Three lectures on Fourier analysis and learning theory

Abstract

Fourier analysis on the discrete hypercubes $\{-1,1{\}}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the context of learning low-degree Boolean functions. In these lecture notes, we explore this line of research and discuss recent progress in discrete quantum systems and classical Fourier analysis.

Expanded lecture notes given at IASM, HIT in summer 2024