Fall School : Metric Embeddings

Description

Scope and Goal of the Fall School

The Fall School is intended to be an intensive school on embedding techniques and obstructions to embeddings. Embeddings of metric spaces into Banach spaces and its applications will be the main topic of the workshop. The Fall School will cover coarse, uniform, bi-Lipschitz embeddings and their applications in geometric group theory, Banach space geometry and quantitative metric geometry. The format of the workshop is based on similar events that have occurred in UCLA (run by Christoph Thiele) and University of Bloomington-Indiana (run by David Fisher). The targeted participants are PhD students, postdocs or young researchers. The goal will be to cover some key techniques in detail, with all lectures given by the active participants. The active participants will also be asked to write a short article on the topic of their talk, prior to attending the Fall School.

Outreach and Interdisciplinary of the Fall School

It is quite remarkable that fundamental subfields of quantum physics, theoretical computer science and pure mathematics share a common feature. Indeed, numerous problems that arose in these fields highly rely at the theoretical level on a deep understanding of the geometric properties of certain metric spaces. For instance, embeddings incurring a small distortion on distances, of large but finite metric spaces, into Banach spaces with an almost Euclidean geometry is a cornerstone in designing fast approximation algorithms. One of the main goal of the Fall School is to invite young mathematicians from three seemingly different communities to interact on a common topic of interest and help them built a broad and significant global knowledge related to the embedding theory. Breaking the barriers between fields and building a community of young researchers acquainted with the numerous techniques and sharing a global knowledge, and a common language, is expected to have a significant impact on the theory.