S4B1 - Graduate Seminar in Analysis - The Calderón problem
Summer term 2023
- Time and place: Wed 16-18 (c.t.), Room N0.007, Endenicher Allee 60 (Annex), first seminar:
Wed 5th AprilWed 12th April
Preliminary meeting:Tue 24.01.23, 16-18, Room 2.008, Endenicher Allee 60
- If there are any questions, please get in touch with one of the organisers. If you are a participating Masters student, please register on Basis.
The Calderón problem is an instance of a nonlinear inverse problem: unknown coefficients of a partial differential equation are to be determined from boundary measurements of the corresponding solutions.
See here for more information, including a list of talks and literature recommendations.
Prerequisites: Basics of linear PDE and functional analysis
TopicsThe seminar will cover a subset of the following topics, depending on the interests of the participants:
1) Introduction ▪ well-posedness of Dirichlet problems, boundary determination
2) Smooth coefficients, Euclidean domains in dimension ≥ 3 ▪ complex geometric optics (CGO) solutions, interior determination, stability and instability, partial data problem
3) Smooth Riemannian surfaces ▪ determination of conformal class, CGO solutions on Riemann surfaces, interior determination of potentials
4) Rough coefficients, Euclidean domains in dimension 2 ▪ d-bar problem, inversion of scattering transforms