Projects
The Internet Analysis Seminar will hold a workshop during Summer 2015. 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 Harmonic Analysis associated to Elliptic Operators
- The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds, by Hofmann, Lacey, and McIntosh.
- The solution of the Kato square root problem for second order elliptic operators on $R^n$, by Auscher, Hofmann, Lacey, McIntosh, and Tchamitchian.
- Duality of Hardy and BMO spaces associated with operators with heat kernel bounds, by Duong and Yan.
- Riesz transforms for $1 \leq p \leq 2$, by Coulhon and Duong.
- Riesz transform on manifolds and heat kernel regularity, by Auscher, Coulhon, Duong, and Hofmann.
- Hardy and BMO spaces associated to divergence form elliptic operators, by Hofmann and Mayboroda.
- Hardy spaces associated to the Schrodinger operator on strongly Lipschitz domains of $R^d$, by Huang.
- Atomic decomposition of $H^p$ spaces associated with some Schrodinger operators, by Dziubanski.
- Heat kernel bounds, conservation of probability and the Feller property, by Davies.
- Hardy spaces of differential forms on Riemannian manifolds, by Auscher, McIntosh, and Russ.
- Hardy spaces and divergence operators on strongly Lipschitz domains of $R^n$, by Auscher and Russ.
- $L^p$ bounds for Riesz transforms and square roots associated to second order elliptic operators, by Hofmann and Martell.
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 July 6 to Friday July 10, 2015 at Georgia Tech in Atlanta, Georgia.
Interested participants should email wick[at]math[dot]gatech[dot]edu before March 28, 2015. In the email, please provide a ranking, in terms of interest, of which of the above projects you would be willing 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.