Energy Minimizing Periodic Point Sets

对于给定的对势函数，最小化能量的点构型出现在数学及其应用的不同背景中。近年来，对普适最优点位形的研究揭示了一些引人注目的新现象。在这个项目中，我们将在研究周期点的配置，也就是说，对于有限联盟的平移的格子。创建和使用改进的数值工具的计算实验，我们希望揭示新的现象，并收集证据的存在或不存在的普遍最佳周期点集。我们将开发和应用新的标准，局部最优的空间中的周期点配置。最近观察到的现象的形式对偶周期点集将进行研究，并尽可能，相应的集将被分类。 该项目期间开发的软件将出版，为其他研究人员提供未来研究的有用工具。

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.