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.

 

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Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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