Date/Time : 18 Mar 2021 14:30
Venue : via Zoom
Speaker : Hao Liu, University of Hong Kong

Join Zoom Meeting https://nus-sg.zoom.us/j/81674259454?pwd=MmtaT2ZWUWlCeDQ1UE5oWXByeUpxZz09&from=addon Meeting ID: 816 7425 9454 Password: 778322 Abstract:  In this talk, we are going to talk about the global weak solutions to the gmCH equations which are constructed through peakons. We use a double mollification to the ODE system for trajectories of N-peakon weak solutions which has the crucial weak consistency property. With the global N-peakon weak solutions, we can use the mean-field approximation method to obtain global weak solutions for general initial data.

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Date/Time : 17 Mar 2021 16:30
Venue : via Zoom
Speaker : Te Li, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83795761997?pwd=ZFdUTXBIVGlHMHZhZlpjRmlFYnRDQT09 Meeting ID: 837 9576 1997 Password: 483694 Abstract:  We study the incompressible Navier-Stokes equations in dimensions d = 2 or 3 and address the hydrodynamic stability problem at high Reynolds. Our talk will mainly focus on the stability of laminar equilibria, around which the fluid moves in well-ordered layers. In joint works with Dongyi Wei and Zhifei Zhang, we established the (nonlinear) stability of Oseen vortices, Kolmogorov flow and Couette flow. In particular, our work on Oseen vortices confirmed Gallay’s conjecture. Pseudospectral bound and wave-operator method play crucial roles in our proofs.

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Date/Time : 23 Dec 2020 22:00
Venue : via Zoom
Speaker : Martin Lesourd, Harvard University

Join Zoom Meeting https://nus-sg.zoom.us/j/82136576826?pwd=TFVpYjhOMGZRMVErdzNSZVI1aVVZUT09 Meeting ID: 821 3657 6826 Password: 706367 Abstract: Christodoulou’s 2008 breakthrough on the formation of trapped surfaces in general relativity has engendered a great deal of activity and has brought the fundamental conjecture of Weak Cosmic Censorship into closer view. This conjecture amounts to a global existence problem for the hyperbolic PDEs of the Einstein vacuum system, and there are currently no non-trivial examples of it. I’ll describe some of the landscape that has arisen since Christodoulou’s seminal result, as well as recent work with Nikos Athanasiou in which we construct examples of the conjecture that are conditional on the validity of another problem in general relativity: the stability of the Kerr black hole solution.

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Date/Time : 17 Dec 2020 15:00
Venue : via Zoom
Speaker : Jue Liu , Tsinghua University

Join Zoom Meeting https://nus-sg.zoom.us/j/83066226180?pwd=NllOVE1TNXZxTXhqVGFyYVRxMlQ1UT09 Meeting ID: 830 6622 6180 Password: 886072 One of the fundamental questions in mathematical relativity is the weak cosmic censorship conjecture proposed by Penrose, which states that for generic asymptotically flat spacetime the singularities are invisible to the infinity observers. This is a global problem involved the whole future evolution of the asymptotically flat initial data. A suitable local version is the trapped surfaces conjecture proposed by Christodoulou, which states that given a first singularity, for generic initial data defined on an arbitrary domain containing the intersection of the past of the singularity and the initial hypersurface, the maximal future development must contain a trapped surface. In this talk, I will review the previous works on the formation of trapped surfaces and introduce the recent work by Junbin Li and me about the trapped surfaces conjecture when the first singularity is a spherical naked singularity constructed by Christodoulou.

