11.09.2007	Alan Carey (Australian National University) Semifinite non-commutative geometry and applications 10:15 in Seminarraum B (room 37), Beringstr. 4.
23.10.2007	Niels Martin Moller (Univ. of Aarhus) Dirac operator determinants: the Bär-Schopka and Branson conjectures. Abstract: A Riemannian (spin) manifold M allows the introduction of natural geometric differential operators: Laplacians and Dirac operators. From the spectrum of these, one defines spectral zeta functions and determinants, which are important both as geometric invariants (Ray-Singer torsion etc.) and in physics (QFT/string actions etc.). This talk deals with two aspects. (1) Explicit values of determinants on S^n: we announce a proof of Bär-Shopka's conjecture on large n asymptotics. The real focus in the talk is (2) Extremal results under variation of the Riemannian metrics: This involves the problem of general changes of metrics in spin geometry, and finding the Hessian of the determinant. In even dimension, M. Lesch's class of pseudodifferential log-polyhomogeneous symbols is needed, and we prove results on semi-boundedness of spectrum in a subclass. The analysis gives the pattern (in the dimension) of extremals. Combining this with results by K. Okikiolu we can verify, with finitely many exceptional directions, a local version (but for general variations) of a conjecture by T. Branson, which stated that the Dirac operator behaves oppositely to the conformal Laplacian. We specialize to round spheres S^n, which we study as our main example.
30.10.2007	Calin Martin (Potsdam) Corner operators and applications to elliptic complexes.
06.11.2007	Maurice de Gosson (Bremen) A Symplectic Approach to Hardy's Uncertainty Principle. Abstract
13.11.2007	Alla Sargsyan (Leipzig) On the $\bar\partial$-problem on unbounded domains and Levi-degenerate hypersurfaces in CP^n.
20.11.2007	Change in schedule: The talk by Nikolai Neumaier has been cancelled due to illness. Instead we are happy to announce Norbert Peyerimhoff (Durham, UK) An integral geometric problem on harmonic spaces. Abstract: In 1929, the Rumanian mathematician D. Pompeiu asked the following question: given a continuous function f on R^2 and a compact set K. Assume that the integral of f over all images of K under rigid motion vanishes. Does this imply that the function f itself is zero? The answer is negative in the case that K is a disk. But it can be shown that the conclusion holds in the case that the integral of f vanishes on all disks of radius r_1 and of radius r_2, as long as the quotient r_2/r_1 avoids a certain countable set of real numbers. It is natural to ask similar questions in more general geometries. In this talk we discuss the same (two radius) problem in harmonic spaces. In particular, we focus on a certain class of harmonic spaces, which were originally intoduced by Damek and Ricci as counterexamples of a conjecture of Lichnerovich.
27.11.2007	Jürgen Eichhorn (Greifswald) Teichmüller Theorie und harmonische Abbildungen für offene Flächen.
11.12.2007	Arthur Wotzke (Bonn) Analytic torsion for hyperbolic manifolds and the Ruelle zeta function. Abstract: In 1986 Fried proved that the Ruelle zeta function $Z_R^\varphi$ , where $\varphi$ is a unitary representation of the fundamental group of a hyperbolic manifold $X$, has a representation by a finite product of Selberg zeta functions. Therefore, by applying the method of the trace formula one yields a meromorphic continuation of $Z_R^\varphi$ to the whole complex plane. In particular, Fried showed that the Ruelle zeta function is regular in the origin and that $Z_R^\varphi(0)=T(\varphi)^2,$ is the analytic torsion. In this talk we discuss a generalization of these results for an induced representation, i.e. the representation of $\pi_1(X)$ is a restriction of an irreducible representation of the isometry group of $X$.
18.12.2007	Andras Vasy (Stanford) Propagation of singularities of the wave equation on manifolds with corners
15.01.2008	Peter Zograf (MPIM and Steklov Institute, St. Petersburg) Kaehler structure on the space of meromorphic functions Abstract: We introduce a natural Kaehler metric on the space of (generic) ramified coverings of the Riemann sphere of a given degree and describe its Kaehler potential.
22.01.2008	Yaroslav Kopylov (z.Zt. MPI Bonn) $L_p$-differential forms and Banach complexes
29.01.2008	Benjamin Himpel (Bonn) Splitting the spectral flow and the SU(3) Casson invariant for spliced sums