• 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.