Cours spécialisé (HFE, Com)
Contact : alexandros.eskenazis à imj-prg.fr
Pas de notes de cours prévues.
In this course we will explore methods showing the (non)embeddability of metric spaces into Banach spaces. This classical direction in nonlinear functional analysis has grown to be a central topic in mathematics having interactions with Banach space theory, discrete analysis, geometric group theory, combinatorics, probability, differential geometry, and noncommutative geometry, while also having powerful applications to theoretical computer science. Our goal is to study fundamental aspects of embedding theory including: Schoenberg’s theory of isometric embeddings, Bourgain’s embedding theorem for finite metric spaces, Assouad’s embedding theorem for doubling spaces, the embeddability properties of Hamming cubes, \(\ell_\infty\) grids, trees and fractals into Banach spaces, the metric geometry of planar graphs and expander graphs, metric notions of Rademacher type, cotype and uniform convexity, dimensionality reduction, topological methods in embedding theory, and applications to algorithms.