Mathematical Sciences: Mathematical Physics of Crystals, andTiling

[9531584] Radin这个项目是关于对欧几里得空间的瓷砖进行分类，这些瓷砖是由一组有限的不同瓷砖的副本产生的。研究者计划将他最近的研究结果应用于平面和空间的旋转对称铺层。所采用的方法是将传统的遍历理论与非周期瓷砖的新技术相结合。在这两个研究领域中，有一些基本的数学问题是共同的：确定低温物质中晶体对称的原因，以及通过有限多块瓷砖的副本对空间瓷砖进行分类。这两个都是优化问题；晶体问题涉及确定使低温高压物质具有实验发现的高度有序和对称的晶体的基本机制。

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.