Conferences & Seminars
Northeastern Topology Seminar
I’m co-organizing “Northeastern topology seminar” (“东北拓扑系列活动”) which meets on Tuesdays at 2 pm (unless informed otherwise). The seminar is held in hybrid mode. If you are interested in participarting the seminar or giving a talk, please shoot me an email. The ads of the past talks can be found on http://cos.neu.edu.cn/ (under the section “学术交流”). The other co-organizers are: 陈亮 （东北师大），鄂强（大连海事），李风玲 （大连理工），张发泽 （东北师大），钟立楠（延边大学）
For recordings of talks in Fall 2022, please visit YoukuFall2022. For recordings of talks in Spring 2023, please visit YoukuSpring2023.Hybrid March 21, 2023 9:30 am - 10:30 am
Fengling, Dalian University of TechnologyTitle: On $H'$-splittings of Seifert manifolds
Abstract: In this talk, we introduce the $H'$-splittings for compact connected orientable $3$-manifolds, and discuss some properties of $H'$-splittings of Seifert manifolds.
Tencent March 28, 2023 2:00 pm - 3:00 pm
Yulan Qing, Fudan UniversityTitle: Boundary of Groups
Abstract: Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this study we introduce a generalization of the Gromov boundary for all finitely generated groups. We construct the sublinearly Morse boundaries and show that it is a QI-invariant topological space and it is metrizable. We show the geometric genericity of points in this boundary using Patterson Sullivan measure on the visual boundary of $CAT(0)$ spaces. Lastly we discuss the connection between the sublinearly Morse boundary and random walk on groups. As applications we answer open problems regarding QI-invariant models of random walk on $CAT(0)$ groups and on mapping class groups.
Tencent April 11, 2023 2:00 pm - 3:00 pm
Yi Liu, Peking UniversityTitle: On profinite properties of $3$-manifolds
Abstract: In this talk, I will discuss recent development in the study of finite covers of $3$-manifolds and profinite properties of their fundamental groups.
Hybrid April 18, 2023 2:30 pm - 3:30 pm
Yi Huang, Tsinghua UniversityTitle: The earthquake metric
Abstract: Earthquakes are natural generalisations of Fenchel-Nielsen twists deformations on Teichmüller space, and Thurston’s remarkable earthquake theorem asserts that any hyperbolic metric on a given closed surface can be deformed to any other by a unique (left) earthquake. This was famously employed by Kerckhoff in his proof of the Nielsen realisation problem, which quickly cemented their importance in Teichmüller theory. Geometrically speaking, however, (long) Earthquake paths are far from being “twist efficient” - indeed, Mirzakhani shows that earthquake flows on Teichmüller space are measure conjugate to the horocyclic flow. Motivated by wishing to understand how one might efficiently “earthquake” between hyperbolic structures, we initiate the first systematic study of the earthquake metric—a Finsler metric first introduced in Thurston’s “Minimal stretch maps between hyperbolic surfaces” preprint, and discover surprising connections to both the Thurston metric and the Weil-Petersson metric. This is work in collaboration with K. Ohshika, H. Pan and A. Papadopoulos.
Hybrid April 18, 2023 3:40 pm - 4:40 pm
Yu Pan, Tianjin UniversityTitle: Augmentations and Exact Lagrangian surfaces
Abstract: Exact Lagrangian surfaces are important objects in the derived Fukaya category. Augmentations are objects of the augmentation category, which is the contact analog of the Fukaya category. In this talk, we discuss various relations between augmentations and exact Lagrangian surfaces. In particular, we realize augmentations, which is an algebraic object, fully geometrically via exact Lagrangian surfaces.
Hybrid April 28, 2023 10:30 am - 11:30 am
Xiaolei Wu, Fudan UniversityTitle: Finiteness properties of surface Thompson groups
Abstract: I will start with an introduction to Thompson groups and their surface version. Then I will explain how one can determine their finiteness properties by calculating the connectivity of some special complexes. This is based on joint works with Javier Aramayona, Julio Aroca, Kai-Uwe Bux, María Cumplido, Jonas Flechsig, Nansen Petrosyan and Rachal Skipper.
Hybrid April 28, 2023 2:00 pm - 3:00 pm
Binbin Xu, Nankai UniversityTitle: Periodic directions on translation surfaces of genus 2
Abstract: One generalization of flat structure on torus to oriented closed surface of genus greater than $1$ is called translation surface structure. When a surface is equipped with such a structure, we call it a translation surface. Given a translation surface $S$, like on a flat torus, there is a globally well-defined notion of direction on $S$, and geodesics on $S$ along a same direction are disjoint from each other, hence induces a flow on $S$. Such flows and their dynamical properties are important in the study of the symmetry group of $S$ which is called Veech group. In particular, when the flow on $S$ along one direction has only periodic regular orbits, we call this direction a periodic direction of $S$. In a joint-work with Anja Randecker, using the close relation between interval exchange transformations and flows on surfaces, we obtain a full classification of translation surfaces of genus $2$ with one singularity according to the size of their periodic directions sets. In this talk, I will first give some necessary background, then I will explain our result and give the rough idea of the proof.
