A Beautiful Journey —— IASM202...

2026-01-06

Seminar by Tony Feng: Higher T...

2025-12-31

 Venue: Lecture Hall of IASM, ZJUTime: 15:00-17:00, December 31Speaker: Tony Feng (UC Berkeley)Title: Higher Theta Functions Over Function Fields15:00 - 15:45  Pre-talk: I will introduce background on theta functions and shtukas which will be helpful for understanding the main talk. This should be accessible to senior undergraduates and graduate students. 16:00 - 17:00 Abstract：The theory of theta functions and arithmetic theta functions is used classically to access the special values and special derivatives of automorphic L-functions. In joint work with Zhiwei Yun and Wei Zhang, we have constructed a theory of higher theta functions over function fields, which we expect to give access to higher derivatives of automorphic L-functions in terms of arithmetic geometry. This has led us, also partly jointly with Adeel Khan, to unexpected and fruitful connections between theta functions, derived algebraic geometry and motivic homotopy theory.

Seminar by Trung Nghiem: An ef...

2025-12-29

 Venue: Room 204, Hai Na Yuan #2, Zijingang CampusTime: 10:30 - 11:50, December 29Speaker: Trung Nghiem (Université Claude Bernard Lyon 1)Pretalk: Introduction to toric Calabi--Yau conesAbstract: A toric variety is a normal algebraic variety that contains an algebraic torus as a dense set, whose action extends to the whole variety. Since their conception, the varieties have provided many insightful examples for important conjectures in algebraic geometry. This pretalk aims to introduce the concept of complex affine toric varieties with Gorenstein singularities; their classification in terms of rational polytopes; and their equivalent metric characterization as toric Calabi--Yau cones (i.e. Ricci-flat Kähler cone metrics with toric isometry).Research talk: An effective construction of asymptotically conical Calabi--Yau manifoldsAbstract: An asymptotically conical Calabi--Yau manifold is a Ricci-flat Kähler manifold whose shape, when zoomed out towards infinity, looks like a Calabi--Yau cone. A recent work of Conlon--Hein shows that an AC Calabi--Yau manifold is obtained either by algebraic deformations or crepant resolution in a reversible and exhaustive process. In terms of the metric on the cone, the behavior of the AC Calabi--Yau metric is said to be quasi-regular or irregular. Examples of the latter are notoriously rare in the literature: in fact the only such example before our work was built by Conlon--Hein using ad-hoc computations; but so far there has been no explicit way to obtain them, and an open question in their paper was whether there exist more metrics of the same kind. In my research talk, I'll present an effective strategy to construct irregular AC Calabi--Yau manifolds via Altmann's deformation theory of isolated toric Gorenstein singularities (i.e. toric Calabi--Yau cones by the previous talk). This is a joint work with Ronan Conlon (University of Texas, Dallas).

Seminar by Yuanyang Jiang: Loc...

2025-12-25

 Venue: Lecture Hall of IASM, ZJUTime: 16:00-17:00, December 25Speaker: 江元旸 Yuanyang Jiang (Université Paris-Saclay)Abstract: We generalize a result of Lue Pan on locally analytic completed cohomology of modular curves to the case of Hilbert modular varieties. As an application, we prove that for parallel weight Hecke classes appearing in the completed cohomology of Hilbert modular varieties, de Rhamness of the associated Galois representation will imply classicality. One central problem is to understand certain partial de Rham cohomology, which we will prove to be classical by developing a version of Jacquet–Langlands transfer of D-modules using theory of analytic de Rham stacks.

Seminar by Fangu Chen: A gener...

2025-12-17

 Venue: Lecture Hall of IASM, ZJUTime: 16:00-17:00, December 17Speaker: 陈梵谷  Fangu Chen (University of California, Berkeley)Abstract: In 1987, Elkies proved that every elliptic curve defined over Q has infinitely many supersingular primes. In this talk, I will present an extension of this result to certain abelian fourfolds in Mumford's families and more generally, to certain families of Kuga–Satake abelian varieties constructed from K3-type Hodge structures with real multiplication. I will review Elkies' proof and explain how his strategy of intersecting with CM cycles can be adapted to our setting. I will also discuss some of the techniques in our proof to study the local properties of the CM cycles.

Seminar by Jiawei An: Slopes o...

2025-12-10

 Venue: Lecture Hall of IASM, ZJUTime: 16:00-17:00, December 10Speaker: 安嘉伟 Jiawei An (Chinese Academy of Sciences)Abstract: In this talk, I will discuss a distribution conjecture (Bergdall–Pollack) concerning the slopes (i.e., the p-adic valuations) of L-invariants attached to p-new eigenforms, which is analogous to the Gouvêa distribution conjecture for the slopes of modular forms. I will also explain how the recent breakthrough – the local ghost theorem of Liu, Truong, Xiao, and Zhao – can be used to compute these slopes and to prove the conjecture under certain generic local conditions on the associated Galois representations.

Seminar by Peihang Wu: Canonic...

2025-12-03

 Venue: Lecture Hall of IASM, ZJU Time: 16:00 - 17:00, December 3Speaker: Peihang Wu 吴沛航 (Peking University)Abstract: In this talk, we discuss the extension of p-adic shtukas on (integral models of) toroidal compactifications of Shimura varieties. We will explain the theory from a more general context and explain how to construct such extensions for toroidal compactifications. We will also discuss its applications for proving that many strata of special fibers are well positioned and for studying the uniqueness and functoriality of compactifications. This is based on a joint work in preparation with Shengkai Mao.

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.