What lattice polytopes can tell us about network of oscillators?

Abstract: Lattice polytopes have found many, often surprising, applications in science and engineering. We begin this talk with a brief review of the connections between symmetric edge polytopes and the Kuramoto equations, which are crucial in the study of networks of coupled oscillators derived from biology, chemistry, and engineering. We highlight the important information about Kuramoto equations that are encoded in the symmetric edge polytopes. We also extend this connection to other families of equations. Finally, we end with an exploration on what symmetric edge polytopes can tell us about the interesting phenomenon of "oscillator death".

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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