Nilmanifolds are compact homogeneous spaces of nilpotent Lie groups. Dynamical systems on nilmanifolds have been used recently in ergodic theory in the study of problems of multiple convergence and recurrence.

In the first talk we define these systems, give examples and describe their properties. In the second talk we summarize the proof of a "structure theorem" linking these objects with some dynamical seminorms similar to the Gowers norms. In the last talk we give some applications.

Lecture #12892

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