Mathematical Sciences: Topics in Symbolic Dynamics

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This supplementary award is to support the mathematical research of Professor Selim Tuncel on the project of the principal investigator, Professor Lind. The subject is a branch of ergodic theory called symbolic dynamics. A symbolic dynamical system is a collection of two-way infinite strings of symbols from a finite alphabet satisfying a formation rule that specifies which symbols are allowed to follow which as one moves along the string. Two such systems are equivalent if there is a well- behaved bijection between them that respects the operation of shifting. A central theme in this area is the classification of symbolic dynamical systems. Professor Tuncel will study invariants for these and related systems, including the beta function for Markov chains and an algebraic invariant resulting from dimension modules and an additional element of structure called the scaffold. Cellular automata and block codes between Bernoulli shifts are additional research topics. The mathematical structures studied in this project have found considerable use as models for communication and data systems.