Title: Two phase free boundary problem of Chris Bishop: how singular integrals and blow up methods solve it.

Date: 10/10/2016

Time: 4:02 PM - 5:00 PM

Place: C517 Wells Hall

This is a report of a joint work with Azzam, Mourgoglou and Tolsa. Harmonic measure was in the focus of attention of many analysts (Bishop, Bourgain, Carleson, Jones, Makarov, Wolff to name a few) in 1985-1995. Beautiful metric properties of harmonic measure were revealed during this period, this concerns especially a 2D case. In higher dimensions the behavior was more enigmatic, and many problems were left for the future. Recently it turned out that the technique of non-homogeneous harmonic analysis developed by (among others) Nazarov-Treil-and the speaker (NTV) is the right tool to clarify several
outstanding questions about harmonic measure in 3 and higher dimensions. We will show how to solve yet another problem formulated by Chris Bishop in 1992.