Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Herbert Spohn
Zentrum für Mathematik, Technische Universität München
The one-dimensional KPZ equation and its universality class
In 1986 Kardar, Parisi, and Zhang proposed a stochastic PDE for the motion of driven interfaces. Bertini
and Giacomin (1997) explained how to approximate the solution to the 1D KPZ equation through the
weakly asymmetric simple exclusion process. Based on work of Tracy and Widom on the PASEP, we
report a formula for the one-point generating function of the KPZ equation in the case of sharp wedge
initial data. The long time limit is given by the Tracy-Widom distribution from GUE random matrices. Of
particular interest are the finite time corrections. This is joint work with Tomohiro Sasamoto.
Rainer Verch
Universität Leipzig
Quantum fields on non-commutative space: non-commutative potential scattering and Wick
rotation
In this talk, two different strands of quantum field theory on non-commutative space will be presented.
First, the scattering of the quantized Dirac field on Minkowski spacetime will be discussed, and it will be
explained how this gives rise to observables of the quantized Dirac field on Moyal-deformed Minkowski
spacetime. Furthermore, it will be argued that this construction is a model for obtaining a correspondence
between more general Lorentzian non-commutative geometries in the sense of spectral geometry and
observables of quantum field theories over such non-commutative Lorentzian geometries. In the second
strand of the talk, the problem of Wick rotation, i.e. the relation between a quantum field theory on
Euclidean space on one hand, and Minkowski spacetime on the other, will be generalized for the Moyal
deformations of Euclidean space and Minkowski spacetime. It will be shown that there is a relation if the
Moyal deformation leaves the time coordinate untouched. These latter results were obtained in joint work
with H. Grosse, G. Lechner and T. Ludwig.
Stefan Weinzierl
Universität Mainz
Hidden mathematical beauty in scattering amplitudes
This talk will be on a topic related to mathematics and (particle) physics. Scattering amplitudes in
particle physics are related to the probability with which a certain scattering process occurs. The
scattering amplitudes are calculable in perturbation theory. Higher orders in the perturbative expansion
are needed for precision predictions for the experiments at the LHC collider. Recent progress in the
calculation of scattering amplitudes has shown that these scattering amplitudes have a much simpler
structure than previously believed. This simplicity is directly related to mathematical structures hiding
underneath. The complexity of scattering amplitudes increases with the number of external legs and
with the number of internal loops. Simplicity with respect to the number of external legs is obtained
by formulating the theory not in space-time, but in twistor space instead. Simplicity with respect to
the number of internal loops is obtained by making use of the algebra of transcendental functions, like
the algebra of multiple poly-logarithms. Here, particle physics touches the domain of the theory of motives.
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