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Seung Yeol Ha (Dept. of Math, SNU) In this talk, we will discuss complete phase-frequency synchronization for the discrete and continuous-time Kuramoto phase models with random interactions. We present sufficient conditions for initial configurations leading to the exponential time-decay toward completely synchronized states which is characterized by initial configurations and natural frequencies. If time is permitted, we will also discuss the kinetic Kuramoto model and provide the global existence of measure-valued solutions and their asymptotic behavior. |