Bi-Co Mathematics Colloquium with Dr. Matthew Mizuhara
Abstract: How do fireflies in Thailand spontaneously begin flashing their lights in unison? Why did the Millennium Bridge in London start wobbling when it opened to pedestrians in 2000? And what do these two situations have to do with each other? In this talk, we explore how mathematics helps us study synchronization and other pattern formation in complex systems. I will first introduce the celebrated Kuramoto model as a simple and natural framework for describing pairwise interactions in complex systems. Through a combination of numerical simulations and analytical tools, we will see how both individual heterogeneity and the network of interactions shape the emergent behaviors. In particular, I will highlight how mean-field limits and bifurcation analysis help us overcome the difficulties of solving these high-dimensional, nonlinear systems. I will conclude with recent results on self-similar networks, where the geometry of fractals opens new directions for the study of synchronization.
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