1st – 3rd April 2019

Organised in collaboration with the School of Mathematics, University of Bristol, UK

Geordie Williamson is a world-leading researcher in geometric representation theory. His groundbreaking work includes the development of Hodge theory for Soergel bimodules and a proof of the Kazhdan-Lusztig conjectures for general Coxeter groups. He is also well known for his spectacular counterexamples to conjectures of Lusztig and James, which have opened up entirely new directions for research.

He is the recipient of numerous awards, including the inaugural Chevalley Prize of the American Mathematical Society, the EMS Prize, a Clay Research Award (all in 2016) and the New Horizons in Mathematics Prize in 2017. Last year he was elected a Fellow of the Royal Society (aged 36, he is the youngest living member of the society) and he was a plenary speaker at the International Congress of Mathematicians in Rio de Janeiro. I can also add that he is an outstanding speaker!

Geordie Williamson, University of Sydney, Australia

Lecture 1 (Colloquium style)

Semi-Simplicity in Representation Theory

Representation theory is the study of linear symmetry. Since the first papers on the representation theory of finite groups by Frobenius at the end of the 19th century, the theory has grown to form a fundamental tool of modern pure mathematics, with applications ranging from the standard model in particle physics to the Langlands program in number theory. Some of the most important theorems in representation theory assert some form of semi-simplicity. Examples include Maschke’s theorem on representations of finite groups over the complex numbers (proved in 1897), Weyl’s theorem on representations of compact Lie groups (proved in 1930), and the Kazhdan-Lusztig conjecture (proved by Beilinson-Bernstein and Brylinski-Kashiwara in 1980). The lectures will provide an introduction to these ideas, with an emphasis on our attempts to uncover further layers of hidden semi-simplicity.

Lecture 2 | slides in pdf

Representation Theory and Geometry

Lecture 3 | slides in pdf

Representation Theory and Geometry