Seminar by Elias Caeiro: (Star...

2025-11-26

 Venue: Lecture Hall of IASM, ZJUTime: 15:00 - 16:00, November 26Speaker: Elias Caeiro (École Normale Supérieure)Abstract: 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.

Seminar by Sheng Rao: A rough ...

2025-11-24

 Venue: Room 204, Hai Na Yuan #2, Zijingang CampusTime: 16:00-17:20, November 24Speaker: Sheng Rao 饶胜 (Wuhan University)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.

Seminar by Si Ying Lee: p-isog...

2025-11-19

 Venue: Lecture Hall of IASM, ZJUTime: 16:00 - 17:00, November 19Speaker: Si Ying Lee (National University of Singapore)Abstract: 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.

Seminar by Langte Ma: Generali...

2025-11-10

 Venue: Room 204, Hai Na Yuan #2, Zijingang CampusTime: 16:00-17:20, November 10Speaker: 马烺特 Langte Ma (Shanghai Jiao Tong University)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.

Seminar by Shih-Yu Chen: On th...

2025-11-05

 Venue: Lecture Hall of IASMTime: 16:00 - 17:00, November 5Speaker: Shih-Yu Chen 陈昰宇(National Tsing Hua University)Abstract: 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.

Seminar by Habib Alizadeh: Bar...

2025-11-03

 Venue: Room 204, Hai Na Yuan #2, Zijingang CampusTime: 16:00 - 17:20, November 3Speaker: Habib Alizadeh (USTC-IGP)Pretalk: Barcodes in geometryAbstract: Barcode 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 ellipsoidAbstract: Consider 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.

Seminar by Masao Oi: Types and...

2025-10-29

 Venue: Lecture Hall of IASM, ZJUTime: 17:00 - 18:00, October 29 Speaker: Masao Oi (National Taiwan University)Abstract: 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).

Seminar by Jingjun Han: Log ca...

2025-10-27

 Venue: Room 204, Hai Na Yuan #2, Zijingang CampusTime: 16:00 - 17:20, October 27Speaker: 韩京俊 Jingjun Han (Fudan University)Pretalk: log canonical thresholds and minimal log discrepanciesAbstract: I will introduce definition and basic properties of log canonical thresholds and minimal log discrepancies. Research talk: On boundedness in general type MMPAbstract: One 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.

IASM Receives "Light Cube" from Class of 1981 COSE Alumni

2025-10-18

On October 18th, a ceremony was held at the Institute for Advanced Study in Mathematics (IASM) to inaugurate the Light Cube, a smart pergola generously donated by the Class of 1981 alumni from th...

IASM Launches Named Lecture Series with Support from Alumni Donors

2025-10-12

On the afternoon of October 12, the Institute for Advanced Study in Mathematics (IASM) held a donation ceremony to launch its Named Lecture Series, celebrating the generous support of its alumni commu...

Professor Liu Yifeng has online published a research paper by Inventiones mathematicae

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...

Professor Sun Song Joined IASM as the Fifth Permanent Member

2024-01-01

Professor Sun Song joined IASM as the fifth permanent member in January, 2024. Professor Sun Song, Chinese, was born in February 1987 in Anqing, Anhui Province. He received his bachelor'...

Prof. Gang Bao of Zhejiang University Selected as an academician of the Chinese Academy of Sciences

2023-11-22

On November 22, the Chinese Academy of Sciences (CAS) released the list of 2023 new members, and Professor Bao Gang of Zhejiang University was elected as CAS member. Congratulations!Bao Gang, born in ...

Prof. Binyong Sun Selected as one of the first "New Cornerstone Investigators"

2023-01-13

 On January 13th, the New Cornerstone Investigator Program announced the list of the first grantees; 58 scientists from Mathematical and Physical Sciences and Biological and Medical Sciences beca...

Prof. Bao Gang and Prof. Sun Binyong to Speak at ICM 2022

2022-04-14

The International Congress of Mathematicians 2022, rescheduled as a fully virtual event, will take place over 6–14 July 2022. Virtual ICM 2022 has just announced the plenary speakers and schedule. We ...

The IASM Post Doctoral Fellow Dr. Shu Cheng has online published a research paper by Advances in Mathematics

2022-04-01

The character table of GLn(Fq)⋊<σ>Volume 403,  by Cheng ShuAbstractWe compute the character table of GLn(Fq)⋊<σ>, σ being an order 2 exterior automorphism....

Professor Liu Yifeng has online published a research paper by Inventiones mathematicae

2022-01-21

On the Beilinson–Bloch–Kato conjecture for Rankin–Selberg motivesInventiones mathematicae volume 228, pages107–375 (2022)  by Yifeng Liu, Yichao Tian, Liang Xiao, Wei Zhang & Xinwen...