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 […]
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.