The main teaching and research activities are focused on dynamical systems and quantitative and qualitative methods for their analysis. A broad range of different model classes is necessary to understand complex phenomena, including models with or without delay, deterministic or random, low-dimensional or generated by partial differential equations, time-invariant or time-varying.

Conceptually different approaches are developed for nonautonomous dynamical systems, for experimentally or numerically observed finite-time systems with time in a bounded interval or generalized models which play a role in biological and network applications.

Some of the key interests are spectral theory, invariant and inertial manifolds, timescale separation, reduction by Hartman-Grobman and normal form results, stability radii, bifurcation theory and attractors. Our group is open to new ideas fostering a broader understanding of complex systems within mathematics and beyond.