MWF 12:35–1:30 in ES-153.
AMAT 520 & 540, or permission of instructor.
Lie groups (i.e., groups that are also smooth manifolds, in such a way that the groups operations are smooth maps) provide the best-developed theory of continuous symmetries of mathematical objects and structures, making them indispensable tools for many parts of contemporary mathematics and modern theoretical physics (Wikipedia).
In this course, which will be driven by a variety of examples, we will learn the fundamental definitions and structure theorems of Lie groups, and then study and classify their representations. The interplay between topology, geometry, algebra, and analysis, which is at the core of the subject, makes Lie group theory fascinating and instructive.
None — but the following book, which can be bought on Amazon.com for less than $20, is an excellent reference:
- J. Frank Adams, Lectures on Lie Groups, University of Chicago Press, 1969 (reprint 1982).
Biweekly homework assignments.