Knizhnik-Zamolodchikov equations
I will give a self-contained exposition of the theory of KZ equations and related topics. I want to focus on the geometry hidden behind solutions of KZ equations, e.g. local systems associated with KZ, the Gauss-Manin connections, monodromy representations of braid groups from KZ. I will also go to the algebra part such as Drinfeid-Kohno theorem which explains the relation between the monodromy representations and the one from quantum groups. I also hope to talk about the current developments.
Lecturer
Date
14th March ~ 4th July, 2022
Website
Prerequisite
representation theory of simple Lie algebra, basic knowledge of differential geometry and algebraic topology.
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Xinxing Tang, received a bachelor's degree in basic mathematics from the School of Mathematics, Sichuan University in 2013, and received a doctorate from Beijing International Center for Mathematical Research, Peking University in 2018. From 2018 to 2021, she worked as a postdoctoral fellow at the Yau Mathematical Sciences Center, Tsinghua University, and joined Beijing Institute of Mathematical Sciences and Applications in 2021 as assistant professor. Research interests include: integrable systems, especially infinite-dimensional integrable systems that appear in GW theory and LG theory, and are interested in understanding the algebraic structure of infinite symmetries and related calculations. Other interests include: mixed Hodge structures, isomonodromic deformation theory, KZ equations.