报告题目：Permutation Groups and Coherent Configurations

报 告 人：Andrey Vasil'ev

时 间：2019年4月18日（周四）下午3:30-4:30

地 点：六号楼二楼报告厅

简 介：Starting in the late 1960s, the theory of coherent configurations has now become one of the central parts of algebraic combinatorics. The main goal of this theory is to provide a common method to study symmetries of combinatorial objects. So it is not surprising that permutation groups provide a rich source of coherent configurations. In fact, there is a natural Galois correspondence between subgroups of symmetric group on a set Ω and coherent configurations defined on Ω. The closed objects with respect to that correspondence are 2-closed permutation groups and schurian coherent configurations. In our talk, we will discuss these notions from various points of view: algebraic, combinatorial, algorithmic.

报告题目：A Geometric Approach to the Modified Milnor Problem

报 告 人：陈丽娜

时 间：2019年4月24号（周三）下午4:00-5:00

地 点：六号楼二楼报告厅

简 介：The Milnor Problem (modified) in the theory of group growth asks whether any finite presented group of vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to the Milnor Problem (modified) is equivalent to the Nilpotency Conjecture in Riemannian geometry: given $n, d>0$, there exists a constant $\epsilon(n,d)>0$ such that if a compact Riemannian $n$-manifold $M$ satisfies that Ricci curvature $\op{Ric}_M\ge -(n-1)$, diameter $d\ge \op{diam}(M)$ and volume entropy $h(M)< \epsilon(n,d)$, then the fundamental group $\pi_1(M)$ is virtually nilpotent. We will verify the Nilpotency Conjecture in some cases, and we will verify the vanishing gap phenomena for more cases i.e., if $h(M)<\epsilon(n,d)$, then $h(M)="0$." This is a joint work with Professor Xiaochun Rong and Shicheng Xu.

报告题目：On thin carpets for doubling measures

报 告 人：文胜友

时 间： 2019年4月19日（周五）上午 9：00-10：00

地 点：六号楼二楼报告厅

简 介：We study thin sets for doubling or isotropic doubling measures in $\R^{d}$. In our results we prove that the self-affine sets satisfying the open set condition with holes are thin for isotropic doubling measures and among them Bara\'nski carpets are thin for doubling measures.