This project aims at substantially advancing the knowledge about Lipschitz-free spaces and their applications to metric geometry and to functional analysis. For a metric space (M,d) the free space F(M) is a Banach space that is built around the metric space M in such a way that M is isometric to a subset F(M) and Lipschitz maps from M into any other Banach space X canonically become bounded linear operators from F(M) into X. Analyzing the linear maps between the free spaces contributes a precious information for the analysis of the Lipschitz maps between the underlying metric spaces. Lipschitz-free spaces appear naturally also in domains such as Optimal Transport, Computer Science or Machine Learning.
Despite the exponentially growing activity concerning Lipschitz-free spaces observed nowadays, many basic questions about them stay without answer. We believe that the right moment for this to change is now. Indeed, several new ideas appeared recently (supports, quotient representations, compact reduction) with the potential to give the needed push. We propose a study of isomorphic and isometric properties of free spaces as well as a pioneering study of linear dynamics in free spaces.
The requested grant will be used to finance the visits and invitations of our national and international collaborators, to organize a conference dedicated to Lipschitz free spaces and their interactions, and to recruit a post-doc fellow for 1 year. We are convinced that our project has the potential to bring together many young scientists in France and around the world with interest in this beautiful fast-growing subject.
Monsieur Antonin Prochazka (LABORATOIRE DE MATHÉMATIQUES DE BESANÇON)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
LMB LABORATOIRE DE MATHÉMATIQUES DE BESANÇON
EA2597 LABORATOIRE DE MATHEMATIQUES PURES ET APPLIQUEES JOSEPH LIOUVILLE
LAMA Laboratoire d'analyse et de mathématiques appliquées
Help of the ANR 92,059 euros
Beginning and duration of the scientific project: December 2020 - 48 Months