Energy Minimizing Periodic Point Sets

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Point configurations minimizing energy for a given pair potential function occur in diverse contexts of mathematics and its applications. In recent years the study of universally optimal point configurations has revealed some striking new phenomena. In this project we will break new grounds in the study of periodic point configurations, that is, for finite unions of translates of a lattice.Creating and using improved numerical tools for computational experiments, we expect to reveal new phenomena and collect evidence for the existence or non-existence of universally optimal periodic point sets. We will develop and apply new criteria for local optimality in the space of periodic point configurations. The recently observed phenomenon of formally-dual periodic point sets will be studied and, as far as possible, corresponding sets will be classified. The software developed during the project will be published, giving other researchers a useful tool for future studies.