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 12 | No seminar. | |
| October 19 | No seminar. | |
| October 26 | No seminar. | |
| November 2 | No seminar. | |
| November 9 | Rizwan Ahmad | Multiplication of distributions. AbstractBased upon M. Oberguggenberger's "Multiplication of distributions and applications to partial differential equations", the focus of my diploma thesis was developing and presenting a hierarchy, describing the relations between several irregular intrinsic products of distributions. After a short introduction i'm going to give an overview on the duality product, the Fourier product and regularization products. |
| November 16 | James Grant | The positive mass theorem. AbstractThe positive mass theorem states that the mass of a complete, asymptotically flat Riemannian manifold with non-negative scalar curvature is non-negative, and that the mass is equal to zero if and only if the manifold is isometric to flat Euclidean space. This theorem was proved in the smooth setting by Schoen and Yau for manifolds of dimension less than or equal to seven, and by Witten for spin manifolds. I will discuss some recent work with Nathalie Tassotti in which we prove that the positivity of the mass can be extended to a class of non-smooth metrics, where one has a compact set on which the metric is required to only be continuous, to live in the Sobolev space $W^{2, n/2}_{loc}$ and to have non-negative scalar curvature in the distributional sense. I will also give some indications of how all of the known proofs of the rigidity result (i.e. that if the mass is zero, the space is Euclidean) seem to break down for metrics with our level of regularity. A brief announcement of this work was contained in the preprint arXiv:1205.1302. |
| November 23 | Eduard Nigsch | Locally convex algebras of nonlinear generalized functions. AbstractWe will discuss a recent preprint by J. F. Colombeau about subalgebras of the special Colombeau algebra which admit Hausdorff locally convex topologies with nice topological properties. These subalgebras are obtained, in a sense, by restricting to analytic representatives. |
| November 30 | Milena Stojkovic | Cone Structures. AbstractThe talk is based on the paper by A. Fathi and A. Siconolfi, "On smooth time functions", where they give a detailed study of cone structures which are used for proving the existence of smooth time functions on space-times that satisfy appropriate causality conditions. We first give an introduction to cone structures on manifolds and then discuss their applications to global hyperbolicity of Lorentzian manifolds. |
| December 7 | Clemens Sämann | Impulsive gravitational waves. |
| December 14 | Paolo Giordano | T.B.A. |
| January 11 | Tobias x | T.B.A. |
| January 18 | Katharina Kienecker | T.B.A. |
| January 25 | Not fixed yet. |