at the

American Institute of Mathematics, Palo Alto, California

organized by

Christopher Bendel, Terrell Hodge, Brian Parshall, and Cornelius Pillen

The workshop thus aims to bring together two groups:

- those with research interests related to the modular representation theory and cohomology of finite groups of Lie type;
- experts in computation and applications whose experience may or may not lie directly in the field, but whose knowledge could add depth to the pool of ideas for this group.

- New developments on the theoretical front, such as the recent work on the Broue conjecture, which may have important implications for the representation theory of the finite groups of Lie type.
- The presence of fundamental theorems, in both defining and cross-characteristic cases, which have have yet to be exploited by powerful computational techniques.
- The rapid development and increasing sophistication of modules for computational algebra packages, such as GAP, and growing use of algebraic approaches to mathematical modeling, e.g., via Groebner bases.
- Promising new results that have arisen from other contexts (e.g., a new program for computing Kazhdan-Lusztig polynomials by the ATLAS project on Lie groups), mandating an examination of their suitability and/or adaptability to the modular theory for finite groups of Lie type.
- Developments in technology and computational packages over the last decade, coupled with theoretical advances in the field, that have made portions of many problems more amenable to adaptation as student research projects, even with students possessing relatively modest backgrounds in algebra.

Through small working groups, demonstrations, large-group discussions, and some lectures, the workshop aims to:

- Assess the current state of past, present, and potential uses for computation in the field, and to identify, assemble, and discuss a list of problems for which progress might significantly hinge on intensified computation.
- Fill in the lack of awareness on computational methods as a tool for theoretical advances on the part of some active researchers (and potential researchers).
- Take steps to address other barriers to employing computational
methods, such as
- the lack of computational expertise on the part of researchers;
- lack of time/manpower to implement computational approaches;
- limitations on individual computing facilities;
- limitations on available algorithms, software, and programming methods.

- Generate for researchers some awareness of potential applications of their work to applied issues.
- Develop collaborative strategies among researchers and potential researchers at various locations ranging from primarily undergraduate institutions to research intensive universities.

The workshop schedule.

A report on the workshop activities.

Introduction to Kazhdan-Lusztig polynomials(Second half of Lin's lecture) (photos)

Monday afternoon discussion I (typed up)

Monday afternoon discussion II (modified version)

Monday discussion (directory of photos)

Calculating cohomology by J. Carlson

Computing (with) characters and respresentations by F. Luebeck

demo.txt Magma demonstration file by D.Roozemond

demo_defs.txt Magma demonstration file by D.Roozemond

magma1.txt Transcript of demonstration given by D.Roozemond(1 of 2).

magma2.txt Transcript of demonstration given by D.Roozemond(2 of 2).

Cohomology of finite groups by R. Guralnick

Reduced standard modules and cohomology by L. Scott

Categorification by B. Srinivasan and P. Webb

An introduction to the cohomology and modular representation theory of the symmetric group by D. Hemmer

LiE.txt a demonstration of the software LiE by D. Roozemond

Photo 1 Photo 2 Photo 3 Photo 4 Photo 5

Photo 6 Photo 7 Photo 8 Photo 9 Photo 10

Photo 11 Photo 12 Photo 13 Photo 14 Photo 15

qua6-25.txt Gap demonstration (QuaGroup package) by C. Bendel

Photo 16 Photo 17 Photo 18 Photo 19 Photo 20

Photo 21 Photo 22 Photo 23 Photo 24 Photo 25

Photo 26 Photo 27 Photo 28 Photo 29 Photo 30

The latest stand alone package Coxeter 3 by Fokko Du Cloux

GAP lessons by P. Webb

Irreducible Modular Representations of Finite and Algebraic Groups Notes by Christopher Drupieski and Terrell Hodge, based on lectures by Leonard Scott.

The organizers have begun a wiki with a bibliography and reference material, located at http://modularrepresentations.wetpaint.com/. That wiki is viewable by anyone and can easily be edited.

Instructions for Downloading GAP