2018代数与几何拓扑研讨会

2018 Workshop on Algebraic and

Geometric Topology

会议手册

2018年 7月 28日-31日

中国 四川 成都

主办单位：西南交通大学数学学院

欢迎辞 为了促进西南交通大学数学学科建设及国内外同行在几何学、拓扑学领域的学术交

流，展示最新研究成果，在成功举办 2017 年几何拓扑研讨会的基础之上，我们 2018 年

继续在西南交通大学峨眉校区举办“2018 年代数与几何拓扑研讨会”，会议时间为 2018

年 7 月 28 日-31 日。本次会议旨在将代数与几何拓扑领域的专家学者们召集起来，就当

前代数与几何拓扑领域的前沿课题及最新成果进行深入而广泛的交流，提高西南地区的

学术影响力，活跃地区学术氛围。

历史会议回顾：西南交通大学 2017 年几何拓扑研讨会合影

Program Committee

The Academic Committee

An-min Li Sichuan University

Fuquan Fang Capital Normal University

Haibao Duan Chinese Academy of Sciences

Zhi Lv Fudan University

Bohui Chen Sichuan University

Bin Zhang Sichuan University

Weiping Li Southwest Jiaotong University

Organizing Committee

Weiping Li Southwest Jiaotong University

Xiaojun Chen Sichuan University

Wenchuan Hu Sichuan University

Xiaobin Li Southwest Jiaotong University

Conference Secretaries

Xiaobin Li Southwest Jiaotong University

Hong Hao Southwest Jiaotong University

Yifan Lu Southwest Jiaotong University

Organizers：School of Mathematics, Southwest Jiaotong University

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2018 代数与几何拓扑会议委员会

学术委员会

李安民 四川大学

方复全 首都师范大学

段海豹 中国科学院

吕志 复旦大学

陈柏辉 四川大学

张斌 四川大学

李维萍 西南交通大学

组织委员会

李维萍 西南交通大学

陈小俊 四川大学

胡文传 四川大学

李晓斌 西南交通大学

会务组

李晓斌 西南交通大学

郝虹 西南交通大学

卢怡帆 西南交通大学

承办单位：西南交通大学数学学院

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2018 代数与几何拓扑会议日程安排 一、会议地点：西南交通大学峨眉校区第五会议室

二、会议日程安排：

1. 2018年 7月 28 日在湖山宾馆报到；

2. 2018年 7月 29-30日学术报告；

3. 2018年 7月 31日离开。

7月 29日 西南交通大学峨眉校区第五会议室

8:30-9:00 开幕式及合影

主持 李维萍（西南交通大学）

9:00-9:50 段海豹（中国科学院） The characteristic classes and Weyl

invariants of the Spin geometry

9:50-10:00 茶歇

10:00-10:50 王向军（南开大学） On the homotopy elements h_0h_n in the

classical ASS

10:50-11:00 茶歇

11:00-11:50 刘秀贵（南开大学） Rational homotopy of the homotopy fixed

point sets of $S^3$ actions

12:00-14:00 午餐（湖山宾馆）

主持 吕志（复旦大学）

14:00-14:50 杨文元（北京大学） Genericity of contracting elements in

groups

14:50-15:00 茶歇

15:00-15:50 于立（南京大学） On the existence of positive scalar

curvature on small covers and real

moment-angle manifolds

15:50-16:00 茶歇

16:00-16:50 许明（首都师范大学） Geodesic and curvature of a piecewise flat

Finsler surface

16:50-18:00 自由讨论（free discussion）

18:00-20:00 晚宴（湖山宾馆）

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7月 30日 西南交通大学峨眉校区第五会议室

主持 段海豹（中国科学院）

9:00-9:50 吕志（复旦大学） On Kosniowski conjecture

9:50-10:00 茶歇

10:00-10:50 李平（同济大学） Kaehler hyperbolic manifolds and Chern

number inequalities

10:50-11:00 茶歇

11:00-11:50 陈庆陶（瑞士苏黎世理

工学院）

Recent progress of various Volume

Conjectures for links as well as

3-manifolds

12:00-14:00 午餐（湖山宾馆）

主持 刘秀贵（南开大学）

14:00-14:50 陈立志（兰州大学）

Systolic volume and complexity of

3-manifolds

14:50-15:00 茶歇

15:00-15:50 Sylvie Paycha（德国

波茨坦大学）

An algebraic approach to locality:

