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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, January 10, 2019}
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\textbf{At} \emph{11:00 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Nishant Chandgotia 
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  (The Hebrew University of Jerusalem)
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will talk about
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{\Large\bfseries Universal models for Z\^{}d actions\par}
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\textsc{Abstract:}
Krieger’s generator theorem shows that any free invertible ergodic measure preserving action $(Y,\mu, S)$ can be modelled by $A^Z$ (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is $A^Z$) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which $Z^d$-dynamical systems are universal. These conditions are general enough to prove that

1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo and recovering recent results by David Burguet)
2) Proper colourings of the $Z^d$ lattice with more than two colours and the domino tilings of the $Z^2$ lattice (answering a question by Şahin and Robinson) are universal. Our results also extend to the almost Borel category giving partial answers to some questions by Gao and Jackson.








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