ROSSI (Universita' di Padova) TITLE: Propagation phenomena for heterogeneous KPP equations The talk is concerned with generalized transition waves for reaction-diffusion equations with monostable nonlinearity. It is well known that in the homogeneous case the family of speeds associated with traveling fronts is given by a right half-line. In collaboration with G. Nadin, we have improved this result to nonlinearities depending in general way on time by introducing a suitable notion of mean. As an application, we have obtained the existence of random traveling waves when the nonlinearity is stationary ergodic. At the end of the talk, we will present some work in progress with L. Ryzhik where also space-dependence is taken into account.