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 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 : 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 : 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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Date/Time : 09 Dec 2019 15:30
Venue : S17 #05-12 SR4
Speaker : Zhao Lifeng, University of Science and Technology of China

Date/Time:09 Dec 2019 15:30 Venue: S17 #05-12 SR4 Speaker: Zhao Lifeng, University of Science and Technology of China Asymptotic behaviours for energy-subcritical damped Klein-Gordon equations In this talk, we will investigate the long-time behaviour of damped Klein-Gordon equation in the energy subcritical case. In fact, we will establish the soliton resolution for this equation which means that the global bounded solution evolves into the super-position of moving solitons. Moreover, we will give some further information about the resolution. The talk is based on joint works with Ze Li, Raphael Cote, Yvan Martel and Xu Yuan. Add to calendar: 

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Date/Time : 25 Oct 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Xiao Zhang, Guangxi University

Date/Time:25 Oct 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Xiao Zhang, Guangxi University Bondi-Sachs Spacetimes and the Bondi Energy Bondi-Sachs spacetimes were originally introduced by Bondi for axi-symmetric spacetimes, and generalized by Sachs to general asymptotically flat spacetimes for the zero cosmological constant. In this framework, Bondi defined the Bondi energy-momentum at null infinity, which represents the rest energy of spacetimes after the loss due to gravitational radiation. In this talk, we shall discuss, for zero cosmological constant, whether the Bondi energy is nonnegative? How the Bondi energy-momentum relates to the ADM energy-momentum defined at spatial infinity? We shall also discuss the natural boundary condition and the peeling property when the cosmological constant is nonzero. The talk is based on some joint works with W-l. Huang, Yau and F. Xie. Add to calendar: 

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Date/Time : 02 Oct 2019 16:00
Venue : S16 #03-09
Speaker : Yin Silu, Hangzhou Normal University

Date/Time:02 Oct 2019 16:00 Venue: S16 #03-09 Speaker: Yin Silu, Hangzhou Normal University Global well-posedness of elastodynamics In this talk, I will present some classical theory of elastic waves. The motion of elasticity is a wave system with multiple speeds, so Lorentz invariant is absent. For incompressible isotropic elasticity with constant density in 3D, the Cauchy problem with small initial datum were studied by a series work of Sideris and Thomases. We studied the inhomogeneous case in Lagrangian coordinate under the assumption that the density is a small perturbation around a constant state. This is a joint work with Xiufang Cui. Add to calendar: 

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Date/Time : 18 Sep 2019 16:00
Venue : S16 #03-09
Speaker : Chen Haoyang, Fudan University

Date/Time:18 Sep 2019 16:00 Venue: S16 #03-09 Speaker: Chen Haoyang, Fudan University Global regularity for Einstein-Klein-Gordon system with $U(1) \times \mathbb{R}$ isometry group In this paper we prove the global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a $U(1)\times \mathbb{R}$ isometry group. We reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1 dimensional system. We prove that the energy of this system cannot concentrate near the first possible singularity, and hence is small. Then, we show that the global regularity holds for the reduced 2+1 dimensional system with initial data of small energy. Add to calendar: 

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