会议地点: 中国科学技术大学五教5104
会议指定酒店: 悦雅江南春酒店(合肥中科大店)

日程安排：
10月25日周六
09:45-10:35 汪湜 
11:05-11:55 叶圣奎

14:00-14:50 何思奇
15:10-16:00 高悦
16:20-17:10 沈洋

10月26日周日
09:45-10:35 明爽
11:05-11:55 王志浩

汪湜
题目: On the Jacobian of the Douady-Earle extension
摘要: Given an isotopy class between two closed hyperbolic surfaces, there is a unique analytic diffeomorphism representative defined by Douady-Earle. We study the Jacobian of the Douady-Earle extension map F. We show that |Jac F|=1 if and only if F is an isometry. We also show that there exists a family of pairs of hyperbolic surfaces such that Jac F tends to infinity. We suspect that the function log|Jac F| should correspond to a certain distance function in the associated Teichmuller space.

叶圣奎
题目: Some questions related to free-by-cyclic groups and tubular groups
摘要: We prove that a CAT(0) free-by-cyclic tubular group with one vertex is virtually special, but many of them cannot virtually act freely and cocompactly on CAT(0) cube complexes. This partially confirms a question of Brady--Soroko and answers a question of Lyman in the negative. Furthermore, we provide examples of free-by-cyclic groups amalgamated along cyclic subgroups that are not virtually free-by-cyclic. This answers negatively a question of Hagen--Wise. Lastly, we exhibit an example of a cyclic-subgroup-separable tubular group that does not have the property (VRC) (i.e. every cyclic subgroup is a virtual retract). This answers a question of Minasyan in the negative. This is a joint work with Xiaolei Wu.

何思奇
题目: Quadratic Differentials and Non-Archimedean Representations of Surface Groups
摘要: Teichmüller space of a compact Riemann surface of genus at least two is closely related to quadratic differentials, measured foliations, and harmonic maps. Important works of Thurston, Hubbard-Masur, and Wolf built these connections. In this talk we study rank-two representations into a non-Archimedean local field and explain how they relate to measured foliations and Jenkins-Strebel differentials. This is joint work with J. Chen. 


高悦
题目：Asymptotics of shortest filling closed geodesics
摘要: We investigate the asymptotics of shortest filling closed multi-geodesics of closed hyperbolic surfaces as systole $\to 0$ or as genus $\to \infty$. We first show that for a closed hyperbolic surface $X_g$ of genus $g$, the length of a shortest filling closed multi-geodesic of $X_g$ is uniformly comparable to $$\left(g+\sum\limits_{\textit{closed geodesic }\gamma\subset X_g, \ \ell(\gamma)<1}\log \left(\frac{1}{\ell(\gamma)}\right)\right).$$ As an application, we show that as $g\to \infty$, a Weil-Petersson random hyperbolic surface has a shortest closed multi-geodesic of length uniformly comparable to $g$. We also show that this is true for a random hyperbolic surface in the Brooks-Makover model. This is a joint work with Yunhui Wu and Zhongzi Wang.  

沈洋
题目: Constructions of expander graphs and surfaces
摘要: In this talk, we will review some relative results of spectrums on graphs and hyperbolic surfaces, and introduce a new model of random graphs. Based on the study of such model, we constructed a sequence of non-compact hyperbolic surfaces with uniform positive spectral gaps. This is a joint work with Qi Guo and Bobo Hua.

明爽
题目: Turaev-Viro invariants from positive representations of quantum SL(2, R)
摘要: In this talk, I will introduce a Turaev-Viro type invariant for hyperbolic three manifolds with totally geodesic boundary. The invariant comes from the positive representations of quantum SL(2, R). I will also discuss the recent results on the asymptotic analysis of the invariant. This is joint work with Tianyue Liu, Xin Sun, Baojun Wu and Tian Yang.

王志浩
题目: The Frobenius maps of the stated SLn skein modules.
摘要: The stated SLn skein algebra can be viewed as a quantization of the coordinate ring of the SLn character variety. This topic lies at the intersection of several active areas of research, including quantum cluster algebras and higher Teichmüller theory.
First I will give an overview of the stated SLn skein module. Then I will discuss the Frobenius maps for stated SLn skein modules, which generalizes the classical Frobenius map for the quantum group Oq(SLn) to the setting of surfaces. Finally, I will show that the image of an oriented framed knot under the Frobenius map is obtained by threading the knot with a generalized SLn-version of the Chebyshev polynomial, which solves the Conjecture by Bonahon-Higgins.

会议组委会：孙哲、张影
会议联系人：唐慧 tanghui@mail.ustc.edu.cn