1. Holomorphic quadratic differentials and Teichmüller theory

主讲人： 苏伟旭（中山大学）

课程介绍：主要围绕黎曼面上的全纯二次微分，介绍Teichmüller空间的构造及其复几何；介绍全纯二次微分的轨线结构和分解定理；介绍Teichmüller测地流在全纯二次微分研究中的应用；介绍全纯二次微分和调和映照的联系。

参考文献：

[1] Hubbard. Teichmüller theory and applications to geometry, topology, and dynamics. Matrix Editions, 2016.

[2] Kerckhoff, Masur, Smillie. Ergodicity of billiard flows and quadratic differentials. Annals of Mathematics, 1986, 124(2): 293-311.

[3] Strebel. Quadratic differentials. Springer Berlin Heidelberg, 1984.

[4] Wolf. The Teichmüller theory of harmonic maps. Journal of differential geometry, 1989, 29(2): 449-479.

主讲人简介：苏伟旭，中山大学教授。苏伟旭2011年在中山大学获得博士学位，之后在复旦大学工作，2022年8月至今在中山大学工作。他的研究领域是Teichmüller空间理论，部分成果发表在Math Ann., Adv. Math. 等著名期刊。

2. Quantum Invariants and the Volume Conjecture

主讲人：杨田（Texas A&M University）

课程介绍：In this series of lectures, I will introduce several quantum invariants of knots/links and 3-manifolds, and their relationship with hyperbolic geometry. In particular, I will talk about the Jones and colored Jones polynomials of knots and links in the 3-sphere, and the Reshetikin-Turaev and the Turaev-Viro invariants of 3-manifolds. The Volume Conjectures for these invariants will also be discussed.

参考文献：

[1] C. Blanchet, N. Habegger, G. Masbaum and, P. Vogel, Three-manifold invariants derived from the Kauffman bracket. Topology 31 (1992), no. 4, 685–699.

[2] W. B. R. Lickorish, The skein method for three-manifold invariants. J. Knot Theory Ramifications 2 (1993), no. 2, 171–194.

[3] N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and theirinvariants derived from quantum groups. Comm. Math. Phys. 127 (1990), no. 1, 1–26.

[4] N. Yu. Reshetikhin and V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), no. 3, 547–597.

[5] V. G. Turaev and O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j -symbols. Topology 31 (1992), no. 4, 865–902.

[6] Q. Chen and T. Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev– Viro invariants. Quantum Topol. 9 (2018), no. 3, 419–460.

主讲人简介：杨田，美国德克萨斯农工大学副教授，博士毕业于罗格斯大学，并曾在斯坦福大学担任博士后。他主要专注于几何拓扑和量子拓扑的理论研究，研究成果发表于Journal of Differential Geometry， Geometry & Topology，Communications in Mathematical Physics, Advances in Mathematics 等一系列国际高水平杂志上。