Mathematical Sciences: Flow Equivalence of Subshifts

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9401079 Huang The proposer has classified up to flow equivalence all 2- component shifts of finite type. He has recently classified n-component shifts of finite type when 1 is not an eigenvalue of the defining matrix. The project is to complete the classification for general n-component shifts of finite type by proving a crucial "two-sided" realization theorem which may also have a new implication to C*-algebras. Moreover, based on the existing results, the proposer intends to study (almost) flow equivalence of sofic shifts, of stochastic Markov shifts and of the more general setting of Laurent polynomial matrices. Especially, he plans to explore more interesting relations between flow equivalence and C*-algebras, including a conjecture he made for the classification of non-simple Cuntz-Krieger algebras associated to 2-component shifts of finite type. 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 of "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 and algebra in their quests to clasify flows and algebraic structures. ***