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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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