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), low-dimensional topology, mathematical optimization, mathematical physics, number theory, and operations research.