Given a positive integer n, what are the primes of the form x^2+ny^2? For n=1, this is a familiar question from elementary number theory. For other values of n, the question becomes more interesting and revealing. We will characterize such primes for an infinite set of n (this is no small task! Gauss only succeeded in doing so for 65 selected values of n), treading into some class field theory along the way.
The talk should be accessible to everybody (elementary algebra required).