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02/06/2024, 19:00
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03/06/2024, 08:50
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Håkan Andreasson03/06/2024, 09:00
In the seminal work by Oppenheimer and Snyder from 1939 it is shown that a homogeneous ball of dust undergoes gravitational collapse. This work has had an enormous impact on the field since it predicts the existence of black holes. In this talk I will show that the Oppenheimer-Snyder type collapse can be approximated arbitrarily well by solutions to the Einstein-Vlasov system. It is crucial...
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03/06/2024, 10:00
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Léo Bigorgne (Université de Rennes)03/06/2024, 10:30
We will be interested in the solutions to the Vlasov-Maxwell system arising from sufficiently small and regular data. In particular, we will compare their asymptotic behavior with the ones of the solutions to the linearised system. Even if the electromagnetic fields have a nontrivial memory effect, they enjoy linear scattering since they approach, for large time, a solution to the vacuum...
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Chiara Saffirio03/06/2024, 11:30
The Vlasov-Poisson system is a non-linear PDE describing the mean-field time-evolution of particles forming a plasma or a galaxy.
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In this talk I will present uniqueness criteria for the Vlasov-Poisson equation in the classical and semi-relativistic setting, emerging as corollaries of stability estimates in strong (L^p) topologies or in weak topologies (induced by Wasserstein distances), and... -
03/06/2024, 12:30
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03/06/2024, 16:00
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Klaus Widmayer03/06/2024, 16:30
While "Landau damping" is regarded as an important effect in the dynamics of hot, collisionless plasmas, its mathematical understanding is still in its infancy. This talk presents a recent nonlinear stability result in this context. We start with a discussion of dynamics in the linearized Vlasov-Poisson equations near certain homogeneous equilibria on R^3, and see how both oscillatory and...
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03/06/2024, 18:30
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03/06/2024, 19:00
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Istvan Kadar (University of Cambridge)04/06/2024, 09:00
The existence of multi black hole solutions in asymptotically flat spacetimes is one of the expectation from the final state conjecture. In this talk, I will present preliminary works in this direction via a semilinear toy model in dimension 3. In particular, I show 1) an algorithm to construct approximate solutions to the energy critical wave equation that converge to a sum of solitons at an...
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04/06/2024, 10:00
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Ryan Unger04/06/2024, 10:30
I will present a proof that extremal black holes arise on the threshold of gravitational collapse. More precisely, I will present a construction of one-parameter families of smooth solutions to the Einstein-Maxwell-charged Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal Reissner-Nordström black hole. This is joint work with...
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Jacques Smulevici04/06/2024, 11:30
Given a quasi-periodic wave operator $\psi_{tt}-\psi_{xx}+\mathcal{B}^{xx}(\omega t,x)\partial_{xx}$, where $\mathcal{B}^{xx}:\mathbb{T}^{\nu+1} \rightarrow \mathbb{R}$ is parity preserving, reversible and small enough and where $\omega$ is diophantine, we explain how to construct \emph{null coordinates} respecting the quasi-periodicity. In these coordinates, the principal symbol of the wave...
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04/06/2024, 12:30
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04/06/2024, 16:00
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Gustav Holzegel04/06/2024, 16:30
I will talk about joint work with Olivier Graf (Grenoble) establishing linear stability of Schwarzschild-anti de Sitter (AdS) black holes to gravitational perturbations. This is the statement that solutions to the linearisation of the Einstein equations $\textrm{Ric} = -\frac{3}{\ell^2} g$ around a Schwarzschild-AdS metric arising from regular initial data and with standard Dirichlet boundary...
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Leonhard Kehrberger04/06/2024, 17:30
In the first part of the talk, I will give a historical overview of various arguments pertaining to Penrose's notion of a smooth null infinity and the peeling property. In the second part of the talk, I will then give an account of my own work: After clearly formulating the mathematically and physically relevant problems, I will explain how to set up a semi-global (i.e.~away from the timelike...
