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Updates:

July 27, 2007:
Updated Notes

Oct 2, 2008:
Added Talk Section

Sept 14, 2008:
Updated Fall 2008 Courses

Aug 28, 2008:
Added Fall 2008 Courses

Aug 05, 2008:
New Format For Website

Course Notes

What follows are course notes for some classes I have taken at the University of Michigan. Let me just say that these are all in various states of completeness. I make no assertion that these are error free. However, if you notice typos, feel free to email me corrections.

Math 612 - Lie Algebras (Last Updated: 7/27/2009)
This course given by Professor Gopal Prasad in the Fall of 2008 covers the standard theory of finite dimensional Lie Algebras with full proofs. The course culminates in classification of complex semi-simple Lie algebras in terms of their root systems. Their finite dimensional representations are also studied.

Math 637 - Lie Groups (Last Updated: 7/11/2008)
This course given by Professor Gopal Prasad in the Winter of 2008 is a comprehensive introduction to the theory of Lie groups. This course proves the basic results and describe the structure of abelian, nilpotent, and solvable Lie groups. It then present results on tori in compact Lie groups and use them to describe their topological and group-theoretic structure and their classification. The course finishes with the study noncompact semi-simple Lie groups in considerable detail by looking at their maximal compact subgroups, proving their conjugacy, and ending with a proof of the Cartan, Iwasawa decompositions.

Talks

What follows are the outlines of talks that I have given at the University of Michigan.

An Introduction to Cohomology Operations (Given Sept. 26, 2008)
Mosher and Tangora describe cohomology operations as a "technique for supplementing and enriching the algebraic structure of the cohomology ring." This talk will be the first of three on cohomology operations and their applications to homotopy theory. We will begin by introducing the notions of a cohomology ring and cohomology operations. Due to the representability of cohomology, these operations are fundamentally related to Eilenberg-MacLane spaces. We will conclude by exploring the correspondence between cohomology operations of a certain type and the cohomology of Eilenberg-MacLane spaces.