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Fix a graph H and denote by Z^d both the group and its Cayley graph with respect to standard generators. By a hom-shift X_H, we mean the space of graph homomorphisms from Z^d to H, that is, vertex maps from Z^d to H which preserve adjacency. It is a dynamical system under translations by Z^d. In joint work with Ron Peled, we prove that they are universal with respect to the (2Z)^d action, meaning that any free ergodic Z^d action, whos entropy is less than 2d times the entropy of X_H, can be realised on X_H under the (2Z)^d action; the main ingredient for the proof being some surprisingly elementary probability. This partially answers a question by Şahin and Robinson. The talk will not assume much background in ergodic theory; familiarity will of course help.
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