent developments in the Langlands program that are of a "categorical'' nature, to the effect that (at least conjecturally), various categories of representations of p-adic Lie groups can be realized inside categories of coherent sheaves on parameter spaces of Galois representations.  In slightly different terms, this amounts to realizing modules over certain non-commutative rings as coherent sheaves on interesting geometric spaces.   The focus of the talk will be on outlining the overall ideas, and then illustrating them through some interesting but accessible examples.