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.

Summer term 2019

Date | Speaker | Title |
---|---|---|

08. Mar. 2019 | First meeting for scheduling | |

15. Mar. 2019 | Zhangwen Guo | G-Manifolds ## AbstractA Lie group action $l: G\times M \mapsto M$ gives rise to an anti Lie algebra homomorphism (i.e. the fundamental vector field) $\zeta: \mathfrak g \mapsto \mathfrak{X}(M)$, which describes how moving $g\in G$ for a small amount will change $g.x$. Conversely, an anti Lie algebra homomorphism $\zeta: \mathfrak g \mapsto \mathfrak{X}(M)$ where $\mathfrak g$ is the Lie algebra of some Lie group $G$ gives rise to a local action $l: G\times M \supseteq U \mapsto M$ with $\{e\} \times M \subseteq U$ and whise fundamental vector field is $\zeta$. If $G$ is simply connected, the action can be defined globally. |

22. Mar. 2019 | Günther Hörmann | What‘s in a Schrödinger equation? ## Abstract1. A rough review of how the Schrödinger equation is embedded into the overall structure of quantum mechanics.
2. A zoo of Banach spaces when messing around with the potential term or the initial value in a generalized function sense.
3. A confusion about where the Schrödinger equation got lost in all the discussions of the double slit experiment. |

29. Mar. 2019 | Clemens Sämann | Warped products with one-dimensional base as Lorentzian length spaces ## AbstractI will report on work in progress with Stephanie Alexander, Melanie Graf and Michael Kunzinger, where we study spaces of the form $I\times X$, with $I$ an interval in $\mathbb{R}$, and $X$ a length space. We establish that the causal properties of such spaces are especially nice and that we can view them as Lorentzian length spaces and thereby opening up the possibility to study curvature bounds in a synthetic way. |

05. Apr. 2019 | No seminar. | |

12. Apr. 2019 | Ondřej Hruška | The study of Kundt geometries in Quadratic Gravity ## AbstractThe Kundt class is geometrically defined to admit a null geodesic congruence with a vanishing expansion, shear, and twist. We analyse these geometries in the so-called Quadratic Gravity (QG): higher-order extension of Einstein’s general relativity with action containing additional terms quadratic in the Riemann tensor and its contractions. We study the restrictions imposed by the QG field equations on the Kundt geometric ansatz and compare the results with those well-known in classic general relativity. In detail we discuss specific solutions, such as pp-waves. In order to provide means of physical interpretation, we investigate the equations of geodesic deviation. |

03. May. 2019 | No seminar | |

10. May. 2019 | Benedict Schinnerl | Limit curve theorems and future boundaries. ## AbstractI will talk about the Limit curve theorems of Lorentzian Causality and how they can be used to describe the boundary of the future of a set in a spacetime. |

17. May. 2019 | Diksha Tiwari | Wavelet and Differential Equation ## AbstractFourier series and the Fourier transform have been around since the 1800s, but the development of wavelets has been much more recent (the 1980s). Fourier ransforms time-based signals to frequency-based signals. A Drawback of Fourier transform is that transforming into the frequency domain, time information is lost because we don't know when an event happened. A possible Solution is a wavelet transform indeed. With the help of Haar wavelet, we obtain numerical solutions of non-linear singular initial value problems. |

24. May. 2019 | Theresa Pöll | Godement’s Theorem on the manifold structure of quotient spaces ## AbstractGodement’s theorem gives a necessary and sufficient condition that quotient spaces of manifolds under equivalence relations have a unique structure of a smooth manifold. To prove the theorem we construct a manifold structure on the quotient space with the help of so-called slices for the intersection of the equivalence classes with a saturated open neighborhood for any point on the manifold. |

31. May. 2019 | No seminar | |

07. Jun. 2019 | Roman Popovych | Parameter-dependent linear ordinary differential equations and topology of domains ## AbstractThe well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or characterizations of such systems via nonvanishing Wronskians are sensitive to the topological properties of the underlying domain of the independent variable and the parameter. We give a complete characterization of the solvability of such parameter-dependent systems in terms of topological properties of the domain. In addition, we also consider this problem in the setting of Schwartz distributions. |

14. Jun. 2019 | No seminar | |

21. Jun. 2019 | Akbarali Mukhammadiev | Supremum, infimum and hyperlimits of Colombeau generalized numbers ## AbstractIt is well-known that the notion of limit in the sharp topology of
sequences of Colombeau generalized numbers $\widetilde{\mathbb{R}}$ does not generalize classical results. In fact, the ring $\widetilde{\mathbb{R}}$ is non-Archimedean and this topology is generated by balls of infinitesimal radii. E.g. the
sequence $\frac{1}{n}\not\to0$ and a sequence $(x_{n})_{n\in\mathbb{N}}$
converges if and only if $x_{n+1}-x_{n}\to0$. This has several
deep consequences, e.g. in the study of series, analytic generalized
functions, or sigma-additivity and classical limit theorems in integration
of generalized functions. The lacking of these results is also connected
to the fact that $\widetilde{\mathbb{R}}$ is necessarily not a complete ordered set,
e.g. the set of all the infinitesimals does not have neither supremum
nor infimum.
We present a solution of these problems with the introduction of the
Robinson-Colombeau ring ${}^{\rho}\widetilde{\mathbb{R}}$ and with the notion of hypernatural numbers ${}^{\rho}\widetilde{\mathbb{N}}:=\left\{[n_{\epsilon}]\in{}^{\rho}\widetilde{\mathbb{R}}\mid n_{\epsilon}\in\mathbb{N}\ \forall\epsilon\right\}$. |

28. Jun. 2019 | Volker Branding | Higher order energy functionals ## AbstractIn the first part of the talk we will give an introduction to the notions of harmonic and biharmonic maps. Harmonic maps are solutions of a semilinear elliptic partial differential equation of second order, whereas the biharmonic map equation is of order four. The second part of the talk is concerned with higher order energy functionals for maps between Riemannian manifolds. The study of such functionals was first proposed by Eells and Sampson in 1965 and, later, by Eells and Lemaire in 1983. We will present several recent results on these higher order functionals and point out many challenging problems that remain to be solved. This is joint work with Stefano Montaldo, Cezar Oniciuc and Andrea Ratto. |