Title: Spheres, primes, and triangles: tales from the interface of harmonic analysis and number theory
Abstract: Pioneered by Bourgain, the fusion of Fourier analytic and number theoretic techniques in novel ways have led to a variety of discrete operator bounds where continuous techniques fail. Moreover, many distributional questions can be answered in a quantitatively strong way by knowing such bounds. We discuss recent work pertaining to distribution of primes on spheres, higher degree spherical maximal functions and three-point configurations.