MAT 638. Topics in Real Analysis.

Geometric measure theory and harmonic analysis.

• Instructor: Raanan Schul
  • Office: Math 3-121.
  • Office hours: here.
• Class: Tu,Th 10:00-11:20am in Physics P125
• The level and specific contents of the course will be modified to fit the level of the participants. Some topics will be
  • Boundedness of Singular integal operators ala Melnikov-Verdera (1995 IMRN)
  • BiLipschitz decomposition of Lipschitz functions ala David and Jones
  • Parametrization ala David-Toro and Edelen-Naber-Valtorta.
  • Stability of Carleson curvature esimates under Big Pieces (as in DS blue book)
  • Carleson curvature estimate for graphs (ala Okikiolu)
  • Christ cubes (1990 paper by M. Christ)
  • Analyst TST in R^n (using Hilbert space proof applied to dyadic cubes)
  • Characterization of 1-rectifiable measures
  • Boundedness of Singular integal operators ala Coifman-Jones-Semmes.
  • Big Pieces and singular integral boundedness
  • more on Uniform rectifiability

• Required Syllabi Statements.