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.
