李琼玲（南开大学）：Higgs bundles and minimal surfaces in non-compact symmetric spaces
助教：陈家煌
课程摘要：The non-Abelian Hodge correspondence relates polystable Higgs bundles over a Riemann surface with reductive representations from the surface group. The correspondence is through looking for harmonic metrics on Higgs bundles, making it harmonic bundle. Conformal harmonic bundles over a Riemann surface X correspond to equivariant minimal branched immersion from the universal cover of X to the symmetric space associated to GL(n,C). In this minicourse, we will explain the non-Abelian Hodge correspondence, and focus on studies related to equivariant minimal surfaces in non-compact symmetric spaces.
Part I: An introduction to the non-Abelian Hodge correspondence
Part III: Various examples of minimal surfaces in non-compact symmetric space
Part III: Anosov representations and Labourie's conjecture
Part IV: Morse index and total curvature of minimal surfaces.
田垠（北京师范大学）：Topological quantum field theory and Khovanov homology
助教：雷子逸
课程摘要：
Lecture 1. Jones and quantum group
Lecture 2. Topological quantum field theory and Khovanov homology (Kh)
Lecture 3. Categorified quantum group
Lecture 4. Application of Kh, symplectic Kh.
吴惟为（浙江大学）：The symplectomorphism groups of 4-manifolds
助教：丁岩峭
课程摘要：
1. The symplectomorphism group of S^2 x S^2
2. Towards rational surfaces: ball-packings and symplectic genus
3. Ball-swappings and uniqueness of Lagrangian spheres
4. Kronheimer-McDuff's trick, the deformation of symplectomorphism groups
杨文元（北京国际数学研究中心）：Groups acting on hyperbolic spaces
助教：杨朝栋
课程摘要：通过双曲空间上等距群作用来研究离散群的几何和代数性质是几何群论中一个重要研究方向。本课程将首先介绍Gromov双曲空间的基本概念和理论，然后研究这类空间上的几何作用即双曲群，以及几何有限作用即相对双曲群这两大类负曲率群。这两类群的代表例子分别是负截面曲率的闭黎曼流形和体积有限黎曼流形的基本群。最后，我们将介绍更广的一类双曲空间上群作用称为无柱双曲群，这类群研究的驱动例子是曲面映射类群和自由群的外自同构群。熟悉经典2维和3维双曲几何将会对本课程内容理解更有助益。
第一次课：Gromov双曲空间基本理论
第二次课：Milnor-Svarc引理和双曲群
第三次课：相对双曲群及例子
第四次课：无柱双曲群概念及前沿介绍
周正一（中科院数学所）：Intersection theory of punctured holomorphic curves and planar open books
助教：杜利特
课程摘要：Using Wendl's theorem on planar open book as an example, we will introduce Siefring’s intersection theory for punctured holomorphic curves.
Lecture 1: Open books, symplectic Lefschetz fibrations, Wendl’s theorem on planar open books and its applications in symplectic fillings.
Lecture 2-3: Siefring’s intersection theory for punctured holomorphic curves.
Lecture 4: Proof of Wendl’s theorem.