Charles Radin

Department of Mathematics
University of Texas
2515 Speedway Stop C1200
Austin, TX 78712-1202

Phone: (512) 471-0174
Office: RLM 12.114
FAX: (512) 471-9038
Email: radin (at) math (dot) utexas (dot) edu

My long-term research interest is the emergence of phases, and especially phase transitions, in large many-component systems as exemplified by the fluid and solid phases of matter in thermal equilibrium. This is a rich subject because of the contrast of scales: phases only emerge at the macroscopic scale yet we want to understand them as based on the microscopic (particle) scale, and the conflict is clarified by the discontinuities of phase transitions. Currently I am concentrating on the emergence of phases in nontraditional settings such as the mathematics of random networks and the physics of soft matter. But over the years this study has included 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 - and their relevance to quasicrystals and, more generally, the rigidity of solids.

Short Curriculum Vitae and professional ancestry


  • Complete list
  • By subject:
  • Packing, tiling and ground states
  • Crystals, soft matter and phase transitions
  • Quantum dynamics
  • Expository papers
  • Book on aperiodic tiling
  • Articles on this work in the popular press, and applications:, Encyclopaedia Britannica etc.

    Some links to matters aperiodic, quasicrystalline, packing/soft matter and random networks