COST action "Mathematical models for interacting dynamics on networks"
Graphs are used to model physical processes - for instance of diffusive, elastic or quantum mechanical nature - that admit a network-type structure. The analysis of evolutionary problems on graphs has a long tradition. Besides a classical approach based on semigroups of operators, variational methods have received a lot of attention.
The currently most interesting research topics in this area include spectral geometry for the asymptotic analysis of parabolic equations, form methods for extension theory, the theory of optimal transport, and numerical methods for the analysis of traffic problems.
These areas form the core of activities of the project "Mathematical models for interacting dynamics on networks" that is financed by COST since 2019 and is dedicated to the fundamental research as well as industrial applications of dynamics on networks. Delio Mugnolo heads the working group 4 "Variational methods on graphs and networks" and represents, jointly with Bálint Farkas (Wuppertal), Germany in the leading committee of the action.