Speaker: Zoltan Buczolich

Title: Divergent Square Ergodic Averages

Abstract:
Answering a question of J. Bourgain we construct
an irrational rotation $T_{\theta}$ of the unit circle $\T$
and a function $f\in L^{1}(\T)$ for which
$\frac{1}N\sum_{n=1}^{N}f(T_{\theta}^{n^{2}}x)$ diverges almost
everywhere. Joint work with Dan Mauldin.