# The Interplay between High-Dimensional Geometry and Probability

**Trimester Program**

**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.

Recent developments emerged from connections between these diﬀerent ﬁelds. To strengthen the ties between these diﬀerent subjects it is important to bring together early-stage researchers and leading experts to discuss these new ideas and foster future collaboration. The trimester will go a long way in helping early-stage researchers navigate the diverse, rapidly-developing literature and wide array of research opportunities. We will also give early-stage researchers a chance to present their own work. Emphasis will be placed on open discussion in an inviting atmosphere.

**Activities during the trimester program: **

The program will include a introductory Winter School addressed to PhD students and postdocs and 2 major workshops: