地點（Place）:kaiyun開云官方網(wǎng)站犀浦校區(qū)綜合樓403

Speaker：Andre Leclair(Cornell University)

Title：The Riemann Hypothesis for Physicists

Abstract：The Riemann Hypothesis is widely considered as the most important unsolved problem in mathematics. It has remained unsolved for over 150 years. In this colloquium I will describe two promising approaches to the problem based on ideas from physics, in particular the universal properties of brownian motion or random walks.

Speaker：Weiqiang He(Sun Yat-sen University)

Title：Equivariant Hikita conjecture for minimal nilpotent orbit

Abstract:The theory of symplectic duality is a kind of mirror symmetry in mathematical physics. Suppose two (possibly singular)manifolds are symplectic dual to each other, then there are some highly nontrivial identities betwe en the geometry and topology of them. One of them is the equivariant Hik ita conjecture. Suppose we are given a pair of symplectic dual conical sy mplectic singularities, then Hikita conjecture is a relation of the quantiz ed coordinate ring of one conical symplectic singularity to the equivariant cohomology ring of the symplectic resolution of the other dual conical sym plectic singularity. In this talk, I will focus on this case: the minimal nilpotent orbit and the slodowy slice of the subregular orbit. This is a joint work with Xiaojun Chen and Sirui Yu.

Speaker：Yaoxiong Wen(KIAS)

Title：Mirror symmetry for nilpotent orbit closure

Abstract：Inspired by the work of Gukov-Witten, we investigate stringy Epolynomials of nilpotent orbit closures of type $B_n$ and $C_n$.Classically, there is a famous Springer duality between special orbits. Therefore,it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special orbits. Unfortunately, such a naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of s pecial orbits. Then, we prove the conjecture for Richardson orbits and obt ain certain partial results in general. In the mirror symmetry, we find an interesting seesaw phenomenon where Lusztig's canonical quotient group plays an important role. This talk is based on the joint work with Baohua Fu and Yongbin Ruan,https://arxiv.org/abs/2207.10533.

報告人：王怡（紐約州立大學(xué)石溪分校）題目：弦拓?fù)浜屠窭嗜兆恿餍?/p>

摘要：Chas和Sullivan在1999年發(fā)現(xiàn)，流形上環(huán)路的不同相交方式可以誘導(dǎo)出自由環(huán)路空間（free loop space）的同調(diào)群上豐富的代數(shù)結(jié)構(gòu)，由此開拓出了弦拓?fù)洌╯ tring topology）這一領(lǐng)域。Fukaya及其合作者在2000年左右研究了一般情形下辛流形中拉格朗日子流形（Lagrangian submanifold）相交的Floer理論，特別地，每個拉格朗日子流形都給出了一個A-無窮代數(shù)，其中蘊(yùn)含了邊界落在該子流形上的偽全純圓盤（pseudo-holomorphic disk）映射的信息。在今天的報告中，基于Fukaya、Irie和我自己的工作，我將闡釋兩者的聯(lián)系。我將從Gromov證明C^n中不存在第一貝蒂數(shù)為零的緊致無邊拉格朗日子流形講起。