Winter Quarter 2003

Tuesdays and Thursdays, 4:40 - 6:00

203 Wellman Hall

Title: From Frobenius to Witten, through Representation of Finite Groups

Lecture notes in .pdf (updated on 2/12/03)

Character Table of the Symmetric Group of Four Letters by Ron Mayer in PDF format

The Two Fundamental Theorems of Invariant Theory by Maya Ahmed in PDF format

Group Theory in Physics by Kramer Akli

Topics to be discussed: Representation theory and character theory of finite groups. If time permits, we may discuss compact Lie groups, too.

Suggested Textbook: None. I hope to produce lecture notes, something similar to the one I did for 280 in 2001, but at this moment let me make no firm promise yet!

Optional Reading: Young Tableaux: with applications to representation theory and geometry, by William Fulton, Cambridge University Press (Paperback, $26). Although this book is assigned, I don't intend to use it at all.

Prerequisite: AB/BS in Mathematics. Thus our 149AB or 150AB or equivalent are required. Undergraduate students who have completed 150AB are welcome!

Course Description: Various aspects of finite groups appear in many curricula used in K-12, but they often fail to explain the true motivation of doing so. We want to discover our own motivation: why representation of finite groups now?

The representation theory of finite groups is an ideal tool to connect historical developments of algebra in the 19th century with modern topology and mathematical physics of the 21st century. I will lecture everything you need to know about the representation theory that I think important (very subjective view, of course) and aim the course at a goal where the audience can appreciate some of the recent developments in topology and mathematical physics.

Grading: A letter grade will be assigned to those who take the course for credit. A student must give a 30-minute presentation on the subject for credit. If you are enrolled as an M.A.T. student, then the topic of your presentation can be anything that is related to algebra, not restricted to the topics of the course.

Let's have fun!