- Dunkl-Cherednik theory and special functions associated with root systems
- harmonic analysis on symmetric spaces
- connections and applications, such as: random matrices, quantum integrable models
- harmonic and geometric analysis on manifolds, in particular on symmetric spaces, and on graphs
- asymptotic harmonic analysis
- convolution algebras and hypergroups
- Macdonald-Cherednik theory
- Probabilistic potential theory, Lévy processes
Current research activities:
Research Seminar "Geometric and Harmonic Analysis" (with T. Weich, J. Hilgert and J. Frahm, Aaarhus)
Editorial activities (M. Rösler):
- Studies in Applied Mathematics, member of the editorial board since 2020.
- C. Dunkl, P. Forrester, M. de Jeu, M. Rösler, Y. Xu (eds.): Special issue on Dunkl operators and related topics, SIGMA, 2009.
- P. Graczyk, M. Rösler, M. Yor (eds.): Harmonic and Stochastic Analysis of Dunkl Processes, Travaux en cours 71, Hermann, Paris, 2008.