Sala Seminari (Dip. Matematica).
In the first part of the talk I will present a comprehensive theory that covers in a unified way a rather large class of (possibly) nonlocal geometric flows bearing a gradient flow structure with respect to suitable generalized perimeters. Within this framework one can establish new existence and uniqueness results as well as recover several examples scattered in the literature. In the second part I will discuss a new distributional formulation that allows one to treat the highly “degenerate” case of crystalline mean curvature motions and to establish the first global-in-time existence and uniqueness results for the crystalline mean curvature flow valid in all dimensions, for arbitrary (possibly unbounded) initial sets, and for general (including crystalline) anisotropies.