Local Representation Theory and Simple Groups

Local representation theory, pioneered by Richard Brauer in the 1930s had its first big successes in the classification of the finite simple groups. Since then, important and deep connections to areas as varied as topology, geometry, Lie theory and homological algebra have been discovered and used. Very recent breakthrough results have now led to the hope that some of the long standing and deep problems, some of which have been open for over five decades, can finally be settled.

Recent results relied crucially on the interplay between the theory of modular representations, the classification of finite simple groups, and Lusztig's powerful geometric machinery built around the Weil conjectures which describes the representation theory of finite reductive groups. At the same time, this has led to a wealth of interesting new questions on finite simple groups and their representation theory, whose solution promises to be useful for many further applications.  The main theme of the programme will be to exploit further this interaction with the aim of eventually solving some of the famous open conjectures, and further developing and applying the representation theory of finite simple groups.

Professor Pham Huu Tiep has been appointed as a Clay Senior Scholar from October to December 2016 to participate in this program.