We study a class of evolution equations, which are derived as a continuum limit of interacting dynamical systems on convergent graph sequences. For systems on random graphs, we present a dynamical law of large numbers and a large deviation principle. We also discuss applications to the analysis of synchronization, pattern formation, and metastability in the Kuramoto model of coupled oscillators.

Biography: Georgi Medvedev received Ph.D. in Mathematics from Boston University in 1999. Before coming to Drexel University in 2002, he was a Veblen Research Instructor at Princeton University and the Institute for Advanced Study.