## Special Colloquium

Karin Melnick

University of Maryland

Normal forms for local flows on parabolic geometries

**Abstract:**The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.

Monday February 3, 2014 at 3:00 PM in SEO 636