Ernesto Estrada (IFISC)

Towards Network Geometrodynamics. Directed Networks.

Friday the 10th of October, 2025, 11:00, NOTICE THE UNUSUAL LOCATION: ICMAT Aula Gris 2.

I will start by motivating the problems emerging for the analysis of diffusion on directed and mixed graphs. Then, I will introduce a model or reaction-diffusion on networks where the diffusive part is controlled by the standard graph Laplacian operator and the reaction one by an imaginary potential. This results in a Hermitian reaction-diffusion operator, which is mathematically identical to the 'magnetic' Laplacian of the graph. By solving the abstract Cauchy problem of the reaction-diffusion based on this operator I will prove how the capacity of the whole network to transporting mass between two vertices is a (real-valued) Euclidean distance in the graph. Although the embedding of the graph induced by this distance is in a complex Euclidean space, we can define some real, Hermitian and complex angles between different planes defined on the graph. In particular, I will focus on the meaning and applications of the Kahler angles formed between pairs of vertices in the graph.

Link for online session (Active on request): https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380