Zoom May 16, 2023 9:00 am - 10:00 am
Hongbin Sun, Rutgers UniversityTitle: Virtual domination of 3-manifolds
Abstract: In this talk, we survey known results on virtual domination of 3-manifolds, i.e. a 3-manifold has a finite cover that admits a non-zero degree to another 3-manifold. We have proved a sequence of results on this topic, in which the domains are closed hyperbolic 3-manifold, closed 3-manifold with positive simplicial volume, cusped hyperbolic 3-manifolds, respectively. The good pants construction initiated by Kahn and Markovic is a crucial tool for all proofs of these results.
Tencent May 23, 2023 2:00 pm - 3:00 pm
Qiang Zhang, Xi'an Jiaotong UniversityTitle: 群自由积的自同态不动子群的显式界
Abstract: 群自同态的不动子群是几何群论中的一个热门课题，自上世纪70年代以来，引起了很多人的关注。本报告将介绍有关不动子群研究的历史及最新进展，特别地，给出一类群的自由积自同态不动子群的显式界。
Tencent May 30, 2023 2:00 pm - 3:00 pm
Zhiqing Yang, Dalian University of TechnologyTitle: Graded knot polynomials
Abstract: 多数纽结不变量的计算不是多项式时间的。但是把纽结多项式变形并按照某种要求分次以后，每一次数的分量可以是多项式时间计算的。这样，以前非常复杂不适合计算的纽结不变量，现在可以计算其低次的分量。这个思想被Jozef H. Przytycki，F. Jaeger，Akio Kawauchi等数学家应用在HOMFLY纽结上，本报告推广这一结果，证明他们给出的纽结多项式变形是报告人的纽结不变量的特殊情形，并讨论更一般的可能。
Hybrid June 5, 2023 8:30 am - 9:30 pm
Seongjeong Kim, Jilin UniversityTitle: On winding parities for knots in $S_{g} \times S^{1}$
Abstract: In knot theory not only classical knots, which are embedded circles in $S^{3}$ up to isotopy, but also knots in other $3$-manifolds are interesting for mathematicians. In particular, virtual knots, which are knots in thickened surface $S_{g} \times [0,1]$ with an orientable surface $S_{g}$ of genus $g$, are studied and they provide interesting properties. In this talk, we will talk about knots in $S_{g} \times S^{1}$ where $S_{g}$ is an oriented surface of genus $g$. We introduce basic notions and properties for them. In particular, for knots in $S_{g} \times S^{1}$ one of important information is “how many times a half of a crossing turns around $S^{1}$”, and we call it winding parity of a crossing. We extend this notion more generally and introduce a topological model, which provide a universal winding parity.
Hybrid June 5, 2023 9:30 am - 10:30 pm
Chao Wang, East China Normal UniversityTitle: Equivariant embeddings of closed surfaces in spheres
Abstract: It is known that every finite group action on a closed surface can extend over some $m$-dimensional sphere via an equivariant embedding. So it is natural to ask what is the minimum possible dimension for a given action. I will discuss some results about this question, and mainly focus on two cases, where the minimum dimension is three or the group action is cyclic.
Hybrid June 5, 2023 10:30 am - 11:30 pm
Zhi Lu, Fudan UniversityTitle: Equivariant bordism of $G$-actions fixing isolated points
Abstract: In this talk, we first recall the history and development of ($G$-equivariant) unoriented bordism, especially for $G$ to be a mod $2$-torus. Then we introduce the recent some progresses for the equivariant unoriented bordism classification of mod $2$-torus-actions fixing isolated points, which are joint works with Bo Chen and Qiangbo Tan.
Hybrid June 27, 2023 10:30 am - 11:30 pm
Zhechi Cheng, Wuhan UniversityTitle: Top group of knot Floer homology and its applications
Abstract: Knot Floer homology is a link invariant introduced by Ozsváth and Szabó. Ni showed that knot Floer homology detects fiberedness of links. Specifically, a link is fibered if and only if the rank of the top group of knot Floer homology is one. The top group plays an important role in the study of knot Floer homology. In this talk, we discuss the development of the study of the top group and discuss some recent applications. This is joint work with Matthew Hedden and Sucharit Sarkar.
Hybrid June 27, 2023 2:30 pm - 3:30 pm
Youlin Li, Shanghai Jiao Tong UniversityTitle: Strongly exceptional Legendrian connected sum of two Hopf links
Abstract: A Legendrian link in a contact 3-manifold is a smooth link that is tangent to the contact structure at every point. In an overtwisted contact 3-manifold, a Legendrian link is called "exceptional" if its complement is tight. It is considered "strongly exceptional" if its complement is tight and does not have Giroux torsion. In this talk, I will completely classify the strongly exceptional Legendrian representatives of connected sum of two Hopf links in contact 3-spheres. This is joint work with Sinem Onaran.