applications in geometry and

renormalisation schemes

15:50-16:00 茶歇

16:00-16:50 郭锂（罗格斯大学） Conical zeta values and double subdivision

16:50-18:00 自由讨论(free discussion)

18:00-20:00 晚宴（湖山宾馆）

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三、报告题目与摘要：

1. 段海豹，中国科学院

Title：The characteristic classes and Weyl invariants of the Spin geometry

Abstract：Based on a pair of new cohomology operations on $2$-formal spaces we

determine the integral cohomology rings of the classifying spaces $%B_{Spin(n)}$ and

$B_{Spin^{c}(n)}$.As applications, we introduce the characteristic classes for the

topological $K_{Spin}$ and $K_{Spin^{c}}$ theories, and present an effective algorithm

to produce of the integral Weyl invariants of the Lie groups $Spin(n)$ and

$%Spin^{c}(n)$.

2. 王向军，南开大学

Title: On the homotopy elements h_0h_n in the classical ASS

Abstract: In this talk, I will introduce the elements $h_0h_n$ in the $E_2$-term

of the classical Adams spectral sequence and of the Adams-Novikov spectral sequence.

I will also introduce the {\it method of infinite descent}, by which we proved that

$h_0h_3$ is a permanent cycle. At last I will introduce our further consideration on

the convergence of elements $h_0h_n$.

3. 刘秀贵，南开大学

Title: Rational homotopy of the homotopy fixed point sets of $S^3$ actions

Abstract: An action of a group $G$ on a space gives rise to two natural spaces, the

fixed point set and the homotopy fixed point set. In this talk, when $G$ is $S^3$ and

$M$ is a $G$-space, we study the rational homotopy type of the homotopy fixed point

set $M^{hG}$, and the natural injection $M^G\rightarrow M^{hG}$. This is a joint work

with Yanlong Hao and Qianwen Sun.

4. 吕志，复旦大学

Title: On Kosniowski conjecture

Abstract: Let M be a unitary closed manifold that admits an action of a circle preserving

the unitary structure and fixing some isolated points. Kosniowski conjectured in 1980

that if M is not a boundary, then the number of isolated points is at least [dim M/4]+1.

This talk will discuss different statements of Kosniowski conjecture and state some

recent progresses.

5. 杨文元，北京大学国际数学中心

Title：Genericity of contracting elements in groups

Abstract：In this talk, I will introduce a class of statistically convex-cocompact

actions for groups with a contracting element. This could be thought of as a statistical

version of convex-cocompact Kleinian groups. This notion includes relatively

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hyperbolic groups, CAT(0) groups with rank-1 elements, mapping class groups on

Teichmuller spaces, etc. Our main result shows that this class of groups have purely

exponential growth, and contracting elements are exponentially generic. This gives many

new classes of groups with these properties, and generalizes some known results.

Strengthening a theorem of Maher, one corollary is that pseudo-Anosov elements are

exponentially generic in mapping class groups. Another is a generalization of a result

of Knieper to singular setting that non-rank-1 geodesics are exponentially small in

CAT(0) groups。

6. 于立，南京大学

Title: On the existence of positive scalar curvature on small covers and real

moment-angle manifolds

Abstract: We study small covers and the real moment-angle manifold over a simple

polytope that admit Riemannian metrics of positive scalar curvature. We first explain

some general facts on the existence of positive scalar curvature on a smooth manifold.

