In 2006 I was one of the organizers of an international conference on anomalous transport, please see below. Because of the big success of this conference we organizers decided to edit a multi-author textbook on the very same topic, as an introduction to this important, very active field of research. The book (584 pages) got published by Wiley-VCH in July 2008. Please see the book's homepage for further details.

In an interdisciplinary collaboration with Peter Dieterich, TU Dresden, A. Schwab, University of Muenster, and R. Preuss, MPI for Plasma Physics, Garching, we showed that biological cells can exhibit a very interesting dynamical behavior: Isolated single cells were put on substrates on which they crawl (with a remote similarly to `caterpillars'). Recording their trajectories with a video camera, the experimental data matches nicely to statistical predictions of a specific theoretical model (a so-called fractional Klein-Kramers equation), which describes a transition from sub- to superdiffusive behavior as time increases. That is, the cell's dynamics is very different from ordinary Brownian motion.
These results have been published as an article in the international top journal Proceedings of the National Academy of Sciences; see PNAS 105, 459--463 (2008).
See the Dresdner Universitaetsjournal 12/2008, p.6 for a short popular science account of our findings.

In 2003 I completed a 300-page summary of my research performed over the previous years. This work got accepted as my Habilitation Thesis at the TU Dresden. An updated and considerably amended 460 page version got recently published as a book in the Advanced Series in Nonlinear Dynamics, World Scientific, Vol.24. Please see the book's homepage for further details.

In September 2006 I awarded a research grant from the British EPSRC council. With this grant (£250,000 or approx. EUR 371000) I am partially funding my own post for two years, I received travel money, money for computers and money for inviting collaborators. This grant includes a 2-year postdoc position.

This very interdisciplinary conference took place at the Physikzentrum Bad Honnef in July 2006 for a duration of 4 days. It was fully sponsored by the Heraeus Foundation and involved about 70 international participants from 17 different countries. I have been organizing this event together with G.Radons and I.M.Sokolov. See also the multi-author textbook related to this conference.

This conference took place at the MPIPKS Dresden in August 2002 for a duration of 3 weeks. It involved about 90 participants from 22 different countries. I have been organizing this event together with P.Gaspard, H.van Beijeren and J.R.Dorfman. All of us were serving as guest editors at the International scientific journal Physica D for the accompanying 400-page Special Issue.

During my Ph.D. thesis work I discovered the phenomenon that diffusion coefficients can be fractal functions of control parameters. At first view this finding appears to be counter-intuitive, since usually one expects physical quantities to change smoothly under parameter variation as, for example, in Ohm's law.
Subsequently it was shown by colleagues, coworkers and myself that this behavior is quite typical not only for diffusion but also for other types of transport coefficients (e.g., electrical conductivities, chemical reaction rates) characterizing transport in low-dimensional deterministic dynamical systems exhibiting spatial periodicities. This class of systems thus exhibits properties that are at the borderline of traditional statistical physics revealing fingerprints of an underlying microscopic deterministic dynamics.
Physical systems of this class being accessible in experiments are, for example, semiconductor devices like antidots and Josephson junctions, certain types of ratchets, and corrugated vibratory conveyors, the latter frequently being used in industrial applications for transporting granular entities. For all these systems there are theoretical predictions of fractal, or at least highly irregular, parameter dependencies of physical transport properties. Although hints on experimental observations of such irregularities already exist in the literature, it still remains to clearly match theory with experiments at this point.

some accounts of this finding in textbooks:

reference:
R.Klages, J.R.Dorfman, Simple maps with fractal diffusion coefficients, Phys. Rev. Lett. 74, 387-390 (1995)