University of Georgia VIGRE Algebra Group

Our research group was initiated in August 2003 under the Vertical Integration of Research and Education (VIGRE)
Program sponsored by the National Science Foundation (NSF) at the Department of Mathematics at the University
of Georgia (UGA).  The group was initially led from 2003-05  by David Benson, Brian Boe and Daniel  Nakano.
The faculty leaders from 2005-08 were Brian Boe, Leonard Chastkofsky, and Daniel Nakano. In 2010-11, the
group will be led by Brian Boe, Jon Carlson, Leonard Chastkofsky, and Daniel Nakano.

The VIGRE Algebra Group consists of faculty members, postdoctoral fellows, graduate students and undergraduates. Our group
operates much like a laboratory in the physical and biological sciences by bringing individuals with varying backgrounds and expertise
to work on a common research project. One of our main educational objectives has been to develop innovative methods for conducting
mathematical research in a large group atmosphere.

During the 2003-04 academic year we focused our efforts on understanding conjugacy classes of nilpotent orbits
via the use of cohomology and representation theory. In 2004-05, our group studied support varieties for modules
over the symmetric group. From 2005-08,  we investigated methods for computing cohomology  for  Lie algebras, quantum
groups and other related objects. Our group has completed seven papers including two software packages:

GAP is available from Versions are available for UNIX/Linux, Windows, or Macintosh OS.

From 2009-11, we will investigate the cohomology of finite groups. In particular we will focus our attention on computations of
low degree cohomology for symmetric groups and finite groups of Lie type.

The details about how our  research was carried out in a large group setting can be found in our biannual reports:

Fall 2003 Report
Spring 2004 Report
Fall 2004 Report
Spring 2005 Report
Fall 2005 Report
Spring 2006 Report
Fall 2006 Report
Spring 2007 Report
Fall 2007 Report
Spring 2008 Report
Fall 2009 Report
Spring 2010 Report
Fall 2010 Report
Spring 2011 Report

Other mathematicians have found the questions that we have worked on interesting and our results useful. Here are some papers where our group's work has been cited.

Click here for a for a detailed list of members of the group (2003-11):  Members of the UGA VIGRE Algebra Group