# Seminar on Wave equations on Lorentzian manifolds and Quantization

Prof. Bernd Ammann,

## News

On May 5th we will visit together the opening of the exhibition at the math department
## Content of the Seminar

The main concern of the seminar is to solve geometrically motivated hyperbolic partial differential equations on curved backgrounds. The simplest example is the wave equation on (flat) ℝ^{n} whose solution will be the starting point of the seminar. These solutions can be used to iteratively construct solutions on curved spacetimes, i.e. Lorentzian manifolds. As soon as we have solved these equations, we will construct natural C^{*}-algebras to a given space-time which is a key step in the quantization of fields in physics, although the seminar is purely of a mathematical nature.
We follow a book by Bär, Ginoux and Pfäffle which is self-contained to a very large degree and didactically very efficient. More information may be found in the program of the seminar.
## Literature

- C. Bär, N. Ginoux, F. Pfäffle. Wave Equations on Lorentzian Manifolds and Quantization, ESI Lectures in Mathematics and Physics, EMS. Available as E-Book in our library.

From a UR computer or via VPN the book can be downloaded at https://doi.org/10.4171/037.
- Further literature is given in the program of the seminar, see below.

## Requirements

The seminar addresses, in particular, to students who have followed my lecture about differential geometry II in the summer term 2021. Students with knowledge of differential geometry I might follow as well, if they are willing to read a bit of additional literature.
### Necessary

- Good knowledge about differential geometry as e.g. taught in "Differential geometry I".
- Some basic knowledge about Lorentzian manifolds or willingness to read into this.

### Helpful (can also be learnt within the seminar)

- Improved understanding of Lorentzian manifold, e.g. de (Anti-) deSitter space
- Basic knowledge about hyperbolic partial differential equations
- Basic knowledge about C
^{*}-algebras
- Basic knowledge about quantization

## Time and Place

Thursday, 14.15 to 16.00 in M009
## Organisational meeting

Monday, Feb 7th, 2022 at 16.15 in M009.

Access via zoom, using the zoom access data of the "Seminar über Abschlussarbeiten und Arbeitsgruppen-Seminar" of Bernd Ammann available here or on the GRIPS page of the seminar.
## Program

The program of the seminar.
## Registration

Come to the organisational meeting -- dates given soon.

Please also register in G.R.I.P.S., as we send announcements
via this system.
## Related web pages

## Formal requirements

see KVV (= kommentiertes Vorlesungsverzeichnis = Commented List of Courses)

Bernd Ammann, 19.10.2022

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