Arlie Oswald Petters  

(Courtesy of Duke University)


Born 
February 8, 1964 Dangriga, Belize 
Residence  United States 
Nationality  United States 
Fields  Mathematical Physics 
Institutions  MIT Princeton University Duke University 
Alma mater  Hunter CollegeCUNY MIT 
Doctoral advisor  Bertram
Kostant David Spergel 
Known for  Mathematical Theory and Mathematical Physics of Gravitational Lensing 
Notable awards 
Alfred P. Sloan Fellowship NSF CAREER Award BlackwellTapia Prize Most Excellent Order of the British Empire 
Arlie Petters (born February 8, 1964) is a Belizean American mathematical physicist, who is the Benjamin Powell Professor and Professor of Mathematics, Physics, and Business Administration at Duke University. ^{[1]}
Contents 
During his childhood in the Central American developing nation of Belize, Petters found his passion for learning and especially mathematics and science. In his own words:
"Imagine majestic night skies filled with sparkling points of starlight scattered like diamonds across the heavens. These were the evening visual experiences of my childhood in the tiny Central American town of Dangriga, Belize. I constantly asked questions about the universe, oftentimes causing my elders to worry about my obsession: Does space continue forever? How did the universe come about? Why do we exist? Is there a God? This early exposure to the profound beauty and mystery of the cosmos has since gripped and steered my intellectual journey." Petters ^{[2]}
He immigrated to the United States in his midteens and became a citizen in 1990. Petters received his B.A and M.A from Hunter College in Mathematics and Physics in 1986 and completed his Ph.D. in Mathematics at MIT in 1991. He was an Instructor of Pure Mathematics at MIT from 1991 to 1993 and an Assistant Professor of Mathematics at Princeton University for five years (19931998). In 1998 Petters joined Duke University as the William and Sue Gross Associate Professor and became a Full Professor in 2003. As of 2008, he has held a triple joint appointment with Duke's Department of Mathematics,^{[3]} Department of Physics,^{[4]} and Fuqua School of Business. ^{[5]} Petters teaches quantitative finance in the Fuqua School of Business and works with MBA students to promote social entrepreneurship in science and technology in Belize and the developing world (see Social Outreach). He is currently the Benjamin Powell Professor at Duke. Petters's work and life were profiled in the New York Times^{[6]} and on NOVA. ^{[7]}
Petters was the only signatory of the Group of 88 who ran controversial ads during the 2006 Duke University lacrosse case to apologize for the group's ads after all players were declared innocent.
Petters is renowned for his pioneering work in the mathematical theory and mathematical physics of gravitational lensing.
Over the ten year period from 19912001, Petters systematically developed a mathematical theory of weakdeflection gravitational lensing, beginning with his 1991 MIT Ph.D. thesis on "Singularities in Gravitational Microlensing" ^{[8]} and followed by the 12 papers [AP1]  [AP12] below. The papers resolved an array of theoretical problems in weakdeflection gravitational lensing covering image counting, fixedpoint images, image magnification, image time delays, local geometry of caustics, global geometry of caustics, wavefronts, caustic surfaces, and caustic surfing. ^{[9]} His work culminated with a 2001 mathematical tome [AP13] that, among other things, systematically created a framework of stability and genericity for kplane gravitational lensing. The book drew upon powerful tools from the theory of singularities and put the subject of weakdeflection kplane gravitational lensing on a rigorous and unified mathematical foundation. ^{[10]}
Following his 19912001 body of mathematical lensing work, Petters turned to more astrophysical lensing issues from 20022005. 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; ^{[11]} ^{[12]} classify the local astrometric (centroid) and photometric curves of an extended source when it crosses fold and cusp caustics due to generic lenses; ^{[13]} ^{[14 ]} predict the quantitative astrometric curves's shape produced by Galactic binary lenses. ^{[13]} ^{[14 ]} The classified local properties of the astrometric curves revealed a characteristic Sshape 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.
During 20052007, 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 (20052006) with the astronomer Keeton, he utilized higherorder gravitational lensing effects by compact bodies to test different theories of gravity with Einstein's general theory of relativity among them. The first two papers computed beyond the standard weakdeflection limit the first and secondorder corrections to the image positions, magnifications, and time delays due to lensing in general relativity and alternative gravitational theories describable within the PPN formalism, ^{[15]} and even determined lensing invariants for the PPN family of models. ^{[16]} Their findings were applied to the Galactic black hole, binary pulsars, and gravitational microlensing scenarios to make testable predictions about lensed images and their time delays. ^{[15]} The third paper took on the difficult issue of how to test hyperspace models like braneworld gravity that postulate an extra dimension to physical space. The paper developed a semiclassical 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 gammaray light. ^{[17]} ^{[18]} Additionally, in a 2007 paper, Petters and Werner found a system of equations that can be applied to test the Cosmic Censorship Hypothesis observationally using the realistic case of lensing by a Kerr black hole. ^{[19]} ^{[20]}
Petters's previous work (19912007) dealt with nonrandom
gravitational lensing. His recent research program (2008present)
has been to develop a mathematical theory of random (stochastic)
gravitational lensing. In two papers, he, Rider, and Teguia took
first steps in creating a mathematical 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 KacRice type formula for the global expected
number of images due to a general stochastic lens system. ^{[21]} ^{[22]} 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 invariants of higherorder caustics
occurring in lensing and caustics produced by generic general maps
up to codimension five. ^{[23]} ^{[24]} ^{[25]} The
invariants hold with probability 1 for random lenses and thereby
form important consistency checks for research on random image
magnifications of sources near stable caustics.
For more information, consult Petters's official Duke University CV ^{[26]} for a very useful road map with detailed and extensive summaries of his research papers.
Selected papers from 19912001: ^{[27]}
[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 DoublePlane Two PointMass 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 PointMass 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)
Petters has given back significantly to the AfricanAmerican community, which has included him serving as Director of the Reginaldo Howard Memorial Scholarship program at Duke. ^{[28]} He has also been active in the AfricanAmerican community particularly through his mentoring, recruiting, and lecturing. ^{[29]} ^{[30]} He has received several community service awards for his social outreach. ^{[31 ]} ^{[32]} Petters is also the first tenured AfricanAmerican professor in Mathematics at Duke University. ^{[31 ]} He is very involved in the Belizean community and in 2005 founded the Petters Research Institute ^{[33]} to train Belizean young people in the mathematics, science, and technology fields and help develop a technologydriven economy in Belize. ^{[34]} ^{[35]} Petters has also authored a number of science and mathematics workbooks for Belizean students. ^{[36]} ^{[37]} Through his joint appointment with Duke's Fuqua School of Business, Petters is promoting entrepreneurship and innovation in science and technology in Belize, a pilot project he plans to extend to other developing nations. ^{[3]}
Petters is the recipient of numerous awards and honors, ^{[38]} which includes an Alfred P. Sloan Research Fellowship in Mathematics (1998), ^{[39]} a CAREER award from the National Science Foundation (1998), ^{[40]} and being the first winner of a BlackwellTapia Prize (2002). ^{[41]} He was selected in 2006 by the National Academy of Sciences to be part of a permanent Portrait Collection of Outstanding AfricanAmericans in Science, Engineering, and Medicine. ^{[42]} In 2008 Petters was also included among the Human Relations Associates' list of "The TwentyFive Greatest Scientists of African Ancestry," which went back as early as the 1700s. ^{[43]} He received an honorary Doctor of Science from his alma mater Hunter College in 2008. ^{[44]} Petters was named by the Queen of England in 2008 to membership in the Most Excellent Order of the British Empire. ^{[45]}
