P-adic Interpolation of the Riemann Zeta Function -- Rebecca Bellovin
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The familiar zeta function $\zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s}$ is a function of the real or complex variable s.  We can also ask whether there is an analogue of the zeta function defined over the p-adic numbers.  I will give an elementary construction of such a function, and if time permits, I will outline a more general technique.  The talk will assume only knowledge of p-adic numbers. 
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The talk should be accessible to everybody (elementary algebra required).