Ph.D., University of Rochester (1970)

Research Interests

Mathematical Physics, Discrete Geometry, Extremal Combinatorics

Current research interest: Hilbert's eighteenth problem - understanding the symmetry of optimally dense packings, of spheres or polyhedra, in Euclidean and hyperbolic spaces, including aperiodic tilings such as the pinwheel, the quaquaversal, and the Penrose kites and darts. I'm also working on the closely related physics problem of the origin of structure in high density/low energy matter, using probabilistic models of sphere packings. In particular I'm interested in phase transitions in various exotic materials in and out of thermal equilibrium, for instance soft matter, such as compacted sand, and quasicrystals. And although direct applications are not yet as compelling, I am also applying similar ideas to random networks and random permutations.