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.

Winter term 2019

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

04. Oct. 2019 | First meeting for scheduling. | |

11. Oct. 2019 | Albert Huber (TU Wien) | On local Spacetimes and geometric Transitions in General Relativity ## AbstractIn the scheduled talk, I will discuss the problem of how to construct local spacetimes in general relativity (or more general theories of gravity) on the basis of so-called metric deformations. Since the treatment of this particular problem requires the solution of appropriate junction conditions, I will give a brief introduction to the underlying subject and discuss its significance for the problem of isolating gravitating physical systems in the theory of Einstein-Hilbert gravity. If time permits, the importance of local models for the construction of special apparent symmetries, also known as phantom symmetries, will be explained, with special attention being paid to so-called generalized Kerr-Schild symmetries. |

18. Oct. 2019 | Benedict Schinnerl | Geodesic Focusing from Averaged Energy Conditions and Index Form methods ## AbstractIn my talk I will discuss the role of an energy assumption on a spacetime and how it is involved in the focusing process of (causal) geodesics. However, many of the classical energy conditions (as e.g. assumed in the standard versions of most singularity theorems) are known to be violated when considering quantum effects. I will shortly discuss possible replacement conditions. The main part of my talk will focus on the so-called index form and how it can be used to prove geodesic focusing. Recent advances with these methods were made by Fewster and Kontou (2019), to obtain singularity theorems under an averaged energy condition. |

25. Oct. 2019 | Darko MitroviÄ‡ | Conservation laws ## AbstractI will talk about development of the theory as well as about different techniques for solving the equations. I will also mention possible research directions and open problems. |

08. Nov. 2019 | Argam Ohanyan | Covering Spaces ## AbstractI will (rather quickly) recall some basic concepts from algebraic topology, such as homotopy, the fundamental group, coverings, the universal covering etc. and then specialize to smooth and (semi-)Riemannian coverings in order to prove some results about the existence of minimizing geodesics in certain homotopy classes. |

15. Nov. 2019 | Michael Kunzinger | Null distance on a spacetime ## AbstractContrary to the case of Riemannian manifolds, for spacetimes it was believed for a long time that there is no natural distance function (metric) that induces the manifold topology, is derived from the spacetime metric and encodes the topology. In this talk I will report on a rather recent paper by C. Sormani and C. Vega that introduces a 'null distance' on spacetimes equipped with a (possible discontinuous) time function. We will then show that in many relevant situations, null distances meet all of the above requirements. |

22. Nov. 2019 | No seminar | |

29. Nov. 2019 | Stanislav Opanasenko | Equivalence of classes of differential equations ## AbstractIn this talk I give a geometric interpretation of differential equations and introduce a group action on them. This would naturally lead to a topic of equivalence of classes thereof, which is a subject of my PhD studies. I will tell how we have advanced theory there and what problems we are still facing. |

06. Dec. 2019 | Tobias Beran | Topology and singularities in cosmological spacetimes obeying the null energy condition. ## AbstractA singularity theorem for 3+1 dimensional spacetimes with compact Cauchy surface which is topologically non-trivial, using a (partial) classification of compact orientable 3 dimensional surfaces. |

13. Dec. 2019 | No seminar | |

10. Jan. 2020 | Andras Bonk | Pseudo-differential operators and parametrices in euclidean space ## AbstractBy recalling some basic definitions and facts regarding Schwartz space, linear diff. operators, symbols etc. I will motivate the notion of Pseudo-differential operators, and then formally introduce them. In the second part of my talk, I will use the developed theory to construct an approximate inverse of an elliptic differential operator in terms of Pseudos. |

17. Jan. 2020 | Beatrice Andreolli | The Ritz-Galerkin method ## AbstractThe talk will focus on finding numerical solutions to second-order elliptic PDEs by introducing suitable finite-dimensional subspaces, according in particular to the Ritz-Galerkin method. We will see that a solution to the Ritz-Galerkin problem exists, is unique, and approximates the solution to the weak formulation of the given elliptic problem. Finally, we will show in which way the Ritz-Galerkin approximation can in fact be viewed as the best possible approximation. |

24. Jan. 2020 | No seminar | |

31. Jan. 2020 | Robert Tiefenbacher | Riemannian version of Hawking's theorem ## AbstractThe talk start by setting the stage for the Riemannian version of Hawkings theorem. Then I will introduce Lorentzian geometrie and give a proof of Hawkings theorem. Finally the two versions will be compared. |