Instructor
Prof. Marco Varisco,
[email protected],
albany.edu/~mv312143
Office: ES-120B,
Office Hours: MWF 9:10–10:00, or by appointment.
Schedule
MW 4:15–5:35 in ES-153.
Prerequisites
AMAT 520 & 540, or permission of instructor. (See the University’s Graduate Bulletin.)
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 online for about $20, is an excellent reference:
- J. Frank Adams, Lectures on Lie Groups, University of Chicago Press, 1969 (reprint 1982).
Grading
Weekly homework assignments.
You are expected to attend all class meetings. The maximum number of absences permitted to receive credit for this course is 5 (five). Excessive tardiness may count as absence.
New York State Education Law (Section 224-A) requires campuses to excuse, without penalty, individual students absent because of religious beliefs, and to provide equivalent opportunities for make-up examinations, study, or work requirements missed because of such absences. I will work directly with you to accommodate religious observances, provided that you notify me in a timely manner.
Reasonable accommodations will be provided for students with documented physical, sensory, systemic, medical, cognitive, learning, and mental health (psychiatric) disabilities. If you believe you have a disability requiring accommodation in this class, please notify the Disability Resource Center ([email protected]). Upon verification and after the registration process is complete, the DRC will provide you with a letter that informs me that you are a student with a disability registered with the DRC and lists the recommended reasonable accommodations.
Of course, you are expected to follow the University’s Standards of Academic Integrity and Medical Excuse Policies. We refer to the Graduate Bulletin for the policies on incomplete grades.