Diploma in Physics (University of Heidelberg)
Ph.D. (University of Heidelberg)
Habilitation in Mathematics (University of Heidelberg)
I graduated in physics with a work on chaotic systems. In particular, I made experimental and numerical studies on the chaotic behaviour of heart cells. Although my interest has in the meantime shifted to more mathematical subjects, I always dream of finding some applications of mathematical theories to physical or biophysical problems.
Starting with my PhD I have been involved in mathematical investigations in the field of non-commutative probability theory, a hybrid of functional analysis and probability theory. In particular, I am fascinated by one of the jewels of that theory, namely by the so-called free probability theory. This theory was introduced and developed by Dan Voiculescu as a tool for studying the structure of a special class of operator algebras (namely von Neumann algebras coming from free products of groups). And indeed this theory has given a lot of new results for operator algebras (especially concerning the von Neumann algebras of free groups). This progress, however, has only been possible because surprising relations between free probability theory and quite different fields of mathematics and physics have emerged.
My own work concentrates on these relations of free probability theory with other fields. In particular, I am studying the combinatorial and probabilistic aspects of free probability and also its applications to problems in quantum statistical physics.
For example, I developed a free stochastic analysis for the free Brownian motion and investigated its relation with random matrices, I showed that the combinatorial side of free probability is governed by the lattice of non-crossing partitions, I derived a master-equation for the description of memory effects in open systems and I considered deformations of the canonical commutation and anti-commutation relations.