Mathematical Sciences: Joinings, Combinatorics and Ergodic Theory

金教授将研究遍历理论中的一些问题。他将考虑基于连接的结构定理的潜在推广。他将研究与Oxtoby和Ulam的工作有关的“连续选择问题”。他将研究两个组合问题：2- 3- 2混合问题和van den Berg-Kesten“盒猜想”。这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。在“动力学”的标题下，可以放置关于抽象变换如何作用于光滑空间的现代理论。通过这种方式，遍历理论在寻求对均匀空间上的流动进行分类时与几何联系在一起。

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.