Instructor
Prof. Marco Varisco,
[email protected],
www.albany.edu/~mv312143/
Office: ES-120C,
Office Hours: by appointment.
Schedule
MWF 12:35–1:30 in ES-153.
Prerequisites
AMAT 520 & 540, or permission of instructor.
Description
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.
Textbook
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).
Grading
Biweekly homework assignments.