Mathematical Sciences: Factor Maps Between Shifts Of Finite Type

特罗教授将在动力系统的一个分支——符号动力学领域进行研究。他的研究将主要关注有限类型位移之间的因子映射。因子映射是连续的、满射的、移位的交换映射。它们是信息论的滑动块代码。特罗教授对这些地图的存在及其可能的程度感兴趣。这些问题与符号动力学的中心问题——有限型位移的拓扑共轭密切相关。符号动力学的研究对象是符号的双无穷序列的集合（称为符号空间）和移位映射。这些空间是一大类动力系统的自然模型。它们引起了遍历理论学家和信息与编码专家的极大兴趣。

Professor Trow will conduct research in the area of symbolic dynamics, a branch of dynamical systems. His research will be primarily concerned with factor maps between shifts of finite type. Factor maps are continuous, surjective, shift commuting maps. They are the sliding-block codes of information theory. Professor Trow is interested in the question of existence of these maps, and their possible degrees. These questions are closely related to topological conjugacy of shifts of finite type, the central problem of symbolic dynamics. The objects of study in symbolic dynamics are sets (called symbol spaces) whose elements are bi-infinite sequences of symbols, together with the shift map. These spaces are natural models for a large class of dynamical systems. They are of great interest to ergodic theorists and information and coding experts.