Max-Planck-Institut für Gravitationsphysik
Am Mühlenberg 1
Curriculum Vitae. This page contains professional information about me. For other material, scientific and otherwise, see my blog Hydrobates.
My publication list can be found here.
Arne Gödeke (PhD student)
In the following I describe some of my research interests. These have to do with the mathematical study of certain problems arising in scientific applications. What follows is a description of my research projects aimed at mathematicians or scientists working in the areas of application I am interested in. There is also a version for non-specialists covering some of the topics.
Recently I have been working on applications of mathematics to biology, in particular immunology. Most of the my earlier work is related to the dynamics of matter interacting by its own gravitational field. The main applications of this are in astrophysics. Often the gravitation is described by the Einstein equations of general relativity, although in some cases the Newtonian theory of gravitation may suffice. My aim is to obtain rigorous mathematical results on these questions. The resulting mathematical problems are often very difficult and in order to make progress it is common to make symmetry assumptions. Another possibility is to restrict to configurations which start close to a configuration which is explicitly known (case of "small data"). The topics I have chosen to describe in more detail are organized under five headings:
1. Mathematical models in immunology
2. Homogeneous cosmological models
3. Systems in one or two space dimensions
4. Linearized perturbations
5. Shock waves in self-gravitating fluids
These descriptions include links to the electronic archives at http://arXiv.org.
Cooperation with the University of Yaounde I
I had a collaboration with the University of Yaounde I in Cameroon. Together Norbert Noutchegueme I led a project funded by the VolkswagenStiftung. A grant of c. 100 000 euro over three years was used to support our collaboration and, in particular, to allow three graduate students from Yaounde (Pierre Noundjeu, Blaise Tchapnda and David Tegankong) to spend time in Golm. Each of them was awarded a PhD by the Technical University in Berlin.
Further background and references on some of the topics discussed above can be found in my review article in Living Reviews in Relativity.
Nonlinear hyperbolic equations, FU Berlin, summer semester 2012. (Details.)
Applied partial differential equations, FU Berlin, summer semester 2011. (Details.)
General relativity, FU Berlin, summer semester 2010. (Lecture notes in English.)
Kinetic equations, FU Berlin, summer semester 2009. (Lecture Notes in English.)
General relativity, FU Berlin, summer semester 2008. (Lecture notes in English and German.)
Systems of conservation laws, FU Berlin, summer semester 2007. (Lecture notes in German.)
Nonlinear hyperbolic equations, FU Berlin, summer semester 2006. (Lecture notes in German.)
General relativity, FU Berlin, summer semester 2005.
Mathematical biology, TU Berlin, summer semester 2004.
General relativity, TU Berlin, summer semester 2003.
Cosmological models, vacation course, AEI, spring 2001. (Lecture notes in English.)
Analysis for computer scientists. TU Berlin, winter semester 2000/01.
Systems of conservation laws, TU Berlin, summer semester 1999.
Nonlinear hyperbolic equations, TU Berlin, winter semester 1997/98.
I have written a text describing selected examples of mathematical modelling, with an emphasis on applications to biology and medicine. The material of the course on hyperbolic equations can be applied to study the Cauchy problem for the Einstein equations. I have written an exposition of the work of Christodoulou and Klainerman on the nonlinear stability of Minkowski space. I have a collection of useful equations related to the 3+1 decomposition of the Einstein equations. I have put a lot of effort into trying to ensure that these equations are correct. If you nevertheless find a mistake please report it to me.
To visit the home page of the Albert Einstein Institute click here.
On 25th November 2010 an interview which I gave featured in a documentary in the series Scobel of the channel 3Sat called "Rätsel Dunkle Materie" [The riddle of dark matter].