Sydney Dynamics Group Seminar: Anthony Dooley, UTS -- Sydney Dynamics group Seminar

Seminar : Sydney Dynamics group Seminar 
Day/time : Thursday, May 7 at 4:00 PM, 
Location : SMRI seminar room (A12 Macleay Room 301) 
Speaker : Anthony Dooley, University of Technology Sydney 

Title: Non-singular actions of amenable groups 

Abstract: In work with Hamachi, I showed that every non-singular measurable dynamical
system is orbit equivalent to a Markov odometer on a Bratteli-Vershik system which is
uniquely ergodic, minimal and induced as a subsystem of a full odometer.  At the same
time, Mortiss and I introduced a new invariant, the critical dimension, for metric
isomorphism of non-singular systems: it is given by the rate of growth of sums of
Radon-Nikodym derivatives.  The critical dimension induces a natural form of equivalence
between systems, Hurewicz equivalence.  Recently, my students Kieran Jarrett and Jie Jin
have been using these ideas to study the Kingman theorem and the Oselede\v c ergodic
theorem for non-singular actions of amenable groups.