Peter Abramenko
( Email - Website )
Professor
Department of Mathematics
PO Box 400137
Dept of Mathematics
Charlottesville, VA 22904
Phone:434-924-4162
Fax:434-924-3084
Education and Experiences:
University of Frankfurt: M.A., 1981;
Ph.D., 1987;
Heisenberg Fellow, University of Bielefeld and Cornell University: 1998-2001;
Researcher, University of Bielefeld: 1997-1998;
Scientific Employee/Assistant Professor, University of Frankfurt: 1991-1997;
Researcher, University of Bielefeld: 1989-1990;
Scientific Assistant, University of Frankfurt: 1988-1989.
Interests:
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. During the last few years, I have done research work on the following subjects:
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