Mathematics Colloquium
Monday, September 30th, 3:00 p.m.
Math Annex 1100
Nike Vatsal
UBC
padic numbers and applications
Let p be a prime number. Then the padic 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 socalled padic metric. Shortly afterwards, Ostrowski
proved that any ``reasonable" metric on the rational numbers is
equivalent to either a padic metric, for some prime p, or the
usual Archimedean metric on the reals. Thus the padic numbers
are in some sense no more or no less natural than the usual
Archimedean metric.
A pervading and fruitful theme in number theory is to study
arithmetic questions from a padic viewpoint, and in this talk
we will discuss the origin of the padics and some recent and
notsorecent results that come from padic methods.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
