Mathematisches Institut

Georg-August-Universität Göttingen

Updates: letztes: 2.5.2007 cgi   nächstes: nach Bedarf      [verantwortlich]

Die Vorträge finden Dienstag, Mittwoch und Donnerstag jeweils um 17.15 Uhr
voraussichtlich im Auditorium Maximum des Mathematischen Institutes statt.

1. Vortrag (Di) : Random surfaces around us.

   We are surrounded by limit shapes --- macroscopic forms produced from microscopic particles by microscopic laws. One can learn about shape formation phenomena from very simple random surface models which can be analyzed exactly. Surprisingly, the same random surface models reappear in other areas of mathematics and physics.
   In the first lecture, we will begin making our acquaintance with the limit shapes by looking at the Wulff shape in the 2-dimensional Ising model.

2. Vortrag (Mi) : Algebraic geometry of random surfaces.

   In zero-temperature 3D Ising model, limit shapes may be described explicitly and turn out to be a plane algebraic curves in disguise. This will be explained in the second lecture, together with the necessary background from algebraic geometry (following a joint paper with Richard Kenyon). Such a connection between probability and geometry leads to a certain synthesis of tools, allowing the analysis to go further.

3. Vortrag (Do) : Instantons, and How Random Surfaces Count Them.

   Instantons are connections that minimize the energy for given topology. They play a very prominent role in gauge theory. Nekrasov proposed a mathematical definition of the partition function of supersymmetric gauge theories in terms of instantons and made a striking conjecture relating it to the work of Seiberg and Witten. In the third lecture, I will explain how it indeed works out and where the limit shapes come into the picture.

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