Steven Sam (Fall 2017):

This course will be an introduction to representation stability, a young growing field. An exposition of this area can be found here: https://arxiv.org/abs/1404.4065

A list of topics to be covered include:

- Representation theory of the symmetric group and general linear group
- Twisted commutative algebras and FI-modules
- Noetherian properties for functor categories
- Applications and examples in algebraic geometry, topology, representation theory, combinatorics

I will cover some open problems in the area as we go. A knowledge of algebraic geometry and/or topology will be useful to appreciate some of the applications, though it won't be strictly necessary if you're willing to take some theorems for granted.

There will be little overlap with the course Math 740 offered in Spring 2017. There is no textbook on the subject. Instead, I will keep a set of notes for the course and offer some references to the literature.