Segnalo il seguente seminario, che si terrà Lunedì prossimo in Sapienza.

*Lunedì 11 Novembre, ore 14:00,* Aula B, Dipartimento di Matematica, Sapienza Università di Roma

*Speaker:* Pablo Groisman (University of Buenos Aires)

*Title: *The Kuramoto Model in Random Geometric Graphs

*Abstract: *The Kuramoto model is a nonlinear system of ODEs that represents the behavior of coupled oscillators. The coupling is determined by a given graph and pushes the system towards synchronization. An important question is whether there is global synchronization (the system converges to a state in which all the phases coincide from almost every initial condition) or if the system supports other patterns. We will consider the Kuramoto model on random geometric graphs in the d dimensional torus and prove a scaling limit. The limiting object is given by the heat equation. On the one hand this shows that the nonlinearities of the system disappear under this scaling and on the other hand, provides evidence that stable equilibria of the Kuramoto model on these graphs are, as n → ∞, in correspondence with those of the heat equation, which are explicit and given by twisted states. In view of this, we conjecture the existence of twisted stable equilibria with high probability as n → ∞. We'll prove this conjecture in dimension d=1.

******************************** Vittoria Silvestri

Assistant Professor Department of Mathematics University "La Sapienza" Piazzale Aldo Moro, 5 00185 - Rome ********************************