Mathematical Application Research Team Meeting #15

Mathematical Application Research Team is delighted to welcome Dr. Pietro De Lellis from University of Naples Federico II, for an upcoming team meeting. We warmly invite everyone to join us for this opportunity to hear about his latest research.

Title: Synchronization and Control in Higher-Order Network Dynamics

Abstract
Understanding how network structure shapes coordinated behavior in coupled dynamical systems is a central question in network science. Although pairwise interactions among identical nodes are well understood, much less is known about the effects of directed higher-order interactions, especially in systems with heterogeneous nodes. In this seminar, I will discuss recent results on the emergence and control of collective behavior in such systems.
I will first present an extension of the standard pairwise framework to higher-order directed interactions and derive conditions for synchronization in the identical-node setting. I will then introduce a mathematically grounded heuristic for steering the system toward a prescribed trajectory. Moving to heterogeneous dynamics, I will present a new notion of network synchronizability that quantifies how hypergraph topology can promote trajectory alignment even when node parameters differ. The resulting metric is analytically derived, agrees closely with numerical observations, and scales efficiently to large networks. This makes it possible to compare higher-order and pairwise interactions systematically, and to identify when multi-body interactions favor or obstruct synchronization. I will conclude with an application to opinion dynamics, where the framework highlights which hyperedges are most conducive to consensus formation.