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Arlie Oswald Petters, MBE né le 8 février 1964, est un physicien et mathématicien américain et belizéen. Il est est le professeur de la chaire de mathématique Benjamin Powell, et un Professeur de physique et d'économie à Université Duke. Petters est un fondateur de astronomie mathématique. Il se concentre sur les problèmes liés à l'intéraction de la gravité et de la lumière, et emploie les outils de l'astrophysique, de lacosmologie, de larelativité générale, de la physique des particules, de la géométrie différentielle, de la les singularités, et de la théorie des probabilités. Sa monographie "Théorie de la singularité et lentilles gravitationnelles" est la première à développer une théorie mathématique de la lentille gravitationnelle. Petters est aussi le doyen des affaires scolaires pour Trinity College des arts et sciences et, et le vice-doyen adjoint pour des études de premier cycle à l'Université Duke.

Biography
Petters was raised by his grandparents in the rural community of Stann Creek Town, British Honduras (now Dangriga, Belize). His mother immigrated to Brooklyn, New York, and married a U.S. citizen, with Arlie joining them when he was 14 years old.

Petters earned a B.A./M.A. in Mathematics and Physics from Hunter College, CUNY in 1986 with a thesis on "The Mathematical Theory of General Relativity", and began his Ph.D. at the Massachusetts Institute of Technology Department of Mathematics in the same year. After two years of doctoral studies, he became an exchange scholar in the Princeton University Department of Physics in absentia from MIT. Petters earned his Ph.D. in Mathematics in 1991 under advisors Bertram Kostant (MIT) and David Spergel (Princeton University). He remained at MIT for two years as an instructor of pure mathematics (1991-1993) and then joined the faculty at Princeton University in the Department of Mathematics. He was an Assistant Professor at Princeton for five years (1993-1998) before moving to Duke University.

Petters's work and life were profiled in the New York Times, on NOVA, by The History Makers, and at Big Think.

Research
Petters is renowned for his pioneering work in the mathematical theory of gravitational lensing.

Over the ten-year period from 1991–2001, Petters systematically developed a mathematical theory of weak-deflection gravitational lensing, beginning with his 1991 MIT Ph.D. thesis on "Singularities in Gravitational Microlensing" and followed by the 12 papers [AP1] - [AP12] below. The papers resolved an array of theoretical problems in weak-deflection gravitational lensing covering image counting, fixed-point images, image magnification, image time delays, local geometry of caustics, global geometry of caustics, wavefronts, caustic surfaces, and caustic surfing. His work culminated with a 2001 mathematical tome [AP13] that, among other things, systematically created a framework of stability and genericity for k-plane gravitational lensing. The book drew upon powerful tools from the theory of singularities and put the subject of weak-deflection k-plane gravitational lensing on a rigorous and unified mathematical foundation. . In collaboration with astronomers, he applied some of the mathematical theory in [AP13] to help develop a practical diagnostic test for the presence of dark substructures in galaxies lensing quasars; classify the local astrometric (centroid) and photometric curves of an extended source when it crosses fold and cusp caustics due to generic lenses;  predict the quantitative astrometric curve's shape produced by Galactic binary lenses. The classified local properties of the astrometric curves revealed a characteristic S-shape for fold crossings, parabolic and swallowtail features for cusp crossings, and a jump discontinuity for crossings over the fold arcs merging into a cusp. A formula for the size of the jump was also found.

[Translating below] Au cours de la période 2005-2007, Petters a collaboré avec des astronomes et des physiciens pour explorer la lentille gravitationnelle dans des directions au-delà de ses limites traditionnelles en astronomie. Dans une série de trois articles de physique mathématique (2005-2006) avec l'astronome Keeton, il a utilisé des effets de lentilles gravitationnelles d'ordre supérieur par des corps compacts pour tester différentes théories de la gravité avec la théorie générale de la relativité d'Einstein. Les deux premiers articles calculés au-delà de la limite de déflexion standard limitent les corrections de premier et de second ordre aux positions d'image, grossissements et retards dus à la lentille en relativité générale et aux théories gravitationnelles alternatives décrivant PPN formalism, même des invariants de lentilles déterminés pour la famille de modèles PPN. Leurs résultats ont été appliqués au trou noir galactique black hole, binary pulsars, et aux scenarios de gravitational microlensing pour faire des prédictions testables au sujet des images lentilles et de leurs retards de temps. Le troisième article a abordé la question difficile de savoir comment tester des modèles d'hyperspace comme la gravité braneworld qui postulent une dimension supplémentaire à l'espace physique. L'article a développé une théorie des ondes semi-classique de la lentille braneworld et a utilisé cette théorie avec la cosmologie braneworld pour prédire une signature testable de trous noirs microscopiques braneworld sur la lumière gamma. En outre, dans un papier de 2007, Petters et Werner ont trouvé un système d'équations qui peuvent être appliquées pour tester l'hypothèse de censure cosmique observationnellement utilisant le cas réaliste de lentilles par un Kerr black hole.

