UW Rainwater Seminar
Winter 2011



Date: Monday, January 31 at 4:00 (note unusual day and time!)

Location: UW Thomson 231 (note unusual room!)

Speaker: Michael Schraudner, Universidad de Chile

Title: Projective subdynamics of (uniformly mixing) Z^d shifts of finite type

Abstract: Motivated by Hochman's notion of subdynamics of a Z^d subshift, we define and examine projective subdynamics of Z^d shifts of finite type (SFTs) where we restrict not only the action but also the phase space. In analogy with the notion of stable and unstable limit sets in cellular automata we distinguish between stable and unstable projective subdynamics.

First we review the classification of Z sofic shifts which can (not) appear as projective subdynamics of Z^2 (Z^d) SFTs both in the stable and unstable regime - these are results obtained jointly with Ronnie Pavlov.

In a second part of the talk we present results on the projective subdynamics of Z^d SFTs with some uniform mixing condition. In particular there is a compatibility condition assuring the projective subdynamics has to be sofic and this condition is met by some of the commonly used uniform mixing properties. If time permits we explain a construction that allows to realize any mixing Z sofic as stable projective subdynamics of some strongly irreducible Z^2 (Z^d) SFT.