Department of Mathematics

Analysis and PDE

  •  Two phase free boundary problem of Chris Bishop: how singular integrals and blow up methods solve it.
  •  10/10/2016
  •  4:02 PM - 5:00 PM
  •  C517 Wells Hall
  •  Alexander Volberg, MSU

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.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science