Previous Seminars

Time： December 27, Wednesday, 14:00-15:00

Venue： Room 203, No.2 Hainayuan

Title: L-functions for Automorphic Forms on Classical Groups

Speaker： Yubo Jin 金雨波(Durham University)

Abstract：The main problem concerned in this talk is the algebraicity of special L-values for automorphic forms on classical groups (Deligne's conjecture). After reviewing this problem, we will present an integral representation for L-functions by the doubling method. Using the integral representation and the Fourier expansion of Eisenstein series, we can prove the algebraicity result in the `holomorphic' case. We will also explain our future plan on studying this problem in full generality.

Time： December 27, Wednesday, 10:30-11:30

Venue： Lecture Hall

Title: On the archimedean arithmetic smooth matching

Speaker： Li Cai 蔡立(Capital Normal University)

Abstract：We will firstly talk about the relative trace formula approach to the Gross-Zagier formula, especially the archimedean arithmetic smooth matching. The archimedean arithmetic smooth matching is a semi-global comparison. Then we discuss the general problem reducing the semi-global comparison to the local one. The talk is based on two joint works:one with Ye Tian, Xinyi Yuan and Wei Zhang，and the another one with Ye Tian.

Time： December 13, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Integral points on the Clebsch-Klein surfaces

Speaker： Rafael von Känel (Tsinghua University)

Abstract：In this talk we present explicit bounds for the Weil height and the number of integral points on classical surfaces first studied by Clebsch (1871) and Klein (1873). Building on Hirzebruch's work in which he related these surfaces to a Hilbert modular surface, we deduced our bounds from a general result for integral points on coarse Hilbert moduli schemes. After explaining this deduction, we discuss the strategy of proof of the general result which combines the method of Faltings (Arakelov, Parsin, Szpiro) with modularity, Masser-Wuestholz isogeny estimates, and results based on effective analytic estimates and/or Arakelov theory. Joint work with Arno Kret.

Time： November 22, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Correspondences between affine Hecke algebras and application to the Howe correspondence

Speaker：Anne-Marie Aubert (CNRS)

Abstract: In the first part of the talk, I will introduce a notion of cuspidality for enhanced Langlands parameters of $p$-adic reductive groups, which conjecturally puts irreducible supercuspidal representations in bijection with such enhanced $L$-parameters.

Next we will use this notion to construct cuspidal support maps and Bernstein series for enhanced $L$-parameters, in analogy with Bernstein’s theory of representations of $p$-adic groups.
One can associate to every Bernstein series of either irreducible representations of a $p$-adic group or enhanced Langlands parameters, an affine Hecke algebra (possibly extended by the twisted group algebra of a finite group) such that its simple modules are naturally in bijection with the members of the Bernstein series.
In the second part of the talk, I will explain how these results can be applied to the study of the Howe correspondence.

Time： November 15, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Theta correspondence and simple factors of global Arthur parameters

Speaker：Chennyan Wu 吴晨彦（The University of Melbourne）

Abstract: Let $\pi$ be a cuspidal automorphic representation of a classical group or a metaplectic group. We show an exact relation between two invariants associated to $\pi$, one called the lowest occurrence index of $\pi$ which is an invariant arising from theta lifts and the other the location of the maximal positive pole of an Eisenstein series attached to $\pi$. As an application, we use this relation to show that certain global Arthur packets cannot contain cuspidal automorphic representations.

Time： October 25, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: A new +/- Iwasawa theory and converse of Gross-Zagier and Kolyvagin theorem

Speaker：Xin Wan 万昕（MCM）

Abstract: We develop a new kind of +/- local Iwasawa theory for characters over quadratic imaginary fields, which is valid in all cases when p is split, inert or ramified. As an application we prove the corresponding converse of the Gross-Zagier and Kolyvagin theorem.

Time：October 18, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Affine Deligne-Lusztig variety of Coxeter type element

Speaker：Yingkun Li 李英琨（Technical University of Darmstadt）

Abstract: By the classical theory of complex multiplication, the modular j-function takes algebraic values at CM points. It is an interesting question to ask about the algebraic nature of other types of automorphic functions at CM points. For the automorphic Green function at integral parameters, Gross and Zagier conjectured in the 1980s that their values at a CM point is essentially the logarithm of an algebraic number. In this talk, we will discuss recent progress toward this conjecture. This is partly joint with Jan Bruinier and Tonghai Yang.

