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 |
|---|---|---|
| 14. Oct. 2016 | Eduard Nigsch | |
| 21. Oct. 2016 | Alexander Lecke | Ph. D. thesis defense |
| 28. Oct. 2016 | No seminar. | |
| 11. Nov. 2016 | Michael Kunzinger | Harmonic coordinates AbstractThis talk is devoted to the question of optimal regularity for Riemannian metrics. We report on a classical paper by Deturck and Kazdan, which, among other results, shows that harmonic coordinates are privileged in the sense that the metric is always most regular when expressed in these coordinates, whereas (maybe somewhat surprisingly) a loss of two orders of regularity may occur for Riemannian normal coordinates. We also discuss isothermal coordinates, give some examples and consider the question whether regularity of the connection or the Ricci tensor imply regularity of the metric itself. |
| 18. Nov. 2016 | Yafet Sanchez Sanchez | What is a gravitational singularity? AbstractIn this talk I will show some of the main issues to describe a singularity in GR. We will show that a spacetime containing cosmic strings can be seen as non-singular even if the curvature is not continuous in the apex. Then, I will comment about some generalizations to QFT. |
| 25. Nov. 2016 | Clemens Sämann | An elementary introduction to Clifford Algebras and Spinors AbstractAfter a brief motivation we give an very elementary introduction to Clifford Algebras and Spinors starting with the Clifford Algebra on (euclidean) R^2. Then discussing the case of R^3, Pauli spin matrices and Pauli spinors. If time permits we discuss higher dimensional cases or more general settings. |
| 04. Nov. 2016 | Eduard Nigsch | Colombeau algebras without asymptotics AbstractColombeau algebras are always constructed by taking the quotient of moderate by negligible elements in some basic space. Classically, moderateness and negligibility are always tested for by evaluating the representatives of generalized functions on nets parameterized by $\varepsilon$, which leads to asymptotic estimates. While a polynomial scale for these estimates gives the desired Colombeau algebras and "just works", it is not yet clarified whether this whole testing procedure is essential for the construction of the algebra or just some intermediate technical tool. In my talk I will present an alternative approach to the quotient construction which replaces the asymptotic estimates by topological properties and hence exposes these estimates as mere auxiliary tools not inherent to the theory at all. |
| 16. Dec. 2016 | No seminar. | |
| 02. Dec. 2016 | Stefan Bognar | Existence and regularity of solutions for linear PDOs AbstractI will give a short introduction to linear PDOs. Then I prove the existence of weak solutions in the L^2 - case. In the second part I introduce the singular support and some properties and finally show the elliptic regularity theorem. |
| 09. Dec. 2016 | No seminar. | |
| 13. Jan. 2017 | James Grant | t.b.a. |
| 20. Jan. 2017 | No seminar. | |
| 27. Jan. 2017 | Paolo Giordano | I see it, but I don't believe it: a Picard-Lindelöf theorem for PDE AbstractL. Luperi Baglini and I already proved a Banach fixed point theorem and a corresponding Picard-Lindelöf theorem for singular nonlinear ODE. So, one could ask himself: why aren't similar theorems available for PDE? Well, we would need free composition of distributions if we want to consider nonlinear PDE. That's not simple at all if we think that generalized functions are functionals. So, we could think at generalized functions as set-theoretical functions that can take infinite values and derivatives. But in that case, the Lipschitz constants could, in the same way, be infinite; so we would need a language with infinitesimal and infinite numbers. But if we have infinitesimals h, then the ODE y'(1+y)h = -t has solution defined only in the infinitesimal interval [-sqrt(h), +sqrt(h)]. Therefore, we would need generalized functions defined only on infinitesimal sets. Finally, if we want to define Fréchet like spaces of generalized functions, we would need a good notion of compact set for generalized functions. Generalized smooth functions are a minimal branch of Colombeau's theory that allows for all these possibilities. So, we proved a Banach fixed point theorem and a Picard-Lindelöf theorem for contractions with loss of derivatives. This seems applicable to a very large class of PDE in normal form, i.e. of the form "maximal time derivative = F(the other derivatives)". |