Description
Speaker: Dr. Nishant Chandgotia, Tel Aviv university
Date & Time - 8-2-18, Thursday, 4 PM
Title: Universal models in ergodic theory
Abstract: In 1970, Krieger proved that any free ergodic probability
preserving invertible transformation of finite entropy can be modelled by
A^Z, the set of unconstrained bi-infinite sequences in some finite alphabet
A. This result has seen many generalisations for more constrained systems
and for actions of other groups. Along with Tom Meyerovitch, we prove that
under certain general mixing conditions $Z^d$-topological dynamical systems
can model all free ergodic probability preserving Z^d actions of lower
entropy. In particular, we show that these mixing conditions are satisfied
by proper colourings of the Z^d lattice (colourings of the Z^d lattice
where adjacent colours are distinct) and the domino tilings of Z^2 lattice,
thus answering a question by Şahin and Robinson. The talk will begin with
an introduction to the terms mentioned in the abstract and should be
accessible to a general audience.