The next geometry seminar will be given by Giovanni Mascellani (Pisa) on 23 May, at 1.30pm, in the Salle des Profs. Giovanni will be joining us as a postdoc this September, so this is a good chance to meet him. His title is *“Fourth-order geometric flows on manifolds with boundary”* and his abstract is below.

Geometric flows are a class of objects that proved very powerful tools for solving problems in geometric analysis (the proof the the Poincaré conjecture by mean of the Ricci flow, completed in 2003 by Perelman, is probably the most famous example). A flow is a smooth evolution of the Riemannian metric on a manifold, regulated by a differential equation usually chosen in order to regularize its geometric features (e.g, the curvature).

I will give a bird’s eye overview on the typical approach for working with flows, taking as an example a class of fourth-order flows first studied by Vincent Bour. Then I will discuss a few problems that arise

when one wants to extend Bour’s theory to manifolds with boundary, particularly considering short time existence.