Title: What is the p-adic Riemann zeta function?

Most mathematicians have heard of the Riemann Zeta function, the subject of arguably the most famous (open) conjecture in number theory. Less well known is its arithmetic cousin - the p-adic Riemann Zeta function - which was also the subject of an important conjecture (now a theorem).

In this talk I would like to explain what the p-adic Riemann zeta function is (spoiler: it's not actually a function!) and how its existence expresses even more deep arithmetic properties of the (complex) Riemann zeta function.

The talk should be accessible to a broad mathematical audience.