Mini-Conference "Representations of finite reductive groups"

Mini-Conference "Representations of finite reductive groups"

Dates: 11th-12th February 2014

Location: TU Kaiserslautern

Organiser: Britta Späth

All talks take place in 48-538. During the breaks there should be some coffee and tea in 48-436 on Tuesday and in 48-519 on Wednesday.

Program:

Tuesday

14:00 - 15:15 Geordie Williamson: Counter-examples to some conjectures in modular representation theory

16:30 - 17:20 Gunter Malle: Local-global conjectures: Recent progress and open questions

17:25 - 18:15 Marc Cabanes: Towards the inductive Alperin-McKay condition for simple groups of type $\mathrm A$

Wednesday

9:00 - 10:15 Sascha Orlik: The cohomology of Deligne-Lusztig varieties for the general linear group

11:00 - 11:50 Michael Livesey: Rouquier blocks for finite unitary groups at unitary primes

13:40 - 14:30 Olivier Brunat: On defining characteristic representations of finite reductive groups

Talks:

Marc Cabanes: Towards the inductive Alperin-McKay condition for simple groups of type $\mathrm A$
Building on former work on the inductive McKay conditions for the special linear and special unitary groups over finite fields one can verify the more involved requirements of the inductive Alperin-McKay conditions for blocks of those groups with maximal defect. In the end I point out the difficulties in generalizing this result to other blocks. This is joint work with B. Späth.

Michael Livesey: Rouquier blocks for finite unitary groups at unitary primes
Rouquier blocks were important in proving Broue's abelian defect group conjecture for symmetric groups and finite general linear groups. We attempt to find an analogue in the case of finite unitary groups at unitary primes.

Gunter Malle: Local-global conjectures: Recent progress and open questions
In the last few years, several counting conjectures in finite group representation theory as well as Brauer's height zero conjecture have been reduced to questions on finite quasi-simple groups. In our survey talk we will present the current state of affairs in the verification of these inductive conditions and discuss the obstacles which have still to be overcome on the way to a complete proof.

Sascha Orlik: The cohomology of Deligne-Lusztig varieties for the general linear group
In my talk I want to present an approach for determining the cohomology of Deligne-Lusztig varieties in the case of the general linear group.

Geordie Williamson: Counter-examples to some conjectures in modular representation theory
I will explain recent counter-examples to Lusztig´s conjecture on modular representations of reductive algebraic groups. I will then sketch a trick (explained to me by Joe Chuang) which allows one to deduce counter-examples to the James conjecture on the dimensions of the simple modules for the symmetric group.

Conference participants:

Olivier Brunat (Université Paris Diderot)
Marc Cabanes (Université Paris Diderot)
Olivier Dudas (Université Paris Diderot)
Ulrike Faltings (TU Kaiserslautern)
Johannes Hahn (Universität Jena)
Frank Himstedt (TU München)
Caroline Lassueur (TU Kaiserslautern)
Michael Livesey (TU Kaiserslautern)
Frank Lübeck (RWTH Aachen)
Pablo Luka (TU Kaiserslautern)
Gunter Malle (TU Kaiserslautern)
Attila Maróti (TU Kaiserslautern)
Carl Mautner (MPI Bonn)
Jürgen Müller (Universität Jena)
Sascha Orlik (Bergische Universität Wuppertal)
Alessandro Paolini (University of Birmingham)
Elisabeth Schulte (TU Kaiserslautern)
Iulian Simion (TU Kaiserslautern)
Britta Späth (TU Kaiserslautern)
Jay Taylor (TU Kaiserslautern)
Geordie Williamson (MPI Bonn)

Registration:

If you would like to participate in the mini conference, please email the organizer.  Also indicate if we should reserve a room at the  B&B Hotel Kaiserslautern (single room 49 EUR per night excluding breakfast, but including internet access) for you.

This meeting is supported by DFG Schwerpunktprogramm "Darstellungstheorie"  and the ERC grant "Counting conjectures and characters of almost simple groups".