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SUMMARY:Nivat's Conjecture and expansive dynamics - Bryna Kra\, Northweste
 rn University\, Chicago
DTSTART:20121024T150000Z
DTEND:20121024T160000Z
UID:TALK39456@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:The Morse-Hedlund Theorem states that an infinite word in a\nf
 inite alphabet is periodic if and only if there is exists a positive\ninte
 ger n such that the complexity (the number of words of length n) is\nbound
 ed by n\, and a natural approach to this theorem is via analyzing\nthe dyn
 amics of the Z-action associated to the word. In two dimensions\,\na conje
 cture of Nivat states that if there exist positive integers n and\nk such 
 that the complexity (the number of n by k rectangles) is bounded\nby nk.  
   Associating a Z^2 dynamical system to the infinite word\, we\nshow that 
 periodicity is equivalent to a statement about the expansive\nsubspaces of
  the action.  As a corollary\, we prove a weaker form of\nNivat's conjectu
 re\, under a stronger bound on the complexity function.\nThis is joint wor
 k with Van Cyr.
LOCATION:MR11\, CMS
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