Click on "Toggle Abstract" to view or hide the abstract for each scheduled talk.
Date
| Speaker
| Topic
|
September 10 |
Jack Sempliner (UCLA) |
On a cohomological Jacquet-Langlands correspondence for Shimura varieties
(Toggle abstract)
Pretalk by Peihang Wu on Introduction to Shimura varieties and Igusa varieties
|
We will discuss a new result on the p-adic geometry of Igusa stacks, which allows one to relate the p-adic geometry of Shimura varieties for a pair of groups $G, G'$ which are global extended pure inner forms. Using this geometric input and the spectral action of Fargues-Scholze, we will discuss how this input may be used to prove the existence of Hecke-equivariant cohomological "Jacquet-Langlands" maps between the cohomology (even with integral or torsion coefficients) of the two Shimura varieties of abelian type associated to $G, G'$.
Pretalk at 10:00-11:30, by Peihang Wu on Introduction to Shimura varieties and Igusa varieties
Outline of the pretalk: We will briefly discuss Shimura varieties by examples, and explain what Igusa varieties are, again by examples.
|
September 17 |
No seminar today
Note: Workshop on p-adic Hodge theory and related topics at Peking University (Sept 17–18) |
September 24
(starts at 2:00 PM) |
Gabriel Dospinescu (Université de Clermont-Auvergne) |
On the boundary of the Drinfeld coverings for GL2(ℚp)
(Toggle Abstract)
Pretalk by Yiwen Ding on Towards a Geometric Realization of the p-adic Langlands Correspondence for GL2(ℚp)
|
I will explain how to recover the global sections of GL2(ℚp)-equivariant sheaves on ℙ1(ℚp) constructed by Colmez for a class of de Rham Galois representations, using the geometry of the boundary of the Drinfeld tower. This is joint work with Benjamin Fleuriault.
Pretalk at 10:00–11:30, by Yiwen Ding on Towards a Geometric Realization of the p-adic Langlands Correspondence for GL2(ℚp)
I will first introduce Colmez’s p-adic Langlands correspondence for GL2(ℚp). I will then discuss the work of Dospinescu and Le Bras on the Breuil–Strauch conjecture, explaining how this correspondence can be realized in the cohomology of coverings of the Drinfeld upper half-plane.
|
October 1 and 8 |
No speakers |
National Day Holiday - No seminars this week |
October 9
(Friday) |
何旭华 Xuhua He（香港大学）
刘一峰 Yifeng Liu（浙江大学） |
Zhongguancun Number Theory Colloquium (at Tsinghua)
何旭华: Cohen–Macaulayness of Local Models
(Toggle Abstract)
刘一峰: L-derivatives for general weights
(Toggle Abstract)
|
Local models describe the singularities of integral models of Shimura varieties. A longstanding question is whether these local models are Cohen–Macaulay. In this talk, I will present a solution for arbitrary parahoric level, valid in every residue characteristic.
The key is a combinatorial result about how the strata in the special fiber fit together, resolving a conjecture of Görtz from over twenty years ago. I will explain the main ideas and how this connection between combinatorics and geometry leads to the Cohen–Macaulay property. |
| In the past 40 years, the Gross–Zagier formula has been vastly generalized. However, (essentially) except the work of S. Zhang on elliptic modular forms of even weights under the Heegner condition, all restrict to minimal weights. In this talk, we will explain our recent discovery on the arithmetic meaning of central L-derivatives of cohomological automorphic forms of general weights over CM fields. |
October 15 |
陈睿 Rui Chen（Johns Hopkins University） |
Spherical Functions on Spherical Varieties for Unramified Groups
(Toggle Abstract)
Pretalk by Daniel Funck on The Satake Isomorphism
|
Let X = H\G be a homogeneous affine spherical variety for an unramified reductive group G over the integers o of a p-adic field k, and K = G(o) a hyperspherical maximal compact subgroup of G = G(k). We compute eigenfunctions ("spherical functions") on X = X(k) under the action of the unramified (or spherical) Hecke algebra of G, generalizing the work of Sakellaridis from split groups to unramified groups.
Pretalk at 10:00–11:30, by Daniel Funck (BICMR) on The Satake Isomorphism
The Satake Isomorphism theorem is a foundational theorem in the representation theory of p-adic groups. It gives an explicit description of the Spherical Hecke algebra, identifying it with the Weyl-fixed vectors of the group algebra of the group of (co)characters of T, and can be interpreted as a p-adic version of the Harish-Chandra isomorphism. It is of extreme import to the story of the Local Langlands correspondence, giving a really good explanation of why smooth G-representations relate to Langlands parameters valued in the Langlands dual group.
In this talk, we will explain what the Satake isomorphism is, and present a proof. We will demonstrate an interpretation of the Satake isomorphism as a kind of “unramified Local Langlands correspondence”, and briefly explore a generalisation known as the “geometric Satake correspondence” in preparation for Rui Chen’s talk.
|
October 22 |
No seminar today |
October 23
(Friday)
14:00–17:00
智华楼 文远堂 |
谢俊逸 Junyi Xie（北京大学）
刘一峰 Yifeng Liu（浙江大学）
周胜铉 Shengxuan Zhou（University of Bonn）
袁新意 Xinyi Yuan（北京大学）
|
算术几何：数论与几何的汇聚
Arithmetic Geometry: where number theory meets geometry
2:10–2:40 PM – 谢俊逸 Junyi Xie
2:40–3:10 PM – 刘一峰 Yifeng Liu
3:15–3:45 PM – 周胜铉 Shengxuan Zhou
3:45–4:15 PM – 袁新意 Xinyi Yuan
4:15–5:00 PM – Panel session
|
October 29 |
邹建迪 Jiandi Zou（哈工大） |
Ramanujan complexes from unitary groups over number fields
(Toggle Abstract)
|
| Ramanujan graphs, as a typical class of the so-called expander graphs, are important in graph theory, number theory as well as computer science. Expander complexes and Ramanujan complexes, as their higher dimensional analogues, have gradually attracted interest in the past decades. In this talk, we give a new construction of Ramanujan complexes from unitary groups over number fields, based on the endoscopic classification of (non-quasisplit) unitary groups. Under the "golden" condition, our construction is explicit, meaning that we have an algorithm that is practically executable on a modern (or future) computer. This is joint work with Rahul Dalal and Alberto Minguez. |
November 5 |
No seminar today
Note: 第四届数学前沿博士生学术交流会议
下午代数方向报告（时间地点 TBD） |
November 12 |
No seminar today |
November 13
(Friday) |
TBD |
Zhongguancun Number Theory Seminar (at Chinese Academy of Sciences)
|
November 19 |
TBD |
TBD
(Toggle Abstract)
|
| Abstract to be announced. |
November 26 |
TBD |
TBD
(Toggle Abstract)
|
| Abstract to be announced. |
December 3 |
No seminar today |
December 10 |
王九亚 Jiuya Wang（University of Georgia） |
TBD
(Toggle Abstract)
|
| Abstract to be announced. |
December 11
(Friday) |
尹洪波 Hongbo Yin（山东大学）
田野 Ye Tian（中科院） |
Zhongguancun Number Theory Colloquium (at Peking University)
|
December 17 |
张志宇 Zhiyu Zhang |
TBD
(Toggle Abstract)
|
| Abstract to be announced. |
December 24 |
杨梓诠 Ziquan Yang |
TBD
(Toggle Abstract)
|
| Abstract to be announced. |