Title: Automorphic forms, motives and periods Abstract: I shall try to give an overview of parts of the Langlands program in a way that suggests future directions and applications. Among these are motivic periods, which I will discuss in general terms. Then, time permitting, I will discuss a conjectural construction of the automorphic and motivic […]
Title: THH(Z) and the image of JAbstract: I will try to overview some ideas from chromatic homotopy theory, including the "redshift" and "blueshift" phenomena therein, and then describe a result, obtained in joint work with Sanath Devalapurkar, that illustrates these phenomena, relating the two objects named in the talk's title.
Title: Solid locally analytic representations Abstract: I will discuss common work with Joaquin Rodrigues Jacinto about new foundations for representation theory of p-adic Lie groups using condensed mathematics. I will explain how different categories of representations fit in the new theory of analytic geometry of Clausen and Scholze, and also how some group cohomological comparisons […]
Title: Unipotent homotopy theory of schemes.Abstract: In this talk, I will present a notion of unipotent homotopy theory for schemes, which is based on Toen's work on affine stacks. I will discuss some general properties of the resulting unipotent homotopy group schemes and explain how over a field of characteristic p>0, they often recover the unipotent completion […]
Title: Analytic de Rham stack Abstract: In this talk I will present a new geometric construction in analytic geometry that encodes different theories of analytic D-modules, analogous to the classical algebraic de Rham stack of Simpson. I will explain some of their main features such as theories of six functors, the relation with more classical theories […]
Title: Introduction to the relative Langlands program, with open problems, II.Abstract: This will be the second of a few talks introducing the "relative" Langlands program, with a view towards open problems, both concrete and speculative.