387:. 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 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 written five books, three of them 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
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theory of stochastic gravitational microlensing. They characterized to several asymptotic orders the probability densities of random time delay functions, lensing maps, and shear maps in stochastic microlensing and determined a Kac-Rice type formula for the global expected number of images due to a general stochastic lens system. The work forms a concrete framework from which extensions to more general random maps can be made. In two additional papers, he and Aazami found geometric universal magnification
411:(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,"going back to the eighteenth century. He received an honorary Doctor of Science from his alma mater,
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higher-order gravitational lensing effects by compact bodies to test different theories of gravity with the general theory of relativity of
Einstein among them. These papers computed beyond the standard weak-deflection limit the first- and second-order corrections to the image positions, magnifications, and time delays due to lensing in general relativity and alternative gravitational theories describable within the
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of higher-order caustics occurring in lensing and caustics produced by generic general maps up to codimension five. The invariants hold with a probability of 1 for random lenses and thereby form important consistency checks for research on random image magnifications of sources near stable caustics.
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During the period from 2005 to 2007, Petters collaborated with astronomers and physicists to explore gravitational lensing in directions beyond its traditional confines in astronomy. In a series of three mathematical physics papers published written with the astronomer
Charles R. Keeton, he utilized
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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
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Over the ten-year period from 1991 to 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". In a series of papers, he and his collaborators resolved an array of
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gravity that postulate an extra dimension to physical space. The paper developed a semi-classical wave theory of braneworld black hole lensing and used that theory along with braneworld cosmology to predict a testable signature of microscopic braneworld black holes on gamma-ray light. Additionally,
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Following his 1991–2001 body of mathematical lensing work, Petters turned to more astrophysical lensing issues from 2002 to 2005. In collaboration with astronomers, he applied some of the mathematical theory in to help develop a practical diagnostic test for the presence of dark substructures in
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Petters's previous work (1991–2007) dealt with non-random gravitational lensing. Starting in 2008, his research program focused on developing a mathematical theory of random (stochastic) gravitational lensing. In two papers, Petters, Rider, and Teguia took first steps in creating a mathematical
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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 in book, entitled
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which he co-authored with Harold Levine and
Joachim Wambganns. This book, which addressed the question, "What is the universe made of?", systematically created a framework of stability and genericity for k-plane gravitational lensing. The book drew upon powerful tools from the theory of
31:
415:, in 2008. Petters was named by the Queen of the United Kingdom 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—
456:"Arlie O. Petters, Benjamin Powell Professor & Professor of Mathematics, Physics, and Business Administration and Bass Fellow and Dean of Academic Affairs of Trinity College of Arts and Sciences and Professor of Economics"
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and swallowtail features for cusp crossings, and a jump discontinuity for crossings over the fold arcs merging into a cusp. Petters, Levine, and
Wambgamnns also developed a formula to calculate the size of the jump.
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905:"A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps," A. O. Petters, B. Rider, and A. M. Teguia, J. Math Phys., 50, 072503 (2009); astro-ph arXiv:0807.0232v2
270:(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.
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825:"Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. II. Probing Post-Post-Newtonian Metrics," C. Keeton and A. O. Petters, Phys. Rev. D 73, 044024 (2006);
808:"Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I. Static, Spherically Symmetric Case," C. Keeton and A. O. Petters, Phys. Rev. D, 72, 104006 (2005);
916:"A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula," A. O. Petters, B. Rider, and A. M. Teguia (2008); astro-ph arXiv:0807.4984
195:. Petters was also the dean of academic affairs for Trinity College of Arts and Sciences and associate vice provost for undergraduate education at Duke University (2016-2019).
925:"A Universal Magnification Theorem for Higher-Order Caustic Singularities," A. B. Aazami and A. O. Petters, J. Math. Phys. 50, 032501 (2009); astro-ph arXiv:0811.3447v2
151:(born February 8, 1964) is a Belizean-American mathematical physicist, who is the Benjamin Powell Professor of mathematics and a professor of physics and economics at
432:
423:. 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
841:"Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. III. Braneworld Gravity," C. Keeton and A. O. Petters, Phys. Rev. D 73, 104032 (2006)
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391:(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).
936:"A Universal Magnification Theorem II. Caustics up to Codimension Five," A. B. Aazami and A. O. Petters, 50, 082501 (2009); math-ph arXiv:0904.2236v4
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scenarios to make testable predictions about lensed images and their time delays. Another paper took on the difficult issue of how to test
875:"Magnification Relations for Kerr Lensing and Testing Cosmic Censorship," M. C. Werner and A. O. Petters, Phys. Rev. D 76, 064024 (2007);
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748:"Identifying Lenses with Small-Scale Structure II. Fold Lenses," C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 635, 35 (2005);
731:"Identifying Lenses with Small-Scale Structure I. Cusp Lenses," C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 598, 138 (2003);
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singularities and put the subject of weak-deflection k-plane gravitational lensing on a rigorous and unified mathematical foundation.
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215:). His mother immigrated to Brooklyn, New York, and married a U.S. citizen, with Arlie joining them when he was 14 years old.
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Section A, "Research Period 1991–2001," Curriculum Vitae of Arlie O. Petters, Department of
Mathematics, Duke University
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Department of
Mathematics in the same year. After two years of doctoral studies, he became an exchange scholar in the
788:"Gravitational Microlensing Near Caustics II: Cusps," B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002);
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768:"Gravitational Microlensing Near Caustics I: Folds," B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002);
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A. O. Petters, Ph.D. Thesis, MIT, Department of
Mathematics (1991): "Singularities in Gravitational Microlensing."
