The VIGRE Algebra Group was led by David Benson, Brian Boe, and Daniel Nakano. The other members
of the group are

Faculty:

Leonard Chastkofsky
Jerome Jungster

Postdocs:

Nadia Mazza
Jonathan Kujawa

Graduate Students:

Irfan Bagci
Phil Bergonio
Kenyon J. Platt
Stephen Winburn
Caroline Wright


The main goal of the VIGRE Algebra Seminar this term was to to study support varieties for modules
over the symmetric group. Support varieties were developed 25 years ago in the pioneering work of
Alperin and Carlson. Since their introduction, these varieties have played a central role in the cohomology
theory of finite groups and restricted Lie algebras. Although these varieties are easy to define once the
finite generation of cohomology is established, they are often very difficult to compute. One of the main
objectives of this project is to make significant progress in computing these varieties for important
classes of modules.

At the start of the semester Benson presented four lectures on the elementary properties of the cohomological
variety theory. This was followed by three lectures by Kujawa on symmetric group representations. Nakano presented
two lectures on the computation of the support varieties for Young and permutation modules (recent results with
David Hemmer). During the last four weeks of the term Benson led the group in making explicit computations of
varieties for symmetric groups. We discovered formulas  for certain Specht modules and have started to compute
the supports for Specht modules for the symmetric group on d letters when d<p^2 (where the characterstic of the
underlying field is p). We are optimistic this case will be solved near the beginning of next semester.

Several students in the group, Bergonio, Platt and Wright, finished up computations on the support varieties of
Weyl modules over bad primes. This effort was initiated and led over the summer by Chastkofsky. Boe and Nakano have
compiled the data and have written up the results. A preprint (the third paper written by our group) is now available.
The first VIGRE Algebra Group paper has now appeared: J. Algebra, 280 (2004), 719-737 and the second
VIGRE Algebra Group paper will appear in the new Journal of Algebra section devoted to computational algebra.

Bagci and Winburn are new members to our group. They are making good progress with the material and we are optimistic
they will contribute further in the spring.