Geometric flows with rough initial data

In the last few decades geometric flows such as the Ricci flow, mean curvature flow and harmonic map heat flow have been successfully applied in the study and resolution of various long-standing open problems, such as the geometrization conjecture and the differentiable sphere theorem. After a very gentle introduction into this area I will talk about some recent results when studying these flows with irregular (or rough) initial conditions. The main results are based on joint works with Herbert Koch (Bonn), Guido Schneider (Stuttgart) and Miles Simon (Magdeburg).