The Symmetry and Order of Densest Packings of Space

PI最近在填料的定性特征上获得了新的结果：证明了平面上某一变形盘的低密度和高密度填料之间的突变（相变），并且实验发现，随着密度的变化，砂填料中的相变（即由重力产生的各向异性）。这些结果提供了一种统一的方法来理解填料几何的某些定性特征，以意想不到的和富有成效的方式将研究领域联系起来，并使用了传统方法中不同寻常的各种数学技术来进行此类研究。

The PI has recently obtained new results on qualitative features of packings : proof of an abrupt change (phase transition) between low and high density packings of a certain deformed disk in the plane, and the experimental discovery of a phase transition in packings of sand (that is, with anisotropy produced by gravity) as density is varied.These results give a uniform approach to understanding certain qualitative features of the geometry of packings, linking research areas in unexpected and fruitful ways, and using a variety of mathematical techniques unusual in the traditional approaches to such studies.