Workshop on Automorphic forms,
Arithmetic, and Geometry
II. p-adic Representation Theory

The second Workshop on Automorphic forms, Arithmetic, and Geometry (WAAG-II) will be held at KIAS on April 23-24, 2026.

WAAG aims to present recent developments in number theory and related areas that are accessible to a broad audience and to promote exchange between researchers, especially those in early careers.

Speakers

• Finn Wiersig (National University Singapore)

• Zhixiang Wu (University of Science and Technology of China)

Schedule & Location

Thursday (April 24)
All talks will be held at Room 8101, KIAS

• 14:00 - 15:00 Wiersig Talk 1

• 15:00 - 15:30 Coffee break

• 15:30 - 16:30 Wu Talk 1

• 16:30 - 17:00 Coffee break

• 17:00 - 18:00 Wiersig Talk 2

• 18:00 - Dinner

Friday (April 25)
All talks will be held at Room 204, Soorim Cultural Foundation (location)

• 14:00 - 15:00 Wiersig Talk 3

• 15:00 - 15:30 Coffee break

• 15:30 - 16:30 Wu Talk 2

• 16:30 - 17:00 Coffee break

• 17:00 - 18:00 Wu Talk 3

• 18:00 - Dinner

Abstract

• Finn Wiersig
  (Talk 1) Title: Coadmissible D-cap modules on rigid-analytic spaces
  Abstract: I give an overview of Ardakov-Wadsley's theory of D-cap-modules on rigid analytic spaces and its applications to admissible locally analytic representations of p-adic Lie groups.
  (Talk 2) Title: Reconstruction theorems for coadmissible D-cap modules
  Abstract: I present a Riemann-Hilbert correspondence for coadmissible D-cap modules. Specifically, we interpret a coadmissible D-cap module as a p-adic differential equation, explain what it means to solve such an equation, and describe how to reconstruct the module from its solutions.
  (Talk 3) Title: Towards a Kashiwara-style constructibility theorem for p-adic D-modules
  Abstract: The constructions made in my second talk are quite abstract, and in this talk, I make them concrete. I compute explicit instances of the Riemann-Hilbert correspondence presented in my second talk. In these examples, we find that the solutions of many D-cap modules have constructible cohomology. This suggests that there is a p-adic version of Kashiwara's constructibility theorem in complex geometry, which states that the solution complexes of holonomic D-modules on complex manifolds have constructible cohomology. This is joint work in progress with Konstantin Ardakov.

• Zhixiang Wu
  (Talk 1) Title: Locally analytic representations and p-adic automorphic forms
  Abstract: I will give an introduction to the application of locally analytic representations of p-adic Lie groups to the study of p-adic automorphic forms and the locally analytic aspect of the p-adic Langlands correspondence.
  (Talk 2 & 3) Title: On supercuspidal locally analytic representations of GL2(Qp)
  Abstract: The Drinfeld upper half plane is a certain p-adic symmetric space. The cohomology of equivariant vector bundles on this one-dimensional rigid analytic space gives rise to locally analytic representations of GL2(Qp). These representations are closely related to two-dimensional p-adic de Rham Galois representations, by the Breuil–Strauch conjecture, proved by Dospinescu and Le Bras. In this talk, I will discuss ongoing work on computing higher extension groups of these locally analytic representations, with a final goal toward a geometrization of their derived category. This is joint work in progress with Benchao Su and Zhenghui Li.

Organizers

• Young-Hoon Kiem (KIAS HCMC)

• Heejong Lee (KIAS HCMC)
  email: heejonglee<at>kias.re.kr

With the support of

• Korea Institute for Advanced Study (KIAS)

• June E Huh Center for Mathematical Challenge (HCMC)