Abstract. Place n nodes on the unit circle and connect some pairs with springs that pull connected nodes toward each other. Which graphs always make all nodes converge to a single point, no matter how they start? This is known as the global synchronization problem of the Kuramoto model and is closely tied to the benign nonconvexity of its synchronization landscape. In this talk, I will demonstrate how this dynamical, continuous question can be reduced to a static, combinatorial one. I will show that certain inductively defined graph classes are globally synchronizing, based purely on a combinatorial analysis of unit vector configurations in the plane. This perspective reveals that global synchronization, despite being a collective phenomenon, unfolds on these graphs through a sequential process of local synchronization that propagates along their structural skeletons.
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Annotated Slides.