为增进拓扑学及相关领域的青年学者之间的学术交流与合作，兹定于2023年7月9日至14日在广西桂林市举办第九届全国青年拓扑学者论坛。本届论坛得到了广西应用数学中心（广西师范大学）、中国科学院数学与系统科学研究院和北京大学的资助。本次会议不收取会务费，参会者食宿费自理。

会议基本信息：

主办单位：中国科学院数学与系统科学研究院   北京大学  广西师范大学

承办单位：广西应用数学中心 广西师范大学数学与统计学院

会议时间：2023年7月9号至14号(报到时间：2023年7月9日；学术交流: 2023年7月10日至13日；离会时间：2023年7月14日)

会议报道地点：桂林市喀舍悦璟酒店大厅

会议地点：广西师范大学（育才校区）田家炳艺术教育学院109室

其他：本次会议为参会者提供自由讨论场地——广西师范大学（育才校区）理科楼306。自由讨论场地开放时间：10号19：00-21：00，12号19：00-21：00，13号全天，14号全天。

交通信息：

1.  高铁（桂林站、桂林北站、桂林西站）

(1) 桂林站距桂林喀舍悦璟酒店约6公里，打车约15元。

(2) 桂林北站距桂林喀舍悦璟酒店约11公里，打车约25元。

(3) 桂林西站距桂林喀舍悦璟酒店约20公里，打车约35元。

2.  机场（桂林市两江国际机场）

(1) 桂林两江机场距桂林喀舍悦璟酒店约35公里，打车约100元。

(2) 乘机场大巴（乘车地点：T2航站楼一楼到达厅6号门外）至民航大厦（20元/人,约50-60分钟，上下班高峰期请预留1小时20分钟的乘车时间），然后打车至桂林喀舍悦璟酒店约3.5公里，打车约10元。

 

第九届全国青年拓扑学者论坛组委会

 

组委会成员（按姓氏拼音排序）：刘登品，卢家宽，苏阳，王家军，徐勐戬，钟立楠

会议日程

会议地点：广西师范大学（育才校区）田家炳艺术教育学院109室

7月10日（周一）

 

7月11日（周二）

会议地点：广西师范大学（育才校区）田家炳艺术教育学院109室

 

 

7月12日（周三）

会议地点：广西师范大学（育才校区）田家炳艺术教育学院109室

 

 

7月13日（周四）

 

 

 

 

 

 

 

 

 

 

 

报告信息

 

报告人：陈海苗  北京工商大学

报告题目：树状纽结的基本群的SL(2,C)-表示

摘要: 纽结基本群的SL(2,C)-表示是重要的研究对象. 但对于给定的纽结, 如何找到具体的表示, 一直被认为是困难的问题, 至今只对少数几类纽结有结果. 我将描述一种方法, 对每个树状纽结, 原则上能确定所有的表示.

 

报告人：陈亮  东北师范大学

报告题目：Singular submanifolds in non-flat space from the viewpoint of Legendrian dualities

摘要：We investigate the geometrical and topological properties of singular submanifolds in non-flat space, such as singular curves in hyperbolic space, singular surfaces in sphere space and so on, from the viewpoint of Legendrian dualities which developed by Izumiya and the speaker.

 

报告人：陈小杨  同济大学

报告题目：Rational ellipticity of Riemannian manifolds

摘要：It was conjectured by Bott-Grove-Halperin that a compact simply connected Riemannian manifold with nonnegative sectional curvature is rationally elliptic, i.e., it has finite dimensional rational homotopy groups. We will discuss some recent progress on this conjecture.

 

报告人：范遥 北京大学

报告题目：Representations of graph manifolds to the Seifert motion group

摘要：In this talk, we mainly consider virtual representations of graph manifolds. And I will give a brief introduction of the Seifert motion group. At last I will prove two theorems in different cases of graph manifolds.

 

报告人：管健云  牡丹江师范学院

报告题目：三维李群的 Gauss-Bonnet 定理和 Ricci 孤立子研究

摘要：主要采用黎曼逼近和洛伦兹逼近的方法研究了具有一般参数族左不变度量的闵可夫斯基平面的刚体运动群和具有典范联络的洛伦兹海森堡群上的 Gauss-Bonnet 定理. 计算并获得了这两类李群中正则曲线的内蕴曲率、曲面的内蕴测地曲率以及曲面的远离特征点的内蕴高斯曲率的具体表达式. 继而综合利用支配收敛定理和经典的 Gauss-Bonnet 公式, 证明了相应版本的 Gauss-Bonnet 定理. 进一步利用代数的方法，探讨了具有典范联络的洛伦兹海森堡群中 Ricci 孤立子的存在性问题. 精细刻画了 Ricci 孤立子等式成立的条件, 并最终找到了一类典范联络下的 Ricci 孤立子.

 

报告人：雷佳麟   西安交通大学

报告题目：Explicit bounds for fixed subgroups of endomorphisms of free products

摘要：For an automorphism of a free group of rank n, Bestvina and Handel showed that the rank of the fixed subgroup is not greater than n (the so-called Scott conjecture). In the past forty years,  their result was generalized by many authors in various directions. In this talk, we introduce some new progress, in particular, the fixed subgroups of endomorphisms of free products, focusing on explicit bounds for their ranks. This is joint work with ZHANG Qiang.

