会议日程

专题系列报告：Theta correspondence 与算术应用

2021年7月4日——2021年7月11日

 (地点：精正楼二楼学术报告厅)

由上海交通大学马家俊老师报告Theta correspondence的表示论知识，由东南大学杜托平老师报告Theta correspondence的算术应用。

2021年7月12日——2021年7月14日系列学术报告

(地点：精正楼二楼学术报告厅)

报告题目与简介

李加宁   中国科学技术大学

Title:  Revisit an old formula of Kida and Ferrero in Iwasawa theory

Abstract:

In 1979, Kida and Ferrero independently proved a formula which describes explicitly the lambda invariants of unramified Iwsawa modules of the cyclotomic Z_2-extension of imaginary quadratic fields. We'll first revisit this formula. Then we will talk about a recent proven analogous formula on Selmer-groups arising from Iwasawa theory of certain elliptic curves with complex multiplications.

秦超     中山大学（珠海校区）

Title: Iwasawa theory over three-dimensional p-adic Lie extensions.

Abstract:

Iwasawa theory is a powerful tool which describes the mysterious relationship between arithmetic objects and the special values of L-functions. A precise form of this relationship is neatly encoded in the so-called Iwasawa Main Conjecture.

In this talk, I will introduce Main Conjecture in the non-commutative setting. Then I will describe the $K_1(\mathbb{Z}_p[[G_{\infity}]])$ and its localizations using $p$-adic congruences, where $G_{\infity}$ is any $p$-adic Lie group with dimension 3.

林明辉   华中师范大学

Title: On fine Selmer groups, etale wild kernels and even K-groups

Abstract:

The fine Selmer group attached to a Galois representation has been a much studied object in Iwasawa theory and occurs in the formulation (and proof) of the Iwasawa main conjecture. Much of the studies revolves around infinite p-adic Lie extensions which contain the cyclotomic Zp-extension. In this talk, we discribe some of the recent works of the speaker concerning on extensions not necessarily containing the cyclotomic Zp-extension. In particular, we are interested in knowing whether the fine Selmer group is still torsion as an Iwasawa module. For Galois representation coming from an abelian variety, we have some partial results (some of which is a joint work with Debanjana Kundu). In the case when the representation is Zp(i), where i is greater or equal to 2, the fine Selmer group is none other than the etale wild kernel in the sense of Kolster and Nguyen Quang Do. In this latter situation, we can make some progress on the torsionness assertion appealing to algebraic K-theory.

邓太旺   清华大学丘成桐数学科学中心

Title: Torsions in Cohomology of arithmetic groups and congruence of modular forms.         

Abstract:

In this talk I will discuss the torsion classes in the cohomology of $SL_2(Z)$  as well as its variant with compact support.

As a consequence, we show how to deduce congruences of cuspidal forms with Eisenstein classes modulo small primes.

This generalizes the previous result on Ramanujan tau functions.

谢兵永   华东师范大学

Title: Noncritical Galois representations

Abstract:

We will introduce what noncritical p-adic Galois representations are, and show that under certain condition Galois representations coming from Hilbert modular forms are noncritical.

齐治     浙江大学

Title: Moments of Central L-values for Maass Forms over Imaginary Quadratic Fields

Abstract:

I will talk about the twisted moments of central L-values for GL(2) Maass forms over imaginary quadratic fields. As a direct consequence, it can be shown that at least 33% of such central L-values do not vanish. This is joint work with Sheng-chi Liu.

苏峰     西交利物浦大学

Title: Rankin-Selberg integrals for principal series representations of general linear groups.

Abstract:

We discuss on a formula which represents the Rankin-Selberg period integral as a product of an explicit multiple scalar and an explicit integral over the open orbit of the Rankin-Selberg subgroup on the flag varieties of Borel. This is joint work with D. Liu and B. Sun.

徐斌     清华大学丘成桐数学科学中心

Title: Stable distributions supported on A-packets

Abstract:

According to Arthur’s conjecture, every A-packet is associated with a stable distribution, which essentially comes from the stabilization of the trace formula. In order to prove Arthur’s conjecture, one sometimes requires a stronger condition that the stable distributions supported on an A-packet is one dimensional. This condition is expected to hold in the tempered case, but is not satisfied in general. We establish this condition for a large class of no tempered A-packets for p-adic classical groups. Similar results also hold for the similitude groups and will play an important role in proving Arthur’s conjecture in that case.

高帆     浙江大学

Title: On a restriction problem for genuine representations

Abstract:

For a linear group G, the restriction of an irreducible representation to its derived subgroup G_0 is semisimple, and the multiplicity (conjecturally) can be read off from the enchanced Langlands parameters. In particular, the dual groups of G and G_0 play an essential role. For covers of G, we speculate that a third group on the dual side should be encoded in a modified functoriality for restrictions to the coveringsubgroup of G_0. We will discuss about this situation.

高辉     南方科技大学

Title: On integral p-adic Hodge theory

abstract:

I will report some progress on integral p-adic Hodge theory (by me and by other mathematicians). These results are closely related with recent constructions of new integral p-adic cohomology theories (by Bhatt-Morrow-Scholze and Bhatt-Scholze).

刘东文   浙江大学

Title: Critical values of automorphic L-functions

Abstract:

Deligne's conjecture predicts period relations for critical values of motivic L-functions, which are expected to hold for automorphic L-functions as well. In this talk we will explain the almost equal rank case of Rankin-Selberg L-functions for general linear groups. This is joint work with J.-S. Li and B. Sun, which uses a previous work with B. Sun and F. Su on Rankin-Selberg integrals.

佘东明   中科院晨兴数学中心

Title: Local Langlands correspondence for the twisted exterior and symmetric square epsilon-factors of GL(n)

Abstract:

We will introduce the local Langlands correspondence, Langlands-Shahidi method, and sketch the proof of the equality of the twisted symmetric and exterior square local arithmetic and analytic L- and epsilon-factors of GL(n) over p-adic fields. These twisted analytic local factors are new and very different from the untwisted case. We use GSpin groups to define them via Langlands-Shahidi method. The proof is a reduction to the stability of Shahidi local coefficients by some globalization method. And the local coefficients stability is obtained by some asymptotic analysis of certain partial Bessel functions.

邀请人：莫忠鹏、彭志峰