I have presented my high potential to acquire new knowledge and my ability to adapt to new environments by performing several research projects in four different European countries. In fact, I finished my PhD thesis with title “A Geometric Approach to Noncommutative Principal Bundles” in Erlangen in 2011 under the supervision of Karl-Hermann Neeb, who is a main authority in infinite-dimensional Lie theory and with whom I still have a strong professional relationship.

 

During my time as a postdoctoral researcher in Münster and Copenhagen, I significantly sharpened my skills in noncommutative geometry and operator algebras, and I became acquainted with colleagues such as Siegfried Echterhoff and Ryszard Nest, who both are leading experts in noncommutative geometry and operator algebras. In Copenhagen, I also got to know Tyrone Crisp and Ehud Meir, who are experts in these fields as well and with whom I had many interesting discussions, for example about free quantum group actions and the interplay between ideas of categorification and noncommutative geometry. I hope to collaborate with both of them in the future.

 

During my time in Helsinki, I worked together with Jouko Mickelsson, who is a main authority in mathematical physics, on non-commutative gerbes resulting in the paper [6]. I also started to work with Kay Schwieger, who is an expert in operator algebras and co-author of the articles [1, 3, 4, 5]. In Hamburg, I further learned from my colleagues Jan Priel and Simon Lentner that non-commutative principal bundles also appear in the study of 3-dimensional topological quantum field theories that are based on the modular tensor category of representations of the Drinfeld double.

 

In my current position in Karlskrona I investigate the algebraic structure of complex group rings together with my co-worker Johan Öinert. More precisely, we are interested in the question whether the complex group ring of a torsion-free group only contains trivial idempotents.  A problem that has regained interest, mainly due to its intimate connection with the Baum-Connes conjecture in operator algebras.