Vorträge in der Woche 09.12.2024 bis 15.12.2024
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Donnerstag, 12.12.2024: Some thoughts on the definition of center of mass and angular momentum
Prof. Dr. Carla Cederbaum (Universität Tübingen)
In the 1960’s, using a Hamiltonian approach, Arnowitt, Deser, and Misner gave very satisfactory definitions of total energy, linear momentum, and mass for asymptotically Euclidean initial data sets sitting in an asymptotically Minkowskian spacetime. By work of Bartnik from the 1980’s, we know that these quantities are well-defined, while by work of Chrusciel around the same time, we know that they transform equivariantly under the asymptotic Poincaré group of the spacetime (at least in a given asymptotic spacetime coordinate chart). In the first part of the talk, we will briefly recall these definitions and the results mentioned before, adding some details ensuring that the mentioned equivariance is indeed correct without assuming that one transforms within a given asymptotic spacetime coordinate chart. In the second part of the talk, we will shift attention to the definitions of angular momentum and center of mass, defined via a Hamiltonian approach by Regge and Teitelboim in the 1970’s and by Beig and O’Murchadha in the 1980’s, respectively. We will compare these definitions with definitions given by Michel in the 2010’s based on Killing initial data. We will discuss known and unknown problems related to both of these definitions and their interrelation. The insights we present rely on ongoing joint work with Senthil Velu and joint work with Nerz and with Sakovich. We will also discuss some preliminary ideas to overcome the shortcomings of these definitions.
| Uhrzeit: | 14:00 |
| Ort: | Seminarraum S09 (C6H05) and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
Donnerstag, 12.12.2024: Towards quantum fields on random structures
Dr. Nicolas Delporte (Okinawa IST, Japan)
Characterizing the effect of disorder on phase transitions of classical or quantum systems is a non-trivial and rich problem. I will begin with a survey of achievements on lattices and classes of random graphs. Afterwards, I will present two directions of research based on random walk expansions, following respectively [arXiv:1905.12783] and [arXiv:2312.10881]. The first establishes upper bounds on completely convergent (in a sense that I will define) correlation functions of a quartic long range scalar field theory on critical Galton-Watson trees, using a multiscale decomposition of the field covariance. Restricting to regular trees of fixed degree, the second calculates Green functions of a Dirac operator taken as the square root of the Laplacian, setting the ground for the study of objects with spin. I will end by drawing the parallels between stochastic homogenization and the renormalization group, suggesting that the techniques of the former can provide a rigorous tool to study the latter for systems in random environments.
| Uhrzeit: | 14:30 |
| Ort: | online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Elena Kabagema-Bilan |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Keppeler, Lemm, Pickl, Teufel, Tumulka |
Donnerstag, 12.12.2024: Gauge Theory for Multi-time Wave Functions
Lukas Nullmeier (Tübingen)
Multi-time wave functions are a relativistic generalization of the wave functions of non-relativistic quantum mechanics. In this talk, I will begin by giving a short introduction to multi-time wave functions. After this and a review of some concepts of classical gauge theory, I will show how analogous concepts show up in the context of multi-time wave functions in quantum electrodynamics and quantum Yang-Mills theory, and how that helps find equations for them. In the end, I will give an outlook to possible generalizations in quantum gravity.
| Uhrzeit: | 16:15 |
| Ort: | C3N14 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Keppeler, Lemm, Pickl, Teufel, Tumulka |
Freitag, 13.12.2024: Discrete approximation of risk-based prices under volatility uncertainty
Michael Kupper (University of Konstanz)
We discuss the asymptotic behaviour of risk-based indifference prices of European contingent claims in discrete-time financial markets under volatility uncertainty as the number of intermediate trading periods tends to infinity. The asymptotic risk-based prices form a strongly continuous convex monotone semigroup which is uniquely determined by its infinitesimal generator and therefore only depends on the covariance of the random factors but not on the particular choice of the model. We further compare the risk-based prices with the worst-case prices given by the $G$-expectation and investigate their asymptotic behaviour as the risk aversion of the agent tends to infinity. The theoretical results are illustrated with several examples and numerical simulations showing, in particular, that the risk-based prices lead to a significant reduction of the bid-ask spread compared to the worst-case prices. The talk is based on joint work with Jonas Blessing and Alessandro Sgarabottolo.
| Uhrzeit: | 14:15 |
| Ort: | Seminarraum S06 (C5H05) |
| Gruppe: | Oberseminar Stochastik |
| Einladender: | Möhle, Teufl, Eckstein |
Freitag, 13.12.2024: Strong cosmic censorship: how singularities restore determinism
Dr. Jan Sbierski (University of Edinburgh)
16:00-16:45 Uhr Vor-Kolloquium im N14 für Studierende und Promovierende, moderiert von Saradha Senthil Velu, Vortragender Dr. Jan Sbierski The breakdown of classical determinism in the interior of black holes The aim of this pre-colloquium is to explain in some detail the mechanism that can lead to the breakdown of classical determinism in the interior of black holes. This mechanism will be demonstrated by the example of the spherically symmetric scalar wave equation. We will recall the notions of Lorentzian causality, introduce the concept of a Penrose diagram, present an example of a black hole spacetime, and work through the initial value problem for the spherically symmetric scalar wave equation. Kolloquium 17:15 Strong cosmic censorship: how singularities restore determinism It has been known for a long time that classical determinism can break down in the interior of rotating black holes. In 1968 Roger Penrose found a heuristic mechanism that leads to an instability and the subsequent formation of a singularity in the interior of such black holes. It is the formation of such a singularity that is expected to generically restore determinism. This scenario is known as the strong cosmic censorship conjecture. In this talk I will review this conjecture and also recent progress towards its resolution.
| Uhrzeit: | 16:00 |
| Ort: | N14 |
| Gruppe: | Kolloquium |
| Einladender: | Cederbaum |