Overview
I am a professor of Mathematics at the University of Georgia. After getting my Ph.D. at Yale University, I did a postdoc at the University of Utah followed by another postdoc at the University of California, Berkeley. I've been at UGA since 1987.
Research
My research interests are in Lie theory, representation theory, and associated geometry. Specifically, I study representations of semisimple Lie algebras, algebraic groups, and Lie superalgebras; cohomology associated to these representations; and support variety theories. I have also worked on cohomology for the Virasoro algebra, Witt algebra, and quantum enveloping algebras, and on geometry of Schubert varieties. I'm a fan of using computers to help with mathematical research, and I've developed various programs over the years, some of which are available.
VIGRE at UGA
From 2003 through 2008, and again beginning in Fall 2009, I have been one of the faculty leaders of the UGA VIGRE Algebra research group. This group of faculty, postdocs, graduate students, and the occasional undergraduate has worked on several open problems involving support varieties for algebraic groups and the symmetric group, cohomology of Lie algebras and quantum enveloping algebras over fields of small prime characteristic, low degree extensions for finite groups of Lie type, and more. We solved quite a few of the problems, and the group has five original research papers published or accepted.
I'm involved in various other aspects of the UGA Mathematics VIGRE II grant, including co-organizing a Summer School Program in May 2010 for graduate students and postdocs on Lie and representation theory. This two-week series of lectures and workshops will be followed by a three-day 2nd annual Southeast Lie Theory conference.
Teaching
I've taught a large variety of courses at UGA, ranging from trigonometry to graduate topics courses. But my favorite class to teach is probably undergraduate abstract algebra. Here are some links to courses I've taught recently.
Service
I have been the Graduate Coordinator for the Mathematics Department since Summer 2007. If you're interested in pursuing graduate studies in our department, have a look at the information on the graduate program website.
The UGA Mathematics Department is an Academic Sponsor of MSRI (the Mathematical Sciences Research Institute in Berkeley, CA). One of the benefits is that MSRI pays for 2-3 of our graduate students to attend their summer workshops every year. I am the institutional representative to MSRI in our department.
I maintain what I believe to be the world's largest list of links to representation theorists' home pages and arXiv preprints. If you would like to be added to the list, or if your entry is out of date, please send me an email (see my Contact page for the address).
