Some open problems on multiple ergodic averages
Updated version (2016) here.
Progress update here (latest update September 2023).
Old version (2011) here.
Progress update
here (latest update September 2023).
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
(Stony Brook).
Open problems in dynamics and related fields
(maintained by M. Hochman).
Open problems in symbolic dynamics
(maintained by M. Boyle).