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.
These 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
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.
The program of the semester is structured around three workshops and one
final conference. Two or three colloquium-style Bernoulli lectures will
take place during the semester. In between the conferences, a small
number of scientists will be in residence at the CIB, thus providing the
opportunity for intensive collaborations.
Semester guest list