## Discrete Structures: Harmonic Analysis and Probability

**Date:**
27 - 28 September 2018

**Location: ** Mathematical Institute, University of Oxford

**Event type:**
CRC Workshop

**Organisers: ** Alexander Volberg (Michigan State) and Paata Ivanisvili (Princeton and UC Irvine)

This workshop will focus on progress in analysis of geometric functional inequalities in particular, but not exclusively, on discrete model: the Hamming cube.

Talks will give an overview of the area, its connections to PDE, combinatorics, martingale methods, stochastic optimization problems, various notions of convexity, and applications to random graphs. The harmonic analysis on Hamming cube is a tool for studying the Renyi random graph model (e.g. sharp threshold results of the type of Margulis graph connectivity theorem).

The geometric functional inequalities are often rooted in their discrete versions on Hamming cube, where the harmonic analysis has many interesting specifics and often uses probabilistic ideas. For example, martingale method leads to important geometric inequalities on Hamming cube and Gauss space, such as e.g. the concentration of measure inequalities. The concentration of measure phenomenon, in its turn, has utmost importance in applied mathematics, in questions of spectral initialization or compressed sensing.

**Speakers: **Franck Barthe (Toulouse), Sergey Bobkov (Minnesota), Dario Cordero-Erausquin (Paris 6), Paata Ivanisvili (UC Irvine), Ryan O’Donnell (Carnegie Mellon), Stefanie Petermichl (Toulouse), Mark Rudelson (Michigan), Ramon van Handel (Princeton), Alexander Volberg (Michigan State)