Olivetti Club

Max Lipton
Conformal group actions on coupled Kuramoto oscillators

Tuesday, February 19, 2019 - 4:30pm
Malott 406

Kuramoto Systems are collections of moving particles on a sphere governed by a global coupling function. They can be used to model neural networks, synchronized chirping, and the focus of a beast with many eyes. In the classical case on a Kuramoto system with $N$ bodies on $S^1$, Watanabe and Strogatz proved there are $N-3$ independent quantities that are conserved over time. Thus, this dynamical system which is ostensibly in $N$ dimensions can be reduced to a system in three dimensions. In 2009, Mirollo et. al. realized these conserved quantities are equivalent to the cross ratios between $4-$tuples of points preserved by the Mobius transformations, also known as fractional linear transformations. Recently, Lohe has shown that cross ratios are still preserved in the higher dimensional Kuramoto systems in $S^d$, and I will explain how this leads to a reduction to a system in a Lie group of conformal transformations.

Refreshments will be served in the lounge at 4:00 PM.