P. O. Box 400137 |
434-924-4162 pa8e@virginia.edu Personal Webpage |
Twin Buildings and Applications to S-Arithmetic Groups, Lecture Notes in Mathematics 1641, Springer (1996).
Buildings: Theory and Applications, Graduate Texts in Mathematics 248, Springer (2008) (with Ken Brown).
I am mainly interested in group theory, (combinatorial) geometry and in the interplay between these two fields. The groups I am investigating are often linear, which means that they are groups of matrices, for instance the special or general linear groups over fields (which are examples of algebraic groups) or over some Dedekind domains known from number theory (which are examples of S-arithmetic groups). I am also interested in (infinite-dimensional) Kac-Moody groups over fields. All these groups come along with BN-pairs, and especially nice geometries associated to BN-pairs are (Tits) buildings. I have been fascinated with buildings, their intrinsic symmetries, and their interplay with groups for several years. Studying the intrinsic geometry of buildings as well as their group-theoretic applications (e.g., certain presentations and homological finiteness properties of groups) forms the major part of my current research work. Education