Florian "ian" Sprung April 12th, 2006.
<p>
Abstract: 

In the ancient past, many clever people looked at quadratic curves
(circles, parabolas, hyperbolas, ellipses) in a certain light, the real
light. Mathematicians started wondering where the rational points (points
with rational coordinates) were, but no one knew how to see them. This all
changed on a sunny day in 1900 or so, when Hensel saw the light of the
stars emerge after the sun set. He cam up with new "p-adic" lights (I'll
explain what these are, and Hilbert was the first to shed these p-adic
lights on quadratic curves to see those rational points that had managed
to escape from the "real light". 

everything will be kept as easy as possible, so no formal math background
necessary.

this talk might also be anice introduction to both Cathy's and my thesis.