Mathematical Sciences: Joinings, Combinatorics and Ergodic Theory

金教授将研究遍历中的一些问题 理论 他将考虑一个潜在的普遍性， 基于连接的结构定理。 他将调查 “连续选择问题”，与Oxtoby的工作有关， 乌拉姆 他将研究两个组合问题：2倍的3- fold混合问题和货车den Berg-Kesten“盒子猜想”。 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 现代理论认为， 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间

Professor King will study a number of questions in ergodic theory. He will consider potential generalizations of a structure theorem based on joinings. He will investigate the "continuous selection problem", related to work of Oxtoby and Ulam. He will study two combinatorial problems: the 2-fold 3- fold mixing problem and the van den Berg-Kesten "box conjecture". This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.