Symmetries and rigidity of dynamical systems
Danijela Damjanovic (KTH,Suécia)

I will talk about the interplay between structure of the symmetry group of a smooth dieomorphism, and dynamical properties of the dieomorphism. Just as symmetries of an object force topological and geometric properties of the object, symmetries of dynamical systems may force imergence of invariant homogeneous structures helping us to better, sometimes even completely, understand the dynamics of the system. I plan to present some recent results with A. Wilkinson and D. Xu concerning symmetry groups and rigidity of partially hyperbolic dieomorphisms.