Geometric Nonlinear Functional Analysis (25w5355)


Alexandros Eskenazis (CNRS, Sorbonne Université)

(Texas A&M University)

Javier Alejandro Chávez-Domínguez (University of Oklahoma)

Audrey Fovelle (Universidad de Granada)

Eva Pernecka (Czech Technical University in Prague)


The Casa Matemática Oaxaca (CMO) will host the "Geometric Nonlinear Functional Analysis" workshop in Oaxaca, from May 4 to May 9, 2025.

Geometric nonlinear functional analysis is a very active research area, having close connections to geometric measure theory, metric geometry, probability, classical analysis, combinatorics, and Banach space theory. Its scope of application is far-reaching and has permeated numerous fields, such as geometric group theory, noncommutative geometry, and topology, as well as theoretical computer science and theoretical physics. This relatively new branch of functional analysis treats a variety of problems whose common feature is to understand the intricate relationship between nonlinear geometric objects (e.g. nonlinear Lipschitz mappings, abstract metric spaces) and their natural linear counterparts. Typical topics include but are not limited to, the classification of Banach spaces under nonlinear notions of equivalences, nonlinear embeddings of graph metrics into Banach spaces, group actions on Banach spaces, existence of differentiability point for Lipschitz mappings, infinite combinatorics and geometry of Banach spaces, the structural theory of metrico-algebraic constructs such as Lipschitz free spaces (a.k.a. transportation cost spaces) or uniform Roe algebras.

Since the beginning of the 21st century which marks the publication of the authoritative monograph by Benyamini and Lindenstrauss aptly named Geometric Nonlinear Functional Analysis, the field has grown tremendously in depth and scope. This event aims to bring together experts as well as young researchers working on various aspects of geometric nonlinear functional analysis and to serve as a diverse forum of discussion and collaboration, where recent advances in the field are presented and new interactions are discovered.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Advanced Education and Technology.