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 |
|---|---|---|
| 03. Mar. 2017 | Scheduling | |
| 10. Mar. 2017 | No seminar. | |
| 17. Mar. 2017 | Eduard Nigsch | Stochastic PDEs and Regularity Structures AbstractAbstract: In this talk I will outline some general principles underlying Hairer's theory of regularity structures in a rather pedestrian way. Avoiding details of stochastic calculus as far as possible, and not yet introducing regularity structures, we will see how for subcritical SPDEs, Picard iteration in combination with renormalization techniques gives a notion of solution to these equations. This is more or less a preparation for next week's talk, where we will see how regularity structures allow to obtain solutions where the pedestrian approach fails. |
| 24. Mar. 2017 | Eduard Nigsch | Stochastic PDEs and Regularity Structures, part 2. |
| 31. Mar. 2017 | Benedict Schinnerl | Length structures on Riemannian manifolds with continuous Riemannian metrics AbstractI will talk about Length structures on riemannian manifolds induced by the class of all piecewise smooth paths and prove the equality of the length of these paths in the riemannian sense and the length in the metric sense (as the total variation). From this on I will identify the class of absolutely continuous paths as another admissible class and prove the above equality for these paths even on riemannian manifolds with merely continuous riemannian metrics. |
| 07. Apr. 2017 | Melanie Graf | The $C^0$-(in-)extendibility of FLRW-spacetimes AbstractIn my talk I will present some results concerning the $C^0$ (in-)extendibility of certain FLRW-models from a recent paper by Galloway and Ling. After a brief introduction to the topic of (in-)extendibility of spacetimes and warped products in general I will discuss some important concepts for $C^0$ inextendibility which will then be used to give sufficient conditions for general FLRW-models to have empty future boundary. Then we will define so called "open" and "Milne like" FLRW-models and prove that any Milne like spacetime has a $C^0$ extension. Finally, if time permits, we will give a sketch of the proof that open FLRW-models generically (i.e., unless their scale factor satisfies a specific condition) do not admit a strongly spherically symmetric $C^0$ extension. |
| 14. Apr. 2017 | No seminar. | |
| 21. Apr. 2017 | No seminar. | |
| 28. Apr. 2017 | Lorenzo Luperi Bagilini | The forbidden topic (combinatorial number theory) AbstractIn the last couple of years, various different techniques have been used to solve some old open problems in the area of the forbidden topic. This has opened it to the interest of a wider mathematical community. The goal of this misterious talk is to pedagogically explain why problems in this area might be of general interest, and how to approach them. This will be done by covering the basics of the forbidden topic, starting with the ancient first central results in the area and arriving to the most recent developments; in between, we will discuss also the various techniques that have been used in this field, from the bygone to the classical to the more exoterical ones. No prior knowledge of the forbidden topic or related arguments is needed. |
| 05. May. 2017 | Clemens Sämann | Causality conditions and relations AbstractIn this talk I will give a somewhat different introduction to causality theory with a focus on the causality relations. If time permits I will also discuss the more abstract settings of the causal spaces of Kronheimer-Penrose and the timelike spaces of Busemann. |
| 12. May. 2017 | Paolo Giordano | Hyperlimits and hyperseries of Robinson-Colombeau generalized numbers AbstractThe Robinson-Colombeau ring of generalized numbers eR is simply the ring of Colombeau generalized numbers where we consider an arbitrary in nitesimal net " ! 0+ instead of the usual " = ". It represents a very natural way to have a scalar ring with in nitesimal and in nite numbers as well as the usual real numbers. In the ring eR one can easily introduce the natural sharp topology, which is generated by balls Br(x) with invertible in nitesimal radii r = da := [a " ] 2 eR>0. This is the natural topology where any generalized function, in particular any Schwartz distribution, is continuous. But then 1=n > da for all n 2 N>0 because 1=n is always nite whereas da is in nitesimal, and hence 1=n 6! 0 in the sharp topP ology as n ! +1. Similarly, it is possible to prove that a series +1 n=0 an converges in the sharp topology if and only if its general term an tends to 0 as n ! +1. This has disruptive consequences in the theory of analytic generalized functions. In this talk, we introduce the notion of hyper nite limit and series, i.e. we let that n 2 eN could be an in nite integer generalized number. We will see several examples showing that, in the sharp topology, these are the correct notions of series and of limit of sequences. For example, if time allows, we'll see that with this concepts we can prove -additivity, monotone and dominated convergence theorems for integrals of generalized functions. We will also present the steps we are planning to prove that every Schwartz distribution is hyperanalytic (i.e. it can be expressed using an hyper nite power series), and hence that the Cauchy-Kowalevski theorem for PDE can be extended to any Schwartz distribution using the notion of hyperanalytic generalized function. |
| 19. May. 2017 | Marlene Hangl | The inverse function theorem for Lipschitz continuous functions |
| 26. May. 2017 | No seminar. | |
| 02. Jun. 2017 | No seminar. | |
| 09. Jun. 2017 | Michael Kunzinger | Cone structures on manifolds. AbstractCone structures play an important role in causality theory and thereby in General Relativity. There are by now quite far-reaching generalizations of results and techniques from causality theory that rely on an interesting blend of techniques from dynamical systems, convexity theory and global analysis. This talk is intended to provide a gentle introduction to and an overview of recent results in this field. |
| 16. Jun. 2017 | No seminar. | |
| 30. Jun. 2017 | Christian Spreitzer | PhD Defense |