Working Group 3 is devoted to the study of dynamical processes on structured spaces, encompassing discrete networks, hybrid discrete–continuous systems, and fully continuous domains. Its central aim is to understand how dynamics evolve across multiple scales and how they interact with the underlying geometry or topology of the space.

A major focus of WG3 lies in the analysis of diffusive and dissipative systems, particularly those governed by gradient flow and variational principles. These frameworks provide powerful tools for studying homogenization, coarse-graining, and discrete-to-continuum limits, thereby clarifying how macroscopic behavior emerges from microscopic interactions. Special attention is given to dynamics in spaces of probability measures equipped with the Wasserstein metric, which naturally connects WG3 to optimal transport theory.

Beyond classical gradient flows, WG3 also investigates more general dynamics, including conservation laws, non-reciprocal interactions, and active systems originating from biology, chemistry, and social sciences. An important aspect of the group’s work is the study of co-evolving systems, where the dynamics and the underlying spatial or network structure influence each other over time. The outcomes of WG3 are expected to provide unifying dynamical models applicable to phenomena such as epidemic spread, opinion formation, and adaptive network design.