# Anne B. Pilkington

### 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

Email: apilking@nd.edu
Office: 242 Hayes-Healy Bldg
Phone: (574) 631-3369
Fax: (574) 631-6579

255 Hurley Bldg
Notre Dame, IN  46556-4618

Class information on Anne Pilkington's personal website.

#### Research Interests

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.

#### Selected Publications

• 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.