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 |
|---|---|---|
| 04. Mar. 2022 | Scheduling | |
| 18. Mar. 2022 | Eleni Kontou (online) | Penrose-type singularity theorems in semiclassical gravity AbstractThe Penrose singularity theorem proves null geodesic incompleteness for spacetimes obeying the null convergence condition, or matter obeying the null energy condition (NEC). The NEC, as with all pointwise energy conditions, is violated by quantum fields. In this talk I will first present a Penrose-type singularity theorem with a weakened energy condition. Next I will discuss two conditions obeyed by quantum fields: the smeared null energy condition and the double smeared null energy condition. Finally, I will present recent progress on using these conditions as assumptions for a Penrose-type semiclassical singularity theorem. Based on: 2012.11569 and 2111.05772 |
| 25. Mar. 2022 | Tobias Beran | Hyperbolic angles (part 2) AbstractWe will define Lorentzian pre-length spaces and hyperbolic angles, introduce timelike curvature comparison via triangle comparison and via the monotonicity condition, and prove they are equivalent. I will present an improved result on branching of timelike geodesics. |
| 01. Apr. 2022 | Alexander Zahrer & E. Stefanescu | Ricci Flow and its applications to black holes AbstractWe will start by a heuristic and rather visual approach to concepts like the Riemann curvature tensor and the Ricci curvature tensor. This will then naturally lead to a definition of Hamilton's Ricci flow. After having done so, we will focus on statements of local existence and some other theorems concerning the Ricci Flow. Finally, we will see applications of the Ricci flow to a model of a black hole. In particular, we will define the entropy of a black hole by means of Perelman's $F$ and $W$ functionals and we will explain in what sense black holes have a prime decomposition. |
| 08. Apr. 2022 | Christian Melder | Minimal surfaces |
| 29. Apr. 2022 | cancelled | |
| 06. May. 2022 | Carla Mladek | The Eightfold way |
| 13. May. 2022 | David Crespo | a geometrical introduction to the de Sitter universe AbstractThis talk should give the listeners an intuition as to how one may model the universe. The beginning will be a small geometrical motivation, which then leads to the definition of de Sitter spaces. After noticing the de Sitters geometrical structures and symmetries, we will take a look at the so-called Anti-de Sitter universe and how one may arrive at such a model. |
| 20. May. 2022 | Christian Ketterer | Synthetic Ricci curvature bounds for metric measure spaces and Spectral Rigidity AbstractIn the first half of this talk I will motivate the definition of synthetic Ricci curvature bounded from below for metric measure spaces and introduce the curvature-dimension condition in the sense of Lott-Sturm-Villani. In the second half of the talk I will present some classical estimates for the spectral gap under lower Ricci curvature bounds. Our main theorem is that the Zhang-Yang spectral estimate for non-negatively curved RCD spaces is attained if and only if the space is 1 dimensional (this is joint work with Yu Kitabeppu and Sajjad Lakzian). |
| 27. May. 2022 | Didier Solis | Causal completions as Lorentzian pre-length spaces AbstractIn this talk we discuss a way to endow the future causal completion of a globally hyperbolic spacetime with a natural Lorentzian pre-length space structure and present some applications. This is joint work with L. Ake and S. Burgos. |
| 03. Jun. 2022 | Felix Rott | A globalization result for upper timelike curvature bounds for Lorentzian pre-length spaces AbstractWe present an analogue to globalization techniques of upper curvature bounds for metric spaces, called Alexandrov's patchwork. Using the gluing lemma for timelike triangles, this result allows for a very nice translation into the synthetic Lorentzian setting. We will very briefly talk about globalization in general, then quickly go over the metric case to get some familiarity and motivation. Then we will look at the Lorentzian case in a bit more detail. |
| 10. Jun. 2022 | Miguel Manzano | General matching across null boundaries and matching across Killing horizons of order zero AbstractNull shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. In this talk, we will present the conditions that allow for the matching of two spacetimes with null embedded hypersurfaces as boundaries. Whenever the matching is possible, it is shown to depend on a diffeomorphism between the set of null generators in each boundary and a scalar function, called step function, that determines a shift of points along the null generators. The particular case of both boundaries being totally geodesic will be analyzed in detail. Moreover, we will provide a definite connection between the original Penrose's cut-and-paste construction and the standard matching formalism. Finally, we will address the problem of matching across Killing horizons of zero order in the case when the symmetry generators are to be identified. We will present the explicit form of the step function for each feasible matching and, as an application of the results, we will study the matching across actual Killing horizons admitting a bifurcation surface. |
| 17. Jun. 2022 | Kevin Islami | Pontryagin's maximum principle for generalized smooth functions AbstractIn this talk we will first give an introduction to generalized numbers and generalized smooth functions, with some properties of the latter. We introduce the non-Archimedean ring of Robinson-Colombeau $^{\rho}\tilde{\mathbb{R}}$ and then give the definition of generalized smooth functions. After having introduced these two key notions, we will discuss the classical Pontryagin maximum principle for the case of a free endpoint. We will also talk about the case of a fixed endpoint problem. Last, we will discuss Pontryagin's maximum principle for generalized smooth functions, how these kinds of functions change the proof and what possibilities of new applications this theorem opens. |
| 24.Jun. 2022 | Florian Müllner | Finsler Geometry AbstractWe will be going over the notion of Finsler geometry, describing manifolds where each tangent space is equipped with a Minkowski norm. Than we will try to find similar structures to (Semi-)Riemanninan geometries, like geodesics and curvature. At the end we will connect it to symplectic geometry which plays a vital roll in theoretical physics. |