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SUMMARY:Elena Giorgi (Princeton University)
DTSTART:20201102T160000Z
DTEND:20201102T170000Z
DTSTAMP:20260404T111102Z
UID:GAuS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/GAuS/
 1/">The stability of charged black holes</a>\nby Elena Giorgi (Princeton U
 niversity) as part of GAuS Seminar on Analysis and PDE\n\n\nAbstract\nI wi
 ll start by motivating the study of black holes and introducing the proble
 m of their stability as solutions to the Einstein equation. I will then co
 ncentrate on the case of charged black holes and their interaction with el
 ectromagnetism. From the prospective of PDEs\, I will especially focus on 
 two aspects of the resolution of the problem: the identification of gauge-
 invariant quantities\, and the analysis of coupled systems of wave equatio
 ns.\n
LOCATION:https://stable.researchseminars.org/talk/GAuS/1/
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SUMMARY:Christian Brennecke (Harvard University)
DTSTART:20201207T160000Z
DTEND:20201207T170000Z
DTSTAMP:20260404T111102Z
UID:GAuS/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/GAuS/
 2/">Bose-Einstein Condensation beyond the Gross-Pitaevskii Regime</a>\nby 
 Christian Brennecke (Harvard University) as part of GAuS Seminar on Analys
 is and PDE\n\n\nAbstract\nIn this talk\, I will consider Bose gases in a b
 ox of volume one that interact through a two-body potential with scatterin
 g length of the order $N^{-1+\\kappa}$\, for $\\kappa >0$. For small enoug
 h $\\kappa \\in (0\, 1/43)$\, slightly beyond the Gross-Pitaevskii regime 
 ($\\kappa =0$)\, I will explain a proof of Bose-Einstein condensation for 
 low-energy states that provides bounds on the expectation and on higher mo
 ments of the number of excitations. The talk is based on joint work with A
 . Adhikari and B. Schlein.\n
LOCATION:https://stable.researchseminars.org/talk/GAuS/2/
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SUMMARY:Lucrezia Cossetti (Karlsruhe Institute of Technology)
DTSTART:20210111T160000Z
DTEND:20210111T170000Z
DTSTAMP:20260404T111102Z
UID:GAuS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/GAuS/
 3/">Absence of eigenvalues of Schrödinger\, Dirac and Pauli Hamiltonians 
 via the method of multipliers</a>\nby Lucrezia Cossetti (Karlsruhe Institu
 te of Technology) as part of GAuS Seminar on Analysis and PDE\n\n\nAbstrac
 t\nOriginally arisen to understand characterizing properties connected wit
 h dispersive phenomena\, in the last decades the method of multipliers has
  been recognized as a useful tool in Spectral Theory\, in particular in co
 nnection with proof of absence of point spectrum for both self-adjoint and
  non self-adjoint operators. In this seminar we will see the developments 
 of the method reviewing some recent results concerning self-adjoint and no
 n self-adjoint Schrödinger operators in different settings\, specifically
  both when the configuration space is the whole Euclidean space $\\mathbb 
 R^d$ and when we restrict to domains with boundaries. We will show how thi
 s technique allows to detect physically natural repulsive and smallness co
 nditions on the potentials which guarantee total absence of eigenvalues. S
 ome very recent results concerning Pauli and Dirac operators will be prese
 nted as well. The talk is based on joint works with L. Fanelli and D. Krej
 cirik.\n
LOCATION:https://stable.researchseminars.org/talk/GAuS/3/
END:VEVENT
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SUMMARY:John Anderson (Princeton University)
DTSTART:20210201T160000Z
DTEND:20210201T170000Z
DTSTAMP:20260404T111102Z
UID:GAuS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/GAuS/
 4/">Stability results for anisotropic systems of wave equations</a>\nby Jo
 hn Anderson (Princeton University) as part of GAuS Seminar on Analysis and
  PDE\n\n\nAbstract\nIn this talk\, I will describe a global stability resu
 lt 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 allo
 w us to prove decay in physical space using decay estimates for the homoge
 neous wave equation as a black box. The final proof will also require us t
 o exploit a certain null condition that is present when the anisotropic sy
 stem of wave equations satisfies a structural property involving the light
  cones of the equations.\n
LOCATION:https://stable.researchseminars.org/talk/GAuS/4/
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