Spring 2021 MATH 257 001 LEC

Group Theory
001 LECTuTh 05:00PM - 06:29PMInternet/OnlineEdward Frenkel31320
UnitsEnrollment StatusSession
4Open2021 Spring, January 19 - May 07
Additional Information: 

Prerequisites 250A

Description We will start with the braid groups, an excellent case study for infinite discrete groups, which can be defined by generators and relations as well as geometrically, as fundamental (or mapping class) groups. Symmetric groups and Hecke algebras appear naturally from braid groups. As an application, we will discuss the Jones polynomial and its generalizations. After a brief survey of simple Lie groups, will look at groups from the Hopf algebra perspective and use it to go from groups to quantum groups. Next, the Tannakian formalism, which enables one to reconstruct an algebraic group from the tensor category of its representations. Time permitting, we will also discuss loop groups, affine Grassmannians, and the geometric Satake correspondence.


Office Hours 

Required Text

Recommended Reading  We will use these books, available electronically from Springer Link (via a UCB login):

Christian Kassel and Vladimir Turaev, Braid Groups, Springer GTM 247

Christian Kassel, Quantum Groups, Springer GTM 155

as well as other materials that will be made available by the instructor in due time.

Grading Letter grade.


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