Information on the EmmyNoether Project
Quantengeometrie: Mathematische Physik auf dem Weg zur Quantengravitation

(Quantum Geometry: Mathematical Physics along the road to Quantum Gravity)

Coordinates
The group was funded by the EmmyNoetherProgramm of the Deutsche Forschungsgemeinschaft under grant FL 622/11 from August 2006 until November 2013.
Since November 2009, the group had been
affiliated to the Mathematics Department
of Paderborn University.
Before, until October 2009, the group had been affiliated to
the Center for Mathematical Physics
and
to the Analysis and Differential Geometry Division of
the Mathematics Department
at Hamburg University.
Group members
Head:

Christian Fleischhack

08/2006 – 11/2013




Postdocs:

Benjamin Bahr

07/2013 – 11/2013


Johannes Brunnemann

10/2006 – 12/2010




Ph.D. students:

Maximilian Hanusch

12/2010 – 11/2013


Diana Kaminski

09/2006 – 12/2010


Heiko Remling

08/2006 – 03/2007

Short Summary
The unification of quantum theory and gravitation is one of the
most important unsolved problems of modern physics.
In particular, due to the lack of experimental data,
it is crucial to investigate this issue mathematically.
Currently, there are three major approaches to attack
this problem: loop quantum gravity, noncommutative geometry, and
string theory. The proposed project is devoted to quantum geometry,
being a main point of the first mentioned area.
At the same time, we strive for an exchange of ideas and methods
with algebraic quantum field theory, being closely related to
noncommutative geometry, and hope to connect both fields this way.
Within the project we are going to investigate, how far the quantization
of classical theories may be unique or whether superselection sectors
may arise. Here, the presence of symmetries will play a crucial role.
At the same time, we are going to study what highly symmetric models
(as known, e.g., from quantum cosmology) can tell us about the full,
but still unknown theory of quantum gravity. Finally, global covariance
of gravity should be treated in a mathematically adequate way and
without separation of space and time. The necessary mathematical
methods will mainly come from analysis (global and functional analysis) and
geometry (differential and algebraic geometry).