Let G be a simply connected algebraic group over an algebraically closed field. A fundamental question in representation theory asks about the characters of the irreducible representations of G. When the base field is of characteristic p, Lusztig recently gave a reformulation of his conjecture from 1979 on the character formulas of irreducible G-representations. In my talk, I will first review this reformulation and give an introduction to Morava K-theory. I will then talk about a construction of quantum groups using the Morava K-theory, which provides a family of new quantum groups parametrized by a prime number and a positive integer. I will explain how those quantum groups are expected to be related to Lusztig’s conjecture

### About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics.

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

#### Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

- computer
- data projector
- chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.