 

报告人：刘勍  南开大学

报告题目：Growth of stable subgroups

摘要：Non-elementary hyperbolic groups grow exponentially faster than their infinite index quasiconvex subgroups. This is a result of Dahmani, Futer, and Wise. For any finitely generated groups, we could investigate the growth of their stable subgroup. In our talk, we will focus on finitely generated groups that have the Morse local-to-global property. We show that the  Morse local-to-global groups grow more quickly than their infinite index satble subgroups. This is a joint work with Suzhen Han and Wenyuan Yang.

 

报告人：柳翔  中国科学院数学与系统科学研究院 数学研究所

报告题目：Braids and linked periodic orbits of disc homeomorphisms

摘要：In 1990, Jean-Marc Gambaudo introduced the notion of linking of two invariant sets of a surface self-map. In this talk, we first survey the known results about linked orbits. Then we concern on orientation-preserving homeomorphisms of the $2$-disc. Based on the forcing relation of braids, we present a method for finding periodic orbits which are linked with a given one. In particular, for $3$-periodic orbits of pseudo-Anosov braid types, we provide new examples of linked orbits of periods at most $4$. It is based on the preprint of arXiv:2303.04570v2.

 

报告人：刘晔   西交利物浦大学

报告题目：Double coverings and local systems of hyperplane arrangements

摘要：Hyperplane arrangements are studied in singularity theory, topology, combinatorics etc. We discuss recent advances on the double coverings of complement of hyperplane arrangement, including our joint work with Yongqiang Liu.

 

报告人：李彦霖  杭州师范大学

报告题目：Geometric topology and singularities of frontal surfaces

摘要：Frontal surfaces are traditionally described as the image of a Legendrian map with singularities, and classified using diffeomorphisms that preserve the Legendrian fibres in the total space. In this presentation, I will talk about geometric topology and singularities of frontal surfaces of corank one and finite frontal codimension.

 

报告人：潘宇  天津大学

报告题目：Wrapped Floer thoery for Immersed Lagrangian surfaces

摘要：We apply wrapped Floer thoery to immersed Lagrangian fillings and generalize the Seidle Isomorphism from embedded Lagrangian fillings to immersed Lagrangian fillings.

 

报告人：王鹏  西安交通大学

报告题目：Iwip endomorphisms of free groups and fixed points of graph selfmaps

摘要：In the paper \cite{JWZ}, Jiang, Wang and Zhang gave a bound for the fixed points and fixed subgroups of a graph selfmap. In this talk, we give a sufficient condition when the bound can be reached, by studying iwip outer endomorphisms of free groups acting on the outer spaces. This is joint work with ZHANG Qiang.

 

报告人：王炜飚  中国科学院数学与系统科学研究院

报告题目：Extendability over the 4-sphere and invariant spin structures of surface automorphisms

摘要：An automorphism f of an oriented closed surface is said to be extendable over the 4-sphere if we can embed the surface in the 4-sphere such that f extends to an automorphism of the 4-sphere.？ It is known that f is extendable over the 4-sphere if and only if f has a bounding invariant spin structure. Using this criterion, for each oriented closed surface of genus g>1 except for g=4, we construct a period-8 map that is not extendable over the 4-sphere. We also show that each surface automorphism has an invariant spin structure. As a consequence, every surface automorphism is extendable over the 4-sphere after a stabilization. It is joint work with Zhongzi Wang.

 

报告人：于立 南京大学

报告题目：A new homology theory of orbifolds from triangulations

摘要：We introduce a new homology theory of orbifolds called stratified simplicial homology (or st-homology for short) from some special kind of triangulations adapted to orbifolds. In the definition of st-homology, the orders of the local groups of an orbifold are encoded in the boundary map so that the theory can capture some structural information of the orbifold. We can prove that st-homology is invariant under orbifold isomorphisms and more generally under weight-preserving homotopy equivalences. It turns out that the free part of st-homology of an orbifold can be computed from the usual simplicial homology of the orbifold. So it is the torsion part of st-homology that can really give us new information of an orbifold. Moreover, we introduce a wider class of objects called pseudo-orbifolds and develop the whole theory of st-homology in this setting.

 

报告人：杨锡柳   北京大学

报告题目：Knot Floer homology and the fundamental group of (1,1) knots

摘要：Knot Floer homology is a categorification of the Alexander polynomial of knots introduced independently by Ozsvath and Szabo and by Rasmussen. The explicit relationship between the fundamental group and the Knot Floer homology is one of the fundamental questions about Heegaard Floer homology raised by Ozsvath and Szabo. We study this question on (1,1) knots. We give an algorithm for computing the knot Floer homology of a (1, 1) knot from a particular presentation of its fundamental group. We also give a way to restore the Heegaard normal form from that presentation.

 

报告人：杨志青   大连理工大学

报告题目：Graded knot polynomials

摘要：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.

 

报告人：曾昊智  华中科技大学

报告题目：On the equivariant cohomology of torus manifolds with locally standard action

摘要：The notation of torus manifolds were introduced by Professor Akio Hattori and Mikiya Masuda. Toric manifolds, quasitoric manifolds, topological toric manifolds, toric origami manifolds and b-symplectic toric manifolds are typical examples of torus manifolds.

In this talk we discuss the equivariant cohomology rings and equivariant Stiefel-Whitney classes of torus manifolds with locally standard action. This is joint work with Yueshan Xiong.

 

报告人：赵旭安 北京师范大学

报告题目：李群的自映射

摘要：Let G be a compact simply connected Lie group. We Consider the Boardman map : [G,G]-->Hom((G),(G)). To understand the image of this map, we take the complex topological K-theory into account. By connecting K-theory and ordinary cohomology via Chern character, we give an approximation of the image of the map . Based on these results, we can classify self-maps of certain compact Lie groups of low rank up to homology.