Title: The Points Between the Primes<br><br>

Abstract: Some of the arithmetic properties of the integers can be
reinterpreted (or rediscovered) using the theory of analytic spaces
invented by Vladimir Berkovich in the late 1980s.

First I'll review Ostrowski's theorem and the product formula:
these tell us all of the different ways to complete the integers and their
relation to each other. Then I'll introduce a construction of Berkovich,
called the Berkovich spectrum (he didn't call it that), that allows one
to glue all of these completions together into a compact, path-
connected, Hausdorff topological space. We can introduce a metric
structure on this space and reinterpret the product formula in terms
of harmonic functions.
* No prior knowledge of any of these concepts will be necessary. *