Joining classification and factor rigidity in infinite volume

Abstract: For a group acting on two spaces, a joining of these systems is a measure on the product space that is invariant under the diagonal action and projects to the original measures on each space. As an important step towards her celebrated measure classification theorem, Ratner proved an early landmark result classifying joinings for horocycle flows on finite volume quotients of PSL(2,R). In this talk, I will discuss joining classification for horospherical flows in the infinite volume, rank one setting, as well as a key factor rigidity theorem that is used in the proof.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar