24 February 2006, Colloquium on Mathematical Logic, Asger Tornquist
(Tram 9 from Central Station, to Plantage Badlaan.)
Abstract: It is a classical result that all conjugacy classes in the group of all measure preserving transformations on [0,1] are meagre, and that the generic transformation is ergodic. Foreman and Weiss showed that the conjugacy relation for ergodic transformations does not allow classification by countable structures, and more recently, Foreman, Weiss and Rudolph showed that it is a complete analytic relation.
In this talk, I will present a modest attempt at extending some of these results to actions of any countable group. We will show that every countable abelian group has "E_0 many" ergodic measure preserving a.e. free actions on [0,1], thus showing that the conjugacy relation is not concretely classifiable. The argument can be extended far enough to show that all countable groups has continuum many non-conjugate actions, though so far without the non-classification part.
This work is joint with Greg Hjorth (UCLA).
For more information, see http://staff.science.uva.nl/~bloewe/CML.html