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, low-dimensional 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.