Vorträge in der Woche 01.05.2023 bis 07.05.2023

Dienstag, 02.05.2023: Cohomology

Daniele Agostini

Donnerstag, 04.05.2023: A generalization of Sylvester's law of inertia

Dr. Stéphanie Cupit-Foutou (Ruhr-Universität Bochum)

Sylvester's law of inertia for real quadratic forms in n variables can be interpreted as a parametrization of the GLn(R)-orbits in the real locus of the set of complex quadratic forms equipped with the real structure defined by the complex conjugation of matrices. The set of non-degenerate complex quadratic forms is an instance of a complex symmetric space and more generally of a spherical space. After having introduced these spaces properly, I will explain how, jointly with D. Timashev, we obtain a generalization of Sylvester's law of inertia for such spaces.

Donnerstag, 04.05.2023: Numerical methods for the fractional Helmholtz equation

Lehel Banjai (Heriot-Watt University)

In this talk we consider the Helmholtz equation where the usual Laplacian is replaced by the spectral fractional Laplacian. The thus obtained fractional Helmholtz equation has applications in geophysical electromagnetics. We describe and analyse two possible numerical methods. Firstly, a direct contour integral method discretised by a sinc quadrature. Secondly a tensor product hp-finite element method. In both cases we show that the cost is equivalent to solving a single standard Helmholtz equation and a fractional Poisson problem. The talk ends with some preliminary numerical experiments showing exponential convergence of the method.

Donnerstag, 04.05.2023: Abstract Lorentzian metric spaces and their Gromov-Hausdorff convergence

Prof. Ettore Minguzzi (University of Florence)

A definition for `bounded Lorentzian metric space’ is presented and discussed. This is an abstract notion of Lorentzian metric space that is sufficiently general to comprise compact causally convex subsets of globally hyperbolic (smooth) spacetimes, and causets. It is shown that a generalization of the Gromov-Hausdorff distance and convergence can be applied to these spaces. Furthermore, two additional axioms of timelike connectedness and existence of maximizers, which are stable under GH-convergence, lead to suitable notions of Lorentzian pre-length and length spaces. Similarly, sectional curvature bounds stable under GH-convergence can be introduced. A (pre)compactness theorem is also mentioned and its limitations are discussed. Talk based on joint work with Stefan Suhr (Bochum).

Freitag, 05.05.2023: Gedenkkolloquium Prof. Dr. Helmut "Reiner" Salzmann

Prof. Dr. Linus Kramer (Münster) und Prof. Dr. Rainer Löwen (Braunschweig)

15:00 Begrüssung --- 15:15 Prof. Dr. Linus Kramer (Münster): Geometrie, Topologie und Liegruppen: Zum Werk von H.R. Salzmann --- Pause --- 17:00 Prof. Dr. Rainer Löwen (Braunschweig): Parallelismen fuer orientierte Geraden im reellen projektiven Raum --- Ab 19:00 besteht die Möglichkeit zur Teilnahme an einer Nachsitzung im Restaurant Waldhäuser Hof. Um Anmeldung bis 26.4. wird gebeten (nerz@mathematik.uni-tuebingen.de).