My current research interest focuses on modular and hierarchical systems and their relation to scales. What causes characteristic scales? How can predominent scales in data guide model development and model simplification? How do the dynamics on one scale influence, determine, and restrict the dynamics on another scale and how can one formalize such "vertical interactions" between scales?
Following these questions, I am interested in various aggregation and dimensional reduction techniques like hierarchical aggregation, singular perturbation methods, meanfield approaches, or Mori-Zwanzig projections, and methods to combine models on different scales in multiscale modeling frameworks as well as methods developed by statistical physics to deal with high dimensional systems and their extensions toward systems with complicated interactions.
Having formerly worked in systems biology and systems ecology, I learned to appreciate the importance of the above mentioned topics when confronted with the hierarchy of living systems, ranging from biomolecules over the organization of cellular organelles and tissue to whole organisms on the one side, and from individuals over communities, populations and metapopulations toward the whole biosphere as one interacting living system on the other side.
Since this hierarchical emergence is an emergence of organizational complexity, I am interested in theories of pattern formation, self-assembly and self-organization as well as chemical based information processing and computation. I am further interested in the origin of life and the transition from non-living matter to fully functional living systems and the emergence of Darwinian evolution from simple self-replicating chemicals.
See also my list of publications.