Mathematical Sciences: Factor Maps Between Sofic Systems

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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.