Special Year Learning Seminar

Sets of recurrence were introduced by Furstenberg in the context of ergodic theory and have an equivalent combinatorial characterization as intersective sets, an observation which has led to interesting connections between these areas.

Originally defined for a single measure preserving transformation, the notion of sets of recurrence makes sense in any semigroup action, including actions by the semigroup of multiplicative natural numbers. We explore some examples and properties of these sets, their connection to combinatorics and number theory, and the many still open questions about them.