The main purpose of this project is to address the problem of optimal networks from different analytical points of view. Optimal networks arise from several contexts and cover mathematical fields such as optimal transport and branched optimal transport problems (particular case of the so-called Gilbert- Steiner problem), the Steiner problem, the singular structure of solutions to certain PDEs, variational problems for maps with values into a manifold, and also physically relevant problems such as crystals dislocations and liquid crystals.
In recent years many different geometric measure theoretical approaches to the problem of optimal networks have been proposed, with different aims (description of the model, existence results, regularity, numerical results...). We plan to strengthen the exchange and collaboration among the communities that adopted some of these approaches.
