On Higher-Dimensional Oscillation in Ergodic Theory

Analysis Seminar
Wednesday, November 6, 2013 - 3:05pm
1 hour (actually 50 minutes)
Skiles 005
We will discuss the fine notion of the pointwise convergence of ergodic averages in setting where one the ergodic transformation is a Z^d action, and the averages are over more exotic sets than just cubes. In this setting, pointwise convergence does not follow from the usual ergodicity arguments. Bourgain, in his study of the polynomial ergodic averages invented the variational technique, which we extend to our more exotic averages.