Seminario - Prof. Spitoni

Topology, noise, and parallelism in circular opinions

Prof. Cristian Spitoni
Department of Mathematics, Utrecht University (NL)
Guest at SBAI, Sapienza Visiting Professors Program 2025

Abstract
This talk explores how topology affects consensus dynamics when opinions take values on a circle. Starting from the Kuramoto model, an asynchronous continuous-space cellular automaton based on local midpoint averaging is introduced. Although the dynamics eventually reaches consensus, periodic boundary conditions can generate long-lived metastable states characterized by a nonzero winding number. The role of this topological trapping is analyzed, together with the effects of stochastic perturbations and parallel updates, revealing the interplay between topology, noise, and relaxation dynamics.