In this talk we present some recent result about the long time behavior of the solutions for some diffusion processes on a metric graph.  We study  evolution problems on a metric connected finite graph in which some of the edges have infinity length. We show that the asymptotic behaviour of the solutions of the heat…

The talk is about oscillatory integral operators on manifolds.  Manifolds of constant sectional curvatures are particularly interesting, and we will see that very good estimates on these manifolds can be expected. We will also discuss Kakeya and Nikodym problems on general manifolds, in particular, manifolds satisfying Sogge’s chaotic curvatures.