# Rafael de la Llave: Non-commutative Coboundary Equations over integrable Systems

**Time: **
Thu 2022-02-24 15.00

**Location: **
Zoom meeting ID: https://kth-se.zoom.us/j/61173989405

**Participating: **
Rafael de la Llave (Georgia Institute of Technology)

**Abstract:** We consider the problem of when a family of cocycles over an integrable system is can be written as a family of coboundaries over the integrable system. This problem has been considered extensively when the dynamics on the base is hyperbolic. Now we consider the case when the dynamics in the base is parabolic.

We show that if there are formal power solutions of the coboundary equation, then there is a convergent family of solutions. When the dynamics on the base is 1 dimensional, this is equivalent to a condition on all periodic orbits.

This is joint work with M. Saprykina (work in progress).