This is a public lecture presented at the XXVth Journées Arithmétiques in
Edinburgh on July 3rd, 2007.
The main body of the lecture appears in these slides.
It is meant as a presentation so you should click fairly rapidly through the slides.
Following further developments this was modified for my 2011 lectures in Haifa
At the bottom of some slides, in small print, are notes to the lecturer reminding him of what comes next.
However, at the bottom of slide 32, is the word, "Conway". This refers to the following animation,
which was kindly
created for me by Anthony Doran. The controls should be
self-explanatory.
I repeated (a version of) this lecture at Northwestern University on May 14th, 2008
Northwestern decide to video it, so see the movie in
high or
low resolution, or
for your iPod