On small abstract quotients of Lie groups and locally compact groups

We prove continuity results for abstract epimorphisms of locally compact groups onto finitely generated groups.

Transitive actions of locally compact groups on locally contractible spaces

Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.

Homogeneous compact geometries

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.

Metric Properties of Euclidean Buildings

This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.

Notes on completely reducible subcomplexes of spherical buildings

A completely reducible subcomplex of a spherical building is a spherical building.