Mathematical Sciences: The Dynamical Theory of Tilings and Quasicrystals

罗宾逊教授将在与平面平铺和高维欧氏空间相关的多维符号动力系统领域进行研究。这些动力系统是n维欧氏空间在紧度量空间上的连续作用。它们与Ambrose-Kakutani-Rudolph表象理论有关。此外，罗宾逊教授将继续他关于各种遍历性质如何提升到扩展的工作。特别是，他将专注于连接如何提升到延伸。上世纪80年代初，S的实验物理学家惊讶地发现，他们认为是周期晶体的晶体具有五重旋转对称性。然而，这在数学上是不可能的，后来人们观察到这种物质不是周期性的，而是“准周期性的”。罗宾逊教授的研究将尝试应用遍历理论和动力系统的技术来理解这种情况。

Professor Robinson will conduct research in the area of multi-dimensional symbolic dynamical systems associated with tilings of the plane and higher dimensional Euclidean spaces. These dynamical systems are continuous actions of n-dimensional Euclidean space on compact metric spaces. They are related to Ambrose-Kakutani-Rudolph representation theory. In addition, Professor Robinson will continue his work on how various ergodic properties lift to extensions. In particular he will concentrate on how joinings lift to extensions. In the early 1980's experimental physicists were surprised to see five-fold rotational symmetry in what they thought to be a periodic crystal. This is however a mathematical impossibility and it was later observed that the substance was not periodic but rather "quasiperiodic". The research of Professor Robinson will attempt to apply techniques from ergodic theory and dynamical systems to understand this situation.