Research interests

My research involves certain types of dimension theories, some of which are classified as geometric topology (more precisely equal parts geometric, general and algebraic topology), and some as metric geometry.

The results I have published so far are related to resolution theorems in topological (or covering or Lebesgue) dimension and cohomological dimension theory, while my recent interests are asymptotic dimension, Assouad-Nagata dimension and their applications in metric geometry and geometric group theory.

The theories of topological dimension dim and cohomological dimension dim_G (for abelian groups G) rely heavily on algebraic topology, homotopy theory, limits of inverse systems of spaces and properties of cell complexes. They can be applied in geometry and geometric group theory, in particular in investigating boundaries of hyperbolic or CAT(0) spaces and groups, especially when combined with asymptotic dimension. Asymptotic dimension asdim is a large scale analog of topological dimension in coarse geometry, while Assouad-Nagata dimension dim_AN can be regarded as a variation on asdim, produced by requiring a certain control on the scale of covering families involved.

Publications