数论与表示论讨论班：Elias Caei...

2025-11-26

 地点: 数学高等研究院报告厅时间: 11月26日，15:00 - 16:00主讲人: Elias Caeiro (巴黎高等师范学院)摘要: The classical class number one problem, conjectured by Gauss and solved by Heegner, Baker and Stark, states that there are only nine imaginary quadratic fields of class number one. In this talk, I will explain how Heegner points and the Gross–Zagier formula may be used to approach geometrically the class number h problem for a fixed h. Assuming Darmon’s conjectural real multiplication theory, this method can be adapted to determine all real quadratic fields of Richaud–Degert type which have class number one, giving a conditional improvement on the work of Biró and Lapkova. This is joint work with Henri Darmon and Jingxuan Geng.

数论与表示论讨论班：Si Ying Le...

2025-11-24

 地点: 数学高等研究院报告厅时间: 11月19日，16:00 - 17:00主讲人: Si Ying Lee (新加坡国立大学)摘要: I will talk about defining the notion of p-isogenies using the theory of F-gauges, and how this allows us to construct integral models of Hecke correspondences. I will also discuss some expected consequences of this, such as constructions of Rapoport–Zink spaces, and a general framework on understanding integral Hecke actions on Shimura varieties. This is joint work in progress with Keerthi Madapusi.

几何与拓扑讨论班：饶胜 A rough...

2025-11-24

 地点：海纳苑2幢204室时间：11月24日，16:00 - 17:20报告人：饶胜 Sheng Rao（武汉大学）摘要:  Pretalk: A rough introduction to deformation theoryAbstract: I will introduce several important notions and theorems in the topics within my research in a rough way.Research talk: Several Rigidity Theorems under Smooth DeformationsAbstract: We report on several rigidity theorems concerning smooth deformations of compact complex manifolds. Two main theorems therein can be described as follows. Let Δ be the unit disk in the complex plane, and consider a smooth family of compact complex manifolds over Δ. We show that the subset of Δ over which the fibers are isomorphic to a fixed hyperbolic manifold is either a discrete subset or all of Δ. Furthermore, for a smooth Kähler family over Δ, we prove a similar rigidity result: the set of points where the fibers are isomorphic to a fixed projective manifold with semiample canonical line bundle is also either a discrete subset or the whole Δ. This talk is based on three preprints jointly authored with Jian Chen, Mu-Lin Li, I-Hsun Tsai, Kai Wang, and Mengjiao Wang.

几何与拓扑讨论班：马烺特 Genera...

2025-11-10

 地点：海纳苑2幢204室时间：11月10日，16:00 - 17:20报告人：马烺特 Langte Ma（上海交通大学）摘要:  Pretalk: Generalized Anti-Self-Dual InstantonsAbstract: ASD instantons are used by Donaldson and others in the 1980s to discover exotic smooth structures on 4-manifolds. In the late 1990s, Donaldson-Thomas proposed to study instantons over Riemannian manifolds with special homolony. I will introduce the notion of such instantons and explain their minimizing property for the Yang-Mills functional, which include HYM connections on Kahler manifolds as examples.Research talk: Instantons on Product ManifoldsWe study the generalized ASD instantons over product manifolds motivated by the fact that many examples of manifolds with special honolomy are built with blocks of product structures. In this talk, I will discuss a generalization of the notion of instanton charge on principal SU(r)-bundle over 4-manifolds to manifolds with special holonomy, and explain how the moduli spaces of instantons over product manifolds are related to this generalized charge, which leads to interaction with instantons on the product factors. This is joint work with Dylan Galt.

数论与表示论讨论班：陈昰宇 On t...

2025-11-05

 地点: 数学高等研究院报告厅时间: 11月5日，16:00 - 17:00主讲人: 陈昰宇 Shih-Yu Chen (台湾清华大学)摘要: The behavior of periods of motives under twisting by Artin motives was studied in depth by Blasius. Building on Deligne's conjecture concerning the critical values of motivic L-functions, Blasius proposed a refined conjecture on the algebraicity of the critical values of twisted motivic L-functions, as well as its automorphic analogue in the setting of standard L-functions of algebraic cuspidal automorphic representations twisted by Artin representations. In this talk, we present results establishing new cases of the automorphic analogue under suitable regularity assumptions.

几何与拓扑讨论班：Habib Alizad...

