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SUMMARY:Elena Giorgi (Princeton University)
DTSTART:20201102T160000Z
DTEND:20201102T170000Z
DTSTAMP:20260422T225754Z
UID:GAuS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GAuS/1/">The
  stability of charged black holes</a>\nby Elena Giorgi (Princeton Universi
 ty) as part of GAuS Seminar on Analysis and PDE\n\n\nAbstract\nI will star
 t by motivating the study of black holes and introducing the problem of th
 eir stability as solutions to the Einstein equation. I will then concentra
 te on the case of charged black holes and their interaction with electroma
 gnetism. From the prospective of PDEs\, I will especially focus on two asp
 ects of the resolution of the problem: the identification of gauge-invaria
 nt quantities\, and the analysis of coupled systems of wave equations.\n
LOCATION:https://researchseminars.org/talk/GAuS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Brennecke (Harvard University)
DTSTART:20201207T160000Z
DTEND:20201207T170000Z
DTSTAMP:20260422T225754Z
UID:GAuS/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GAuS/2/">Bos
 e-Einstein Condensation beyond the Gross-Pitaevskii Regime</a>\nby Christi
 an Brennecke (Harvard University) as part of GAuS Seminar on Analysis and 
 PDE\n\n\nAbstract\nIn this talk\, I will consider Bose gases in a box of v
 olume one that interact through a two-body potential with scattering lengt
 h of the order $N^{-1+\\kappa}$\, for $\\kappa >0$. For small enough $\\ka
 ppa \\in (0\, 1/43)$\, slightly beyond the Gross-Pitaevskii regime ($\\kap
 pa =0$)\, I will explain a proof of Bose-Einstein condensation for low-ene
 rgy states that provides bounds on the expectation and on higher moments o
 f the number of excitations. The talk is based on joint work with A. Adhik
 ari and B. Schlein.\n
LOCATION:https://researchseminars.org/talk/GAuS/2/
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SUMMARY:Lucrezia Cossetti (Karlsruhe Institute of Technology)
DTSTART:20210111T160000Z
DTEND:20210111T170000Z
DTSTAMP:20260422T225754Z
UID:GAuS/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GAuS/3/">Abs
 ence of eigenvalues of Schrödinger\, Dirac and Pauli Hamiltonians via the
  method of multipliers</a>\nby Lucrezia Cossetti (Karlsruhe Institute of T
 echnology) as part of GAuS Seminar on Analysis and PDE\n\n\nAbstract\nOrig
 inally arisen to understand characterizing properties connected with dispe
 rsive phenomena\, in the last decades the method of multipliers has been r
 ecognized as a useful tool in Spectral Theory\, in particular in connectio
 n with proof of absence of point spectrum for both self-adjoint and non se
 lf-adjoint operators. In this seminar we will see the developments of the 
 method reviewing some recent results concerning self-adjoint and non self-
 adjoint Schrödinger operators in different settings\, specifically both w
 hen the configuration space is the whole Euclidean space $\\mathbb R^d$ an
 d when we restrict to domains with boundaries. We will show how this techn
 ique allows to detect physically natural repulsive and smallness condition
 s on the potentials which guarantee total absence of eigenvalues. Some ver
 y recent results concerning Pauli and Dirac operators will be presented as
  well. The talk is based on joint works with L. Fanelli and D. Krejcirik.\
 n
LOCATION:https://researchseminars.org/talk/GAuS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Anderson (Princeton University)
DTSTART:20210201T160000Z
DTEND:20210201T170000Z
DTSTAMP:20260422T225754Z
UID:GAuS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GAuS/4/">Sta
 bility results for anisotropic systems of wave equations</a>\nby John Ande
 rson (Princeton University) as part of GAuS Seminar on Analysis and PDE\n\
 n\nAbstract\nIn this talk\, I will describe a global stability result for 
 a nonlinear anisotropic system of wave equations. This is motivated by stu
 dying phenomena involving characteristics with multiple sheets. For the pr
 oof\, I will describe a strategy for controlling the solution based on bil
 inear energy estimates. Through a duality argument\, this will allow us to
  prove decay in physical space using decay estimates for the homogeneous w
 ave equation as a black box. The final proof will also require us to explo
 it 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.\n
LOCATION:https://researchseminars.org/talk/GAuS/4/
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