ZUMA-NR

The seminar will meet at 4:00–5:00 pm, Wednesday (almost) every week during semesters, in the lecture room of IASM (East 7 Bldg, Zijingang Campus), unless otherwise noted. The seminar is organized by the NT&RT Group at Zhejiang University.

Here are the past talks.

Click on a title to reveal its abstract.

Schedule (2025–26 Spring)

Mar 4

Speaker: Yinchong Song 宋寅翀 (Peking University 北京大学)
Title: Height theory, Arakelov geometry and Beilinson–Bloch heights
In this talk we first give an introduction to height theories and Arakelov geometry, including heights on elliptic curves, various ways to define a height function, and some important theorems and applications of Arakelov geometry. After that we focus on Yuan–Zhang's adelic line bundles and Beilinson–Bloch heights. In the end we will discuss my recent work about Beilinson–Bloch heights.

Mar 11

Speaker: Ziqi Guo 郭子棋 (Peking University 北京大学)
Title: Modular heights of unitary Shimura varieties
The goal of our work is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also delve into a thorough investigation of the arithmetic generating series of divisors on unitary Shimura varieties. Therefore, we will also obtain the so-called "arithmetic Siegel–Weil formula" in our setting.

Mar 18 (3:30–4:30pm!)

Speaker: Jiajun Ma 马家骏 (Xiamen University 厦门大学)
Title: Local theta correspondence and endo-parameters
The theory of semisimple characters and endo-parameters provides a powerful framework for studying smooth representations of p-adic classical groups. Initiated by Bushnell, Kutzko, and Henniart for general linear groups, this theory was later extended to classical groups through the work of Kurinczuk, Skodlerack, and Stevens. Endo-parameters can be viewed as restrictions of Langlands parameters to the wild inertial group, and they provide a decomposition of the category of smooth representations into subcategories that are coarser than the classical Bernstein decomposition. In this talk, I will present the results on a theta correspondence for semisimple characters and show that endo-parameters are compatible with theta correspondence. Furthermore, I will present a reduction-to-depth-zero theorem for theta correspondence. This is joint work with Loke, Stevens, and Trias.

Mar 25

Speaker: Yuta Takaya 髙谷悠太 (University of Tyoko 東京大学)
Title: Categorification of local relative Langlands duality
The relation between period integrals and L-functions, studied since the work of Hecke and Tate, has recently been reformulated by Ben-Zvi–Sakellaridis–Venkatesh as relative Langlands duality. In this talk, I will present a version of this duality, the normalized period conjecture, in the framework of the categorical local Langlands correspondence à la Fargues-Scholze. I will describe computations for the Iwasawa–Tate and Hecke periods that support this conjecture, and discuss how it leads to a relation between distinguished representations and distinguished L-parameters. This talk is based on joint work with Milton Lin.

Apr 1

Speaker: Wenxuan Qi 齐文轩 (Peking University 北京大学)
Title: Kudla's modularity theorem and higher Chow group version of theta lifts
Kudla has made a conjecture that a certein generating series with coefficients in Chow group will be a Siegel modular form. A key ingredient in proving this modularity conjecture is Borcherds' work on singular theta lifts. In this talk, we first intruduce Borcherds' work, and use the language of our framework to give the proof of Borcherds to the modularity theorem. Then we give a generalization of Borcherds' work to a higher Chow group version: we hope to construct a similar generating series with values in higher Chow groups. This is an ongoing series of joint works with Haocheng Fan, Linli Shi, Peihang Wu, Liang Xiao and Yichao Zhang.

Apr 8

Speaker: Haocheng Fan 范浩程 (Peking University 北京大学)
Title: Coherent cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms
In this talk, we provide an upper bound of the coherent cohomological dimension of the Siegel modular variety. As a corollary, we show that the boundary of the compactified Siegel modular variety satisfies the Grothendieck–Lefschetz condition. This implies, in particular, that every formal Siegel modular forms of genus at least 2 and cogenus 1 is classical.

Apr 22

Speaker: Ian Gleason (National University of Singapore 新加坡国立大学)
Title: On the schematic and analytic constructions of the local Langlands category
We prove a folklore conjecture relating two geometrizations of the automorphic side of the local Langlands category (with torsion coefficients). The emphasis of this talk will be in explaining the overall strategy to construct the functor that compares the two categories.

Apr 29

Speaker: Klaus Künnemann (Universität Regensburg)
Title: A tropical formula for non-archimedean local heights
We report on joint work with José Burgos and Walter Gubler. Let X be a smooth projective variety over a non-archimedean field. Using tropicalization, one can introduce real-valued forms and currents on the non-archimedean analytification of X. We discuss how these can be used to compute non-archimedean local heights.

