Mathematics

Quintic

The symbol of these pages is a cross section through the Calabi-Yau manifold known as the quintic. This manifold is defined by the equation a⁵+b⁵+c⁵+d⁵+e⁵=0 in CP⁴, and - as all real 6 dimensional Calabi-Yau manifolds - plays an important role in the compactification of the ten dimensions in which the superstring lives to the four space-time dimensions we observe. For more details, see also D-Branes On The Quintic.

Aesthetics and Mathematics

Inspired by Ernst Peter Fischer's book Das Schöne und das Biest and the less valuable Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler, I spent some time thinking about beauty in mathematics and physics, the results of which can be read here.

Miscellaneous

For a seminar in mathematics, I wrote a small comment about Eulers Formel und Picks Theorem. Fascinated by the golden section and its relation to many aspects of mathematics, I wrote some short notes.

Physics

String Theory

To obtain a good idea of what string theory is all about, you should have a look at the official string theory homepage. In brief, string theory is the (only really promising) attempt to unify general relativity (the theory of gravity and big things like black holes and galaxies) with the principles of quantum mechanics (the theory of small particles like atoms, electrons and quarks). There are many strong arguments which seem to show that string theory can in fact achieve this. However, the description is not unique, but one has infinitely many possibilities of modelling our universe in string theory, which renders its predictive power close to zero. Surprisingly, there has been a development recently called twistor string theory that inspired methods to calculate certain quantities in quantum field theory which was impossible up to then. As these quantities will be needed for understanding the new results of the LHC at CERN, it seems, that for the first time, physicists have really to listen to the string community.

N=1 superfield calculations with Mathematica

This is a Mathematica notebook which can perform superfield calculations for ordinary d=4, N=1 superfields (even if they take values in a Lie algebra). The conventions used in the definitions are those of Wess and Bagger. Although entering a superfield expansion can be rather cumbersome, this notebook helps particularly when one needs to be flexible with conventions. (I wrote and used it to verify coefficients in the Freedman-de Wit transformation). Furthermore, most of the standard definitions are already included and the notebook can be extended to other situations. This notebook is still in an alpha-stage, so I do not guarantee for any of the results. Feel free to use it for your scientific computations; I'd be very happy about being mentioned in the acknowledgments, though.

Miscellaneous

Among the things you might find interesting, there are some short notes on spinors, a review on two-dimensional string theory (however, in French) and transparencies on reconstructions of trajectories for double star systems (this one is in German).

Electric Fields

Quite some time ago, I wrote a small JAVA applet for calculating and visualizing electric fields.