Time：September 20, Wednesday, 16:10-17:10

Venue： Lecture Hall

Title: Affine Deligne-Lusztig variety of Coxeter type element

Speaker：Qingchao Yu 余庆超（The University of Hong Kong）

Abstract: Affine Deligne–Lusztig variety (ADLV) is an important object in arithmetic geometry and plays an important role in Langlands program. While ADLV with hyperspecial level has been extensively study, people know little about ADLV with Iwahori level. In this talk, I will give a survey to the recent progress in the study of Iwahori Level ADLV, and explain how it is related to hyperspecial level. In my recent joint work with Xuhua He and Sian Nie, we study ADLV of Coxeter type element and prove that it is an iterated fiberation over union of classical Deligne-Lusztig varieties of Coxeter type.

Time： September 20, Wednesday, 15:00-16:00

Venue： Lecture Hall

Title:  Families of D-modules and arithmetic models of Harish-Chandra modules

Speaker：Fabian Januszewski (Paderborn University）

Abstract: I will report on joint work with Takuma Hayashi (Osaka   University) on a general theory of D-modules over arbitrary base   schemes. As a motivation and an application, I will explain how to   apply our results to the construction of Harish-Chandra modules over   Z[1/2] with nice properties. This then implies the existence of global   1/2-integral structures on global spaces of automorphic cusp forms.

Time： July 19, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Wavefront Sets and Generic L-parckets

Speaker：Lei Zhang 张磊（National University of Singapore）

Abstract: In this talk, we introduce a notion of arithmetic wavefront sets for admissible representations of classical groups over local fields of characteristic 0. Conjecturally, via local Langlands correspondence, this arithmetic wavefronts coincide with the classical wavefront sets in sense of Harish-Chandra characters. Hence this conjecture proposes an algorithm to explicate the wavefront sets of representations in generic L-packets, by computing local symplectic root numbers. In particular, we verify the analogue conjectures over finite fields. This is a joint project with Dihua Jiang (The University of Minnesota), Dongwen Liu (Zhejiang University), Zhicheng Wang (Soochow University).

Time： June 28, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: A local twisted trace formula for Whittaker induction of coregular symmetric pairs

Speaker：Chen Wan万忱（University of Minnesota）

Abstract: In this talk, I will discuss the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur and Waldspurger. As a consequence of the trace formula, we prove a simple local trace formula of those models for strongly cuspidal test functions which implies a multiplicity formula for these models. I will also present various applications of the trace formula and multiplicity formula, including a necessary condition for a discrete L-packet to contain a representation with a unitary Shalika model (resp. a Galois model for classical groups) in terms of the associated Langlands parameter, and we also compute the summation of the corresponding multiplicities for certain discrete L-packets. This is a joint work with Raphael Beuzart-Plessis.

Time： June 28, Wednesday, 15:00-16:00

Venue： Lecture Hall

Title: On the structure of Arthur packets for real symplectic and orthogonal groups

Speaker：Bin Xu 徐斌（Tsinghua University）

Abstract: The irreducible admissible representations of Arthur class are the local components of automorphic representations. They are conjectured to be parametrized by the Arthur parameters, and the set of irreducible representations associated with a single Arthur parameter is called an Arthur packet. For symplectic and orthogonal groups, the Arthur packets have been determined by Arthur, and their structure in the p-adic case can be understood in a very complicated way by the works of Moeglin, Xu, Atobe. In this talk, we would like to introduce some conjectures on their structure in the real case, which are motivated by the results in the p-adic case. This is an ongoing project with Taiwang Deng and Chang Huang.

Time： June 21, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Bracelets are theta functions for surface cluster algebras

Speaker：Yihang Zhu 朱艺航（University of Maryland）

Abstract: I will first recall the general expectations of Shimura, Langlands, and Kottwtiz on the shape of the zeta function of a Shimura variety, or more generally its etale cohomology. I will then report on some recent progress which partially fulfills these expectations, for Shimura varieties of unitary groups and special orthogonal groups. Finally, I will give a preview of some foreseeable developments in the near future.

