Dominique Maldague, of Cambridge University and UCLA, continues a two-part talk given at the Institute for Advanced Study's WAM program on Fourier restriction theory. She builds from the classical use of Fourier series in solving the wave and Schrodinger equations, then shows how imposing frequency constraints turns these series into objects with real geometric structure. From there she connects the subject to three concrete problems: the distribution of prime numbers, the size of arithmetic progressions inside sets, and the Kakeya problem in fractal geometry, which asks how small a set can be while still containing a line in every direction. The talk traces how one analytic framework threads through number theory, combinatorics, and geometric measure theory, aimed at an audience already comfortable with graduate-level analysis.