Current trends in representation theory of finite groups

The objectives of the program are to give talks by experts dealing with recent important trends in representation theory of finite groups. Some examples of these trends are the following: 1. Work of Rickard, Okuyama and others dealing with applications of derived categories to representation theory; in particular, work toward Broue's conjectures on blocks with abelian defect groups. In the case of finite groups of Lie type, there are connections between the complexes providing derived equivalence and braid groups actions on Deligne- Lusztig varieties, leading to "cyclotomic Hecke algebras". 2. Recent work of Ariki, Grojnowski, and others which connects representation theory of Iwahori-Hecke algebras at roots of unity with representation theory of affine Kac-Moody Lie algebras. This is related to representations of symmetric groups and perhaps other finite Coxeter groups. 3. Continued work, especially by G. Robinson, on Alperin's conjecture. There is also work dealing with stronger conjectures of Dade. This could explain some of Brauer's problems. 4. Work of Broue-Malle-Michel and Shoji on character-like functions coming from complex reflection groups. 5. Applications of representation theory and cohomology of finite groups to topology, especially by Benson, Carlson, and Adem.

Confirmed Participants

Videos

Final Report (PDF)