Title: On the vanishing of Selmer groups for odd orthogonal Galois representations Abstract: Let $pi$ be a cuspidal automorphic representation of $Sp_2n$ over $mathbb{Q}$ which is holomorphic discrete series at infinity, and $chi$ a Dirichlet character. Then one can attach to $pi$ an orthogonal $p$-adic Galois representation $rho$ of dimension $2n+1$. Assume $rho$ is irreducible, […]
Title: Introduction to the relative Langlands program, with open problems, I.Abstract: This will be the first of a few talks introducing the "relative" Langlands program, with a view towards open problems, both concrete and speculative.
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.
Title: The Drinfeld and Quillen formal groupsAbstract: The Cartier–Witt stack, introduced recently by Drinfeld and Bhatt–Lurie, is a geometric object whose quasicoherent sheaves provide a natural target category for prismatic cohomology. Over this stack, Drinfeld has defined a certain formal group involved in the construction of prismatic Chern classes, and conjectured that this formal group […]
Title: Test ideals in mixed characteristic via the p-adic Riemann-Hilbert correspondence.Abstract: Multiplier ideals in characteristic zero and test ideals in positive characteristic are fundamental objects in the study of commutative algebra and birational geometry in equal characteristic. We introduce a mixed characteristic version of the multiplier / test ideal using the p-adic Riemann-Hilbert functor of Bhatt-Lurie. Under […]
Title: The (oo,2)-category of internal (oo,1)-categories Abstract: Results which concern the classification of parametrized structures over a given base by means of internal constructions within that base are fairly ubiquitous in logic, algebra and topology. These results are by and large formal consequences of reflection properties of an associated externalization functor. In this talk, we define the […]