9:00-10:00 Yu Min  (Hong Kong University of Science and Technology)

Title: Prismatic construction of potentially crystalline deformation ring up to p-power torsion

Abstract: Kisin proved that there exists a quotient of the unrestricted local deformation ring, which parametrizes potentially semistable representations with Hodge—Tate weights lying in a fixed interval. We will introduce how to use prismatic theory to give a moduli construction of this deformation ring up to p-power torsion. This is work in progress.

10:30-11:30 Ben Savoie (Peking University)

Title: Components of the Moduli Stack of Galois Representations

Abstract: In this talk, I will introduce the Emerton-Gee stack for GL_2(K), which serves as a moduli space for 2-dimensional p-adic representations of the absolute Galois group of K, where K is a finite, unramified extension of Qp. Understanding the geometry of this moduli space is pivotal to advancing the categorical p-adic Langlands conjecture formulated by Emerton, Gee, and Hellmann.

I will present recent joint work with Kalyani Kansal, where we determine which of the irreducible components of the Emerton-Gee stack are smooth. Among the non-smooth components, we also identify those which are normal or Cohen-Macaulay. This allows us to show that the normalization of each component has fairly mild (resolution-rational) singularities.

The talk will begin with a review of Galois representations and modular forms, followed by an outline of the key ideas behind the construction of the Emerton-Gee stack. I will conclude the talk by describing how our results update expectations about the categorical p-adic Langlands conjecture.

11:30-13:00 Lunch&Discussion

13:00-14:00 Vytautas Paškūnas (University of Duisburg-Essen)

Title: Infinitesimal characters and Lafforgue's pseudocharacters

Abstract: We associate infinitesimal characters to p-adic families of Lafforgue's pseudocharacters of the absolute Galois group of a p-adic local field by extending a construction of Dospinescu, Schraen and the first author. We use this construction to study the action of the centre of the universal enveloping algebra on the locally analytic vectors in the Hecke eigenspaces of the completed cohomology. (Joint work with Julian Quast.)

14:30-15:30 Arnaud Vanhaecke (Morningside Centre)

Title : Factorization of the cohomology of étale local systems on the p-adic half plane

Abstract : Combining our previous work and following the argument of Colmez, Dospinescu and Niziol’s paper on the factorization in the trivial coefficient case, we compute the first cohomology group of certain étale local systems on the p-adic plane in a factorized form using Kisin rings and the p-adic local Langlands correspondence in families. I will stress on certain differences concerning Kisin rings at the exceptional point.