Title: Twisted recurrence in measurable dynamical systems

Abstract: In the study of some dynamical systems, the limsup set of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limsup sets. However, the zero-one laws for the shrinking targets and recurrence are usually treated separately and proved differently. In this talk, I will talk about twisted recurrence, which can specialize into both shrinking targets and recurrence. I will introduce some known results about twisted recurrent sets, including their zero-one laws and Hausdorff measures.