Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Stefan Müller
Korea Institute for Advanced Study
Continuous Hamiltonian and contact dynamics
Continuous Hamiltonian and contact dynamics is an extension of smooth Hamiltonian and contact dynamics
to continuous flows with nonsmooth ‘generating’ Hamiltonian functions. Although there does no
longer exist a vector field linking a flow to its Hamiltonian, each continuous flow possesses a unique Hamiltonian
in the appropriate sense, and vice versa. Moreover, the usual transformation laws continue to
hold, and in fact, many other fundamental properties of smooth dynamics unexpectedly persist in this
continuous framework.
This survey will introduce the main players of the theory together with their most important properties,
followed by a selection of interesting applications. As much as time permits, the initial motivation for this
approach to some of the known C 0 -phenomena in symplectic topology will be explained. The talk is based
on joint work with Peter Spaeth, earlier joint work with Yong-Geun Oh, and work of Augustin Banyaga and
Spaeth.
Frank Pfäffle
Universität Potsdam
On torsion, gravity and the spectral action principle
In this talk closed Riemannian manifolds equipped with orthogonal connections (with torsion) will be
considered. First, I will review the classical Einstein-Cartan-Hilbert theory. Then, I will consider Dirac
operators which are induced by orthogonal connections. By Connes’ spectral action principle all physically
relevant actions should be deducible from the spectral data of a suitable Dirac operator. The
Chamseddine-Connes action is motivated by eigenvalue counting, and it predicts the right form of the Lagrangian
of the standard model of particle physics. I will present a formula for the Chamseddine-Connes
action in presence of torsion and discuss critical points. This project is joint work with Christoph Stephan.
Thomas Schick
Universität Göttingen
Metrics of positive scalar curvature: existence and classification
Fix a compact smooth manifold without boundary. Does it admit a Riemannian metric with positive scalar
curvature? The index of the Dirac operator and the (non)-existence of harmonic spinors, as well as
many “higher” refinements give rise to obstructions. On the other hand, it there are Riemannian metrics
of positive scalar curvature, how does the space of all such metrics look like? What are its homotopy
groups? In the talk, we will present new developments concerning obstructions. The focus, however will
be on the construction and detection of interetsting topological features of the space of metrics of positive
scalar curvature and of its moduli space.
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