Flows on 1-graded parabolic geometries

Karin Melnick (Maryland)

Abstract: Conformal and projective structures are examples of parabolic geometries. These geometries may admit a nonlinearizable flow by automorphisms, but according to some recent rigidity theorems, such flows can only occur in a particular case. In this talk I will discuss the question of determination of an automorphism by its 1-jet at a point, for 1-graded parabolic geometries, and survey some of the significant previous results. I will give a new rigidity theorem, joint with K. Neusser, in the case of almost-Grassmannian structures.