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. Radin is also working on the closely related physics problem of the origin of structure in high density matter using probabilistic models of sphere packings. For instance he is interested in proving phase transitions in statistical mechanics models such as hard spheres, used in modelling both thermal equilibrium and various forms of soft matter such as sand piles or crumpled sheets.