Representing Integers by Ternary Quadratic Forms

This talk will give an introduction to the current state of knowledge of "What integers are represented by a quadratic form in 3 or more variables?". Along the way we will explore the close connections
with Gauss sums, special values of zeta functions, the Riemann hypothesis, modular forms (of integral and half-integral weight), and even Galois representations. We will conclude by characterizing the set of numbers represented by a ternary quadratic form, and explore
several interesting subtleties that exist only in the case of 3 variables.