From phase reduction to hypergraphs: the higher-order dynamics of coupled phase oscillators

Networks are powerful tools in the modeling of complex systems, but they do not always capture the right interactions when multiple units are involved simultaneously. Such many-body interactions are encoded by higher-order structures which can be thought as extensions of networks. Over the last years, higher-order networks have been the focus of great excitement, since this novel framework has enormous potential for applications. In this talk, I will give an overview of higher-order interactions and their effects on nonlinear dynamics. I will introduce the basics of dynamics on networks and its extension to the case of higher-order interactions. As examples of the effects on nonlinear dynamics, I will discuss the case of phase reduction for systems with higher-order interactions and show the effects on synchronization dynamics.