Oberseminar Globale Analysis / Research Seminar

Prof. Dr. Matthias Lesch

Winter semester 2005/2006

Tuesday, 14:15-15:45 (talks last for about an hour plus discussion)

Seminarraum D (via Beringstr. 1)



01.11.05 All Saints Day. No seminar
08.11.05 Time change: 13:15 - 14:45
Philip Foth (Univ. of Arizona, z.Zt. MPIM Bonn)
Poisson geometry of homogeneous spaces and applications

Abstract: This will be an introductory talk, in which I will explain basic concepts of Poisson geometry and present a variety of examples. The emphasis will be placed on Poisson homogeneous spaces. As examples of applications, we will consider certain integrals appearing in harmonic analysis.
15.11.05 Alexander Strohmaier (Bonn University)
The index of projective families of elliptic operators: 1.1 Brauer groups and the Dixmier Douady invariant (research seminar)

This is the first talk as part of the research seminar on the recent work of Varghese Mathai, Richard B Melrose and Isadore M Singer: The index of projective families of elliptic operators. Everybody who is interested, is welcome to attend.
Abstract: An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup of the third cohomology of X with values in Z. The Chern character of the index class is then computed.
22.11.05 Time change: 13:15 - 14:45
Benjamin Himpel (Bonn University)
The index of projective families of elliptic operators: 1.2 Twisted K-Theory (research seminar)

This talk is part of the research seminar on the recent work of Varghese Mathai, Richard B Melrose and Isadore M Singer: The index of projective families of elliptic operators. Everybody who is interested, is welcome to attend.
29.11.05 Dmitry Jakobsen (McGill University, z.Zt. MPIM Bonn)
Lower bounds in local Weyl's law

Abstract: We will discuss proofs of the results on lower bounds for spectral functions and local Weyl law (stated in the MPI Oberseminar talk on October 27). We shall concentrate on the proof in negative curvature case, and explain connections to results of Parry-Pollicott on weighted dynamical zeta functions that are used in the proof.
06.12.05 Bernhard Kroetz (MPIM Bonn)
Transcendenting Cartan-Helgason theory for spherical representations

Abstract: Cartan-Helgason theory gives us methods and classification of finite dimensional spherical representations. In this talk I will extract its essence in order to modify it for infinite dimensional unitary modules.
13.12.05 Alexandra Mozgova (Univ. d'Avignon, z.Zt. MPIM Bonn)
Incompressibility in dim 4

Abstract: A standard fact about two incompressible surfaces in an irreducible 3-manifold is that one can move one of them by isotopy so that their intersection becomes $\pi_1$-injective. We extend it on $\pi_1$-injective maps of some 3-dimensional manifolds and $\mathbb{Z}_n$-manifolds into 4-manifolds and give applications to 4-manifolds with big fundamental groups.
10.01.06 Yoonweon Lee (Inha Universitaet Korea, z.Zt. MPIM Bonn)
The zeta-determinants of Dirac Laplacians on a compact manifold with boundary

Abstract: In this talk we briefly review the gluing formula for the zeta-determinants of Laplacians on a closed manifold given by Burghelea, Friedlander and Kappeler, which was established for the Dirichlet boundary condition. We next discuss, on a compact manifold with boundary, the difference of log of two zeta-determinants of Dirac Laplacians subject to the Dirichlet bounday condition and a boundary condition on the smooth, self-adjoint Grassmannian. Combining these two results, we try to establish the gluing formula for the zeta-determinants of Dirac Laplacians with respect to boundary conditions on the smooth, self-adjoint Grassmannian. We also discuss some related topics.
24.01.06 Roland Friedrich (Institute for Advanced Study Princeton, z.Zt. MPIM Bonn)
On some recent applications of Riemann surfaces in light cone gauge presentation
31.01.06 Raphael Ponge (RWTH Aachen)
Noncommutative residue and new invariants for CR and contact manifolds








B. Himpel, 11/2005