This seminar is an informal forum where members of the DIANA group meet to discuss topics of interest. We meet on a weekly basis. The programme for these meetings will be advertised below, and by email.
If you wish to be added to (or removed from) our email list, please contact tobias.beran@univie.ac.at: subscribe or unsubscribe.
The the seminar takes place every Friday at 09:45 am in SE 07 and streamed via moodle and will be announced by email weekly.
Anyone interested is welcome to attend.
| Date | Speaker | Title |
|---|---|---|
| October 14 and 21 | No Seminar. | |
| October 28 | Michael Kunzinger | Sprays. |
| November 4 | No seminar. | |
| November 11 | M. Ringbauer and T. Moser | The Schwartz kernel theorem. AbstractWe prove in detail the Schwartz kernel theorem, which establishes a correspondence between sequentially continuous linear maps and distributional kernels. We also discuss the case of regular kernels and fundamental kernels as major applications of the Schwartz kernel theorem. |
| November 18 | Walter Simon | Properties of marginally outer trapped surfaces in spacetime. AbstractA "marginally outer trapped surface" (MOTS) S in a spacetime is a compact2-surface such that one of the two families of null geodesics emanating orthogonally from S (called the outgoing one) has vanishing expansion everywhere on S. For an "outer trapped surface" (OTS) this expansion is negative on S. OTS and MOTS play a role e.g. in the singularity theorems of General Relativity by Hawking and Penrose. I define and discuss "stability" for MOTS, in particular the property that an interior neighbourhood of a stable MOTS can be foliated by OTS, whereas such OTS are absent in an exterior neighbourhood. This result is based in essence on properties of quasilinear and linear elliptic operators. Moreover, in a spacetime foliated by hypersurfaces and with a MOTS on the initial leaf of the foliation, I describe the propagation of this MOTS to adjacent leaves, which depends crucially on its stability. Here the basic result is an application of the implicit function theorem. |
| November 25 | Ronald Quirchmayr | Hörmander's approach to the Malgrange-Ehrenpreis theorem. |
| December 2 | Clemens Sämann | The geodesic problem in metric spaces. AbstractThis talk will be about the (parametric) geodesic problem in metric spaces, i.e., finding minimizers of $\{Var(\gamma) :\gamma\in Lip([a,b],E),\gamma(a) =x,\gamma(b) =y\}$, where $(E,d)$ is a metric space, $x,y\in E$, $Lip([a,b],E)$ denotes the Lipschitz continuous functions from $[a,b]$ to $E$ and $Var$ denotes the variation. After setting up the tools needed (metric derivative, reparametrization) I will give an existence proof for certain metric spaces. |
| December 9 | Clemens Hanel | Ph.D. Defence: On singular wave equations. |
| December 16 | Paolo Giordano | Topologies on Colombeau generalized numbers. Abstractthe slogan of this Diana seminar will be: "the sharp topologyis not horrible, but the e-norm is disgusting". We will see that it is possible to study the sharp topology using the order topology on CGN, i.e. using its absolute value, which has properties very similar to the usual Euclidean one. We will also see that some counter intuitive properties of the sharp topologies comes from general and simple results valid for topological spaces with infinitesimals, and hence cannot be avoided. In case of sufficient time, we will also sketch some ideas concerning a (potentially) interesting subfield of the ring of CGN. [the work is done in collaboration with M. Kunzinger] |
| January 13 | Prof. Norbert Ortner | Gedanken zu einer Vorlesung über partielle Differentialgleichungen. |
| January 20 | Nathalie Tassotti | $C^\alpha$-convergence of Riemannian manifolds. |
| January 27 | Milena Stojkovic | The meaning of curvature. |