Seminar on microlocal analysis
Prof. Bernd Ammann, Zimmer 119
Content of the Seminar
Microlocal analysis is a strong tool in geometric analysis. It refines the notion of the singular support of a distribution to the "wave front set", which is a subset of the cotangent bundle T*M of the underlying manifold M, whereas the singular support is a subset of M itself.
Knowledge on the wave front set leads to a better understanding of the singular behavior by adding information in which direction the singularity occurs.
A main tool for microlocal analysis is the algebra of pseudodifferential operators. This algebra includes differential operators. It also includes operators of negative degrees, e.g. the inverse of an invertible elliptic differential operator is again a pseudodifferential operator. It will be important to understand their symbols.
In the seminar we follow a new book on microlocal analysis by Peter Hintz. One objective of this book is to apply the powerful machinery of microlocal analysis for studying hyperbolic evolution equations, both for hyperbolic systems on ℝn and for natural hyperbolic partial differential equations on Lorentzian manifolds.
Literature
- Peter Hintz, An Introduction to Microlocal Analysis, Springer
Requirements
The seminar addresses to advanced master students and PhD students. We will require:
- Riemannian and Lorentzian geometry
- Distribution and Fourier transform
- Some facts about partial differential operators and the associated equations
Program
Time and Place
Tuesday, 16-18, M101
Registration
Interested students are asked to send an email to Bernd Ammann. In mid-September there will be a meeting for discussing the content of the seminar and for distributing the talks. More information about this will follow on the seminar homepage.
Verbundene Webseiten
Formal requirements
see KVV
Bernd Ammann, 06.08.2026
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