Jonathan Kujawa

I am a member of the faculty of the University of Oklahoma Department of Mathematics. Previously I was an NSF postdoctoral fellow and Franklin Fellow at the University of Georgia with Dan Nakano as my sponsoring scientist. Prior to that I was a postdoctoral fellow at the University of Toronto for six months. Going back even further, I was a graduate student at the University of Oregon.  I received my Ph.D. from Oregon in 2003 under the guidence of Jon Brundan. Finally, a long, long time ago I received my B.A. in mathematics from Gustavus Adolphus College.

Broadly speaking, my research is in the area of representation theory. The general idea is to study the mathematics of symmetry. For example, taken together, the transformations of the plane which leave the background of this page unchanged is a mathematical object called a group. One can study this group to better understand the pattern in the background or, vice versa, use the symmetries of the background to study that group. As one might imagine, this field involves algebra, geometry, combinatorics, and many other areas of mathematics (which makes it interesting!).

My research interests include Lie theory, algebraic combinatorics, crystal/canonical bases, representations of finite and algebraic groups, Lie algebras, cohomology and support varieties, and the super analogue of these topics. This naturally leads to questions in algebraic geometry, quantum groups, finite dimensional algebras, homological algebra and derived categories, and myriad other topics. Below is a two dimensional shadow of the root system of type E7 (borrowed from John Stembridge). The combinatorics and symmetries of this picture reflect the rich theory of the associated Lie group and Lie algebra.