Due to COVID-19 restrictions on travel, this workshop will be conducted via ZOOM and will be reduced to only the minicourses.
This concentration week is part of the
Workshop in Analysis and Probability.
Overview: Boolean functions defined on the hypercube - also known as the Hamming cube - are foundational objects in many
applied fields, such as circuit design, cryptography, theoretical computer science, or social choice theory.
Analysis of such boolean functions is now a powerful and indispensable tool. A fascinating new direction has recently
emerged in this field, involving Poincaré type and log-Sobolev type inequalities for the Hamming cube. Very surprising
recent works by A. Volberg, F. Nazarov, D. Li, P. Ivanisvili and others have made great strides by taking a duality approach
via Bellman functions. Loosely speaking, Bellman functions resulting from estimates for the dyadic square function
can be "dualized" via a Legendre type transform to obtain a corresponding estimate for the gradient on the Hamming cube.
This workshop is aimed at graduate students and postdocs in analysis, probability and related fields, but also to anyone wishing to learn this subject.
The goal is to introduce the main tools, current results, and open problems in
functional inequalities on the Hamming cube through a series of minicourses by
Alexander Volberg,
Paata Ivanisvili, and
Irina Holmes.
The participants are not expected to have prior knowledge
on these specific topics, but a standard background in graduate analysis and probability is assumed.