Explore the intricacies of the discrete cube in this illuminating lecture by Ramon van Handel from Princeton University. Delve into methods of Fourier analysis, the Poisson inequality, and interpolation techniques as they apply to this fundamental mathematical structure. Gain insights into random walks on the discrete cube and follow a comprehensive proof that ties these concepts together. Part of the "Probability, Geometry, and Computation in High Dimensions Boot Camp" series, this talk offers a deep dive into advanced mathematical concepts with applications in high-dimensional probability and geometry.