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04/06/2024, 19:00
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Mihalis Dafermos05/06/2024, 09:00
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05/06/2024, 10:00
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Benoit Pausader05/06/2024, 10:30
We consider the Vlasov-Poisson with a perfectly conducting wall in a class of convex infinite domains and we show that small initial data lead to global solutions which satisfy a form of modified scattering, with the asymptotic data supported on a maximum cone in the domain. This is joint work with W. Huang and M. Suzuki.
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Maciej Maliborski05/06/2024, 11:30
We consider the cubic nonlinear wave equation on an interval with Dirichlet boundary conditions. First, we review the perturbative construction of small-amplitude time-periodic solutions. Furthermore, using an appropriate numerical construction algorithm, we explore large solutions. By analysing the underlying equations, we propose a systematic approach for describing the complex structure of...
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05/06/2024, 12:30
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05/06/2024, 14:00
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05/06/2024, 16:00
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05/06/2024, 19:00
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05/06/2024, 20:30
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Thomas Stucker06/06/2024, 09:00
The late-time behavior of solutions to the wave equation on Kerr spacetime is governed by inverse polynomial decay. However, at earlier time-scales, numerical simulations are found to be dominated by quasinormal modes. These are exponentially damped oscillatory solutions with complex frequencies characteristic of the system. In this talk, I will present a rigorous characterization of...
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06/06/2024, 10:00
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Pascal Millet (Ecole Polytechnique)06/06/2024, 10:30
The study of wave propagation on black hole spacetimes has been an intense field of research in the past decades. This interest has been driven by the stability problem for black holes and by questions related to scattering theory. On Kerr black holes, the analysis of Maxwell's equations and the equations of linearized gravity, can be simplified by introducing the Teukolsky equation, which...
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Dejan Gajic06/06/2024, 11:30
Quasinormal modes (QNMs) are damped oscillations that play an important role in the dynamics of perturbations of stationary black hole spacetimes. They are governed by frequencies that are characteristic to the black hole under consideration and are analogous to the characteristic overtones of a vibrating drumhead. Although extensively featured in the physics literature for over fifty years, a...
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06/06/2024, 12:30
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06/06/2024, 16:00
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Andrea Nützi06/06/2024, 16:30
I will describe a differential graded Lie algebra tailored to study perturbations of Minkowski spacetime, including asymptotics. This differential graded Lie algebra is defined on the conformal compactification of Minkowski spacetime. Its Maurer-Cartan equation is equivalent to the vacuum Einstein equations, and is symmetric hyperbolic including across the boundary of Minkowski spacetime. I...
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Hamed Masaood (Imperial College London)06/06/2024, 17:30
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06/06/2024, 19:00
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David Fajman (University of Vienna)07/06/2024, 09:00
We are interested in the dynamical behaviour of relativistic fluids towards the expanding direction of cosmological spacetimes.
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It is known that the expansion of spacetime induces a friction-like term in the fluid equation, which can prevent the formation of shocks, yielding future global solutions for small initial data.
This phenomenon is referred to as fluid stabilization. While this... -
07/06/2024, 10:00
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Grigorios Fournodavlos07/06/2024, 10:30
In cosmology, the equation of state of a perfect fluid is considered to be p = c_s^2 \rho, where c_s is the speed of sound. The simplest solution to the Einstein-Euler system, known as FLRW, representing a cosmological fluid, was discovered by Friedmann already in 1922. There is an extensive literature in physics concerning the dynamics of cosmological fluids. However, rigorous mathematical...
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John Anderson07/06/2024, 11:30
In this talk, I hope to describe elements of proving a certain stable singularity formation result for the Einstein—Euler system, which is the topic of work in progress with Jonathan Luk. I will first describe where this fits into the big picture of the study of multidimensional shocks, and why it is appropriate to call this a shock formation result. Then, I will try to describe some of the...
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07/06/2024, 12:30
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Lili He
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