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DTSTART;TZID=America/New_York:20230427T103000
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DTSTAMP:20260416T020736
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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
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DTSTART;TZID=America/New_York:20230427T130000
DTEND;TZID=America/New_York:20230427T140000
DTSTAMP:20260416T020736
CREATED:20230824T183024Z
LAST-MODIFIED:20240209T052245Z
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SUMMARY:Competition at the front of expanding populations
DESCRIPTION:Active Matter Seminar\n\n\nSpeaker: Mehran Kardar\, MIT \nTitle: Competition at the front of expanding populations \nAbstract: When competing species grow into new territory\, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on the reproductive advantage (fitness)\, as well as ability and opportunity to colonize new domains. (1) Based on symmetry considerations\, we present a model that  integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored\, providing a framework to study spatial competition\, fixation\, and differentiation\, In particular\, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory. (2) Variations of fitness\, as well as fixation time upon differentiation\, are shown to belong to distinct universality classes depending on limits to gain of fitness.
URL:https://cmsa.fas.harvard.edu/event/am-42723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Active Matter Seminar
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