High Dimensional Probability (17w5080)

Arriving in Oaxaca, Mexico Sunday, May 28 and departing Friday June 2, 2017

Organizers

(Washington University in St. Louis)

(Université Paris 5 - René Descartes)

(University of Delaware)

(University of Nice Sophia Antipolis)

(University of Warsaw)

Objectives

The aim of this workshop is to bring together leading experts in high dimensional probability and a number of related areas to discuss the recent progress in the subject as well as present the major open problems and questions. We want to deepen contacts between several different communities with common research interests focusing on probability inequalities, empirical processes, strong approximations, Gaussian and related chaos processes of higher order, Markov processes, concentration of measure techniques and applications of these methods to a wide range of problems in other areas of mathematics, statistics and computer science. We would like also to foster and develop interest in this area of research by new researchers and recent Ph.D.'s. There are many exciting open problems in the area that may be formulated in a way that can be understood by graduate students. We hope that they will attract attention of young people taking part in this workshop.

Particular areas of focus and interest for the meeting include:

- Application of generic chaining techniques to study the regularity of stochastic processes and lower and upper bounds on norms of random vectors and matrices - Interactions between small ball probabilities, approximation theory, and Bayesian nonparametrics - Applications of modern empirical process and strong approximation methods to treat problems of machine learning and inference in high- and infinite-dimensional statistical models - Interactions between information-theoretic inequalities, convex geometry and high-dimensional probability - Stein’s method and its use in high-dimensional probability - Super-conconcentration phenomena in high dimension: new tools, examples and open problems - Identification of major problems and areas of potentially high impact for applications and use in other areas of mathematics, statistics, and computer science