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337:, and even determined lensing invariants for the PPN family of models. Their findings were applied to the Galactic
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Computer assembly course for
Belizean students by Petters Research Institute and the Belize Defence Force
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in a 2007 paper, Petters and M.C. Werner found a system of equations that can be applied to test the
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191:. His monograph "Singularity Theory and Gravitational Lensing" developed a mathematical theory of
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and the first Belizean American to be Grand Marshal of the Central American Day Parade in
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Petters has served as director of the Reginaldo Howard Memorial Scholarship program at
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Arlie Petters, official Curriculum Vitae, Department of Mathematics, Duke University
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720:, A. O. Petters, H. Levine, and J. Wambsganss (Birkhauser, Boston, 2001). Amazon.com
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Human Relations Associates, The Twenty-Five Greatest Scientists of African Ancestry
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Many media outlets have profiled Arlie Petters and his scholarship, including
266:(Princeton University). He remained at MIT for two years as an instructor of
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Publications of Arlie O. Petters, Department of Mathematics, Duke University
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A CONVERSATION WITH: ARLIE PETTERS; A Journey to Bridge Math and the Cosmos
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A CONVERSATION WITH: ARLIE PETTERS: A Journey to Bridge Math and the Cosmos
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from MIT. Petters earned his Ph.D. in mathematics in 1991 under advisors
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Research Fellowship in Mathematics (1998), and a CAREER award from the
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National Science Foundation, Science360 News Server, April 16, 2009
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The Reginaldo Howard Memorial Scholarship program, Duke University
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Petters was raised by his grandparents in the rural community of
1232:"National Academy of Sciences, African-American History Program"
1193:"National Science Foundation, FY 98 CAREER Awardes (New Jersey)"
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Petters has received numerous awards and honors. He was won an
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Massachusetts Institute of Technology School of Science faculty
858:"Scientist Predict How to Detect a Fourth Dimension," Duke News
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Massachusetts Institute of Technology School of Science alumni
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http://hrassoc.net/blog/modules/news/article.php?storyid%3D17
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Petters is known for his work in the mathematical theory of
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Government of Belize Official Press Release, April 28, 2010
499:"Arlie O. Petters - Mathematicians of the African Diaspora"
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Arlie O. Petters - Mathematicians of the African Diaspora
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observationally using the realistic case of lensing by a
1123:"Amandala Newspaper | "Belize's Leading Newspaper""
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893:""Seeking Objects Weirder than Black Holes," Duke News"
431:, where he received honors from the mayor and from the
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effective September 1, 2020. Petters is a founder of
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List of Fellows of the American Mathematical Society
1348:"Arlie Petters wins award | Channel5Belize.com"
475:"Arlie Petters Selected as Provost of NYU Abu Dhabi"
1175:"Alfred P. Sloan Foundation, list of past fellows"
287:), Big Think, and Duke University's news outlet,
1333:"Duke Research Blog: Putting His Name on the Map"
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1011:Service to Underrepresented Minority Community,
419:, Belize—honored him in 2009 by naming a road
240:"The Mathematical Theory of General Relativity
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320:galaxies lensing quasars; classify the local
1509:Fellows of the American Mathematical Society
718:Singularity Theory and Gravitational Lensing
309:Singularity Theory and Gravitational Lensing
93:Mathematical theory of gravitational lensing
1013:Department of Mathematics, Duke University
978:. Archived from the original on 2008-09-07
972:"Math Professor Reaches Out to Minorities"
111:Most Excellent Order of the British Empire
1479:21st-century African-American scientists
407:(1998), and was the first winner of the
16:Belizean-American mathematical physicist
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1544:20th-century African-American academics
1499:Belizean emigrants to the United States
1437:Mathematicians of the African Diaspora
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439:as a Black History Month 2017 Honoree.
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1331:Bates, Karl Leif (January 13, 2010).
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970:Prabhu, Malavika (December 4, 2002).
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435:(COFECA). Petters was recognized by
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1484:Scientists from New York (state)
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155:. Petters became the provost at
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211:(formerly Stann Creek Town,
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66:(formerly Stann Creek Town,
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644:"Arlie Petters's Biography"
615:"About | The HistoryMakers"
405:National Science Foundation
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101:Alfred P. Sloan Fellowship
995:: CS1 maint: unfit URL (
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597:"Profile: Arlie Petters"
421:Dr. Arlie Petters Street
389:Fuqua School of Business
1504:Duke University faculty
1363:, retrieved 2013-05-05.
1421:Profile: Arlie Petters
1051:services.math.duke.edu
254:Department of Physics
161:mathematical astronomy
1514:Hunter College alumni
1346:Louisville, ky Says.
409:Blackwell-Tapia Prize
301:gravitational lensing
193:gravitational lensing
181:differential geometry
108:Blackwell-Tapia Prize
1534:People from Dangriga
503:www.math.buffalo.edu
252:Princeton University
145:Arlie Oswald Petters
42:Arlie Oswald Petters
1296:www.hunter.cuny.edu
285:Library of Congress
177:high energy physics
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568:The New York Times
276:The New York Times
189:probability theory
173:general relativity
1272:Missing or empty
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1069:www.pribelize.org
648:The HistoryMakers
395:Awards and honors
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218:Petters earned a
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351:hyperspace
339:black hole
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