Title: Regular Lip(1,1/2) Approximation of Parabolic Hypersurfaces

Abstract: A classical result of David and Jerison states that a regular, n-dimensional set in R^{n+1} satisfying a two sided corkscrew condition is quantitatively approximated by Lipschitz graphs.  After reviewing this result, we will discuss some recent advances in extending this result to the parabolic setting.  The proofs of these results are quite difficult, but many of the underlying principles are easy to understand and quite geometric and presenting these geometric ideas will be the focus of this talk.  As such, this talk will feature lots of pictures!  Crucially, we highlight how fundamental differences of the parabolic setting require us to consider additional nuances which are not present in the elliptic setting.  We will sketch the ideas of how to circumvent these difficulties.

This talk is based on joint work with Simon Bortz, José Luis Luna Garciá, Steve Hofmann, Kaj Nyström.