Special Erdős Memorial Lecture
The next Erdős Memorial Lecture will be given by Jeffrey Lagarias,
University of Michigan, at this meeting on Saturday, March 28, 2009.
Title: From Apollonian circle packings to Fibonacci numbers
Abstract: Apollonian circle packings are infinite packings of
circles, constructed recursively from a initial configuration of four
mutually touching circles by adding circles externally tangent to triples
of such circles. If the initial four circles have integer curvatures,
then so do all the circles in the packing. If in addition the circles
have rational centers, then so do all the circles in the packing. This
talk describes results in number theory and group theory arising from
such packings. In particular, the integer curvatures in a packing are
determined by the orbit of an integer vector under the action of an integer
matrix group. Recently, strong results on factorization and primality
of these integers were obtained by Bourgain, Gamburd and Sarnak. We contrast
these properties with those of Fibonacci and Lucas numbers, which are
also describable by an orbits of an integer vectors under a different
integer matrix group. (Some results presented were obtained with Ron Graham,
Colin Mallows, Allan Wilks, Catherine Yan, and Jon Bober.)
Short biography: Jeffrey Lagarias received his Ph.D. in Mathematics
from Massachusetts Institute of Technology in 1974. In 1975 he joined
AT&T Bell Laboratories as a member of the technical staff. From 1995
to 2003, he was a Technology Consultant at AT&T Research Laboratories.
He joined the faculty at the University of Michigan in 2003. While his
recent work has been in theoretical computer science, his original training
was in analytic algebraic number theory. He has since worked in many areas,
both pure and applied, and considers himself a mathematical generalist.
Area of specialty: Number Theory
Research: While my original training was in analytic algebraic
number theory, I have since worked in many areas, both pure and applied,
and consider myself a mathematical generalist. My interests include discrete
geometry, dynamical systems, harmonic analysis (wavelets), lowdimensional
topology, mathematical optimization, mathematical physics, number theory,
and operations research.
