A p-adic Gathering
--A Joint Workshop on p-adic Arithmetic
July 16th-July 17th, 2026 MCM, CAS & Peking University
Invited Speakers:
|
Lucrezia Bertoletti |
Universite Paris-Saclay |
|
Yang Chen |
Tsinghua University |
|
Pierre Colmez |
Universite Sorbonne |
|
Changjiang Du |
Universite Paris-Saclay |
|
Zhenghui Li |
Universite Sorbonne |
|
Lue Pan |
Columbia University |
|
Arnaud Vanhaecke |
Morningside Center of Mathematics, CAS |
|
Yitong Wang |
University of Toronto |
|
Deding Yang |
University of Chicago |
Organizers:
|
Yiwen Ding |
Peking University |
|
Yongquan Hu |
MCM, CAS |
Time & Venue:
July 16, 2026 (Thursday)
Morning sessions (Room 410, Morningside Center of Mathematics)
Afternoon sessions (Room 110, Morningside Center of Mathematics)
July 17, 2026 (Friday)
Ding Shisun Conference Room, Zhihua Building, Peking University
Schedule:
|
July 16 (Thur) |
July 17 (Fri) | ||
|
9:30-10:30 |
Deding Yang (MCM410) |
9:30-10:30 |
Pierre Colmez (PKU) |
|
10:00-10:30 |
Tea Break |
10:00-10:30 |
Tea Break |
|
11:00-12:00 |
Lucrezia Bertoletti (MCM410) |
11:00-12:00 |
Zhenghui Li(PKU) |
|
12:00-13:30 |
Lunch Break |
12:00-14:00 |
Lunch Break |
|
13:30-14:30 |
Lue Pan (MCM110) |
14:00-15:00 |
Arnaud Vanhaecke(PKU) |
|
14:30-15:00 |
Tea Break |
15:00-15:30 |
Tea Break |
|
15:00-16:00 |
Changjiang Du (MCM110) |
15:30-16:30 |
Yitong Wang(PKU) |
|
16:20-17:20 |
Yang Chen (MCM110) |
Titles and Abstracts:
Speaker: Dr. Deding Yang (The University of Chicago)
Title: On Galois Representations associated with mod p Hilbert eigenforms
Abstract: Given a modular eigenform of weight k, it is well known that there exists an associated l-adic Galois representation satisfying certain compatibility conditions away from l and the level. There are several natural questions to ask: What happens for the behavior at p=l? What about the converse? What about mod p cases? In the mod p world, the desired weight k of which \rho is modular is encoded in the weight part of Serre's conjecture (For the Hilbert case, this is the Buzzard-Diamond-Jarvis conjecture), also referred to as "algebraic modularity" by Diamond and Sasaki. They also defined "geometric modularity" for mod p Hilbert eigenforms, and conjectured that the two notions of "modularity" are equivalent when the weight k satisfies certain conditions. In this talk, we prove this conjecture for all quaternionic Shimura varieties. This is a joint work in progress with Siqi Yang.
Speaker: Lucrezia Bertoletti (Universite Paris-Saclay)
Title: Finite length for unramified GL2: beyond multiplicity one
Abstract: For K a finite unramified extension of Qp, a natural place to look for a conjectural mod p Langlands correspondence for GL2(K) are Hecke eigenspaces in the mod p cohomology of a tower of Shimura curves. These are hoped to be a direct sum of copies of purely local representation of GL2(K), i.e. depending only on the restriction at p of the Galois representation attached to the system of Hecke eigenvalues. The number of copies (called the multiplicity) should then be computed by counting modular Serre weights in the socle.
In the multiplicity one case, a recent work of Breuil, Herzig, Hu, Morra and Schraen establishes the finite length of the above Hecke eigenspaces, under mild genericity assumptions. In this talk we will discuss how to extend this finite length result when the multiplicity one assumption is removed.
Speaker: Prof. Lue Pan (Columbia University)
Title: Prescribed lifts of 2-dimensional representations
Abstract: Let p be a prime. I will discuss my recent work with Matt Emerton, Toby Gee, and Xinwen Zhu concerning lifts of irreducible, totally odd, 2-dimensional mod p representations of the absolute Galois group of a totally real field.
