BELLMAN FUNCTION METHODS FOR THE HYPERCUBE

Concentration Week: August 3 - 7, 2020.
Organizers: Irina Holmes and Alexander Volberg

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Due to COVID-19 restrictions on travel, this workshop will be conducted via ZOOM.

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. 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, as well as problem sessions and times set aside for discussion and collaboration. The participants are not expected to have prior knowledge on these specific topics, but a standard background in graduate analysis and probability is assumed.

We are also eager to know more about the research of the participants, so we will have afternoon sessions of 30 minute talks where participants can present their current or completed projects.

Financial Support: We expect to cover the local expenses (hotel/dorm accommodation and a modest per diem) for registered participants who request financial support. We are unable to cover travel expenses for most participants.