Invited speakers:

Participants:

Title：Topology and geometry of submanifolds from duality viewpoint

Speaker: Liang Chen, Northeast Normal University 

Abstract：Singularity and degeneracy destroy the structure of manifolds and give rise to essential difficulties in researching the deteriorative manifolds. Thus, it is crucial to develop new methods for investigating the singular or degenerate submanifolds. By characterizing the inner connection between pseudo spheres in semi-Euclidean space, the Legendrian duality is an effective method developed by Chen and Izumiya in 2009 for studying the submanifolds in non-flat space. Specially, the Legendrian duality is applicable for studying the singular or degenerate submanifolds. In this talk, using the singularity theory of mappings, we investigate the geometrical properties of the (singular or degenerate) submanifolds immersed in non-flat space from the viewpoint of duality. The part results in this talk is a joint work with Haibo Yu.

Title: Cablings, Homotopy Groups, and A Question on Virtual Braid Groups

Speaker: Jie Wu, Hebei Normal University

Abstract: In this talk, we will discuss the homotopy aspects of braid groups. In the first section, we will give a review on the classical connections between braids and homotopy theory. Then we talk the connections between Brunnian braids and homotopy groups in the second section. In the last section, we will discuss the theory of classical and virtual Brunnian braids.

Title: On links with Khovanov homology of small rank

Speakers: Yi Xie, BICMR

         Abstract: In this talk I will discuss a classification result on the links whose Khovanov homology has rank no greater than 8, where the coefficient ring is Z/2. Moreover, I will show that Khovanov homology detects all links in the Thistlethwaite Link Table whose Khovanov homology has rank no greater than 12. This is joint work with Zhenkun Li and Boyu Zhang.

Title：Distinguishing 4-dimensional geometries via  profinite completions

Speaker: Jiming Ma,Fudan University

    Abstract：It is well-known that there are 19 classes of geometries for 4-dimensional manifolds in the sense of Thurston. We could ask that to what extent the information is revealed by the profinite completion of the fundamental group  of a closed  smooth geometric 4-manifold. In this paper, we show that the geometry of a 4-manifold in the sense of Thurston could be detected by the profinite completion of its fundamental group except for geometries $ \mathbb{H}^{4}$, $\mathbb{H}^{2}_{\mathbb{C}}$ and $\mathbb{H}^2 \times \mathbb{H}^2$. Moreover, despite the fact that not every smooth 4-manifold could admit one geometry in the sense of Thurston, some closed orientable 4-dimensional Seifert manifolds with general fibre $T^2$ are associated with one. For a Seifert 4-manifold $M$, we show that whether $M$ is geometric could be detected by the profinite completion of its fundamental group. This is joint work with Zixi Wang.

Title: Optimal lower bounds for first eigenvalues of Riemann surfaces for large genus

Speaker: Yunhui Wu, Tsinghua  University

   Abstract: In this article we study the first eigenvalues of closed hyperbolic surfaces for large genus. We show that for every closed hyperbolic surface $X_g$ of genus $g$ $(g\geq 2)$, the first eigenvalue of $X_g$ is greater than $\frac{L_1(X_g)}{g^2}$ up to a uniform positive constant multiplication. Where $L_1(X_g)$ is the shortest length of simple closed multi-geodesics separating $X_g$. Moreover,we also show that this new lower bound is optimal as $g \to \infty$. This is a joint work with Yuhao Xue.

Title: Some recent progress of virtual knots

Speaker:Zhiyun Cheng, Beijing Normal University

    Abstract: Virtual knot theory studies the embeddings of S^1 in thickened surfaces up to stable equivalence, which can be regarded as a generalization of classical knot theory. In this talk, I will briefly discuss some recent virtual knots invariants derived from chord index.

Title: Croke-Kleiner admissible groups: Property (QT) and quasiconvexity

Speaker:Wenyuan Yang, Peking University

     Abstract: Croke-Kleiner admissible groups firstly introduced by Croke-Kleiner belong to a particular class of graph of groups which generalize fundamental groups of 3--dimensional graph manifolds. In this talk, we will present a characterization of strongly quasiconvex subgroups by the finiteness of height in a CKA group.  With further assumption on the vertex groups, we show that a CKA group satisfies a property (QT) introduced by Bestvina-Bromberg-Fujiwara that the group admits an equivariant quasi-isometric embedding into a finite product of quasi-trees. This is a joint work with Hoang Nguyen.

Title: Extending periodic maps on surfaces over 4-sphere

Speaker: Wang Shicheng, Peking University

    Abstract: Let $F_g$ be the closed orientable surface of gunus $g$, and $w_g$ be a periodical map of the maximum order on $F_g$. We show that (1) for each $g$, $w_g$ is periodically extendable over $S^4$ for some non-smooth embedding $e: F_g\to S^4$, and not periodically extendable over $S^4$ for any smooth embedding $e: F_g\to S^4$. (2) for $g=4k+1, 4k+2$, $w_g$ is not extendable over $S^4$ for any smooth embedding  $e: F_g\to S^4$; and for $g=4k, 4k+3$, $w_g$ is extendable over $S^4$ for some smooth embedding $e: F_g\to S^4$ .

