Programme on "Minimal Energy Point Sets, Lattices, and Designs"

September 29 - November 22, 2014

organised by

Christine Bachoc Peter Grabner Edward B. Saff and Achill Schürmann

Participants of the first workshop

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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