Time： June 14, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Bracelets are theta functions for surface cluster algebras

Speaker：Qin, Fan 覃帆 (Shanghai Jiao Tong University)

Abstract: The skein algebra of a marked surface possesses the basis of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cluster algebra, it also admits the theta basis from the cluster scattering diagram by Gross-Hacking-Keel-Kontsevich. 

In this talk, we show that the two bases coincide except for the once-punctured torus. It is based on a joint work with Travis Mandel. Long-standing conjectures on strong positivity and atomicity follow as corollaries. We also connect our results to Bridgeland's stability scattering diagrams.

Time： May 31, Wednesday, 15:00-16:00

Venue： Lecture Hall

Title: Zeta Functions of Shimura Varieties: Past, Present, and the Near Future

Speaker：Sian Nie 聂思安 (Academy of Mathematics and Systems Science)

Abstract: Let G be a simply connected semisimple group of rank r over an algebraically closed field. Steinberg has associated to each minimal length Coxeter element an r-dimensional affine space in G, which is a cross-section of all regular conjugacy classes of G. In this talk, we will consider natural analogues of Steinberg’s cross-sections in the context of a loop group equipped with a Frobenius automorphism. We will show how Steinberg’s cross-sections intersect Frobenius twisted conjugacy classes (which are parameterized by Newton polygons). Some interesting applications will also be discussed.

Time： May 31, Wednesday, 15:00-16:00

Venue： Lecture Hall

Title: Harder-Narasimhan stratification in p-adic Hodge theory

Speaker：Miaofen Chen 陈苗芬 (East China Normal University)

Abstract: we will talk about the construction of Harder-Narasimhan stratification on the B_{dR}^+-Grassmannian and study its basic geometric properties, such as non-emptiness, dimension and relation with other stratifications, which  generalizes the work of Dat-Orlik-Rapoport,  Cornut-Peche Irissarry, Nguyen-Viehmann and Shen.  This is a joint work in progress with Jilong Tong.

Time： May 17, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Robba site and Robba cohomology

Speaker： Koji Shimizu (Tsinghua University, YMSC)

Abstract: We will discuss a p-adic cohomology theory for rigid analytic varieties with overconvergent structure (dagger spaces) over a local field of characteristic p. After explaining the motivation, we will define a site (Robba site) and discuss its basic properties.

Time： April 26, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Arakawa-Suzuki functor and applications

Speaker： Chan Keiyuen 陈佳源（The University of Hong Kong）

Abstract: The Arakawa-Suzuki functor gives a generalization of the classical Schur-Weyl duality. I shall explain some background and development on this subject. Then I will explain some joint work with Kayue Daniel Wong on this topic.

Time： April 19, Wednesday, 16:00-17:00

Venue： Lecture Hall

Title: Motohashi's Formula with Applications

Speaker： Wu Han 吴涵（University of Science and Technology of China）

Abstract: Spectral reciprocities are equalities between moments of automorphic L-functions in different families. They are powerful tools for the study of the moment problem and the subconvexity problem. The first spectral reciprocity formula is Motohashi's formula, which relates the cubic moment of L-functions for GL_2 with the fourth moment of L-functions for GL_1. The exploitation of this formula (over $\mathbb{Q}$) has led Conrey-Iwaniec and Petrow-Young to the uniform Weyl bound for all Dirichlet L-functions. In this talk, we will present and compare two recent approaches to the general form of Motohashi's formula over arbitrary number fields. Applications, such as the generalization of Petrow-Young's result over totally real number fields, the further generalization to some families of L-functions for PGL_2, and the new error term bound of the Partition function etc., will be discussed as much as time permits.

Time：March 29, Wednesday, 16:00-17:00

Venue：Lecture Hall

Title: Ext-Bessel model vanishes for tempered representations

Speaker：Chen, Rui 陈睿（Zhejiang University）

Abstract: In this talk I will show that the Ext-analogue of Bessel model vanishes for tempered representations. As a corollary, this implies that Waldspurger's integral formula gives the Euler-Poincare characteristic of the Bessel model. If time permits, I will also talk about the Fourier-Jacobi case.