Teaching & Supervision

Seminar (Hauptseminar)

In the first part of this seminar we cover the main concepts of distribution theory (distributions with compact support, tempered, and classical distributions) following the book of Hörmander. In the second part we study the Littlewood–Paley theory and Besov spaces and related function spaces following the books of Triebel and Bahouri–Chemin–Danchin. The focus will be the application of these function spaces to the study of the existence and regularity of solutions to (nonlinear) PDEs.

Lecture Course

Elements of phase space analysis: equilibria, periodic orbits, concepts of stability, invariant sets, local vs global dynamics. Linearization. Poincaré-Bendixon theory. Steady state bifurcations: Fold, Hopf. Perturbation theory, asymptotics, averaging. Examples of chaotic dynamics: one-dimensional maps, three-dimensional flows; basics of symbolic dynamics. Applications (from engineering, natural sciences, etc.)