The Kuramoto model is used to describe synchronization behavior of a large set of oscillators. The equilibria of this model can be computed by solving a system of polynomial equations using algebraic geometry. Typical methods for solving such polynomial systems compute all complex equilibrium points when only the real equilibrium points are of physical interest,…

Mixtures of Gaussians are ubiquitous in data science. We give an introduction to the geometry of these statistical models, with focus on the tensors that represent their higher moments. The familiar theory of rank and borderrank for symmetric tensors is recovered when all covariance matrices are zero. Recent work with Carlos Amendola and Kristian Ranestad…