Speaker:  Cesar Silva

Title:  "Mixing on a Class of Rank One Transformations"

Abstract: We will discuss a theorem that shows  that a rank one transformation satisfying a 
condition called restricted growth is a mixing transformation if and only if
the spacer sequence for the transformation is uniformly ergodic.
Uniform ergodicity is a generalization of the notion of ergodicity
for sequences, in the sense that the mean ergodic theorem holds
for what we call dynamical sequences.  The application of our
theorem shows that the class of  polynomial rank
one transformations, rank one transformations where the spacers
are chosen to be the values of a polynomial with some  
conditions on the polynomials, that have  restricted growth are mixing transformations,
implying in particular Adams' result on staircase transformations.
Another application yields a new proof that Ornstein's class of
rank one transformations constructed using ``random spacers'' are
almost surely mixing transformations.  This is joint work with Darren Creutz.