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:

• Varieties for Nilpotent Matrices over Simple Lie Algebras I: Good Primes, J. Algebra 280, (2004), 719-737. 
  
• Varieties for Nilpotent Matrices over Simple Lie Algebras II: Bad Primes, J. Algebra  292, (2005), 65-99.
  
• Support Varieties for Weyl Modules over Bad Primes, J. Algebra  312, (2007), 602-633. 
• On Kostant's Theorem for Lie Algebra Cohomology, Cont. Math. 478, (2009), 39-60.
  
• An Analog of Kostant's Theorem for the Cohomology of Quantum Groups, Proceedings of the AMS 138, (2010), 85-99.
• First Cohomology for Finite Groups of Lie Type: simple modules with small dominant weights, arXiv:1010.1203, to appear in the Transactions of the AMS.
  
• Second Cohomology for Finite Groups of Lie Type, submitted. 


• GAP program UGA3, companion to the paper "Support varieties for Weyl modules over bad primes", (gzipped tar or zip format) to determine support varieties of induced modules for exceptional groups over bad primes. 
• GAP code for calculations used in the papers on "First and Second Cohomology for Finite Groups of Lie Type": UGAVIGRE6-7code
  
• A minor correction to a table at the top of page 732 in the paper "Varieties for Nilpotent Matrices over Simple Lie Algebras I: Good Primes": Revised Table
  

• J.F. Carlson, Z. Lin, D.K. Nakano, Support varieties for modules over Chevalley groups and classical Lie algebras, Trans. AMS, 360, (2008), 1879-1906. 
• I. Bagci, J.R. Kujawa, D.K. Nakano, Cohomology and support varieties for Lie superalgebras of type W(n), IMRN, (2008), Art. Id rnn115.
  
• A.G. Elashvili, V.G. Kac, On exceptional nilpotents in semisimple Lie algebras, J. Lie Theory, 19, (2009), 371-390.
  
• D.J. Hemmer, The complexity of certain Specht modules for the symmetric group, J. Alg. Comb., 30, (2009), 421-427.
  
• K.J. Lim, The varieties of some Specht modules, J. Algebra, 321, (2009), 2287-2301.
  
• K.J. Lim, The complexity of the Specht modules corresponding to hook partitions, Arch. Math, 93,  (2009), 11-22.
  
• B.D. Boe, J.R. Kujawa, D.K. Nakano, Cohomology and support varieties for Lie superalgebras II, Proc. LMS, 98, (2009), 19-44.
• B.D. Boe, J.R. Kujawa, D.K. Nakano, Cohomology and support varieties for Lie superalgebras, Trans. AMS, 362, (2010), 6551-6590.
  
• J. Feldvoss, S. Witherspoon, Support varieties and representation type of small quantum groups, IMRN, (2010), 1346-1362.
  
• T. Arakawa, Associated varieties of modules over Kac-Moody algebras and C_2 finiteness of W-algebras, arXiv1004.1554.