Mathematical Sciences: Factor Maps Between Sofic Systems

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移位之间的因子映射。这些映射是连续的、满射的、移位交换的映射。它们是信息论中的滑动块码。特罗教授对这些地图的存在及其可能程度的问题很感兴趣。这些问题与符号动力学的核心问题--有限移位的拓扑共轭密切相关。符号动力学的研究对象是集合(称为符号空间)，其元素是符号的双无限序列，以及移位映射。这些空间是一大类动力系统的自然模型。遍历理论家以及信息和编码专家对它们非常感兴趣。

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. These 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 a 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.