Upcoming Seminar

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).

Previous Seminar

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 (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 (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.