Bernhard Riemann (1826 - 1866) conjectured in 1859 that the analytic extension of \[ \zeta(s):= 1 + \frac{1}{2^s} +\frac{1}{3^s} + \frac{1}{4^s} + \frac{1}{5^s} + \frac{1}{6^s} + \dots = \prod_{p \ {prime}} \Big(1-\frac{1}{p^s}\Big)^{-1} \] to the complex plane has its zeros ONLY at the negative even integers and complex numbers with real part 1/2.

Because of its connection to the distribution of prime numbers, this is one of the major unsolved problems in mathematics, worth $1M (per the Clay Mathematics Institute).

The talk will explain what all this is about.

Pizza will be served.

Riemann's notes (click for full size)

First nontrivial zeros (click for full size) [source of images]

Colloquium sponsored by the NSM Dean's office DUSEM grant