Petter's travaille precedent (1991–2007) traité avec lentilles gravitationnel non-aléatoires. Son récent programme de recherche (2008-présent) a été de développer une théorie mathématique de lentilles gravitationnelles aléatoires (stochastiques). Dans deux articles, lui, Rider et Teguia ont fait les premiers pas dans la création d'une théorie mathématique de la microlentille gravitationnelle stochastique. Ils ont caractérisé à plusieurs ordres asymptotiques les densités de probabilité de temporisations aléatoires, de cartes de lentilles et de cartes de cisaillement en microlentilles stochastiques et ont déterminé une formule de type Kac-Rice pour le nombre global attendu d'images dues à un système stochastique général. Le travail forme un cadre concret à partir duquel des extensions à des cartes aléatoires plus générales peuvent être faites. Dans deux articles supplémentaires, lui et Aazami ont trouvé des invariants géométriques de grossissement universel de caustiques d'ordre supérieur se produisant dans les lentilles et caustiques produites par les cartes générales génériques jusqu'à codimension cinq. Les invariants se maintiennent avec une probabilité de 1 pour les lentilles aléatoires et forment ainsi des vérifications de cohérence importantes pour la recherche sur les grossissements aléatoires des sources proches des caustiques stables.

For more information, consult Petters's official Duke University CV for a very useful road map with detailed and extensive summaries of his research papers.

Selected papers from 1991–2001:

[AP1] "Morse Theory and Gravitational Microlensing," A. O. Petters, J. Math. Phys., 33, 1915 (1992).

[AP2] "Arnold's Singularity Theory and Gravitational Lensing," A. O. Petters, J. Math. Phys., 34, 3555 (1993).

[AP3] "Multiplane Gravitational Lensing I: Morse Theory and Image Counting," A. O. Petters, J. Math. Phys., 36, 4263 (1995).

[AP4] "Multiplane Gravitational Lensing II: Global Geometry of Caustics," A. O. Petters, J. Math. Phys., 36, 4276 (1995).

[AP5] "Multiplane Gravitational Lensing III. Upper Bound on Number of Images," A. O. Petters, J. Math. Phys., 38, 1605 (1997).

[AP6] "Caustics of the Double-Plane Two Point-Mass Gravitational Lens with Continuous Matter and Shear," A. O. Petters and F.J. Wicklin, Mon. Not. R. Astron. Soc., 277, 1399 (1995).

[AP7] "Lower Bounds on Image Magnification in Gravitational Lensing," A. O. Petters, Proc. R. Soc. Lond. A, 452, 1475 (1996).

[AP8] "Counting Formulas and Bounds on Number of Fixed Points due to Point-Mass Lenses," A. O. Petters and F.J. Wicklin, in Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 1997).

[AP9] "Bounds on Number of Cusps due to Point Mass Gravitational Lenses with Continuous Matter and Shear," A. O. Petters and H. Witt, J. Math. Phys., 37, 2920 (1996).

[AP10] "Mathematical Aspects of Gravitational Lensing," A. O. Petters, in Proceedings of the Seventh Marcel Grossmann Meeting on General Relativity, vol. B, eds. R. T. Jantzen and G. M. Keiser (World Scientific, Singapore, 1996).

[AP11] "Fixed Points due to Gravitational Lenses," A.O. Petters and F.J. Wicklin, J. Math. Phys., 39, 1011 (1998)

[AP12] "Stable Lens Systems, Lensed Image Magnification, and Magnification Cross Sections," A. O. Petters, in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).

[AP13] Singularity Theory and Gravitational Lensing, A. O. Petters, H. Levine, and J. Wambsganns (Birkhauser, Boston, 2001)

Social Outreach
Petters a donné arriéré considérablement a la communauté Afro-Americaine, qu'est inclus lui en servant comme que le Directeur du le 'Reginaldo Howard Memorial Scholarship' programme à Duke University. He has also been active in the African-American community particularly through his mentoring, recruiting, and lecturing. He has received several community service awards for his social outreach. Petters is also the first tenured African-American professor in Mathematics at Duke University. He is very involved in the Belizean community and founded the Petters Research Institute in 2005 to help train Belizean young people in STEM fields and foster STEM entrepreneurship. He has also written five books, three of which were science and mathematics problem-solving books for Belizean students. Some of his entrepreneurial work was conducted while he was a Professor of Business Administration at Duke’s Fuqua School of Business (2008-2017). Petters also served the Government of Belize as Chairman of the Council of Science Advisers to the Prime Minister of Belize (2010-2013).

Awards and honors
Petters is the recipient of numerous awards and honors, which includes an Alfred P. Sloan Research Fellowship in Mathematics (1998), a CAREER award from the National Science Foundation (1998), and being the first winner of a Blackwell-Tapia Prize (2002). He was selected in 2006 by the National Academy of Sciences to be part of a permanent Portrait Collection of Outstanding African-Americans in Science, Engineering, and Medicine. In 2008 Petters was also included among the Human Relations Associates' list of "The Twenty-Five Greatest Scientists of African Ancestry," which went back as early as the 18th century. He received an honorary Doctor of Science from his alma mater Hunter College in 2008. Petters was named by the Queen of England in 2008 to membership in the Most Excellent Order of the British Empire. In recognition of his scientific accomplishments and service to society, Petters's birthplace—Dangriga, Belize—honored him in 2009 with the Dr. Arlie Petters Street. He became in 2011 the first Belizean to receive the Caribbean American Heritage Award for Excellence in Science and Technology. In 2012 he became a fellow of the American Mathematical Society and the first Belizean American to be Grand Marshal of the Central American Day Parade in L.A., where he received honors from the mayor of L.A. and COFECA.