# The Calderón Problem

**Lecturer:**Angkana Rüland**Date:**Thursday 13:15 - 14:45**Room:**Augusteum A314**Language:**English**Target audience:**MSc students, PhD students, Postdocs**Prerequisites:**Basic knowledge from the courses "PDE" and "Functional Analysis I".**Remarks:**If desired it is possible to switch to German as the language of the lecture.

## Abstract:

Do invisibility cloaks only exist in the world of Harry Potter? Or is it maybe possible to realise such cloaks? Or can we prove that material behaviour of this type is impossible? Can one obtain information on the content of a box without opening it?

This lecture will deal with problems which are related to the above questions from a mathematically rigorous point of view. Studying the Calderón problem as a model problem we will acquaint ourselves with techniques and results on inverse problems. In general, these are problems in which one seeks to recover properties of a system by means of indirect measurements. This for instance finds important applications in medicine (e.g. in non-invasive strategies such as x-ray tomography) or geoprospection (oil discovery).

Mathematically, inverse problems often display strong "ill-posedness" features. This leads to interesting mathematical challenges, which we will discuss in this course. In this context, we will in particular deal with the following topics:

- Fourier series and Sobolev spaces.
- Uniqueness for the Calderón problem.
- Stability for the Calderón problem.
- The partial data problem.
- Cloaking.

## Regular Lectures (Summer 2018)

**Geometric and topological methods of data analysis**- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01

**Regularity theory for nonlinear, degenerate partial differential equations**- Benjamin Gess
- Monday, 16:15 - 17:45, MPI MiS A3 01

**The signature of iterated integrals: algebra, analysis and machine learning**- Joscha Diehl
- Thursday, 09.00-10.30, A3 02

**Geometric Variational Problems**- Ulrich Menne
- Monday & Friday, 9:15 - 10:45, Augusteum, Room 314

**The Calderón Problem**- Angkana Rüland
- Thursday, 13:15-14:45, Augusteum, Room 314

**Introduction to the KPZ Equation**- Scott Smith
- Monday, 10:30 - 12:30, MPI MiS A3 01

**Low-rank tensor approximation**- André Uschmajew
- Thursday, 11:00 - 12:30, MPI MiS G3 10

**Data: crush course**- Ivan P. Yamshchikov
- Friday, 12.00-13.30, A3 02

**Stochastic homogenization**- Felix Otto
- Wednesday, 09:15 - 11:00, MPI MiS A3 01

**Reading seminar on “J-holomorphic curves”**- Enno Keßler and Ruijun Wu
- Wednesday, 13:00 - 14:30, MPI MiS A3 01

**IMPRS-Ringvorlesung: Introduction to Nonlinear Algebra**- Bernd Sturmfels and Mateusz Michałek
- Tuesday, 10:00 - 12:00, MPI MiS G3 10