855 Evans Hall, office hours MWF 11-12 or by appointment.
The spring semester should be of interest to a variety of students with some prior knowledge of Lie groups and Lie algebras, not limited to those continuing from 261A this past fall.
The official but not really necessary prerequisite for this course is Math 214 (Differential Geometry). In practice a strong general background in basic algebra and topology is sufficient for 261A, and 261A or equivalent is sufficient for 261B.
We will use Vardarajan in the spring semester for structure of reductive and compact Lie groups and their representations. All material on other topics will be presented in the lectures.
Introduction to differential geometry:
General references on Lie groups and algebras:
Algebraic groups and related topics
The first portion completes the foundational material we began in the fall and can serve as review for students joining the course this spring:
After that:
Other possible topics, depending on time: algebraic groups over Z and finite Chevalley groups; Hecke algebras and Kazhdan-Lusztig theory.
For a grade of A, you should do about half of the homework problems, including some of the more challenging ones; or proportionally fewer for a lower passing grade.
Alternatively, you can earn a grade of A by studying any open research problem connected to the subject matter. You don't have to solve the problem, but should make a serious attempt to understand it and work out some special cases.
TBA