Speakers:  Bernard Host and Bryna Kra

Title: Non-conventional ergodic averages 

Abstract: We give an overview of
recent results on non-conventional ergodic averages.  We consider averages
evaluated at different times, such as along arithmetic progressions,
polynomial values and combinatorial cubes.  For each average, the L^2
convergence is determined by a certain factor of the system.  We describe
these factors, showing that they are nilsystems, meaning a translation on
the quotient of a nilpotent Lie group by a uniform subgroup, and use this
characterization to obtain convergence.