Projects related to Hausdorff Geometry and Singular Integral Operators
The second part of this Internet Analysis Seminar is a workshop held during Summer 2014. A participant in this workshop will be responsible for presenting one of the papers below, via two lectures, to the other participants. A typical participant will be an advanced graduate student or postdoc who is interested in learning more about the themes related to the lectures. More precise details about the workshop appear below the projects.
Projects related to Hausdorff Geometry and Singular Integral Operators
- The s-Riesz transform of an s-dimensional measure in $R^2$ is unbounded for 1<s<2 by Eiderman, Nazarov and Volberg.
- Almost-additivity of analytic capacity and Cauchy independent measures by Eiderman, Reznikov and Volberg.
- Reflectionless measures and the Mattila-Melnikov-Verdera uniform rectifiability theorem by Jaye and Nazarov.
- Three revolutions in the kernel are worse than one by Jaye and Nazarov.
- Rectifiable sets and the traveling salesman problem by Jones.
- Menger curvature and rectifiability by Leger.
- On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of Codimension 1 by Nazarov, Tolsa, and Volberg.
- The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions by Nazarov, Tolsa, and Volberg.
- The Tb-Theorem on non-homogeneous spaces that proves a Conjecture of Vitushkin by Nazarov, Treil, and Volberg.
- Characterization of subsets of rectifiable curves in $R^n$ by Okikiolu.
- Painleve's problem and the semiadditivity of analytic capacity by Tolsa.
Participants selected to work on these projects will have to prepare two one-hour long lectures based on the contents of the paper. Additionally, they will have to write a 5 page summary of the topic before the meeting. These lectures will be presented at a week long workshop that will take place Monday August 4 to Friday August 8, 2014 at Georgia Tech in Atlanta, Georgia.
Interested participants should email wick[at]math[dot]gatech[dot]edu before April 15, 2014. In the email, please provide a ranking in terms of interest of which of the above projects you would like to present. Due to funding limits, there will be approximately 10 participants selected to attend the workshop and present one of the above projects. Selected participants will be notified of the project they are assigned and the exact details for the workshop. Local and travel expenses will be provided for participation.