S4B1 - Graduate Seminar in Analysis - The Calderón problem
Summer term 2023
Organisational details
- Time and place: Wed 16-18 (c.t.), Room N0.007, Endenicher Allee 60 (Annex), first seminar:
Wed 5th AprilWed 12th April
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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.
Overview
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
Topics
The 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
Schedule of talks
April 12 - Jan Bohr - Introduction, DN-maps and boundary determination
April 19 - Sophia Heimann - CGO solutions in dimension ≥ 3 via Fourier analysis
April 26 - Javier Duran Fernandez - Interior determination in dimension ≥ 3
May 3 - Jakob Wilden - Logarithmic Stability
May 10 - Lorenzo Pompili - Optimality of Logarithmic Stability
May 17 - Marven Korte - The partial data problem in dimension ≥ 3 - Part 1
May 24 - Cancelled
May 31 - Pentecost Holiday
June 7 - Xiaopeng Cheng - The partial data problem in dimension ≥ 3 - Part 2
June 14 - Cancelled
June 21 - Double Seminar:
Nils Behrmann - Determination of the conformal class in dimension 2
Jan Bohr - Schrödinger equation on Riemann surfaces - Part 1
June 21 - Double Seminar:
Rongxuan Deng - Schrödinger equation on Riemann surfaces - Part 2
Matteo Ravot Licheri - Reduction to Scattering Transform in dimension 2
July 5 - Anjana Edavazhikkal Jeevanand - Inversion of Scattering Transform - Part 1
July 12 - Shao Liu - Inversion of Scattering Transform - Part 2
Aktuelles
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Catharina Stroppel erhält Gottfried Wilhelm Leibniz-Preis 2023
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Jessica Fintzen erhält einen Whitehead Prize der London Mathematical Society