**Title**: What’s new in rigidity

**Speaker**: Andrey Gogolev (Ohio State University)

**Abstract**: A dynamical system is called *rigid* if a weak form of equivalence to a nearby system, such as coincidence of some simple invariants, implies a strong form of equivalence. For Anosov dynamical systems smooth rigidity theory was initiated by Rafael de la Llave and collaborators who were motivated by the spectral rigidity program. We will discuss smooth rigidity of hyperbolic dynamical systems and related geometric questions such as marked length spectrum rigidity of negatively curved manifolds.

In the first talk (April 4) I will explain what the problem is and explain some of the old results. Then I will state the new results. In particular, I will report on several improvements on Croke-Otal marked length spectrum rigidity.

In the second talk (April 11) I will present the proof ideas in their most basic form. Based on joint work in progress with Federico Rodriguez Hertz. I will make it accessible and explain all necessary background, everybody with interest in dynamics or geometry is welcome.