Mathematical Sciences: Mathematical Physics of Crystals, andTiling

9531584雷丁这个项目涉及对欧几里得空间的瓦片进行分类，欧几里德空间可以通过复制有限组不同的瓦片来产生。这位研究人员计划将他最近在平面和空间的旋转对称平铺方面的结果应用于此。将使用的方法是传统遍历理论和来自非周期平铺的新技术的组合。这两个研究领域之间有一些基本的数学问题是相同的：确定低温物质中结晶对称性的原因，以及根据有限数量的瓷砖的副本对空间的瓷砖进行分类。这两个都是最优化问题；晶体问题涉及到确定迫使低温和高压物质具有高度结晶有序性和对称性的基本机制，这是通过实验发现的。

9531584 Radin This project has to do with classifying the tilings of Euclidean space produceable by copies of a finite set of distinct tiles. The investigator plans to apply his recent results on rotation symmetric tilings of the plane and space. The methods to be used are a combination of traditional ergodic theory and new techniques from aperiodic tilings. There are fundamental mathematical questions in common between the two areas of investigation: determining the causes of crystalline symmetry in low temperature matter, and classifying the tilings of space by copies of finitely many tiles. These are both optimization problems; the crystal problem is concerned with determining the basic mechanisms which force low temperature and high pressure matter to have the high degree of crystalline order and symmetry which is found experimentally.