Heather Harrington (MPI-CBG Dresden and Oxford): Kuramoto Oscillators - Dynamical Systems meets Computational Algebraic Geometry (and Topology)

The Kuramoto model describes synchronisation in graphs of coupled oscillators. A central question is which graphs lead to complete synchronisation and which admit other stable equilibria, known as exotic solutions. In this talk, I will review and present tools from computational algebraic geometry to investigate these questions, characterise equilibrium spaces, and classify graphs exhibiting exotic solutions. Time permitting, I will present a topological data analysis perspective on dynamics of Kuramoto oscillators.