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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 College-CUNY
Doctoral advisor Bertram Kostant
David Spergel
Known for Mathematical Theory and Mathematical Physics of Gravitational Lensing
Notable awards Alfred P. Sloan Fellowship
Blackwell-Tapia 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]



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 mid-teens 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 (1993-1998). 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 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" [8] 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. [9] 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. [10]

Following his 1991-2001 body of mathematical lensing work, Petters turned to more astrophysical lensing issues from 2002-2005. 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 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.

During 2005-2007, 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 (2005-2006) with the astronomer Keeton, he utilized higher-order 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 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 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 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. [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 (1991-2007) dealt with non-random gravitational lensing. His recent research program (2008-present) 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 Kac-Rice 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 higher-order 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 1991-2001: [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 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 has given back significantly to the African-American 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 African-American 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 African-American 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 technology-driven 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]

Awards and honors

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 Blackwell-Tapia Prize (2002). [41] 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. [42] 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 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]


  1. ^ Duke University
  2. ^ Mathematicians: An Outer View of the Inner World, Mariana Cook (Princeton U. Press, Princeton, 2009), p. 186. [1]
  3. ^ a b Department of Mathematics, Duke University
  4. ^ Department of Physics, Duke University
  5. ^ Fuqua School of Business, Duke University
  6. ^ New York Times
  7. ^ NOVA ScienceNow
  8. ^ A. O. Petters, Ph.D. Thesis, MIT, Department of Mathematics (1991): "Singularities in Gravitational Microlensing." [2]
  9. ^ Section A, "Research Period 1991-2001," Curriculum Vitae of Arlie O. Petters, Department of Mathematics, Duke University [3]
  10. ^ Singularity Theory and Gravitational Lensing, A. O. Petters, H. Levine, and J. Wambsganss (Birkhauser, Boston, 2001). [4]
  11. ^ "Identifying Lenses with Small-Scale Structure I. Cusp Lenses," C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 598, 138 (2003); astro-ph/0210318. [5]
  12. ^ "Identifying Lenses with Small-Scale Structure II. Fold Lenses," C. Keeton, S. Gaudi, and A. O. Petters , Astrophys. J., 635, 35 (2005); astro-ph/0503452. [6]
  13. ^ a b "Gravitational Microlensing Near Caustics I: Folds," B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); astro-ph/0112531. [7]
  14. ^ a b "Gravitational Microlensing Near Caustics II: Cusps," B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002); astro-ph/0206162. [8]
  15. ^ a b "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); gr-qc/0511019. [9]
  16. ^ "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); gr-qc/0601053 [10]
  17. ^ "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) gr-qc/0603061 [11]
  18. ^ "Scientist Predict How to Detect a Fourth Dimension," Duke News
  19. ^ "Magnification Relations for Kerr Lensing and Testing Cosmic Censorship," M. C. Werner and A. O. Petters, Phys. Rev. D 76, 064024 (2007); gr-qc/0706.0132 [12]
  20. ^ "Seeking Objects Weirder than Black Holes," Duke News
  21. ^ "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 [13]
  22. ^ "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
  23. ^ "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 [14]
  24. ^ "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 [15]
  25. ^ National Science Foundation, Science360 News Server, April 16, 2009
  26. ^ Curriculum Vitae of Arlie O. Petters, Department of Mathematics, Duke University [16]
  27. ^ Publications of Arlie O. Petters, Department of Mathematics, Duke University: [17]
  28. ^ The Reginaldo Howard Memorial Scholarship program, Duke University [18]
  29. ^ The Chronicle, Math Professor Reaches out to Minorities
  30. ^ Arlie O. Petters, Curriculum Vitae--Service to Underrepresented Minority Community, Department of Mathematics, Duke University [19]
  31. ^ a b Duke Magazine, "Star Professor"
  32. ^ Arlie O. Petters, Curriculum Vitae-- Awards and Honors
  33. ^ Petters Research Institute, Dangriga, Belize
  34. ^ 7 News Belize
  35. ^ Computer assembly course for Belizean students by Petters Research Institute and the Belize Defence Force [20]
  36. ^ Amandala News
  37. ^ Publications of Arlie O. Petters, Department of Mathematics, Duke University [21]
  38. ^ Arlie Petters, official Curriculum Vitae, Department of Mathematics, Duke University [22]
  39. ^ Alfred P. Sloan Foundation, list of past fellows
  40. ^ National Science Foundation, FY 98 CAREER Awardees (New Jersey)
  41. ^ SIAM News
  42. ^ National Academy of Sciences, African-American History Program
  43. ^ Human Relations Associates, The Twenty-Five Greatest Scientists of African Ancestry [23]
  44. ^ Hunter College News 2008
  45. ^ London Gazette, Duke Today

External links



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