召集人：田野，中国科学院数学与系统科学研究院

时间：2024.10.13—2024.10.19

会议日程

报告摘要

10月14日

题目： Harmonic analysis on reductive p-adic groups and Lie algebras

报告人： 蔡立，首都师范大学    上午9：00-10：00

摘要：We review basic results in harmonic analysis on reductive p-adic groups and Lie algebras.

题目： Local trace formula and branching problems

报告人： 佘东明，雁栖湖应用数学研究院    上午10：30-11：30

摘要： Branching problems study representations of reductive groups which are distinguished by certain subgroups. They play important roles in representation theory, arithmetic geometry, and the Langlands program. Many such problems over local fields are solved by purely local techniques using the local trace formula. We will introduce the local trace formula, and discuss its application in the proof of the local multiplicity formula.

自由讨论主题： 局部调和分析和重数公式

10月15日

题目： Arithmetic Rallis inner product formula for (S0(3), Mp(2))  

报告人： 熊玮，湖南大学    上午9：00-10：00

摘要：In this talk, I will consider the arithmetic theta lifting for (S0(3), Mp(2)) and present an arithmetic Rallis inner product formula. This is joint work with Wei He and Ye Tian.

题目： Comparison of periods in local theta lifting

报告人： 何伟，中国科学技术大学    上午10：30-11：30

摘要：In this talk, we consider explicit local theta lifting for (SO_3,SL_2) and give relations between linear forms in the same one dimensional space come from difference sources. As a consequence, we prove the local index of explicit Waldspurger local theta lifting is equals to the local index of the explicit local lifting defined by doubling zeta integral.

自由讨论主题： 精确公式及其算术应用

10月16日

题目：chirality of 3-dimensional hyperbolic manifolds

报告人：尹航，中国科学院数学与系统科学研究院    上午9：00-10：00

摘要: We study chiral properties of 3-dimensional hyperbolic manifolds of finite volume. We provide necessary conditions for a commensurable class of hyperbolic 3-manifolds to contain a achiral member, using the associated quaternion algebra of that class. In each commensurable class, we find a chiral manifold. In each commensurable class that contains an achiral member, we find a non-orientable manifold. The main tool is to transform the properties about 3-dimensional hyperbolic manifolds to properties about rational points of an algebraic group. Then use strong approximation theorem to construct finite index subgroups meeting certain requirements.

题目： Introduction to Khayutin's proof of the mixing conjecture

报告人： 闫旗军，雁栖湖应用数学研究院    上午10：30-11：30

摘要： In this talk I will introduce the mixing conjecture of Michel and Venkatesh and present Khayutin's proof of this conjecture for two products of modular curves, under assumptions.

自由讨论主题： 拓扑，统计与算术

10月17日

题目： Nearly overconvergent modular forms and Rankin-Selberg p-adic L-functions

报告人： 范洋宇，北京理工大学   上午9：00-10：00

摘要： In this talk，we review the theory of nearly overconvergent modular forms and explain its application to the construction of two variable p-adic L-functions for Rankin pairs..

题目：p-part of the BSD formula in rank one CM case

报告人：颜晓军，中国科学院数学与系统科学研究院    上午10：30-11：30

摘要: In this talk, we introduce our work on the  $p$-part BSD formula for rank one  CM abelian varieties over an imaginary quadratic field $K$ and a prime $p$ splits in $K$. This is  joint work with Yongxiong Li, Yu Liu and Ye Tian.

自由讨论主题： p-进方法与BSD 猜想

10月18日

题目：Hypergeometric sheaves on reductive groups

报告人：李宣佑，清华大学   上午9：00-10：00

摘要: To a family of representations of a reductive group, we define a hypergeometric sheaf. It is a perverse sheaf. Under the homogeneity condition, we calculate its lisse locus and its rank. We use theory of Fourier transform over general base to relate this problem to a problem about hypergeometric D-modules, where explicit computation can be done. We use our results to estimate exponential sums on reductive groups.

题目： Generalized Bogomolov conjecture and Equidistribution theorem for semi-abelian varieties.

报告人：薛威，中国科学院数学与系统科学研究院    上午10：30-11：30

摘要：In this talk, I will introduce Arakelov geometry on semi-abelian varieties.  We will mainly talk about the Bogomolov conjecture and equidistribution theorem in Arakelov geometry.