May 6

Speaker: David Hansen (National University of Singapore 新加坡国立大学)
Title: Cohomology of p-adic period domains for GL_n
Since the pioneering work of Drinfeld, p-adic period domains have been a driving force behind many developments in non-archimedean geometry. However, despite many advances, the basic question of computing their cohomology has remained completely open outside of a few very special cases treated by Drinfeld and Schneider–Stuhler over 30 years ago. In this talk I will present a general formula for the cohomology of these spaces for GL_n. This formula is elementary, and it has several unusual features which suggest some very rich phenomenology. I will explain this formula and where it comes from, present several examples, and take the first steps towards unraveling the patterns this formula is hiding. Joint with Dai Wenhan.

May 20

Speaker: Wei He 何伟 (Xi'an Jiaotong University 西安交通大学)
Title: Non-vanishing of L-values and arithmetic applications
In this talk, we discuss the question of non-vanishing of L-values for CM Hecke characters and several arithmetic applications, such as variation of arithmetic invariants and the Iwasawa main conjecture for CM fields. Some parts are joint work with Ashay Burungale, Ye Tian, and Xiangdong Ye.

May 27 (Two talks, starting at 15:30!)

Speaker: Mattia Cavicchi (Université Bourgogne Europe)
Title: (15:30–16:30) Bloch–Beilinson conjectures for Hecke characters and Eisenstein cohomology of Picard surfaces
When a motivic L-function L(M,s) vanishes at the central point of its functional equation, conjectures of Bloch and Beilinson predict the existence of a non-trivial extension of a suitable twist of the motive M by the unit motive. When M arises from certain Hecke characters of a quadratic imaginary imaginary field F, we will describe a construction of candidates for the Hodge realization of the predicted extensions, using the cohomology of Picard modular surfaces attached to F. This is joint work with Jitendra Bajpai.

Speaker: Johannes Anschütz (Université Paris–Saclay)
Title: (16:45–17:45) Analytic prismatization over Q_p
I will report on joint work with Arthur-César Le Bras, Juan Esteban Rodriguez Camargo and Peter Scholze. The aim of this project is the development of a theory of prismatization à la Drinfeld, Bhatt/Lurie for rigid analytic varieties over Q_p (and Q_p-coefficients), that we call analytic prismatization. Our main theorem describes perfect complexes on the analytic prismatization of a smooth rigid-analytic variety as perfect complexes on the pro-étale site.

Jun 3

Speaker: Elad Zehlinger (University of Michigan)
Title: Degenerate Whittaker functions, Hall–Littlewood polynomials, and matrix Kloosterman sums
Whittaker models are important objects in the representation theory of reductive groups. In the last decade, degenerate Whittaker models of Speh representations of general linear groups have been used for new constructions of integral representations of L-functions. In this talk I will explain my results regarding explicit computations of special values of special degenerate Whittaker functions attached to Speh representations of two different types: unramified Speh representations and Speh representations of depth-zero supercuspidal representations. In both cases the formula expresses a special value of a distinguished Whittaker function in terms of modified Hall–Littlewood polynomials evaluated at the representation data. Moreover, In the depth-zero/finite field case, the special values are given by non-abelian versions of exotic Kloosterman sums. The proofs of these results rely on an integral construction, due to Ginzburg and Kaplan, for the tensor product L-function for GL_n×GL_m, generalizing the construction of Godement–Jacquet for the standard L-function.

Jun 9 (Tuesday!)

Speaker: Grigory Andreychev (Chinese Academy of Sciences 中国科学院)
Title: Stacky approach to Galois representations
In ongoing joint work with Maximilian Hauck and Tasos Moulinos, we investigate the étale realization functor from prismatic F-gauges to Galois representations of Q_p with coefficients in Z_p; in the course of this study, we construct an analytic stack in the sense of Clausen–Scholze whose category of quasi-coherent sheaves, or to be more precisely, its category of perfect complexes, is equivalent to the bounded derived category of finitely generated Galois representations.

Jun 17

Speaker: Zhiyou Wu 吴峙佑 (Chinese Academy of Sciences 中国科学院)
Title: Operators on cohomology and topological Hochschild homology
Topological Hochschild homology is a generalization of the classical Hochschild homology in the algebraic setting to stable homotopy theory. In recent years, after pioneering work of Hesselholt and Bhatt–Morrow–Scholze, we learned that topological Hochschild homology is closely related to cohomology theories on algebraic varieties. I will talk about how to produce operators on cohomology theories in certain cases from this topological perspective.

Jun 24

Speaker: Weixiao Lu 卢维潇 (Aix Marseille Université)
Title: Twsited Jacquet–Zagier trace formula and Applications
The trace formula developed by Jacquet and Zagier can be related to the Arthur–Selberg trace formula on GL_n. In this talk, we discuss a twisted version of the Jacquet–Zagier trace formula, which admits a comparison with the stable trace formula on unitary groups. We also present an application to the study of diagonal cycles on unitary Shimura curves. Most of the work presented is joint with Ryan Chen and Wei Zhang.