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 |
|---|---|---|
| 07. Mar. 2014 | Scheduling | |
| 14. Mar. 2014 | No seminar | |
| 21. Mar. 2014 | Alexander Lecke | An Introduction to Direct Methods in Variational Calculus AbstractI will give a short introduction to direct methods in the calculus of variations, answering questions like: 'What is a direct method?', 'Do solutions exist?', and 'Where are problems?' |
| 28. Mar. 2014 | Michael Oberguggenberger | Stochastic Fourier integral operators |
| 04. Apr. 2014 | Milena Stojković | Causality Theory for $C^{1,1}$ Lorentzian metrics AbstractIn the standard references to causality theory smoothness of the metric is usually assumed. However, it was of interest for some time to determine the minimal degree of regularity of the metric for which standard results of causality theory remain valid. A reasonable candidate is given by metrics of class $C^{1,1}$ since it represents the threshold where one still has unique solvability of the geodesic equation. The first part of the talk is going to be about the main results of causality theory with smooth metrics and the second part is about the key ingredients and techniques used to develop it for $C^{1,1}$ metrics and show that fundamental results hold true in this case. |
| 11. Apr. 2014 | Paolo Giordano | How many big-Os do you know? I.e. how to get rid of quantifiers in the full Colombeau algebra AbstractThe full Colombeau algebra (CA) has been introduced to have an intrinsic embedding of Schwartz distributions. The resulting definition is usually perceived as more complicated w.r.t. the special CA, first of all for the greater number of quantifiers involved. We'll see how a suitable definition of "set of indices" permits to introduce new notions of big-O formally behaving as the usual one and allowing a unification of several CA. This is a typical work of foundational nature, i.e. rising from the collision of a lacking of beauty and the searching for a better understanding in topics usually taken for granted. I hope this will also give us the opportunity to discuss about the comparative difficulty in creating definitions, statements, and proofs in Mathematics. |
| 02. May 2014 | No seminar | |
| 09. May 2014 | Lorenzo Luperi Baglini | Asymptotic Gauges AbstractIn some sense, two of the basic ingredients in the Colombeau constructions are the set of indeces $(0,1]$ and of choice of the "growth condition" given by the net $1/\varepsilon$ with $\varepsilon \in (0,1]$. The idea behind the notion of asymptotic gauges is that the usual Colombeau constructions can be generalized by taking (almost) any set of indeces and (almost) any growth condition defined starting from that set of indeces. This generalization can be done by preserving in a quite natural way many of the constructions and results of the usual Colombeau case. In particular, we will show how to generalize the notions of Colombeau special and full algebras and how they can be applied to solve some very easy differential equations with generalized coefficients. If time permits, we will also show that, in some sense, from this generalized point of view the distinction between special and full algebras vanishes. |
| 16. May 2014 | Melanie Graf | Distributions with support in a semi-Riemannian hypersurface AbstractIt is well-known that any distribution on $\mathbb{R}^n$ with support in a single point can be expressed as a sum of derivatives of Dirac's delta distribution. The goal of this talk is to present a similar result for distributions with support in a hypersurface. In the beginning we will quickly review some basic facts about distributions on manifolds (taking into account the added structure given by a semi-Riemannian metric). Then we are going to define single- and multilayer distributions and use them to give alternate expressions for both the pullback of delta on a submanifold and the exterior derivative of a function with a jump discontinuity across a hypersurface. Last but not least we will show that any distribution with support in a (closed, oriented, semi-Riemannian) hypersurface can be written as a locally finite sum of such multilayers (sketching the proof if time permits). |
| 23 May 2014 | Albert Huber | Allgemeine Relativitätstheorie, niedrige Regularität |
| 06. Jun. 2014 | Michael Kunzinger | Geodesics in low regularity AbstractIn this talk I will mainly elaborate a very instructive example, due to Hartman and Wintner, showing how standard properties of geodesics may fail if the regularity of the Riemannian metric is below $C^2$. If time permits I will also make some general remarks on the existence of shortest paths as well as on the relation between shortest paths and geodesics for $C^1$-metrics. |