The DIANA seminar

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.

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The the seminar takes place every Friday at 09.45 am in SE 10 and streamed via moodle and will be announced by email weekly.

Anyone interested is welcome to attend.

Winter term 2021

Date Speaker Title
01. Oct. 2021Scheduling
08. Oct. 2021cancelled
15. Oct. 2021Anton BaldingerPenrose Diagrams
22. Oct. 2021ArgamLorentzian Length Spaces and Time Functions
AbstractI will begin the talk by introducing Lorentzian length spaces as a synthetic analogue to classical spacetimes. Then, following the recent paper by Annegret Burtscher and Leonardo Garcia-Heveling, time functions on Lorentzian length spaces will be introduced and their connection to various levels of the causal ladder will be discussed. The talk will conclude by a discussion of a result which characterizes globally hyperbolic Lorentzian length spaces by means of Cauchy time functions and Cauchy sets.
29. Oct. 2021TobiasHyperbolic angles in Lorentzian pre-length spaces
AbstractI will define hyperbolic angles in Lorentzain pre-length spaces, and do some properties (triangle inequality of angles, semi-continuity), and some applications (space of directions, future timelike tangent cone, exponential and logarithmic map). We probably won't be able to cover all.
05. Nov. 2021Benedict SchinnerlOn the causal hierarchy of Lorentzian Length Spaces
AbstractFollowing the paper titled "On the causal hierarchy of Lorentzian Length Spaces" by Hau, Pacheco and Solis, I will introduce several causality notions for Lorentzian Length Spaces and establish a causal hierarchy similar to the case of spacetimes. The talk will mainly focus on the upper levels of the causal ladder (i.e. stable causality, causal continuity and causal simplicity) as these have not been previously studied in the setting of Lorentzian Length Spaces.
12. Nov. 2021Florian Lang, Stephan SchneiderJump formulas in distributions
19. Nov. 2021Gunter WirthumerOn cosmic censorship
AbstractLargely following the review paper "Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose" by Klaas Landsman (Jan. 2021), I will present the concept's key notions and ideas, and also address some of the difficulties in defining and proving it.
26. Nov. 2021Clemens SämannA Lorentzian analog for Hausdorff dimension and measure
AbstractWe define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to the Hausdorff dimension for metric spaces - that distinguishes between e.g. spacelike and null subspaces of Minkowski spacetime. The volume measure corresponding to its geometric dimension gives a natural reference measure on a synthetic or limiting spacetime, and allows us to define what it means for such a spacetime to be collapsed (in analogy with metric measure geometry and the theory of Riemannian Ricci limit spaces). As a crucial tool we introduce a doubling condition for causal diamonds and a notion of causal doubling measures. Moreover, applications to continuous spacetimes and connections to synthetic timelike curvature bounds are given.
03. Dec. 2021Clemens SämannLorentz meets Lipschitz
AbstractWe show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a $C^{1,1}$-parametrization and that they solve the geodesic equation in the sense of Filippov in this parametrization. Our proof shows that maximal causal curves are either everywhere lightlike or everywhere timelike. Furthermore, the proof demonstrates that maximal causal curves for an $\alpha$-Hölder continuous Lorentzian metric admit a $C^{1,\frac{\alpha}{4}}$-parametrization.
10. Dec. 2021DjamelHahn-Banach Theorem in Colombeau GF
17. Dec. 2021Milos Vujicicde Sitter and anti de Sitter space
07. Jan. 2021CezaryWagner-Paper on Jump formulas for Manifolds
15. Jan. 2021KevinPontryagin’s Maximum Principle
21. Jan 2021FelixGluing constructions in Lorentzian length spaces
28. Jan 2021MatteoOptimal transport in Lorentzian length spaces