Interactions and Topological Synchronization in Simplicial Kuramoto Model

Watch a 43-minute research lecture exploring the dynamics of simplicial Kuramoto models and their role in understanding interacting oscillators on simplicial complexes. Delve into the mathematical foundations using discrete differential geometry to uncover the relationships between topology, geometry, and dynamics. Learn about the microscopic interpretation of interaction terms, including higher-order and self interactions, and understand the equivalence between simplicial Kuramoto models and standard Kuramoto models on pairwise networks when dealing with pseudomanifold simplicial complexes. Explore the concept of simplicial synchronization, its connection to simplicial homology, and examine the mathematical bounds necessary for achieving oscillator coupling strength and synchronization.