I earned my bachelor’s degree in mathematics from the University of California, Berkeley in 1986 and my Ph.D. at Yale University in 1990.
I’m a Distinguished Research Professor (DRP) in the Mathematics Department. My primary departmental duties include conducting mathematical research, presenting my work outside of UGA, advising Ph.D. students, mentoring postdoctoral fellows and teaching graduate and undergraduate courses. I’m also actively involved with serving on college and university committees.
Representation theory has emerged as a central area of modern mathematics with connections to combinatorics, algebraic geometry, topology, number theory, along with applications to chemistry and physics. Representations are mappings, regarded as snapshots, of complicated algebraic objects (such as groups and Lie algebras) to an array of numbers (matrices). These realizations by matrices encode local data that can yield deep insights into these complicated algebraic objects.
Recent developments have included using the representation theory of Lie groups to better understand signal processing and the translation of the P versus NP Problem in computer science via geometric complexity theory into questions about decomposing representations for the general linear group.
My research is at the interface between representation theory, geometry and homological algebra. Collecting all the representations for a certain algebraic object forms a tensor triangulated category. Methods from homological algebra can be used to build a bridge between tensor triangulated categories and geometric objects. Uncovering this “hidden geometry” often leads to new insights about the algebraic object and its representations.
|1986||A.B.||Mathematics||University of California, Berkeley|
1992-95 National Science Foundation Postdoctoral Fellowship
2007 Creative Research Medal, University of Georgia
2007 American Mathematical Society One-Hour Invited Address
2008 McCay Award, Dept. of Mathematics, University of Georgia
2010 Distinguished Research Professorship, University of Georgia
2013 Fellow of the American Mathematical Society (Class of 2013, Inaugural Class)
2016 Lamar Dodd Creative Research Award, University of Georgia