Periodicity, complexity and shifts.
Seminar Room 2, Newton Institute Gatehouse
AbstractA beautiful example of a global property being determined by a local one is the Morse-Hedlund Theorem; it gives the relation between the global property of periodicity for an infinite word in a finite alphabet and local information on the complexity of the word. I will discuss higher dimensional versions of this problem, and the use of local conditions on complexity to determine global properties of the configuration, and applications of this to the automorphism group of shifts. This is joint work with Van Cyr.
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