This is a joint work with Wang Zhongzi.

We thank Ding Fang, Liu Yi and Wang Chao for mathematics they taught us. 

Title: A presentation of the fundamental groups of three manifolds from certain braid group actions

Speaker: Zhi Chen, Hefei University of Technology

     Abstract: There is a way to present the knot groups from the natural action of braid groups on free groups. We give a very similar way to presenting the fundamental groups of three manifolds, by using another action of the braid groups. Possibly we also investigate applications of that presentation.

Title: On the structure of the Kauffman bracket skein algebras of planar surfaces

Speaker: Haimiao Chen, Beijing Technology and Business University

    Abstract:Let R be a ring containing an invertible element A. For a sur-face Σ, its Kauffman bracket skein algebra S(Σ; R) is the R-module generated by framed links L in Σ × [0, 1], modulo some local relation-s; the multiplication L1 · L2 is defined by stacking L1 over L2. For each n ≥ 5, we give a presentation for S(Σ0,n; Q(A)) by generators and relations. When g ≥ 1, some partial results on the structure of S(Σg,n; Q(A)) are obtained.

Title:Fixed Points of G-CW-complex with Prescribed Homotopy Type
Speaker:Min Yan, Sustech

   Abstract:Suppose G is a finite group, and f is a map from a finite CW-complex F to the fixed point set of a finite G-CW-complex Y. Is it possible to extend F to become the fixed point set of a finite G-CW-complex X, and extend f to become a G-map from X to Y, such that g is a homotopy equivalence after forgetting the G-action? In the problem, Y is the prescribed homotopy type of the desired G-CW-complex X.
For the case Y is a point, the problem becomes the fixed point set of contractible G-CW complex. In 1942, Smith gave the necessary homological condition for the fixed point set. In 1971, for semi-free actions by cyclic groups, Jones proved the sufficiency of Smith condition. In 1975, for actions by groups of not prime power order, Oliver gave necessary and sufficient condition in terms of the Euler characteristic of the fixed set.  We extend these classical theories to general Y, and also give some examples.

Stavros Garoufalidis (ICM SUSTech)

Ingrid Irmer              (ICM SUSTech)

Yi Liu                         (BICMR)

Jiping Zhang             (ICM SUSTech)

SUSTech International Center for Mathematics

SUSTech Mathematics Department 

Friday 13th of November

8:00-8:30     Registration

8:30-8:40     Welcome Speech

8:40-9:40     Shicheng Wang   

Extending periodic maps on surfaces over 4-sphere

9:40-10:40    Min Yan              

Fixed Points of G-CW-complex with prescribed homotopy type

10:40-11:00  Tea Break

11:00-12:00  Yang Jingling                                         

Distance one surgeries on the lens space L(p, 1) and band surgeries on the torus knot T(2,p)  

12:00-14:00  Lunch

14:00-15:00  Jiming Ma         

Distinguishing 4-dimensional geometries via profinite completions

15:00-15:20  Tea Break

15:20-16:20  Yunhui Wu        

Optimal lower bounds for first eigenvalues of Riemann surfaces for large genus

16:20-17:20 Zhi Chen            

A presentation of the fundamental groups of three manifolds from certain braid group actions

Saturday 14th of November

8:30-9:30 Yifei Zhu         

Generalized modular forms in topology

9:30-10:30 Jie Wu           

Cablings, homotopy groups, and a question on virtual braid groups

10:30-11:00  Conference photo +Tea break

11:00-12:00  Haimiao Chen   

On the structure of the Kauffman bracket skein algebras of planar surfaces

12:00-14:00  Lunch

14:00-15:00  Yi Xie         

On links with Khovanov homology of small rank

15:00-16:00  Zhiyun Cheng   

Some recent progress of virtual knots

16:00-17:00  Liang Chen        

Topology and geometry of submanifolds from duality viewpoint

18:00  Conference Dinner

Sunday 15th of November

8:30-9:30 Yin Tian          

The Drinfeld center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory

9:30-10:30 Wenyuan Yang      

Croke-Kleiner admissible groups: Property (QT) and quasiconvexity

10:30-11:00  Tea Break

11:00 -12:00 Yi Liu                 

To be announced

Address: 201 Jinqizhigu Building, No.1 Tangling Road, Nanshan District, Shenzhen City, Guangdong Province.

(Please take lift No. 5 or 6（low-rise）to the 2nd floor)

Postcode: 518055

Tel: 26920864-8027

By Metro: Tanglang Station (Exit D), follow Liuxian Avenue (westbound) to Tangling Road (about 900 metres), then turn right

By Bus: Tanglang Depot North Station, Line M554, M343

Please send an email to Ms Zheng Jiayi  zhengjy@mail.sustech.edu.cn 

  There are funds available for graduate students and postdocs to attend.

   Please email your CV to Ms Zheng Jiayi zhengjy@mail.sustech.edu.cn to apply.

Jiayi Zheng (SUSTech):zhengjy@mail.sustech.edu.cn