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DTSTART;TZID=America/New_York:20230406T093000
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DTSTAMP:20260501T105811
CREATED:20230818T042449Z
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SUMMARY:Rough solutions of the relativistic Euler equations
DESCRIPTION:General Relativity Seminar \nSpeaker: Sifan Yu\, Vanderbilt University \nTitle: Rough solutions of the relativistic Euler equations \nAbstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations\, which has geo-analytic structures. In this geometric formulation\, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics\, including the existence of low-regularity solutions. Then\, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0\,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof\, as well as a comparison of the relativistic and non-relativistic scenarios.
URL:https://cmsa.fas.harvard.edu/event/gr_4623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230413T093000
DTEND;TZID=America/New_York:20230413T103000
DTSTAMP:20260501T105811
CREATED:20230818T042744Z
LAST-MODIFIED:20240228T081413Z
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SUMMARY:Resolving the photon ring
DESCRIPTION:General Relativity Seminar \nSpeaker: Shahar Hadar (University of Haifa) \nTitle: Resolving the photon ring \nAbstract: In the past few years\, the Event Horizon Telescope has released the first close-up interferometric images of two supermassive black holes\, M87* and SgrA*. It is believed that within these images is embedded a fine\, yet-unresolved brightness enhancement called the photon ring. The ring is a universal consequence of strong lensing by the black hole and thereby conveys information on its spacetime geometry\, potentially providing a new independent avenue for tests of general relativity in the strong-field regime. In the talk I will briefly review the theory of the photon ring and its corresponding spacetime region\, the photon shell\, which governs the universal lensing structure. I will then describe some current efforts and future prospects for resolving the ring\, which include both the construction of transformative new instruments and the development of novel analysis methods. Focusing on the latter\, I will present an upcoming proposal to use spectro-temporal autocorrelations in signals emitted from black hole environs as a probe of strong lensing effects.
URL:https://cmsa.fas.harvard.edu/event/gr_41323/
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-04.13.23.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230424T133000
DTEND;TZID=America/New_York:20230424T143000
DTSTAMP:20260501T105811
CREATED:20230818T043218Z
LAST-MODIFIED:20240119T052608Z
UID:10001261-1682343000-1682346600@cmsa.fas.harvard.edu
SUMMARY:Recent advances in scalar curvature and positive mass theorems
DESCRIPTION:General Relativity Seminar \nSpeaker: Tin Yau Tsang\, University of California Irvine \nTitle: Recent advances in scalar curvature and positive mass theorems\n\nAbstract:  First\, we have a review of classical tools for studying scalar curvature and positive mass theorem. Then we are going to discuss some advances and new perspectives on these tools which lead to a deeper understanding of geometry and initial data sets.
URL:https://cmsa.fas.harvard.edu/event/gr_42423/
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-04.24.23-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230427T103000
DTEND;TZID=America/New_York:20230427T113000
DTSTAMP:20260501T105811
CREATED:20230818T043803Z
LAST-MODIFIED:20240119T052918Z
UID:10001262-1682591400-1682595000@cmsa.fas.harvard.edu
SUMMARY:The localized seed-to-solution method for the Einstein constraints
DESCRIPTION:General Relativity Seminar \nSpeaker: Philippe G. LeFloch\, Sorbonne University and CNRS \nTitle: The localized seed-to-solution method for the Einstein constraints \nAbstract: I will discuss advances on asymptotically Euclidian initial data sets and the variational method introduced by J. Corvino and R. Schoen. This talk is based on joint papers with The-Cang Nguyen (Montpellier) and Bruno Le Floch (Sorbonne Univ. and CNRS). In the vicinity of any given reference data set\, we define a “localized seed-to-solution” map\, which allows us to parametrize the initial data sets satisfying the Einstein constraints (possibly with matter fields). The parametrization is defined over classes of data sets understood modulo the image of the dual linearized constraints. Our main contribution concerns the sharp behavior of solutions at infinity\, which we can arbitrarily localize in asymptotic cones in the sense of A. Carlotto and R. Schoen. Most importantly\, as we prove it\, the solutions enjoy sharp decay estimates at the harmonic and super-harmonic levels. In the course of this analysis\, we discover the notion of ‘asymptotic modulators’\, as we call them\, or “correctors” to the standard ADM invariants.
URL:https://cmsa.fas.harvard.edu/event/gr_42723/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-04.27.23.png
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