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 |
|---|---|---|
| 03.10. | Scheduling | |
| 10.10. | David Lenze | Isometric rigidity of the Ebin metric AbstractIn 1970, Ebin introduced a natural L2-type metric on the infinite-dimensional space of Riemannian metrics over a given manifold. Though the infinite dimensional geometry of this space has been extensively-studied, a new metric perspective emerged in 2013 when Clarke showed that the completion with respect to the Ebin metric turns out to be a CAT(0) space.Recently, Cavallucci provided a shorter and more conceptual proof of a strengthened result that in addition to being CAT(0) establishes the completion of the space of Riemannian metrics to depend only on the dimension of the underlying manifold. In this talk I will sketch some of this recent progress and present new results which provide a complete characterization of the self-isometries of the space of Riemannian metrics with respect to the Ebin metric. |
| 17.10. | (Lausanne) | |
| 24.10. | Tobias Beran | Coordinates for Lorentzian CBB – an overview Abstract(joint work with John Harvey, Felix Rott and Clemens Sämann) I will define strainers and the corresponding coordinate map, and show it is continuous and open. If this map is not a local homeomorphism, a way of increasing of the dimension of the strainer is presented. This then gives a coordinate theorem for finite dimensional LLS with CBB: near each point there is either an open set homeomorphic to $\mathbb R^n$, or a nested sequence of open sets and corresponding sequence of strainers (which one should interpret as the space being infinite dimensional). If time permits, I will show that the time separation function lies between two flat time separation functions, making the coordinate map weakly bi-Lipschitz. |
| 31.10. | Paul Haberger | Null Geometry Abstract(Smooth) Null hypersurfaces of spacetimes play a prevalent role in General Relativity, where they describe various kinds of horizons. When it comes to studying the geometry of null submanifolds in general, the degeneracy of the metric causes technical difficulties that must be properly addressed. The goal of the talk is to give an introduction to the geometry of null hypersurfaces and to develop the necessary tools to handle their degenerate structure. In particular, this will be applied by presenting a proof of the Penrose Incompleteness Theorem which makes heavy use of the structure of achronal boundaries. We will closely follow ideas by Prof. Dr. Gregory J. Galloway; see especially "https://www.math.miami.edu/~galloway/vienna-course-notes.pdf". |
| 07.11. | Davide Manini | On the geometry of synthetic null hypersurfaces and the Null Energy Condition AbstractIn the talk, I will present a joint work with Fabio Cavalletti (Milan) and Andrea Mondino (Oxford), where we develop a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent advances in Lorentzian geometry and causality theory, we define a synthetic null hypersurface as a triple $(H, G, m)$: $H$ is a closed achronal set in a topological causal space, $G$ is a gauge function encoding affine parametrizations along null generators, and m is a Radon measure serving as a synthetic analog of the rigged measure. This generalizes classical differential geometric structures to potentially singular spacetimes. A central object is the synthetic null energy condition ($NC^e(N )$), defined via the concavity of an entropy power functional along optimal transport, with parameterization given by the gauge $G$. This condition is invariant under changes of gauge and measure within natural equivalence classes. It agrees with the classical Null Energy Condition in the smooth setting and it applies to low-regularity spacetimes. A key property of $NC^e(N )$ is the stability under convergence of synthetic null hypersurfaces, inspired by measured Gromov--Hausdorff convergence. As a first application, we obtain a synthetic version of Hawking’s area theorem. Moreover, we extend the celebrated Penrose singularity theorem to continuous spacetimes and we prove the existence of trapped regions in the general setting of topological causal spaces satisfying the synthetic null energy condition. |
| 12.11. (extra) | Roland Steinbauer | Colloquium ? |
| 14.11. | Mauricio Adrian Che Moguel | Topological data analysis and spaces of persistence diagrams AbstractIn this talk, I will give an introduction to topological data analysis (TDA), with an emphasis on the notion of persistence diagrams. These objects, arising in algebraic topology, provide a concise, quantitative way to visualise the homological information carried by filtrations of topological spaces. In TDA, filtrations are often built from data sets using Vietoris-Rips complexes or similar constructions.One can study persistence diagrams from a geometric point of view, by equipping the space of diagrams with metrics inspired by optimal transport. I will discuss this connection and what it reveals about the metric structure of spaces of persistence diagrams. |
| 21.11. | Stefano Saviani | Wasserstein gradient flows |
| 28.11. | Leonardo Garcia-Heveling | (Lie) Group actions on spacetimes |
| 05.12. | Marta Sálamo Candal | tba |
| 12.12. | Miguel Manzano | Conformal something |
| 19.12. | Waiho Yeung | Laplacian of the distance function |
| 09.01. | Joe Barton, Samuël Borza, Jona Röhrig | Causal set something |
| 16.01. | (student of Mathias visits) | |
| 23.01. | Karim Mosani | C^0 extensions ? |
| 30.01. | Peter Michor |