The aim of this programme is to bring together mathematicians and scientists
(especially physicists and chemists) for the purpose of gaining a better
understanding of the structure of particle systems under a variety of physical
constraints. The subject includes, for example, classical ground states for
interacting particle systems, best-packing, random packings, jammed states,
granular and colloidal systems, as well as minimal discrete and continuous
energy problems for general kernels. The common thread that runs through these
subjects is that they are related to problems of optimality under various
physical constraints. Of particular interest is that of systems of particles
interacting through a pairwise potential and restricted to the unit sphere
S^d in R^(d+1). This is the classical Thomson problem in the
case d=2 with the Coulomb potential. Such problems on the sphere are
related to spherical designs, coding theory, viral morphology and Voronoi
decompositions. Specifically, the programme will focus on (i) relationships
between geometrical, topological, and combinatorial properties of a manifold
that are reflected in the asymptotics of minimal energy problems; (ii) the
analysis and development of statistical mechanical models from first
principles; (iii) tilings and Voronoi decompositions; (iv) high dimensional
sphere packings; (v) the geometry of the structure of jammed and near optimal
configurations.
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