2025-11-03

 地点：海纳苑2幢204室时间：11月3日，16:00 - 17:20报告人：Habib Alizadeh（中国科学技术大学几何与物理研究中心）摘要:  Pretalk: Barcodes in geometryBarcode is a notion introduced first in Topological Data Analysis (TDA) and it captures the topology (holes) of a data set. In a different form this notion appeared long before TDA in the works of Morse where he uses functions on spaces to study their topology. Inspired by TDA and Morse, barcodes were re-introduced in geometry and are vastly studied with many significant applications, e.g., they can be used to detect periodic points of certain maps on manifolds; this is in the same spirit as the Morse inequality that states the number of critical points of a smooth non-degenerate function on a manifold is at least the sum of the Betti numbers of the manifold. In this talk we will define barcodes, using simple linear algebra that should be accessible by undergraduate students, and if time permits we will mention some applications of barcodes in geometry. Research talk: Spectral diameter of a symplectic ellipsoidConsider a diffeomorphism of an even-dimensional Euclidean space, that is compactly supported in a given convex open subset X, and preserves the standard symplectic form; in dimension two in particular it preserves the area. Using barcodes we define an invariant of such a diffeomorphism that we call the spectral norm of the diffeomorphism. The space of such diffeomorphisms of X equipped with the spectral norm has a finite diameter which is called the spectral diameter of X. This number defines a symplectic capacity for X, an object defined axiomatically in symplectic geometry to capture the “symplectic size” of a domain; the first symplectic capacities were defined by Gromov using pseudo-holomorphic curves. In this talk, we compute the spectral diameter for all symplectic ellipsoids and polydisks, and in dimension four, for all convex toric domains. Exact computations of symplectic capacities are useful in obstructing symplectic embeddings.

数论与表示论讨论班：大井雅雄 T...

2025-10-30

 地点：数学高等研究院报告厅时间：10月29日，17:00 - 18:00报告人：Masao Oi (台湾大学)摘要：In this talk, I would like to discuss a comparison of two kinds of representations of p-adic reductive groups arising from different origins. One is Yu's algebraic construction, further developed by Kim-Yu and Kaletha. The other is a geometric construction recently established by Chan-Ivanov, which generalizes the classical Deligne-Lusztig construction to the positive-depth setting. Our basic strategy is to compare the trace characters of those two representations. A central idea in our argument is to introduce an analogue of the classical Green function (in the context of Deligne-Lusztig theory) for both the algebraic and geometric representations, which enables us to get a character formula completely parallel to the classical Deligne-Lusztig character formula. This talk is based on my joint work with Charlotte Chan (University of Michigan).

几何与拓扑讨论班：韩京俊 Log c...

2025-10-27

 地点：海纳苑2幢204室时间：10月27日，16:00 - 17:20报告人：韩京俊 Jingjun Han（复旦大学）摘要:  Pretalk: Log canonical thresholds and minimal log discrepanciesI will introduce definition and basic properties of log canonical thresholds and minimal log discrepancies. Research talk: On boundedness in general type MMPOne of the main open problems in the Minimal Model Program (MMP) is the termination. Motivated by local volumes introduced by Chi Li, we introduce log canonical volume which is non-decreasing in any sequence of MMP for general type varieties. As a result, in such kind of MMP, we show that (1) the Cartier index of any Weil Q-Cartier is uniformly bounded; (2) every fiber of the extremal contractions or the flips is bounded (3) the set of minimal log discrepancies belongs to a finite set. This is a joint work with Lu Qi, and Ziquan Zhuang.

捐赠仪式 | 求是之光 智映未来

2025-10-18

捐赠仪式 | 以数学之名，赴一场秋日之约

2025-10-12

数与对称——2024未来科学大奖与浙江大学联合学术报告会举行

2024-10-09

数高院孙崧教授在Acta Mathematica上发表文章

2024-09-09

Collapsing geometry of hyperkähler 4-manifolds and applicationsActa Math., 232 (2024), 325–424 by Song Sun, Ruobing Zhang AbstractWe investigate the collapsing geometry of hyperkähler 4-mani...

祝贺！数高院孙斌勇教授获“2024未来科学大奖”

2024-08-16

数高院刘一峰教授接连取得重大学术突破

2024-03-29

数高院刘一峰教授在Inventiones mathematicae上发表文章

2024-02-23

A p-adic arithmetic inner product formulaInventiones mathematicae volume 236, pages 219–3751 (2024)  by  Daniel Disegni & Yifeng LiuAbstractFix a prime number p and l...

孙崧教授正式加入浙江大学数学高等研究院

2024-01-01

   2024年1月1日，研究院迎来第五位永久成员孙崧教授。孙崧，1987年2月出生，中国籍，安徽安庆人，教授。中国科技大学学士（2003年-2006年），美国威斯康星大学麦迪逊分校博士（2006年-2010年）。先后任职...

祝贺！浙江大学包刚教授当选中国科学院院士

2023-11-22