表示论与自守型学术论坛

时间：2019 年 6 月 27 日－ 28 日

地点：数学高等研究院（紫金港校区东 7 教学楼）

日程	6 月 27 日
9:30-10:30	张磊
11:00-12:00	高帆
2:00-3:00	余君
3:30-4:30	万忱
4:40-5:40	罗之麟
日程	6 月 28 日
9:00-10:00	林秉辰
10:20-11:20	彭志峰
11:30-12:30	齐治

Organizers: 江迪华，刘东文 (maliu@zju.edu.cn)

Introduction

This two-day workshop at IASM, Zhejiang University, invites eight excellent young mathematicians to discuss a wide range of topics in Representation Theory and Automorphic Forms. It includes: archimedean local Gan-Gross-Prasad conjecture for orthognal groups, construction of cohomological test vectors for standard L-functions of GL(m), endoscopy classification for automorphic represen- tations of exceptional groups, local Langlands conjecture and local descent theory, automorphic L-functions and their poles, Shahidi theory of local coefficients, and applications to number theory.

报告人：张磊（新加坡国立大学）

题目：Local Descent and Algebraic Wavefront Set

摘要：In this talk, we will discuss the local descents for the classical groups of Hermitian type over local fields of characteristic zero. By using the results on local Gan-Gross-Prasad conjecture, we may obtain explicit spectral decomposition of the local descents at the first occurrence index in terms of the local Langlands parameters by explicating calculations of the relevant local root numbers. Conjecturally, this first occurrence indexes of irreducible admissible representations in generic local Vogan packets equals the largest part of the partition in their algebraic wavefront set. This is a joint work with Dihua Jiang and Dongwen Liu.

报告人：高帆（浙江大学）

题目：On the local coefficients matrix via some simple examples

摘要：We will highlight a question arising from (potentially) generalizing Shahidi’s theory of local coefficients matrix from linear group to their finite-degree covers. We will also discuss several examples from SL2.

报告人：余君（北京大学）

题目：Classification  of  acceptable  groups

摘要：A group G is called acceptable if any two homorphisms from any group H to G which have conjugate images at each element are actually conjugate. This notion arises from studying Galois homomorphisms. We show a classification of connected compact Lie groups that are acceptable.

报告人：万忱（麻省理工）

题目：The residue method for period integrals

摘要：In this talk, I will explain how to use the residue method and Langlands-Shahidi’s theory for residues of Eisenstein series to study the period integrals of spherical varieties. In joint works with Aaron Pollack and Michal Zydor, we applied this method to seven spherical varieties. For each case, we proved a relation between the period integrals and certain automorphic L-functions.

报告人：罗之麟（明尼苏达大学）

题目：Regular Germ of Orbital Integrals and the Local Gan-Gross-Prasad Conjecture for Special Orthogonal Groups: Archimedean case

摘要：In this talk, we will give a formula for the regular germ of orbital integrals for any connected reductive algebraic groups over any local field of characteristic zero in terms of endoscopic invariants. As an application, we prove the tempered part of the local Gan-Gross-Prasad conjecture for special orthogonal groups. The results are known for the non-archimedean situation, where the regular germ formula is due to D. Shelstad, and the tempered part of the local GGP conjecture for special orthogonal groups is due to J.-L. Waldspurger, so the result is new only for Archimedean local field. For the proof of the tempered part of the local Gan-Gross-Prasad conjecture for special orthogonal groups, we follow the local trace formula approach initiated by J.-L. Waldspurger and later refined by R. Beuzart-Plessis.

报告人：林秉辰（四川大学）

题目：Non-vanishing of Archimedean local integrals of Friedberg-Jacquet (complex case) 摘要：In a recent work joint with D. Jiang, we explicitly constructed a cohomological vector v and established the non-vanishing property of the archimedean local Friedberg-Jacquet integral for GL2n(R) when evaluating at v. In this talk, we will study the same problem for complex case and give similar results to the real case.  The strategy is similar, but there are still some unforeseen difficulties to conquer in our situation. This is a joint work with Fangyang Tian.

报告人：彭志峰（苏州大学）

题目：An endoscopic classification of automorphic representations of G2

摘要：In this talk, we will introduce the endoscopic theory of the exceptional group of G2.  We

well know that Arthur has given the endoscopic classification of automorphic representations of orthogonal groups and symplectic groups. We will show that the difference part and the same part compared with Arthur work.

报告人：齐治（浙江大学）

题目：The Bessel δ-method and subconvexity for L-functions

摘要：In this talk, I will introduce a new δ-method by a certain Bessel integral and a simple proof of the Weyl-type subconvex bound for modular form L-functions in the t-aspect. This is joint work with Aggarwal, Holowinksy and Lin.