Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Michael Baake
Universität Bielefeld
Kinematic diffraction from a mathematical viewpoint
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure
and the corresponding inverse problem of structure determination. In recent years, the understanding of
systems with continuous and mixed spectra has improved considerably, while their relevance has grown
in practice as well. Here, the phenomenon of homometry shows various unexpected new facets, particularly
so in the presence of disorder. After an introduction to the mathematical tools, we review pure
point spectra, based on the Poisson summation formula for lattice Dirac combs, aiming at the diffraction
formulas of perfect crystals and quasicrystals. We continue by considering classic deterministic examples
with singular or absolutely continuous diffraction spectra, and we recall an isospectral family of structures
with continuously varying entropy. We close with a summary of more recent results on the diffraction of
dynamical systems of algebraic or stochastic origin.
Literatur
Baake, M. and Grimm, U. (2011). Kinematic diffraction from a mathematical viewpoint, Z. Krist. 226, in
press; arXiv:1105.0095.
Baake, M., Birkner, M. and Moody, R.V. (2010). Diffraction of stochastic point sets: Explicitly computable
examples, Commun. Math. Phys. 293, 611–660; arXiv:0803.1266.
Volker Bach
Institut für Analysis und Algebra, Technische Universität Braunschweig
Existence and construction of resonances in minimally coupled nonrelativistic QED
An excited eigenvalue of an atom is believed to be unstable and turn into a resonance under a perturbation.
In this talk the precise definition of such resonances is given and their existence and construction
is outlined in case the atom is minimally coupled to the quantized radiation field. This model is infrared
singular and notoriously difficult to treat. We review Sigal’s recent construction of resonances based on
the “Feshbach map" and present a novel, alternative construction based on “Pizzo’s method".
Dorothea Bahns
Universität Göttingen
String theory outside the critical dimension
I will review some recent developments in string theory in a setting initiated by Klaus Pohlmeyer in the
1980s. Here, a Poisson algebra is assigned to surfaces of extremal area immersed in Minkowski space,
e.g. to the world sheet of a string. Two deformations of this Poisson algebra (quantization schemes) have
been proposed. One is based on the quantization of an auxiliary Lie algebra in terms of its universal
enveloping algebra, the other is based on the deformation theory of quasi-Lie-bialgebras. Contrary to
the ordinary setting of string theory, which is based on conformal field theory, these two quantization
schemes do not require a critical dimension for consistency.
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