Monday, September 30th, 3:00 p.m.
Math Annex 1100
p-adic numbers and applications
Let p be a prime number. Then the p-adic numbers were discovered by
Hensel in the early part of the twentieth century, as the Cauchy
completion of the rational numbers Q with the respect to a certain
metric, the so-called p-adic metric. Shortly afterwards, Ostrowski
proved that any ``reasonable" metric on the rational numbers is
equivalent to either a p-adic metric, for some prime p, or the
usual Archimedean metric on the reals. Thus the p-adic numbers
are in some sense no more or no less natural than the usual
A pervading and fruitful theme in number theory is to study
arithmetic questions from a p-adic viewpoint, and in this talk
we will discuss the origin of the p-adics and some recent and
not-so-recent results that come from p-adic methods.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).