Faculty Detail
Jeffrey Lagarias
Professor
3086 East Hall
Phone: (734) 7631186
Email:
lagarias@umich.edu

Affiliation(s)

Combinatorics
Computer Science
Geometry and Topology
Number Theory

Combinatorics

About
My research interests are diverse. My initial training was in analytic and algebraic number theory. After receiving the PhD in 1974, I worked at Bell Laboratories and AT &T Labs until 2003, on problems in many pure and applied fields. Besides number theory, I have made contributions in harmonic analysis (wavelets and fractals), mathematical optimization (interior point methods), discrete geometry (tilings and quasicrystals), ergodic theory, lowdimensional topology (complexity of unknotting), and theoretical computer science.
At Michigan I have been active in the number theory group over the last few years, with additional work in other fields. My last 25 postings on the arXiv were in: Number Theory (16), Dynamical Systems (3), Classical Analysis and ODE?s (3), Metric Geometry (1), Optimization and Control (1), Spectral Theory (1). My doctoral students typically work on their own topics. Some have worked in topics in number theory: integer factorial ratios, character sum estimates, Diophantine equations with two separated variables; Others have worked in topics in discrete geometry: packings of regular tetrahedra, rigidity of circle configurations.
News
Jeffrey Lagarias is appointed a George Polya Lecturer for the Mathematical Association of America. 2011
The Polya lectureships were established to uphold the high expository standards set by George Polya. The lectureship entails giving invited talks at selected MAA Section meetings over the two year appointment period.
Jeffrey Lagarias gives the Erdos Memorial Lecture at the Spring Central Section Meeting of the American Mathematical Society. 2009
His talk, "From Apollonian Circle Packings to Fibonacci Numbers", described results in number theory and group theory that arise from Apollonian circle packings, and contrasted some of the properties relating to the circles' curvatures with those of Fibonacci and Lucas numbers. The Erdos Memorial Lecture is an annual invited address named for the prolific mathematician Paul Erdos.
The Mathematical Association of America awards Jeffrey Lagarias a Lester R. Ford Award. 2008
Established in 1964, the award, which includes a citation and cash prize, is presented for articles of expository excellence published in the American Mathematical Monthly. Lagarias received the recognition for his article "Wild and Wooley Numbers," vol. 113, No. 2, 2006.
Jeffrey Lagarias received an award for the Best Paper of the Year for 2005 in the area of Difference Equations from the International Society of Difference Equations. 2005
The award recognizes a series of three papers written jointly with Eric Rains entitled "Dynamics of a Family of Piecewiselinear Areapreserving Plane Maps" that were published in Volume 11 of the Journal of Difference Equations and Applications.