纪念华罗庚诞辰110周年活动

今年是华罗庚先生 （1910.11.12-1985.6.12）诞辰110周年。数学所举办“纪念华罗庚诞辰110周年活动”，以缅怀华先生献身科学事业的精神，活动日程如下：

地点：南楼N204教室

报告人：周向宇院士

题目：多复变研究在中国

摘要：介绍华先生、陆先生在多复变与复几何的贡献，以及近期进展。

报告人：刘劲松 研究员

题目：Extensions of quasi-isometries between complex domains

摘要：Recall that we have the important Caratheodory theorem in one dimension. If f maps a Jordan domain D conformally onto a bounded Jordan domain in the complex domain, then f has a continuous injective extension to D. In general, this result does not hold in higher dimensions. In this talk, we will discuss holomorphic homeomorphisms （or quasi-isometries） between two kinds of higher complex domains.

报告人：张平 研究员

题目： 3D anisotropic VS classical Navier-Stokes equations

摘要： 在此报告的第一部分，我将综述经典Navier-Stokes方程的正则性结果；继而我将介绍我们在3维各向异性Navier-Stokes方程方面的适定性结果；最后我将介绍我们从各向异性的观点研究经典Navier-Stokes 方程所得出的

报告人：张志涛

题目：Henon-Lane-Emden conjecture and related Schrodinger systems

摘要：We have proved Henon-Lane-Emden conjecture is true for space dimension    by scaling invariant of the solutions and Sobolev embedding on  . Then we obtained new Liouville-type theorems and showed Henon-Lane-Emden conjecture for polyharmoic system holds in a new region,  and also  proved the generalized Henon-Lane-Emden conjecture in   and  .  Moreover, we prove some new results on symmetry breaking via Morse index for ground state solutions of related Schrodinger systems.

报告人：孙斌勇 院士

题目：Cohomological test vectors and arithmetic of automorphic L-functions

摘要：It was known to Euler that ζ(2k) is a rational multiple of π^2k , where ζ is the Euler-Riemann zeta function, and k is a positive integer. Deligne conjectured that similar results hold for motives over number fields. Algeraic automorphic representations of GL(n), as defined by Clozel, correspond to motives (at least conjecturally). I will explain an analogue of Deligne’s conjecture for these algeraic automorphic representations, as well as some recent progresses on it. The Archimedean theory of cohomological representations and cohomological test vectors will also be explained, as they play a key role in the proof.

报告人：付保华 研究员

题目：Rigidity of wonderful group compactifications under Fano deformations

摘要: For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification \bar{G}, which is a smooth Fano G \times G-variety of Picard number n enjoying many interesting properties. In this talk, it is shown that the wonderful compactification \bar{G} is rigid under Fano deformations. Namely, for any family of smooth Fano varieties over a connected base, if one fiber is isomorphic to \bar{G}, then so are all other fibers. This is a joint work with Qifeng LI.

报告人：田野 研究员

题目：Goldfled Conjecture for Congruent Number Elliptic Curves

摘要：Recall that a positive integer  n is called a congruent number if it is the area of a right triangle with rational side lengths, or equivalently, the group of rational points on the elliptic curve E_n: ny^2=x^3-x has positive rank. The (even parity) Goldfeld conjecture for these elliptic curves can be stated as that among all integers n congruent to 1, 2, 3 mod 8, there is a subset of density one consisting of n such that among the integral solutuons to 2x^2+y^2+8z^2=n, the number of solutuons with z odd is not equal to the number of solutions with z even. In this talk, we introduce recent progress on this conjecture.（It is based on our joint works with A. Burungale and with Yuan-Zhang.）

报告人：万昕 研究员

题目：岩泽理论和BSD猜想

摘要：在这个报告中，我将介绍我们对于岩泽理论的一系列最新研究进展及其在BSD猜想的应用，并概述主要的新想法。

（按报告时间顺序排序）

以下报告以“Zoom会议”线上形式进行，N202、N204作为会议的主会场，欢迎大家参加！