课程名称：Title: Undergraduate Student Seminar - Categorification and TQFT
授 课 人：田垠 教授 北京师范大学
课程时间：2022年8月11-17日 14:00 - 16:00
课程地点：腾讯会议 ID：722-8452-0851; PW: 220726
校内联系人：王骁 wangxiaotop@jlu.edu.cn
课程安排：
1.2022年8月11日 14:00 - 16:00，The Jones polynomial and 3D TQFT.
We give an introduction to the Jones polynomial from algebraic and topological perspectives. We also explain the idea of a generalization to 3-manifold invariants, Witten-Reshetikhin-Turaev invariant.
2. 2022年8月13日 14:00 - 16:00，Khovanov homology, a categorification of the Jones polynomial.
We introduce a celebrated example of categorification, Khovanov homology, as a categorification of the Jones polynomial. As an application, we explain Rasmussen's combinatorial proof of the Milnor conjecture.
3.2022年8月15日 14:00 - 16:00， Soergel bimodules and Khovanov-Rozansky homology
We introduce a generalization of Khovanov homology as a categorification of the HOMFLY-PT polynomial. It is closely related to Hecke algebras and its categorification.
4. 2022年8月17日 14:00 - 16:00，Quantum groups and categorification
We discuss the representation theory of quantum groups behind the link invariants. We also explain the categorified quantum group based on the notion of canonical bases.
授课人简介：田垠，2014博士毕业于美国南加州大学，现就职于北京师范大学。研究方向为低维拓扑、范畴化、辛几何。在Geom. Topol.，Int. Math. Res. Notices，J. Symplectic Geom. ，Advances in Mathematics，Quantum Topology，JOURNAL OF ALGEBRA等杂志发表学术文章。