Then we show a class of simple polytopes over which the small covers and the real

moment-angle manifolds admit metrics of positive scalar curvature. In

particular, these examples give all the 3-dimensional small covers that admit

metrics of positive scalar curvature. In addition, our study leads to an interesting

problem in combinatorics.

7. 李平，同济大学

Title：Kaehler hyperbolic manifolds and Chern number inequalities

Abstract：In this talk we will review two well-known conjectures due to Hopf and S.-T.

Yau respectively, and explain their connections via the concept of “Kaehler

hyperbolicity” introduced by Gromov. Then we shall report our recent work around

Kaehler hyperbolic manifolds.

8. 陈庆陶，苏黎世联邦理工学院

Title：Recent progress of various Volume Conjectures for links as well as 3-manifolds

Abstract： The original Volume Conjecture predicts a precise relation between the

asymptotics of the colored Jones polynomials (Kashaev invariants) of a knot in S^3 and

the hyperbolic volume of its complement. I will discuss two different directions that

lead to generalizations of this conjecture.

The first direction concerns different quantum invariants of knots, arising from the

colored SU(n) (with the colored Jones polynomial corresponding to the case n= 2). I

will first display subtle relations between congruence relations, cyclotomic

expansions and the original Volume Conjecture for colored Jones polynomials of knots.

I will then generalize this point of view to the colored SU(n) invariant of knots.

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Certain congruence relations for colored SU(n) invariants, discovered in joint work

with K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume

Conjecture for these colored SU(n) invariants. I will also discuss similar ideas for

the superpolynomials that arise in HOMFLY-PT homology as well as other different

situations.

Another direction for generalization involves the Witten-Reshetikhin-Turaev and

(modified) Turaev-Viro quantum invariants of 3-manifolds. In a joint work with T. Yang,

we formulated a new Volume Conjecture for the asymptotics of these 3-manifolds

invariants evaluated at certain roots of unit, and numerically checked it for many

examples. Interestingly, this conjecture uses roots of unity that are different from

the one usually considered in literature. This may indicate that the understanding of

this new phenomenon requires new physical and geometric interpretations that go beyond

the usual quantum Chern-Simons theory. I will also introduce recent progress in this

direction.

9. 许明，首都师范大学

Title：Geodesic and curvature of a piecewise flat Finsler surface

Abstract：This talk is based on my joint work with S. Deng. The idea was inspired from

lunch-chatting and dinner-chatting with Huibin Chang, Ju Tan and Lei Zhang respectively.

I would also like to sincerely thank Fuquan Fang and the referee of this paper for precise

advices. The purpose of this talk is to show how the combinatoric methods can be

introduced to the study of Finsler geometry. Firstly, I will introduce the concept of

piecewise flat Finsler surface. Secondly, I will show the local behavior of the

geodesics. Thirdly, I will define a (Riemannian type) curvature from the process of

extending geodesics. Lastly, I will define the notions of Berwald space and Landsberg

space in the piecewise flat context, and show a combinatoric Gauss-Bonnet formula.

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10. 陈立志，兰州大学

Title： Systolic volume and complexity of 3-manifolds

Abstract：The systolic volume is a topological invariant of manifolds, defined as the

optimal constant in a systolic inequality. It shows there are various relations between

systolic volume and other topological invariants. We investigate the relation between

systolic volume and complexity of 3-manifolds. The complexity of a closed 3-manifold

is defined to be the minimum number of tetrahedron in a triangulation. We prove the

systolic volume of aspherical 3-manifolds can be upper bounds in terms of complexity.

11. 郭锂，罗格斯大学

Title：Conical zeta values and double subdivision

Abstract：Conical zeta values are special values of a class of multi-variable analytic

functions at integers points. They give a natural generalization of the well-known

multiple zeta values from a geometric viewpoint. We discuss multiple zeta values and

their double shuffle relations. We then generalize these relations to double

subdivision relations for conical zeta values. This is joint work with Sylvie Paycha

and Bin Zhang.

