Saturday Morning Plenary Lecture:

"Diophantine Analysis of Apollonian Packings"

Abstract:
The curvatures of the circles in certain Apollonian packings are all integers.After reviewing the plane geometry and group theory that underlies this remarkable fact, we will examine the diophantine properties of these integral packings. As is the case with most diophantine problems, the "obvious" questions that present themselves are difficult to answer but one can make progress.