Periodicity and Complexity

Bryna Kra, Northwestern University
Fine Hall 314

A 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, using local conditions on complexity to determine global properties of configurations. This is joint work with Van Cyr.