Aperiodic Tiling

非周期性平铺

• 批准号: 0071643
• 负责人: Charles Radin
• 金额: $ 8.4万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071643&HistoricalAwards=false
• 关键词: Aperiodic; Tiling

A class of tilings of Euclidean spaces, the best known being the Penrose tilings of the plane, have proven to be a fertile subject of research with impact in a broad range of directions. The investigator continues his interdisciplinary research of these tilings, emphasizing consequences of the statistical rotational symmetry of the tilings, in particular the full rotational symmetry of tilings such as the pinwheel tilings of the plane. The methods are a combination of ergodic theory, ring theory and algebraic topology.Tilings of space have been an important tool to understand the geometric relationships that are possible between many small components within a larger whole. In particular tilings help us understand geometric symmetries. In recent years tilings with unexpected symmetries have been discovered, and used successfully in modeling the atomic structure of new types of physical materials. The investigator studies these new symmetries, and, making use of the way tilings interface with various parts of mathematics, uses the symmetries as a tool to investigate structures in diverse parts of mathematics.

欧氏空间的一类拼接，最著名的是平面的彭罗斯拼接，已被证明是一个肥沃的研究课题，在广泛的方向产生影响。调查员继续他的跨学科研究这些平铺，强调后果的统计旋转对称的平铺，特别是充分旋转对称的平铺，如风车平铺的飞机。这些方法是遍历理论、环理论和代数拓扑学的结合。空间的倾斜是理解一个更大的整体中许多小部分之间可能存在的几何关系的重要工具。特别是平铺帮助我们理解几何对称性。近年来，人们发现了具有意想不到的对称性的镶嵌，并成功地用于模拟新型物理材料的原子结构。研究者研究这些新的对称性，并利用镶嵌与数学各个部分的接口方式，使用对称性作为工具来研究数学不同部分的结构。