中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

几何拓扑会议学术报告

报告一

报告人：刘贝贝 （The Ohio State Univeristy）

时间：2024.5.25 （周六）9:30-10:30

地点：N702

题目：Heegaard Floer homology of plumbed L-space links

摘要：The well-known L-space conjecture proposed a connection between Heegaard Floer homology of closed orient 3-manifolds, the left orderability of its fundamental group, and the existence of taut foliation. I will focus on the Heegaard Floer homology side of this conjecture. Every closed 3-manifold is obtained by Dehn surgeries on some links in S^3, so we will focus on the Heegaard Floer theory on links in S^3. The computation becomes very complicated when the number of components of links increases, however, we find for the plumbed L-space links, there is a simple and practical algorithm to compute the Heegaard Floer package. Part of this talk is joint work with Borodzik and Zemke. 

报告二

报告人：陈大任 California Institute of Technology

时间：2024.5.25 （周六）10:45-11:45

地点：N702

题目：Some variations of Khovanov homology for null homologous links in RP^3

摘要：In this talk, I will describe two variations of Khovanov homology for null homologous links in RP^3 from two different perspectives: First, we will introduce a Bar-Natan deformation of the homology theory and define the corresponding s-invariant, which provides a genus bound for a certain class of slice surfaces. Second, we will explore an extension of the Ozsváth-Szabó spectral sequence on Heegaard Floer homology of branched double covers for null homologous links in RP^3, and generalize the E_2 page of it. 

报告三

报告人：张凝川，Indiana University Bloomington

时间：2024.5.25 （周六）14:00-15:00

地点：N702

题目：Equivariant algebraic K-theory and Artin L-functions

摘要：The celebrated Quillen-Lichtenbaum Conjecture (QLC), proved by Rost and Voevodsky, connects special values of the Dedekind zeta function of a number field to sizes of its algebraic K-groups. In this talk, I will explain how to generalize the QLC to Artin L-functions of Galois representations of finite, function, and totally real number fields. On the K-theory side, we compute equivariant algebraic K-groups with coefficients in equivariant Moore spectra attached to those Galois representations. This is joint work with Elden Elmanto.

报告四

报告人：董欣 University of Connecticut

时间：2024.5.25 （周六）15:15-16:15

地点：N702

题目：Characterizations of the Euclidean ball by invariant metrics

摘要：I will mention some recent results on characterizations of the Euclidean ball by invariant metrics and their curvature properties. These include the Bergman metric and the Carathéodory metric on pseudoconvex domains. This talk is based on the joint work with Ruoyi Wang and Bun Wong at UC Riverside.

报告五

报告人：王季康，University of California, Berkeley

时间：2024.5.25 （周六）4:30-5:30

地点：N702

题目：The local and global fundamental group of Ricci limit spaces.

摘要：Assume that $(M_i,p_i)$ is a sequence of $n$-manifolds satisfying Ric$\ge -(n-1)$ and converges to $(X,p)$ in the Gromov-Hausdorff sense. We shall show that $X$ is semi-locally simply connected.  In particular, if $M_i$ is simply connected and $X$ is compact, then $X$ is simply connected.

In the case that $M_i$ is simply connected and $X$ is non-compact, $X$ is not necessarily simply connected; so we further assume that there is a discrete isometric group action $G_i$ on $M_i$ so that the diameter of $M_i/G_i$ is uniformly bounded, we may assume $G_i$ equivariantly converges to an isometric group $G$ on $X$. We can show that $G_0$, the identity component of $G$, is a nilpotent group and there is a maximal torus $T^k$ in $G_0$. We can show $\pi_1(X)$ is generated by the $T^k$ orbit of $p$.