RESEARCH 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:

- Topological properties (homotopy type) of subcomplexes of Tits buildings
- Investigations of affine (Bruhat-Tits) buildings (with G. Nebe)
- Characterizations of spherical and of twin buildings (with H. Van Maldeghem)
- Homological finiteness properties of (certain) S-arithmetic groups
- Homological finiteness properties of Kac-Moody groups over finite fields
- Presentations of and Levi decompositions in Kac-Moody groups over arbitrary fields (with B. Muehlherr)

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