Discrete harmonic analysis (vignettes)

Boolean function analysis is a tremendously useful topic with many applications to TCS. Traditionally, the functions being studied reside on the Boolean hypercube. Nowadays the horizons have broadened, with domains as varied as Gaussian space, association schemes, and locally testable codes being studied from a Fourier-theoretic angle. We will shine a spotlight on some of these advances, focusing on the underlying theory rather than on particular applications.