Some open problems on multiple ergodic averages
Updated version 2016.
Older version 2011 (with progress updates).
Other open problem webpages in ergodic theory
Open problems in dynamical systems and ergodic theory
(maintained by S. Kolyada and M. Misiurewicz).
Open problems in dynamical systems
Open problems in dynamics and related fields
(maintained by M. Hochman).
Open problems in symbolic dynamics
(maintained by M. Boyle).