View AbstractAbstract: "Tate Days" is a one-day graduate student seminar centered around a paper of John Tate. This seminar, the fifth in the series, is centered around the Ph.D. thesis of Tate (Princeton, 1950).
The talks will be an exposition of Tate's thesis which used harmonic analysis and Fourier transforms to prove results in number theory, namely, the proof of the meromorphic continuation and functional equation of the zeta function of number fields; these properties for the Riemann zeta function were proved by Riemann.
The talks will be mostly self-contained, beginning with the basics of Fourier analysis on locally compact groups (especially p-adic numbers, adeles, ideles) and then Poisson summation, Riemann-Roch theorems and ending with the functional equation and meromorphic continuation of the zeta function of number fields.
There will be a break for lunch and coffee. Speakers are our own graduate students: D. Bekkerman, S. Gilles, D. Kaufman, D. Zollers, R. Cowan, N. Dykas