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Geometric evolution equations like the Ricci flow and the mean curvature flow have played an important role in the solution of several major open conjectures in geometry and topology like for instance the Poincare conjecture and Thurston's geometrization programme. We shall present some selected techniques related especially to the work of Perelman on Ricci flow on closed manifolds and discuss adaptations of this when boundary terms are involved. This will in particular include the lecturer's own research carried out over the last few years, part of which has been published and some of which is still work in progress. Although this lecture course is aimed at students at the MSc and PhD level (postdocs are also welcome) it does not require a lot of background material except for the one listed below.
Note that this lecture course is NOT a replacement for Partielle Differentialgleichungen 3!
Prerequisites: Diff. Geom. 1, Partielle Differentialgleichungen 1, Familiarity with Riemannian manifolds, hypersurfaces, curvature, Sobolev spaces and inequalties and some basic regularity thory for PDE will definitely be assumed. More advanced background material will be presented in lectures.
Literature: To be advised in class