One of the many things John Tate is famous for is his 1950 PhD thesis. In it, Tate reproves results of Hecke (functional equations for certain L-functions) using novel and powerful tools (abstract fourier analysis over adeles and ideles). In this talk, I will attempt to give a sense of these methods, and use them to show that the Riemann zeta function satisfies a functional equation. I will try to make this talk accessible to as broad an audience as possible. In particular, no special knowledge of algebraic number theory will be required beyond basic field theory. Knowledge of the p-adic numbers will be helpful, but I can explain what it is needed here as well if necessary.
(Bagels and refreshments will be served.)