Bohnenblust--Hille inequalities and low-degree learning

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• Haonan Zhang (University of South Carolina)
• Friday 06 December 2024, 11:10-11:50
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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