Quivers are directed graphs with loops and multiple arrows between vertices. We will look at networks of dynamics, located at vertices, where the arrows indicate certain influences and dependencies. The theory is driven by many examples in science and technology including, but not limited to, metabolic and neural networks, electronic circuits and power grids, animal gaits and locomotion in robots. Dynamical systems with a network structure display a wealth of spatio-temporal patterns such as synchrony, phase-locked cluster states, multi-frequency patterns, and partial amplitude death. The representation theory of groups, groupoids, and quivers serves as an exciting algebraic framework which we will combine with background from Dynamical Systems to explore the above phenomena. We will focus on hidden symmetries as described by groupoids and quivers, subnetwork structures and quotient relations. Prerequisite: some background on Dynamical Systems or Algebra or Graph Theory. Schließen