Focus Event on the Geometry of Wasserstein Spaces

The goal of this focus event is to study certain fundamental geometric properties of Wasserstein spaces and to explore further the intimate relationship between the theory of Lipschitz-free spaces and optimal transportation.

This week is dedicated to discussions and joint research, possibly after some introductory talks.

Participants:

• Ramón J. Aliaga (Universitat Politècnica de València)   
• Zoltán Balogh (University of Bern, Switzerland)
• Nicolas Juillet (Université de Haute-Alsace)
• Eva Pernecká (Czech Technical University in Prague) 
• Tamás Titkos (Rényi Institute)
• Dániel Virosztek (Rényi Institute)

Report:

This focused event on the geometry of Wasserstein spaces was organized by T. Titkos and D. Virosztek within the framework of the Optimal Transport on Quantum Structures semester at the Erdos Center, Budapest.
The aims of this week included exploring synergy effects between optimal transport and Lipschitz-free spaces (R. J. Aliaga and E. Pernecka are experts in the latter field) and gaining a deeper understanding of optimal transport in non-Euclidean geometries like the Heisenberg group (an area of expertise of Z. Balogh and N. Juillet).
We had a dense week of fruitful discussions and informal presentations concerning, e.g., the notoriously hard problem of possible isomorphisms between (seemingly) different Lipschitz-free spaces and the classification of isometries of Wasserstein-Heisenberg spaces. Among others, we made significant steps forward to describe the Wasserstein-Heisenberg isometries.