# Mathematical Sciences Research Institute

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# Workshop

Introductory Workshop on the Representation Theory of Finite Groups February 04, 2008 - February 08, 2008
 Registration Deadline: January 20, 2008 about 6 years ago November 04, 2007 over 6 years ago
Parent Program: Representation Theory of Finite Groups and Related Topics
Organizers Jonathan Alperin(chair), Robert Boltje, Markus Linckelmann
Speaker(s)

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Description

The workshop will focus on surveying main active areas of representation theory of finite groups, especially highlighting major unsolved problems. It is meant to be accessible for graduate students and non-specialists with some background in representation theory. The bulk of the week's program will be four short series of lectures:   Course 1. Block theory and counting conjectures. The course will introduce the basic ideas of modular representations, including block theory, the main theorems of Brauer and the Green correspondence. Special theories for cyclic and nilpotent blocks will be covered. Subsequently, several counting conjectures will be discussed. These include the Alperin-McKay conjecture, Alperin's weight conjecture, the Knorr-Robinson synthesis via alternating sums, Dade's conjecture and recent subtle refinements.   Course 2. Representation theory of groups of Lie type. While emphasizing the general linear group, this course covers topics including representations in characteristic zero, p and "el" and related structures such as Hecke algebras.   Course 3. Representation theory and topology. The purpose of this course is to describe some of the important tie-ins between representation theory and algebraic topology through topics from cohomology of groups applied to representation theory, homological algebra (e.g. derived categories), fusion systems and p-local finite groups.   Course 4. Broue's abelian defect group conjecture. This course will focus on equivalences between derived categories of blocks and on Broue's isotypies between blocks. In the case of finite groups of Lie type, related geometric structures enter the picture. These include Deligne-Lusztig varieties and complex reflection groups. As another illuminating example, the case of the symmetric groups will be discussed. The four courses will be supplemented by a number of single lectures on a variety of topics. Accommodations: A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Simply go to the reservations & availability, click on corporate at the bottom, enter the word math & proceed from there. Please put the following code in the Guest Comment field; group code CGMS56 (this code is not case sensitive). The cut-off date for reservations is January 13, 2008. A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: C20000. The cut-off date for reservations is January 4, 2007.

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

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Schedule
Feb 04, 2008
Monday
 09:30 AM - 10:30 AM Blocks and Counting Conjectures Burkhard Kuelshammer 11:00 AM - 12:00 PM Representations of Algebriac Groups in Characteristic p Jonathan Brundan 02:45 PM - 03:45 PM Representation Theory and Topology Markus Linckelmann (City University) 04:15 PM - 05:15 PM Broué's Abelian Defect Group Conjecture Joe Chuang
Feb 05, 2008
Tuesday
 09:30 AM - 10:30 AM Blocks and Counting Conjectures Burkhard Kuelshammer 11:00 AM - 12:00 PM Representations of Algebriac Groups in Characteristic p Jonathan Brundan 02:45 PM - 03:45 PM Representation Theory and Topology Markus Linckelmann (City University) 04:15 PM - 05:15 PM Broué's Abelian Defect Group Conjecture Joe Chuang
Feb 06, 2008
Wednesday
 09:30 AM - 10:30 AM Blocks and Counting Conjectures Burkhard Kuelshammer 11:00 AM - 12:00 PM Introduction to Deligne-Lusztig Theory Cedric Bonnafe
Feb 07, 2008
Thursday
 09:30 AM - 10:30 AM Introduction to Deligne-Lusztig Theory Cedric Bonnafe 11:00 AM - 12:00 PM Representation Theory and Topology Markus Linckelmann (City University) 02:45 PM - 03:45 PM Broué's Abelian Defect Group Conjecture Joe Chuang 04:15 PM - 05:15 PM On Duality Inducing Automorphisms and Sources of Simple Modules in Finite Classical Groups Radha Kessar
Feb 08, 2008
Friday
 09:30 AM - 10:30 AM Around the McKay Conjecture Gabriel Navarro (University of Valencia) 11:00 AM - 12:00 PM A Bijection towards Counting Conjectures in Finite Reductive Groups Paul Fong (University of Illinois at Chicago) 02:45 PM - 03:45 PM Biset Functors Serge Bouc 04:15 PM - 05:15 PM Squeezed Resolutions over the Group Algebra of a Finite Group David Benson (University of Aberdeen)