January 5 - April 23, 2021

dedicated to Elizabeth Meckes

Organizers: Ronen Eldan, Assaf Naor, Matthias Reitzner, Christoph Thäle, Elisabeth M. Werner

Description: The last ten years have seen a merger of ideas and techniques from analysis, geometry and probability and have led to breakthrough results. It is the goal of this trimester program to bring together senior and junior researchers in these areas for mutual exchange of ideas and methods, to intensify the already existing ties and to stimulate substantial progress at the crossroads of these disciplines. Asymptotic geometric analysis is concerned with geometric and linear properties of finite dimensional objects, studying their characteristic behavior when the dimension, or a number of other relevant free parameters, grows to infinity. High dimensional systems appear naturally and play an essential role in mathematics and applied sciences. It is from the shared need to better understand similar phenomena that many breakthrough results have occurred in the last decade. The roots of asymptotic geometric analysis are essentially in functional analysis but the area is now closely tied to convex and discrete geometry, several branches of probability including stochastic geometry, random graph theory and random matrix theory, among others. By virtue of the general framework of asymptotic geometric analysis and its methods, it is situated at the “crossroads” of these fields.

Associated Events: 

• Winter School on The Interplay between High-Dimensional Geometry and Probability (January 11-15, 2021)
• Workshop: High dimensional spatial random systems (February 22-26, 2021)
• Workshop: High dimensional measures: geometric and probabilistic aspects (March 22-26, 2021)