# Research in Groups: Lorentz Geometry

## Summer term 2016

#### News

The
WueCampus homepage
of this RiG is now available.

#### Programme

In this Research in Groups, we discuss Lorentzian geometry: every
manifold can be equipped with a Riemannian metric. However, it needs
some additional features that a manifold can also be equipped with a
Lorentzian metric, where the signature is now (+, -, ..., -). Such
inner products on every tangent space are now the crucial
ingredient for a geometric formulation of general relativity: our
spacetime carries a Lorentz metric which encodes not only the
propagation of light but the whole causal structure of the
spacetime. We will discuss the geometry arising from such a metric in
detail. Particular emphasize will be put on the causal structure,
Cauchy hypersurfaces and globally hyperbolic spacetimes, and, if time
permits, propagation of linear waves.

The course consists of essentially two components: first, a lecture
where the basic notions of Lorentz geometry are explained. The
preliminary program for
the lecture component includes the following topics:

- Lorentz metrics and their geodesics
- Submanifolds
- Causality
- Globally hyperbolic spacetimes
- Symmetries
- Wave equations

The second component will be a seminar by the students on more
particular topics. We expect the participants to write a small
proceeding-like summary of their seminar talks.

#### Prerequisites

This Research in Groups addresses master students in mathematics or in
mathematical physics with a reasonable background in differential
geometry. Here the lecture notes on differential geometry from the last
semesters will be a good starting point. They will be on WueCampus as soon
as the course is enabled.

However, if you are in doubt, please contact me directly and we will find a
solution. I will explain the necessary things either in the lecture
part or directly.

#### Literature

The following list of
references will be discussed in the first
meeting. More references will be given individually.

#### Dates

If there are collisions with other lectures or seminars, please
contact me early: maybe one can still shift things around a bit.

- Lecture: Maybe Tuesdays
- Seminar: The seminar will take place at one or two days at the end of the
semester. The precise date will be announced.

#### Links

- On WueCampus there will be a
homepage
for this RiG. The WueCampus homepage will replace this site as soon as
it is activated.

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