Professor of the Practice
B.A. (Hons) Mathematics and Economics, 1984
M.A. University College Dublin, Ireland, 1985
Ph.D., University of Notre Dame, 1991
Algebra and Algebraic Geometry
My research uses results from Classical groups, K-theory, Number theory, Quadratic forms, Coxeter groups and representation theory. In particular, with respect to classical groups, my work has focused on the theory of the group SL_2 over number rings and the behavior of its subgroups related to ideals in the rings. I am still interested in some unresolved questions from K-theory, concerning SL_2 over rings. More recently I have done some work on convex geometries on root systems related to Coxeter groups. I have compared several natural convex closure operators on these root systems, and considered the question as to when they satisfy an anti-exchange condition, defined by Edelamn and Jamison.
I am currently working on the representation theory of an interesting algebra related to the n by n matrices over the ring R $\otimes$ R, where R is the ring of integers of a number field. The representation theory can be explored using the results of Dyer on Category C, and has interesting connections with the number theory of the rings.
- The E_2® – Normalized Subgroups of GL_2®: Journal of Algebra 172, 584-611 (1995).
- The E_2® – Normalized Subgroups of GL_2® II: Journal of Algebra 177, 619-626 (1995)
- The highest weight representations from number ring.: In preparation.
- Convex closures on root systems: Submitted for publication.