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Date/Time : 16 Dec 2020 22:00
Venue : via Zoom
Speaker : Pengyu Le, University of Michigan

Join Zoom Meeting https://nus-sg.zoom.us/j/87148806876?pwd=VXlaNjlIaGNpK0c1SnY4YTQ1WUs1QT09 Meeting ID: 871 4880 6876 Password: 380377 Abstract: The Penrose inequality is a renowned inequality in GR proposed by Penrose in 1973. It conjectures a simple relation between the total mass of the spacetime and the mass of a black hole inside it. The original physical reasoning supporting this inequality by Penrose relates it to some most important and difficult problems in GR, i.e. the final state of the evolution of black holes and naked singularities (the weak cosmic censorship conjecture). A major breakthrough was achieved independently by Huisken, Ilmanen and by Bray, proving the Riemannian Penrose inequality. The Riemannian Penrose inequality is of course not the end of the story. There is another important case of the inequality on null hypersurfaces which is still open. The speaker will present his work confirming the null Penrose inequality on null hypersurfaces in a perturbed Schwarzschild spacetime. A major ingredient of the work is the study of perturbations of null hypersurfaces.

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Date/Time : 20 Nov 2020 22:30
Venue : via Zoom
Speaker : Elena Giorgi, Princeton University

https://princeton.zoom.us/j/93296784920 (Joint online mathematical general relativity and hyperbolic PDE seminar) Abstract: The Kerr-Newman spacetime is the most general explicit black hole solution, and represents a stationary rotating charged black hole. Its stability to gravitational and electromagnetic perturbations has eluded a proof since the 80s in the black hole perturbation community, because of “the apparent indissolubility of the coupling between the spin-1 and spin-2 fields in the perturbed spacetime”, as put by Chandrasekhar. We will present a derivation of the Teukolsky and Regge-Wheeler equations in Kerr-Newman in physical space and use it to obtain a quantitative proof of stability

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Date/Time : 20 Nov 2020 23:30
Venue : via Zoom
Speaker : John Anderson, Princeton University

https://princeton.zoom.us/j/93296784920 (Joint online mathematical general relativity and hyperbolic PDE seminar) Abstract: In this talk, I hope to show a global stability result for a nonlinear anisotropic system of wave equations. This is motivated by studying phenomena involving characteristics with multiple sheets. For the proof, I will describe a strategy for controlling the solution based on bilinear energy estimates. Through a duality argument, this will allow us to prove decay in physical space using decay estimates for the homogeneous wave equation as a black box. The final proof will also require us to exploit a certain null condition that is present when the anisotropic system of wave equations satisfies a structural property involving the light cones of the equations.

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Date/Time : 19 Nov 2020 15:00
Venue : via Zoom
Speaker : Haoyang Chen, Fudan University

Join Zoom Meeting https://nus-sg.zoom.us/j/87823796442?pwd=eHBhYmc4Mi9NNlhTczlCdk5neGROQT09 Meeting ID: 87823796442 Password: 132921 Abstract:  In this talk, we generalize a classic result of Lindblad on the scalar quasilinear wave equation and we show that the Cauchy problem for 3D elastic waves, a physical quasilinear wave system with multiple wave-speeds, is ill-posed in $H^3(R^3)$. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. The main difficulties arise from the multiple wave-speeds and its associated non-strict hyperbolicity. We design and combine a geometric approach and an algebraic approach to overcome these difficulties. This is based on joint work with Xinliang An and Silu Yin.

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Date/Time : 15 Jan 2020 15:00
Venue : S17 #06-11
Speaker : Georgios Moschidis, UC Berkeley

Date/Time:15 Jan 2020 15:00 Venue: S17 #06-11 Speaker: Georgios Moschidis, UC Berkeley A proof of the instability of AdS spacetime for the Einstein–scalar field system The AdS instability conjecture is a conjecture about the initial-boundary value problem in general relativity. It states that there exist arbitrarily small perturbations to the initial data of AdS spacetime which, under evolution by the vacuum Einstein equations with reflecting boundary conditions on conformal infinity, lead to the formation of black holes after a sufficiently long time. In this talk, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein–scalar field system. The construction of the unstable family of initial data will require working in a low regularity setting, carefully designing a family of initial configurations of localised matter beams and estimating the exchange of energy taking place between interacting beams over a long period of times, as well as estimating the decoherence rate of the beams. Add to calendar: 

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