**Abstract:**We construct a set which is dense in the Bohr topology on the group of integers and which is not a set of measurable recurrence, answering a question asked by Bergelson, Hegyvári, Ruzsa, and the author, in various combinations. This talk will provide a broad overview and explain details of the construction. We will see similarities to many other examples in additive combinatorics and ergodic theory, such as Igor Kriz's construction showing topological recurrence does not imply measurable recurrence, and Ruzsa's niveau sets. New problems on sets of recurrence will be posed, and connections will be made to well known open problems.

## Date:

Tue, 16/06/2020 - 14:00 to 15:00