My field of research are cohomological structures in global analysis in the presence of symmetry. These symmetries are mostly described by Lie groups (which may be infinite-dimensional) or Lie groupoids and their associated Lie algebras and Lie algebroids. More precisely, I often work with the following concepts:
Cohomology of Lie groups (continuous, smooth, topological, Segal-Mitchison, bounded, measurable, ...) and the related differential geometric structures (flat bundles, symmetric spaces, ...)
Lie groupoids, Lie algebroids and their relation to infinite-dimensional Lie theory
String geometry, in particular the string (2-)group, its representations and higher gauge theory in general
Infinite-dimensional Lie groups (mapping- and gauge groups, diffeomorphism groups) and their cohomological invariants
02.11.2006, Approximation Theorems for Locally Convex
Manifolds, Lie Groups and Principal Bundles,
Seminar Sophus Lie 2006 (Vienna, Austria)
slides
16.06.2006, Equivalences of continuous and smooth principal
bundles, 31. Süddeutsches Kolloquium
über Differentialgeometrie (Darmstadt, Germany),
slides
(in German)