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 |
|---|---|---|
| 13. Mar. 2009 | Prof. Günther Hörmann | The fundamental theorem of calculus. |
| 20. Mar. 2009 | Dr. James Grant | Injectivity radius estimates. |
| 27. Mar. 2009 | Eduard Nigsch | Point Values in the full Colombeau Algebras Ge and Gd |
| 03. Apr. 2009 | Eduard Nigsch | Point Values in the full Colombeau Algebras Ge and Gd Part II - featuring smooth bump functions on nuclear spaces |
| 10. Apr. 2009 | No seminar | |
| 17. Apr. 2009 | No seminar | |
| 24. Apr. 2009 | Dr. Shantanu Dave | Some Functoriality Problems for Regularization |
| 01. May 2009 | No seminar | |
| 08. May 2009 | No seminar | |
| 15. May 2009 | Dr. Shantanu Dave | Comparison of various regularisation processes |
| 22. May 2009 | No seminar | |
| 29. May 2009 | Martina Glogowatz | Pseudodifferential factorization of PDEs with non-smooth coefficients |
| 05. Jun. 2009 | Clemens Hanel | Wave equations and singular spacetimes. AbstractThe topic of this talk is existence theory of hyperbolic second order systemsof partial differential equations with coefficients of low regularity in suitablealgebras of generalized functions (in the sense of J. F. Colombeau, cf. [1]).We start with an existence theorem by Grant, Mayerhofer and Steinbauer(see [2]) for a linear scalar wave equation on the special Colombeau algebra.From a geometrical viewpoint this is an existence result for the Laplace-Beltramioperator of a (generalized) Lorentzian metric. We extend this result to a certainclass of tensorial linear hyperbolic equations, that are classically treated in [3]and [4], and give an outlook how to use this result for systems of quasilinearhyperbolic equations to solve the Cauchy problem for Einstein’s field equationson a Colombeau-Algebra. |
| 12. Jun. 2009 | No Seminar | |
| 19. Jun. 2009 | No Seminar | |
| 26. Jun. 2009 | Todor D. Todorov | Algebraic Approach to Non-Standard Analysis and Colombeau Theory of Generalized Functions. AbstractWe construct a chain (of infinitely many) algebras of generalized functions and show theyare spacial Colombeau algebras in the sense that for each of these algebras there exists aColombeau type of embedding of the space of Schwartz distributions (the proof is based onconvolution, but also on Zorn lemma). One of these algebras is a full Colombeau algebra (withan explicit embedding). What is different from most of the similar constructions is that thescalars of these algebras form algebraically closed Cantor complete non-Archimedean fields.Our framework is the so calleddistributional non-standard modelof the real numbers especiallydesigned for the purpose of non-linear theory of generalized functions. No background onnon-standard analysis is required by the audience; the language will be essentially algebraic:ordered fields, algebraically closed fields, maximal ideals, etc.For supporting material we refer to Todor’s webpage http://web.me.com/ttodorov (under“Current Research Projects”), where you will findlinks to: 1. Todorov & Vernaeve,Asymptotic Fields and Power Series(under preparation). The reading requires a background in non-standard analysis. 2. For a“gentle” introduction to non-standard analysiswe refer to the Master Thesis ofRay Cavalcante, where the non-standard analysis is presented in terms ofnets of complexnumbers $\mathbb{C}^{\mathbb{R}_+}$(notationally similar to Colombeau theory).3. For themore advanced introduction to distributional non-standard modelof analy-sis we refer to the Master Thesis of Guy Berger, where the non-standard analysis is presentedin terms of nets of complex numbers $\mathbb{C}^D$.4. For anup-to-date versionof thedistributional non-standard modelwe refer to Sec-tion 6 in Todorov & Vernaeve,Full Algebra of Generalized Functions and Non-StandardAsymptotic Analysis, Logic and Analysis, Vol. 1, Issue 3, 2008.5. For the terminology on ordered fields we refer to any textbook on abstract algebra; inparticular to S. Lang (Chapter XI). |