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DTSTART;TZID=America/New_York:20230309T093000
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DTSTAMP:20260415T201701
CREATED:20230817T185018Z
LAST-MODIFIED:20240228T091310Z
UID:10001256-1678354200-1678357800@cmsa.fas.harvard.edu
SUMMARY:Pseudospectrum and black hole quasinormal mode instability: An ultraviolet universality conjecture
DESCRIPTION:General Relativity Seminar \nSpeaker: Jose Luis Jaramillo (Bourgogne U.) \nTitle: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture \nAbstract: Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations\, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties\, Nollert and Price found evidence of a BH QNM instability phenomenon\, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically\, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities\, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines\, therefore probing the analytic structure of the resolvent\, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable\, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity\, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon\, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.
URL:https://cmsa.fas.harvard.edu/event/gr_3923/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.09.23.png
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DTSTART;TZID=America/New_York:20230309T110000
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DTSTAMP:20260415T201702
CREATED:20230807T171904Z
LAST-MODIFIED:20240215T105139Z
UID:10001191-1678359600-1678363200@cmsa.fas.harvard.edu
SUMMARY:On the free energy of spin glasses with multiple types
DESCRIPTION:Probability Seminar \n\nSpeaker: Jean-Christophe Mourrat (ENS Lyon) \nTitle: On the free energy of spin glasses with multiple types \nAbstract: In the simplest spin-glass model\, due to Sherrington and Kirkpatrick\, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups\, which we can visualize as forming two layers\, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins\, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there\, and some partial progress.
URL:https://cmsa.fas.harvard.edu/event/probability-3923/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-03.09.23.png
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