Moduli Spaces in Representation Theory - Math 797RM

Instructors: Chris Elliott and Owen Gwilliam

Course Description

This course will be a guided tour of moduli spaces that have played a central role in topology, differential geometry, and representation theory. The emphasis will be on explicit examples rather than theory.

The approach will be a hybrid between a lecture class and a seminar. For the first few weeks, we will give lectures laying foundations and introducing terminology. But we will also have you form small groups, focused around a common interest, in which you will read a key text (e.g., a paper by Atiyah) and work together to master it. In the latter part of the course, each group will give presentations, so you get a chance to practice speaking and so that we can all benefit from what your group has learned. We expect the class to be highly interactive and dynamic, and we will create a welcoming atmosphere to discuss confusions and to grow as mathematicians.

We will start out with the following:

Later topics may include:


Basic notions of differential geometry and algebra.

Possible Topics for Exploration

The following list of topics is only a suggestion, other topics that the participants are interested in are also welcome.


Chris Elliott:
Owen Gwilliam:

Last modified Wednesday October 28th, 2020.

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