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 - Xiaopeng Cheng - The partial data problem in dimension ≥ 3 - Part 2
May 31 - Pentecost Holiday
June 7 - Nils Behrmann - Determination of the conformal class in dimension 2
June 14 - Jan Bohr - Schrödinger equation on Riemann surfaces - Part 1
June 21 - Rongxuan Deng - Schrödinger equation on Riemann surfaces - Part 2
June 28 - 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
News
Prof. Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Hirzebruch lecture by Rahul Pandharipande on Monday, May 15, 2023
Lucas Mann recevices the Hausdorff memorial award 2021/22
Bachelor Prize 2021/22 of the BMG awarded
Prof. Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Prof. Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Rajula Srivastava receives Association for Women in Mathematics Dissertation Prize
Prof. Ana Caraiani wins a New Horizons in Mathematics Prizes 2023
Pius XI Medal awarded to Professor Peter Scholze
Prof. Valentin Blomer und Prof. Georg Oberdieck erhalten ERC grants
Grants for Mathematics students from Ukraine
Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant