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 […]
Title: Rigid inner forms and the Bernstein decomposition for L-parametersAbstract: The purpose of this talk is to explain the construction of the Bernstein decomposition for enhanced L-parameters (first introduced by Aubert-Moussaoui-Solleveld using Arthur’s enhancements of L-parameters) in Kaletha’s framework of rigid inner forms. This is the first step in a general strategy to reduce local Langlands correspondences to the […]
Title: Introduction to the relative Langlands program, with open problems, III.Abstract: This will be the third (and probably last) of a few talks introducing the "relative" Langlands program, with a view towards open problems, both concrete and speculative.
Title: Exodromy beyond conicality Abstract: Let (X, P) be a stratified space. The most general version of the exodromy equivalence between constructible sheaves on (X, P) and functors out of the exit-path ∞-category of (X, P) currently available requires that the stratification of X be conical. Unfortunately, many stratifications naturally arising in geometry are not conical. […]
Title: How to invent pyknotic/condensed mathematics
Title: Quantum ergodicity on the Bruhat-Tits building for PGL(3, F) in the Benjamini-Schramm limit Abstract: Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic. More recently, several authors have investigated quantum ergodicity for sequences of spaces which "converge" to their common universal cover […]
Title: Introduction to the relative Langlands program, with open problems, IV.Abstract: This will be the fourth and last talk introducing the "relative" Langlands program, with a view towards open problems, both concrete and speculative.
Title: Ways to write a positive integer into sums of positive integers Abstract: Take a positive integer, say 4; we can write it as a sum of positive integers in the following five ways: 4, 3+1, 2+2, 2+1+1, 1+1+1+1. Among these five ways, how many have only odd numbers as summands? How many of them […]
Title: K-Theory of Adic SpacesAbstract: We will explain a new approach to the K-theory of analytic adic spaces via condensed mathematics. Its main advantage is that it allows us to define K-theory in that context as the (continuous) K-theory of a certain dualizable stable infty-category associated to an analytic adic space (as opposed to previous […]
Title: The Geometry of the Hitchin Fibration for Symmetric Spaces Abstract: Motivated by questions in relative Langlands and relative endoscopy, we study generalized Hitchin systems associated to symmetric spaces. We will use two new techniques in invariant theory, the regular quotient and the parabolic cameral cover, in an effort to describe the geometry of such […]