Speaker: Changjiang Du (Universite Paris-Saclay)
Title: Multivariable $(\varphi_q,\mathcal{O}_K^{\times})$-modules associated to $p$-adic Galois representations
Abstract: Let $K$ be an unramified extension of $\mathbb{Q}_p$ with absolute Galois group $G_K$, and $E$ a finite extension of $K$ with ring of integers $\mathcal{O}_E$. In this talk, we will explain how to associate an étale $(\varphi_q,\mathcal{O}_K^{\times})$-module over $A_{\mathrm{mv}}$ to every continuous $\mathcal{O}_E$-representation $\rho$ of $G_K$ of finite type, where $A_{\mathrm{mv}}$ is a certain multivariable coefficient ring. We will prove that this construction defines a fully faithful exact functor. The construction is based on the theory of Lubin-Tate $(\varphi,\Gamma)$-modules and relies on two different descent arguments. We expect this functor to be related to $p$-adic Banach representations of $\mathbf{GL}_2(K)$.
Speaker: Yang Chen (Tsinghua University)
Title: Homological branching laws for mod $p$ representations of $\mathrm{GL}_2(F)$
Abstract: In this talk, we investigate the homological branching law for mod $p$ representations of $\mathrm{GL}_2(F)$ restricted to the multiplicative group $L^\times$ of a quadratic extension $L/F$, as well as to the torus $T$, where $F$ is a finite extension of $\mathbb{Q}_p$.
We will present a complete solution to the homological branching problem for the case $F = \mathbb{Q}_p$. For a general field $F$, we resolve the problem for principal series and the special series. Time permitting, we will discuss the key techniques used, including the existence of adjoints for compact inductions in the derived category, translating the category of smooth representations into the category of pseudocompact modules via Pontryagin duality, and utilizing Mackey decompositions to reduce the problem to explicit calculations within the category of pseudocompact modules. Ultimately, this approach provides a unified theoretical framework for understanding branching laws in the mod $p$ context.
Speaker: Prof. Pierre Colmez (Universite Sorbonne)
Title: Hodge-podge of (\varphi,\Gamma)-modules
Abstract: We will present various results about (\varphi,\Gamma)-modules and their cohomology
Speaker: Zhenghui Li (Universite Sorbonne)
Title: Bernstein-Zelevinsky duality for equivaraint vector bundles on Drinfeld spaces
Abstract: We show that Serre duality for equivariant vector bundles on the Drinfeld space induces a locally analytic Bernstein-Zelevinsky duality on the compactly supported cohomology. It is a generalization of the result of Fargues and Mieda in l-adic case. This is a joint work with Benchao Su and Zhixiang Wu.
Speaker: Dr. Arnaud Vanhaecke (MCM, CAS)
Title: Bounded vectors and sheaves on the coverings of Drinfeld’s half plane
Abstract: A fundamental construction in the p-adic Langlands correspondence for GL2(Qp) is the universal unitary completion, which associates a Banach representation to a locally analytic representation. Unfortunately, this "functor" is often poorly behaved, especially beyond the case of GL2(Qp).
One of the first effective constructions of such a completion was given by Breuil and Mézard in their 2010 Astérisque paper. They constructed a Zariski sheaf on a formal model of the p-adic half-plane whose global sections are dual to the universal unitary completion of certain special series representations. This realizes the completion in terms of bounded vectors in the dual of the locally analytic representation. In this talk, I will explain how this idea can be used to derive the bounded vectors functor in specific settings where the representations arise from sheaves on coverings of Drinfeld's half-plane.
Speaker: Dr. Yitong Wang (University of Toronto)
Title: Multivariable (phi,gamma)-modules and local-global compatibility
Abstract: Let K be a finite unramified extension of Qp. Let pi be an admissible smooth mod p representation of GL2(K) occuring in some Hecke eigenspaces of the mod p cohomology of a Shimura curve, and r be its underlying global 2-dimensional Galois representation. When r is sufficiently generic, we prove that the associated multivariable (phi,gamma)-module D_A(pi) defined by Breuil-Herzig-Hu-Morra-Schraen is completely determined by the restriction of r to the decomposition group at p in an explicit way, generalizing their results.
