課程名稱：Title: Undergraduate Student Seminar - Categorification and TQFT
授 課 人：田垠 教授 北京師範大學
課程時間：2022年8月11-17日 14:00 - 16:00
課程地點：騰訊會議 ID：722-8452-0851; PW: 220726
校内聯系人：王骁 wangxiaotop@jlu.edu.cn
課程安排：
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.
授課人簡介：田垠，2014博士畢業于美國南加州大學，現就職于北京師範大學。研究方向為低維拓撲、範疇化、辛幾何。在Geom. Topol.，Int. Math. Res. Notices，J. Symplectic Geom. ，Advances in Mathematics，Quantum Topology，JOURNAL OF ALGEBRA等雜志發表學術文章。
