Math 683 (Spring 2011)

Instructor: Ben Webster
Office: 151 Susan Campbell Hall
Office Hours: T 1-2, W 10-11, R 2-3
Class times: Monday, Wednesday, Friday, 11am-12pm.

For basic information about the course, see the course syllabus.

Since students will have to write a paper for the course, here's a list of suggested topics.

Class Schedule

March 28: Smooth manifolds, vectors on manifolds. Optional reading: Bump, Chapter 6

March 30: Derivations, vector fields and flows. Optional reading: Bump, Chapter 6

April 1: Lie brackets of vector fields, commutators of flows. Lie algebras of Lie groups. Optional reading: Bump, Chapter 7,8

April 4: Lie algebras and Lie groups, examples, the Campbell-Baker-Hausdorff formula. Optional reading: Bump, Chapter 5

April 6: Uniqueness of Lie groups for Lie algebras, universal covers. Optional reading: Bump, Chapter 13

April 8: Fundamental groups of classical groups. Optional reading: Bump, Chapter 13

April 11: Fundamental groups and weight lattices.

April 13: The Weyl group and normalizers of tori.

April 15: Uniqueness of Cartans and Borels.

April 18: Compact groups, Peter-Weyl. Optional reading: Bump, Chapters 1-4

April 20: Compact Lie groups and Cartan involutions.

April 22: Uniqueness of compact forms, split forms.

May 9: Borel-Weil theorem.

May 11: Borel presentation of cohomology of G/B.