Research Seminar Global Analysis

Jun.-Prof. Dr. Michael Dreher

Prof. Dr. Matthias Lesch

Prof. Dr. Werner Müller

Summer semester 2008

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

Seminarraum D (via Beringstr. 1)



15.04.08 Toshikazu Sunada (Meiji Univ. /MPIM)
Pinning down a diamond twin: an application of discrete geometric analysis

Abstract: A random walker on a crystal lattice X detects the most natural way for X to sit in space. Using this fact, I will pin down a diamond twin which has the same property of symmetry as the diamond crystal. I also mention a relationship with a graph version of Abel-Jacobi map.
22.04.08 Michael Dreher (Konstanz/Bonn)
Elliptische Systeme gemischter Ordnung mit Anwendungen
29.04.08 Matthias Lesch (Bonn)
The Calderón Projection: New Definition and Applications
06.05.08 Alessandro Portaluri (Milan)
The homology of path spaces and Floer homology with conormal boundary conditions
27.05.08 Dan Freed (Univ. of Texas, Austin)
Dirac operators and differential K-theory
03.06.08 Tilmann Wurzbacher (Metz)
Some remarks on the geometry of loop spaces
10.06.08 Werner Hoffmann (Bielefeld)
Application of asymptotic and descent formulas for weighted orbital integrals
24.06.08 Dan Mangoubi (MPI Bonn)
On the Inner Radius of Nodal Domains

Abstract: Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplacian on M with eigenvalue k. The k-nodal set is the zero set {f=0}. A k-nodal domain is a connected component of the set f<>0. Faber-Krahn Inequality shows that the volume of any k-nodal domain is > C/k^{n/2}, where C depends only on the metric. We ask whether it is possible to insert a ball of radius >C/k^{1/2} in a k-nodal domain. We give an affirmative answer in dimension two, and give a partial answer in dimension n>=3. In fact, we prove that the inner radius of a k-nodal domain > C/k^{(n-1)/2}. We show that this problem is closely related to a connection between zeroes of harmonic functions and their growth.
01.07.08 Stefan Haller (Wien)
Non-selfadjoint Laplacians and analytic torsion

Abstract: We will discuss an approach to analytic (Ray-Singer) torsion which is based on non-selfadjoint Laplacians associated to a flat vector bundle over a closed Riemannian manifold. Essentially, this analytic torsion is a non-vanishing complex number which depends holomorphically on the flat connection. We will then turn to comparison results, relating it to the combinatorial (Milnor-Turaev) torsion as well as the "refined analytic torsion" introduced by Braverman and Kappeler.
08.07.08 Atle Hahn (Lissabon)
From the Chern-Simons path integral to the Reshetikhin-Turaev invariant
10.07.08
Special Date!
14:15-15:15, Seminarraum E (via Beringstr. 1)
Mark Malamud (Donetsk National University, Ukraine)
Absolutely continuous spectrum, scattering matrices and Weyl functions
15.07.08 Henri Moscovici (Columbus, Ohio)
Relative Connes-Chern character for manifolds with boundary







B. Himpel, 04/2007