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 Wu Talk 1

• 15:00 - 15:30 Coffee break

• 15:30 - 16:30 Wiersig 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. Here, D-cap refers to the sheaf of infinite order differential operators, whose definition I explain in detail. Then, I discuss the category of coadmissible D-cap-modules, as an analog of the coherent D-modules in the classical algebraic theory. Finally, I speak about applications to the admissible locally analytic representation theory of p-adic Lie groups, in particular, the Beilinson-Bernstein localisation theorems of Ardakov-Wadsley and Ardakov.

• (Talk 2) Title: Reconstruction theorems for coadmissible D-cap modules
  Abstract: D-cap modules can be regarded as differential equations on rigid-analytic spaces. In this talk, I explain a framework for solving these differential equations. My main theorem is that this framework gives rise to a fully faithful embedding, from coadmissible D-cap as defined in the first talk, into a certain category of complexes over the overconvergent almost de Rham period ring. This result may be regarded as a Riemann-Hilbert correspondence for coadmissible D-cap modules.

• (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: The p-adic local Langlands correspondence investigates the relationship between p-adic representations of p-adic Lie groups and p-adic representations of Galois groups. Its locally analytic aspect studies locally analytic representations of p-adic Lie groups. In this talk, I will give an introduction to the application of locally analytic representations to the construction of p-adic families of automorphic forms, as well as to the study of the classicality of p-adic automorphic forms and the Fontaine-Mazur conjecture.

• (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)