Monday, May 6, 2013, 3:30 B113 VV, Tuesday, May 7, 2013, 4:00 p.m., B139VV Wednesday, May 8, 2013. 3:30 p.m., B317 VV Diego Cordoba (ICMAT Madrid) will give three lectures on Interface dynamics for incompressible fluids. Abstract: We consider the evolution of an interface generated between two immiscible, incompressible and irrotational fluids. Specifically we study the Muskat equation (the interface between oil and water in sand) and water wave equation (interface between water and vacuum). For both equations we will study well-posedness and the existence of smooth initial data for which the smoothness of the interface breaks down in finite time. We will also discuss some open problems.