Nonlinear stability results for nonlocal gradient flows Massimilano Morini (Parma) Abstract: We consider two different nonlocal flows. We first investigate the long-time behavior of the so-called nonlocal Mullins-Sekerka flow, that is the gradient flow, with respect to a suitable Riemannian structure, of the Ohta-Kawasaki energy. In the second part of the talk we consider the evolution of interfaces of elastic materials driven by surface diffusion and elastic stress, establishing new short-time existence and asymptotic stability results.