(What is strange is wonderful.)
The symbol on the right 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.
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.
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.
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).
Quite some time ago, I wrote a small JAVA applet for calculating and visualizing electric fields.
If you are doing (theoretical) physics, it is fortunately most of the time enough to rely on information you can obtain from the internet. First of all, one has to mention the arXives, which provide you with most of the papers written since 1991. If you are doing high-energy physics, there is the further useful database of inSPIRE, which allows you to search through most of the hep papers ever published. It also comes with a powerful citation database which makes the search for relevant literature really convenient. Furthermore, there is a huge collection of lecture notes and review papers in all areas of physics found at The Net Advance of Physics.
Whenever you are in need of a mathematical definition or some background information on a certain class of objects, one should try MathWorld, Planet Math and - surprisingly - the allmighty Wikipedia. Furthermore, there are the math sections of the famous arXiv, a helpful frontend for the latter and the homepage of MathSciNet.
Science related blogs
Some blogs have developed into quite a useful source for news in the string and high-energy physics community. Here is a short selection:
Another classic is Musings by Jacques Distler, which people used to check out all the time during the Strings2004 conference for reading summaries of the talks they missed because they read blogs.
Closely related is the String Theory Coffee Table on which you find mostly reporst on recent developments in rather remote corners of the mathematical universe.
The currently most famous (or notorious?) blog is probably Lubos Motl's reference frame, which reliably reports on all important developments in high-energy physics and string theory from the point of view of a true believer. The political attitudes brought forth in this blog are, however, weird in the best case but most of the time quite shocking.
Lubos traditional opponent in the blogosphere is apparently Peter Woit, who writes about all kinds of issues related to high-energy physics. Most of the time, however, he will complain about how bad string theory is in predicting anything.
Cosmic Variance is a nice blog of a group of scientists on all kinds of topics.
Institutes I visited or worked at
Mostly for my own convenience, here is a list of the scientific
institutes I had some relation to:
- Physikalisches Institut der Universität Würzburg
- Physics Department of The University of Texas at Austin
- Institut des Hautes Études Scientifiques, Paris
- Departement des Mathematiques et applications of the Ecole Normale Superieure, Paris
- Centro de Estudios Cientificos, Valdivia, Chile
- Institute for Theoretical Physics of the University of Hanover
- The Abdus Salam ICTP in Trieste
- Bogoliubov Laboratory of Theoretical Physics in Dubna, Russia.
- Dublin Institute for Advanced Studies
- School of Mathematics, Trinity College Dublin
- Department of Mathematics, Heriot Watt University, Edinburgh
- Maxwell Institute, Edinburgh
- International Centre for Mathematical Sciences, Edinburgh
- Isaac Newton Institute Cambridge