The study of estimating the size of a solution to a linear dispersive partial differential equation, called the Strichartz estimate, has been of interest in both partial differential equations and harmonic analysis.

In this talk, I will focus on Strichartz estimates for the Schrödinger equation on a flat two-dimensional torus, which has rich connection to discrete mathematics. I will briefly introduce some of the connections, ranging from number theory to, more recently, incidence geometry and additive combinatorics.