Upcoming： 

Venue: C548, Tsinghua University Shuangqing Complex Building A

15:00-16:00
Masao Oi (NTU)

Title: Local Langlands conjecture and positive-depth Deligne-Lusztig theory

Abstract: The local Langlands conjecture predicts that irreducible representations of a p-adic reductive group can be classified in terms of certain arithmetic data involving local Galois representations. One possible approach to the local Langlands conjecture is to find some nice parametrization of irreducible representations of a p-adic reductive group because it typically enables us to construct the corresponding local Galois representations in an explicit manner.
On the other hand, by Deligne-Lusztig theory, it is known that any irreducible representation of a finite reductive group can be realized on the etale cohomology of an algebraic variety called the Deligne–Lusztig variety. Recently, Chan–Ivanov established a generalization of Deligne–Lusztig theory, which provides representations of open compact subgroups of a p-adic reductive group.
In this talk, I would like to discuss the relationship between Chan–Ivanov’s representations and a certain class of representations of a p-adic reductive group, especially, from the viewpoint of the local Langlands conjecture.
This talk is based on my joint work with Charlotte Chan (University of Michigan).

16:30-17:30
Wee Teck Gan (NUS)

Title: Global Langlands parameters for G_2

Abstract: I will discuss a joint work with Erez Lapid which gives a characterization of those automorphic representations of GL(7) which arise as the functorial lifts from globally generic cuspidal representations of the exceptional group G_2. This refines earlier results of Joseph Hundley and Baiying Liu and gives rise to a notion of global L-parameters for G_2. 

Past： 

Venue: Room 110, Morningside Building, Chinese Academy of Sciences 

15:00-16:00, Ziquan Yang

Title: Some Arithmetic Applications of Functional Transcendence

Abstract: A classical question in number theory is whether there are algebraic relations among given transcendental numbers. In functional transcendence theory, transcendental numbers are replaced with power series. Of particular interest is the case when the power series arise from variations of Hodge structures. I plan to give a survey talk on the arithmetic applications of functional transcendence results, including one from my joint work with Urbanik last year.

16:30-17:30, Yousheng Shi

Title: The Kudla-Rapoport Conjecture: knowns and unknowns
Abstract: The Kudla-Rapoport Conjecture is a precise identity between the arithmetic intersection number of special cycles on unitary or orthogonal Shimura varieties and the central derivative of Eisenstein series. It sheds light on the relation between L-functions and algebraic cycles. In this talk, I will discuss known results about this conjecture and some open problems.

Venue: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR

15:00-16:00 Yiwen Ding (Peking University)

Title: Hodge filtration and p-adic Langlands programme

Abstract: A basic problem in p-adic Langlands programme is to find the information of Hodge filtration in p-adic automorphic representations. In the talk, we will discuss some results, conjectures and speculations towards the problem. 

16:30-17:30 Ping Xi (Xi'an Jiaotong University)
Title: Exponential/character sums in analytic number theory

Abstract: Applications of Fourier analysis to number theory create exponential and character sums. Estimates for such sums turn out to be very crucial in analytic number theory. We would like to show how the deep works of Weil, Deligne, Laumon, Katz, et al can be adapted to deal with such (incomplete) sums. 

Time：Fri., 15:00-17:30, Sept. 27, 2024

Venue: Shuangqing C654 (note that the lecture room was changed)

15:00-16:00, Gerard van der Geer
Title: Picard modular forms and curves of genus three
Abstract: We discuss how to calculate traces of Hecke operators on Picard modular forms by the use of point counting of curves of genus three over finite fields. This is joint work with Jonas Bergstroem and Fabien Clery. 

16:30-17:30, Yifeng Liu

Title: Bessel periods and Selmer groups over ordinary eigenvariety

Abstract: We (re)construct the ordinary part of the eigenvariety for a reductive group G from the module of integral ordinary distributions. For G=U(n)xU(n+1), we construct the Bessel periods as H-invariant distributions, in both definite and indefinite cases, where H is the diagonal subgroup of G appearing in the Gan-Gross-Prasad conjecture. Finally we relate such period to the characteristic divisor of the Selmer group of the standard Galois representation over the eigenvariety.