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 |
|---|---|---|
| 10. Mar. 2023 | Scheduling | |
| 17. Mar. 2023 | skipped (ESI) | |
| 24. Mar. 2023 | skipped (ESI) | |
| 31. Mar. 2023 | Chiara Rigoni | Metric measure spaces satisfying the CD condition for negative values of the dimensional parameter AbstractIn this talk we present an appropriate setting to introduce the CD(K, N)-condition for N < 0, allowing metric measure structures in which the reference measure can have some pathologies. Then in this class of spaces we introduce the distance $d_{\mathsf{iKRW}}$, which extends the already existing notions of distance between metric measure spaces. Finally, we prove that if a sequence of metric measure spaces satisfying the CD(K, N)-condition with N < 0 is converging with respect to the distance $d_{\mathsf{iKRW}}$ to some metric measure space, then this limit structure is still a CD(K, N) space. |
| 21. Apr. 2023 | Phillip Bachler | Ricci bounds and Optimal transport AbstractWe will start right with the Monge and Kantorovich problem. Then, we take a look at quadratic cost on the Wasserstein space of $\mathcal{R}^n$. The main ideas of the proof will then be compared with the techniques used to prove the existence of optimal transport maps on compact Riemannian manifolds. If time is left, we take a glance at the relative entropy and its connection with Ricci bounds on metric measure spaces. |
| 28. Apr. 2023 | Jiri Podolski | New metric for all type-$D$ spacetimes AbstractWe present an improved metric form of the complete family of exact black hole spacetimes of algebraic type D, including any cosmological constant. This class was found by Debever in 1971, Plebanski and Demianski in 1976, and conveniently reformulated by Griffiths and Podolsky in 2005. In our new form of this metric the key functions are simplified, partially factorized, and fully explicit. They depend on seven parameters with direct physical meanings, namely m, a, l, alpha, e, g, Lambda which characterize mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges of the black hole, and the cosmological constant, respectively. Moreover, this general metric reduces directly to the familiar forms of (possibly accelerating) Kerr-Newman-(anti-)de Sitter spacetime, charged Taub-NUT-(anti-)de Sitter solution, or (possibly rotating and charged) C-metric with a cosmological constant by simply setting the corresponding parameters to zero. In addition, it shows that the Plebanski-Demianski family does not involve accelerating NUT black holes without the Kerr-like rotation. The new improved metric also enables us to study various physical and geometrical properties, namely the character of singularities, two black-hole and two cosmo-acceleration horizons (in a generic situation), the related ergoregions, global structure including the Penrose conformal diagrams, parameters of cosmic strings causing the acceleration of the black holes, their rotation, pathological regions with closed timelike curves, or thermodynamic quantities. |
| 05. May. 2023 | Matteo Calisti | Ricci curvature bounds in warped products using optimal transport AbstractI will present a work of Christian Ketterer where he proved that a warped product between a space with curvature bounded by below and Finsler manifold with Ricci curvature bounded by below satisfies the so-called curvature dimension condition. |
| 12. May. 2023 | Robert Švarc | Expanding impulsive waves AbstractWe study the geometric properties of spacetimes with expanding gravitational impulses which are generated by snapped cosmic strings and propagate on a flat background. The construction of the line element is reviewed, and suitable string-generating complex mappings are derived for various configurations such as previously studied cases of a pair of snapping strings. Moreover, these mappings are related to the topology of the flat half-space in front of the wave and their understanding seems crucial for the analysis of global geometry, the relationship between half-spaces on both sides of the impulse, and the physical interpretation of, in principle, observable effects. Such spacetime structure is also closely connected with the motion of free test particles crossing the impulse which we describe in detail. |
| 19. May. 2023 | Tobias Beran | The Null distance encodes causality AbstractI prove null distance encodes causality locally using null cone coordinates. Global causality preservation follows if the time function is proper. |
| 26. May. 2023 | Carla Mladek | The null distance encodes causality in globally hyperbolic spacetimes AbstractIn my talk I will briefly introduce the null distance and then prove the following result from A. Burtscher and L. Garcia Heveling (2022):In a globally hyperbolic spacetime the null distance with respect to a Cauchy temporal function encodes causality. |
| 02. Jun. 2023 | Argam Ohanyan | Cosmological spacetimes without CMC Cauchy surfaces and Bartnik's splitting conjecture AbstractIn 1988, Robert Bartnik conjectured the rigidity of the Hawking-Penrose singularity theorem in the cosmological case. More precisely, he conjectured that any timelike geodesically complete cosmological spacetime must split isometrically as a product. This conjecture, while having been solved under various additional assumptions throughout the years, remains open in full generality to this day. Bartnik showed that under the assumptions of the conjecture, the splitting happens if and only if there exist CMC Cauchy surfaces. Moreover, he constructed cosmological (albeit timelike geodesically incomplete) examples without such CMCs.In this talk, we will go over the conjecture, its meaning as a rigidity statement and some of its history. We will then go on to discuss Bartnik's no-CMC example and some possible generalizations of his construction. This talk is based in part on recent ongoing joint work with Eric Ling. |
| 09. Jun. 2023 | Roman Brem | Visibility of Marginally Outer Trapped Surfaces AbstractThe aim of this talk is to present aspects of the theory of (marginally, outer) trapped surfaces and sets. A closed spacelike surface in a spacetime is called trapped if both congruences of normal (future directed) null geodesics are converging. If the spacetime contains such a trapped surface, satisfies the null energy condition and admits a non-compact Cauchy surface, the spacetime is singular by Roger Penrose’s singularity theorem. Marginally outer trapped surfaces (MOTS) serve as a generalisation of trapped surfaces, in the sense that one of the null congruences has zero convergence. They are an integral part in the mathematical study of black holes.Here we focus on the issue of (non-)visibility of MOTS from conformal future null infinity and explain corresponding known results especially in asymptotically de Sitter spacetimes. Next we restrict attention to de Sitter space itself and discuss MOTS of spherical and toroidal topology and their (non-)visibility. Finally we explain why the singularity theorems do not apply in this case. |
| 16. Jun. 2023 | Darius Erös | First order calculus in metric measure spaces AbstractIn their book "Lectures on Nonsmooth Differential Geometry" Nicola Gigli and Enrico Pasqualetto present a first-order calculus for metric measure spaces via normed modules. Starting with an outline of their approach to Sobolev spaces using the notion of test plans, we will cover some basics of theory of normed modules and finally prove the existence and (essential) uniqueness of the cotangent module together with its differential for an arbitrary metric measure space. |
| 23. Jun. 2023 | skipped (Nijmegen) | |
| 30. Jun. 2023 | Sekar Nugraheni | Complex integration of generalized holomorphic functions AbstractGeneralized smooth functions (GSF) theory is a branch of Colombeau theory where generalized functions share a number of fundamental properties with smooth functions, in particular with respect to composition and nonlinear operations. They allow us to prove a number of analogues of theorems of classical analysis, especially for integrals via primitives and multidimensional integrals.In this talk, we will introduce and discuss the integral over a path of a generalized holomorphic function using the better theory of integration of GSF, if compared with the one in Colombeau theory. |