Arlie Petters
Encyclopedia
Arlie Oswald Petters, MBE
(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
.
He is currently Chairman of the Council of Science Advisers to the Prime Minister 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
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 appointment at Duke with the Department of Mathematics, Department of Physics, and Fuqua School of Business
.
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. He currently holds the Benjamin Powell endowed Chair at Duke University. Petters's work and life were profiled in the New York Times, on NOVA
,
and at Big Think.
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.
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.
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;
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 curves'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.
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,
and even determined lensing invariants for the PPN family of models.
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.
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.
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.
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.
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.
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.
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)
as Director of the Reginaldo Howard Memorial Scholarship program at 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 in 2005 founded the Petters Research
Institute
to train Belizean young people in the mathematics, science, and technology fields
and help develop green technologies as a serious contributor to the economy of Belize.
Petters has also authored a number of science and mathematics workbooks for Belizean students.
Through his joint appointment with Duke's Fuqua School of Business,
Petters is promoting entrepreneurship and innovation in science and green technology
in Belize, a pilot project he plans to extend to other developing nations.
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.
Order of the British Empire
The Most Excellent Order of the British Empire is an order of chivalry established on 4 June 1917 by George V of the United Kingdom. The Order comprises five classes in civil and military divisions...
(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
Duke University
Duke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
.
He is currently Chairman of the Council of Science Advisers to the Prime Minister of Belize.
Biography
During his childhood in the Central American developing nation of BelizeBelize
Belize is a constitutional monarchy and the northernmost country in Central America. Belize has a diverse society, comprising many cultures and languages. Even though Kriol and Spanish are spoken among the population, Belize is the only country in Central America where English is the official...
, 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
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
Hunter College
Hunter College, established in 1870, is a public university and one of the constituent colleges of the City University of New York, located on Manhattan's Upper East Side. Hunter grants undergraduate, graduate, and post-graduate degrees in more than one hundred fields of study, and is recognized...
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
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
for five years (1993–1998).
In 1998 Petters joined Duke University
Duke University
Duke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
as the William and Sue Gross Associate Professor
and became a Full Professor in
2003. As of 2008, he has held a triple appointment at Duke with the Department of Mathematics, Department of Physics, and Fuqua School of Business
Fuqua School of Business
The Fuqua School of Business is the business school of Duke University in Durham, North Carolina, United States. It currently enrolls 1,340 students in degree-seeking programs...
.
Petters teaches quantitative finance in the Fuqua School of Business and works with MBA students to promote social entrepreneurship
Social entrepreneurship
Social entrepreneurship is the work of social entrepreneurs. A social entrepreneur recognizes a social problem and uses entrepreneurial principles to organize, create and manage a venture to achieve social change . While a business entrepreneur typically measures performance in profit and return, a...
in science and technology in Belize and the developing world. He currently holds the Benjamin Powell endowed Chair at Duke University. Petters's work and life were profiled in the New York Times, on NOVA
NOVA (TV series)
Nova is a popular science television series from the U.S. produced by WGBH Boston. It can be seen on the Public Broadcasting Service in the United States, and in more than 100 other countries...
,
and at Big Think.
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.
Research
Petters is renowned for his pioneering work in the mathematical theory and mathematical physicsMathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
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.
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;
classify the local astrometric (centroid) and photometric
Photometry (astronomy)
Photometry is a technique of astronomy concerned with measuring the flux, or intensity of an astronomical object's electromagnetic radiation...
curves of an extended source when it crosses fold and cusp caustics due to generic lenses;
predict the quantitative astrometric curves'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.
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,
and even determined lensing invariants for the PPN family of models.
Their findings were applied to the Galactic black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
, binary pulsars, and gravitational microlensing
Gravitational microlensing
Gravitational microlensing is an astronomical phenomenon due to the gravitational lens effect. It can be used to detect objects ranging from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers can only detect bright objects that emit lots of light ...
scenarios to make testable predictions about lensed images and their time delays.
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.
Additionally, in a 2007 paper, Petters and Werner found a system of equations that can be applied to
test the Cosmic Censorship Hypothesis
Cosmic censorship hypothesis
The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....
observationally using the realistic case of lensing by a Kerr black hole.
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.
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.
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.
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 has given back significantly to the African-American community, which has included him servingas Director of the Reginaldo Howard Memorial Scholarship program at Duke University
Duke University
Duke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
.
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 in 2005 founded the Petters Research
Institute
to train Belizean young people in the mathematics, science, and technology fields
and help develop green technologies as a serious contributor to the economy of Belize.
Petters has also authored a number of science and mathematics workbooks for Belizean students.
Through his joint appointment with Duke's Fuqua School of Business,
Petters is promoting entrepreneurship and innovation in science and green technology
in Belize, a pilot project he plans to extend to other developing nations.
Awards and honors
Petters is the recipient of numerous awards and honors,which includes
an Alfred P. Sloan
Alfred P. Sloan
Alfred Pritchard Sloan, Jr. was an American business executive in the automotive industry. He was a long-time president, chairman, and CEO of General Motors Corporation...
Research Fellowship in Mathematics (1998),
a CAREER award
from the National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
(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
Hunter College
Hunter College, established in 1870, is a public university and one of the constituent colleges of the City University of New York, located on Manhattan's Upper East Side. Hunter grants undergraduate, graduate, and post-graduate degrees in more than one hundred fields of study, and is recognized...
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.
External links
- NOVA scienceNOWNOVA scienceNOWNOVA scienceNOW is a newsmagazine version of the long running and venerable PBS science program Nova. Premiering on January 25, 2005, the series was originally hosted by Robert Krulwich, who described it as an experiment in coverage of "breaking science, science that's right out of the lab, science...
http://www.pbs.org/wgbh/nova/sciencenow/3411/04.html - New York Times http://www.nytimes.com/2003/05/27/science/a-conversation-with-arlie-petters-a-journey-to-bridge-math-and-the-cosmos.html
- National Academy of Sciences http://www.nasonline.org/site/PageServer?pagename=AAHP_Database_Bio_Petters
- Mathematicians of the African Diaspora http://www.math.buffalo.edu/mad/PEEPS/petters_arlie.html