Research Seminar Global Analysis
Prof. Dr. M. Lesch, Prof. Dr. W. Müller
Sommersemester 2012
Next Talk
Forthcoming Talks
| 15.05.12 | Hans Boden (McMaster Univ., MPI) Title: Spliced sums and the SU(3) Casson invariant |
| Abstract: Given two knots in the 3-sphere, one can construct the spliced sum (a generalization of connected sum), and the resulting 3-manifold can be easily seen to be a homology 3-sphere. For instance, the SU(2) Casson invariant is additive under both connected sum and spliced sum. On the other hand, the SU(3) Casson invariant is not additive under connected sum, but subtracting a suitable multiple of the square of the SU(2) Casson invariant gives something that is additive under connected sum but not under spliced sum. In this talk we present methods for computing the SU(3) Casson invariant for certain spliced sums. The examples include splicing along complements of (p,q) torus knots, and the techniques involve developing a good working description of the SU(3) flat and perturbed flat moduli spaces and providing methods to compute the relevant spectral flows. This is a report on joint work with Chris Herald and Ben Himpel. | |
| 22.05.12 | Michael Gruber (Hannover) Title:Absolutely continuous spectrum for periodic magnetic fields |
| Abstract: The spectral theory of Schrödinger operators with periodic magnetic fields (non-zero flux) still poses surprisingly many unsettled questions. We review the main methods and results pertaining to the measure theoretic nature of the spectrum (absolutely continuous vs. pure point) and present new results for AC spectrum. | |
| 05.06.12 | Martin Olbrich (Luxemburg) Title: |
| Abstract: | |
| 12.06.12 | Gerardo Mendoza (Temple University) Title: Complex b-manifolds and their boundary |
| Abstract: A complex b-structure on a manifold with boundary is an involutive subbundle b^T^{0,1}M of the complexification of b^TM with the property that \C b^TM = b^T^{0,1}M + \overline{b^T^{0,1}M} as a direct sum; the interior of M is a complex manifold. The complex b-structure induces a rich structure on the boundary of M similar to that of the circle bundle of a Hermitian holomorphic line bundle over a complex manifold, however generically the circle action is replaced by an \R action. I will briefly show how the structure is obtained and then discuss a classification theorem for such boundary structures similar to that of line bundles by their first Chern class, and embedding (i.e., ampleness) and vanishing theorems similar to Kodaira's well known theorems for positive line bundles. | |
| 26.06.12 | Henri Moscovici (Ohio State University, Columbus) Title: |
| Abstract: |
Past Talks
| 28.03.12 | S. Wakatsuki i (Kanazawa Univ., Japan) Title: On coefficients of unipotent orbital integrals for the symplectic group of rank 2 |
| 03.04.12 | Jens Kaad (Paris VII) Title: An index theorem for commuting Toeplitz operators |
| Abstract: For a large class of Hilbert spaces of holomorphic functions on a domain in n-dimensional complex space there is an associated index problem for tuples of Toeplitz operators with holomorphic symbols. However, outside the strictly pseudoconvex world, concrete computations of the index seems quite scarce. This leaves out classical function spaces such as Bergman and Hardy spaces over the polydisc. The purpose of this talk is to prove an index theorem for a general class of Hilbert spaces satisfying appropriate boundary and density conditions. In this context the index only depends on the behaviour of the symbols near their common roots and can be computed as a sum of intersection numbers (or equivalently of local degrees). The main tool applied in the proof is an algebraic reduction theorem due to Douglas, Paulsen, Sah and Yan. The talk is based on an ongoing project with Ryszard Nest. | |
| 17.04.12 | Jean Raimbault (Jussieu) Title:Analytic torsion for hyperbolic 3-manifolds defined by congruence subgroups of the Bianchi groups |
| Abstract: For finite-volume hyperbolic (three)-manifolds one can define "regularized analytic torsion" simply by using the constant term of the Maass-Selberg expansion for the trace of the heat operator on forms. We are interested in the behaviour of this torsion (with coefficients in a fixed local system) for sequences of manifolds as the systole tends to infinity. More precisely we would like to generalize a recent result of Bergeron and Venkatesh from the compact to the noncompact setting, and we get the following kind of result: Let V be the tautological representation of G=SL_2(C), then if \Gamma_n are an infinite sequence of principal congruence subgroups of a fixed Bianchi group, M_n=\Gamma_n\backslash H^3, the normalized analytic torsion log T(M_n;V)/vol(M_n) tends to 11\pi/12. I will show how to define the regularized analytic torsion and try to explain some of the difficulties arising when studying its asymptotics." |
Informations
• Tuesday, 14:15 in room 0.008, Endenicher Allee 60
• Talks last for about an hour plus discussion
Past semester program
• Winter semester 2011/2012
• Summer semester 2011
• Winter semester 2010/2011
• Summer semester 2010
• Winter semester 2009/2010
• Summer semester 2009
• Winter semester 2008/2009
• Summer semester 2008
• Winter semester 2007/2008
• Summer semester 2007
• Winter semester 2006/2007
• Summer semester 2006
• Winter semester 2005/2006