Bohnenblust--Hille inequalities for cyclic groups

Haonan Zhang (University of South Carolina)

Thursday 21st November 16:00-17:00 Maths 311B

Abstract

A fundamental problem from computational learning theory is to efficiently reconstruct an unknown Boolean function. One classical result of this problem for the random query model is the low-degree algorithm of Linial, Mansour, and Nisan in 1993. This method saw exponential improvement in 2022 by Eskenazis and Ivanisvili via a family of dimension-free polynomial inequalities named after Bohnenblust and Hille dating back to Littlewood's work in 1930. In this talk, I will review the recent progress along this line of research on discrete quantum systems, and discuss parallel advances in classical harmonic analysis. This is based on joint work with Alexander Volberg and Joseph Slote.

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