12. Sylvie Paycha，德国波兹坦大学

Title：An algebraic approach to locality: applications in geometry and renormalisation

schemes

Abstract：According to the principle of locality in physics, events taking place at

different locations should behave independently, a feature expected to be reflected

in the measurements. The talk will present an algebraic approach to this principle

transposed to a mathematical context. We will discuss how it relates to locality in

geometry and hint to how it can be used to evaluate a priori divergent multiple

integrals and sums in accordance with the locality principle. This talk, which is

related to Li Guo's presentation, is based on joint work with P. Clavier, Li Guo and

Bin Zhang.

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住宿及交通情况：

一、住宿信息

1. 下榻酒店：交大湖山宾馆。（注：百度地图上可以查到交大湖山宾馆的位置）

酒店地址：四川省峨眉山市黄湾乡西南交通大学峨眉校区内（近西南交大东门）

联系电话：0833-5198510

注意事项：1. 入住和离店：入住时间 14:00 以后，离店时间 12:00 以前。

2. 宠物：不可携带宠物。

2. 下榻酒店：峨眉山大酒店（2 号楼）。

酒店地址：峨眉山市报国寺景区路二段 322 号 ，近峨眉山山门口。

联系电话： 0833-5526888

3. 周边的其他酒店：如红珠山宾馆、途家酒店、秀湖度假大酒店、青庐等等。

二、交通信息

1. 第一种方式：乘坐飞机到成都双流机场（国内航班只有川航在 T1 航站楼，其它航班在

T2 航站楼）；在成都双流机场 T2 航站楼乘坐城际高铁到达峨眉山站（注意：峨眉山站与

峨眉站是两个不同车站，相距约 7 公里，高铁只到达峨眉山站），全程大约 1 小时 20 分

钟，二等座票 68 元，到达峨眉山站（又称峨眉山高铁站）后，可以打车至交大湖山宾馆（车

程应该 5 分钟之内），也可以步行（大约 15-20 分钟），也可以坐 12 路公交车到峨眉山旅

游车站（或报国寺站）下，步行至宾馆。从双流机场站到峨眉山站最后一班城铁 C6315 是

20:23 分到达双流机场站 20:25 分从双流机场站出发。

2. 第二种方式：如果从成都市里出发，在成都东站（或成都南站）乘坐城际高铁到峨眉山

站，打车或步行至交大湖山宾馆即可。

3. 第三种方式：在成都双流机场乘坐 304 路机场大巴（15 元/人）进入得成都市区岷山饭

店后，再打出租车（8 元左右）到成都新南门旅游客运中心，或直接打车到成都新南门旅

游客运中心（50 元左右），然后乘坐成都—峨眉的大巴车（45 元/人），前后大约花 4 个

小时到达峨眉山市区的峨眉山报国寺旅游客运中心。从报国寺旅游客运中心打车或步行至

交大湖山宾馆即可。另外，成都新南门旅游客运中心每天发往峨眉的班车时间 07：15—18：

10 ，每隔 20 分钟一班 ， 全程 2 个小时，终点站有两个：一个是峨眉山市客运中心（票

价 40 元），另外一个是峨眉山报国寺旅游客运中心（票价 43 元）。除此之外，新南门车

站还有到达乐山、峨眉的桑塔纳轿车 65 元/人，坐满 4 人就走。

注备：如果遇到飞机晚点等特殊情况，错过当天高铁和汽车最后一班车，建议在成都住下，

坐第二天早上的高铁或大巴即可，这时记住若坐高铁提前买高铁票，若坐汽车可以到了成

都新南门旅游客运中心后再买票。

此时如果有任何问题，可以电话联系会务组成员：李晓斌：13880423473。

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Notebook

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Notebook

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Notebook

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从峨眉山高铁站到交大湖山宾馆

西南交通大学峨眉校区第五会议室位于主楼二层