Arlie Petters
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Arlie Oswald Petters, MBE (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
Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...
. Petters became the provost at New York University Abu Dhabi effective September 1, 2020. Petters is a founder of
mathematical astronomy Theoretical astronomy is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretica ...
, focusing on problems connected to the interplay of gravity and light and employing tools from
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
,
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...
,
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
,
high energy physics Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the stu ...
,
differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
, singularities, and
probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
. His monograph "Singularity Theory and Gravitational Lensing" developed a mathematical theory of
gravitational lensing A gravitational lens is matter, such as a galaxy cluster, cluster of galaxies or a point particle, that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein's Ge ...
. 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).


Biography

Petters was raised by his grandparents in the rural community of
Dangriga Dangriga, formerly known as Stann Creek Town, is a town in southern Belize, located on the Caribbean Sea, Caribbean coast at the mouth of the North Stann Creek River. It is the capital of Belize's Stann Creek District. Dangriga is served by the ...
,
Belize Belize is a country on the north-eastern coast of Central America. It is bordered by Mexico to the north, the Caribbean Sea to the east, and Guatemala to the west and south. It also shares a maritime boundary with Honduras to the southeast. P ...
(formerly Stann Creek Town,
British Honduras British Honduras was a Crown colony on the east coast of Central America — specifically located on the southern edge of the Yucatan Peninsula from 1783 to 1964, then a self-governing colony — renamed Belize from June 1973
). His mother immigrated to Brooklyn, New York, and married a U.S. citizen, with Arlie joining them when he was 14 years old. Claudia Dreifus
A CONVERSATION WITH: ARLIE PETTERS: A Journey to Bridge Math and the Cosmos
''
The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...
'', May 27, 2003.
Petters earned a B.A./M.A. in
Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
and
Physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
from
Hunter College Hunter College is a public university in New York City, United States. It is one of the constituent colleges of the City University of New York and offers studies in more than one hundred undergraduate and postgraduate fields across five schools ...
,
CUNY The City University of New York (CUNY, pronounced , ) is the Public university, public university system of Education in New York City, New York City. It is the largest urban university system in the United States, comprising 25 campuses: eleven ...
in 1986 with a thesis on "The Mathematical Theory of General Relativity", and began his Ph.D. at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
Department of Mathematics in the same year. After two years of doctoral studies, he became an exchange scholar in the
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
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 Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...
(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. Many media outlets have profiled Arlie Petters and his scholarship, including ''
The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...
'',
NOVA A nova ( novae or novas) is a transient astronomical event that causes the sudden appearance of a bright, apparently "new" star (hence the name "nova", Latin for "new") that slowly fades over weeks or months. All observed novae involve white ...
, The HistoryMakers (a digital archive of oral histories featuring African-Americans and preserved at the
Library of Congress The Library of Congress (LOC) is a research library in Washington, D.C., serving as the library and research service for the United States Congress and the ''de facto'' national library of the United States. It also administers Copyright law o ...
), Big Think, and Duke University's news outlet, ''The Chronicle''.


Research

Petters is known for his work in the mathematical theory of
gravitational lensing A gravitational lens is matter, such as a galaxy cluster, cluster of galaxies or a point particle, that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein's Ge ...
. 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 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 ''Singularity Theory and Gravitational Lensing'' (Springer 2012)'','' 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 singularities and put the subject of weak-deflection k-plane gravitational lensing on a rigorous and unified mathematical foundation. ''Singularity Theory and Gravitational Lensing'', A. O. Petters, H. Levine, and J. Wambsganss (Birkhauser, Boston, 2001). Amazon.co

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 P13to help develop a practical diagnostic test for the presence of dark substructures in galaxies lensing quasars; classify the local
astrometric Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. History ...
(centroid) and photometric curves of an extended source when it crosses fold and cusp caustics due to generic lenses;"Gravitational Microlensing Near Caustics I: Folds," B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); . "Gravitational Microlensing Near Caustics II: Cusps," B. S. Gaudi and A. O. Petters, Astrophys. J., 580, 468 (2002); . 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. Petters, Levine, and Wambgamnns also developed a formula to calculate the size of the jump. 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 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 PPN formalism,"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); . and even determined lensing invariants for the PPN family of models. Their findings were applied to the Galactic
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
, binary pulsars, and
gravitational microlensing Gravitational microlensing is an astronomical phenomenon caused by the gravitational lens effect. It can be used to detect objects that range from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronom ...
scenarios to make testable predictions about lensed images and their time delays. Another 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 M.C. Werner found a system of equations that can be applied to test the
Cosmic Censorship Hypothesis The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity. Singularities that arise in the solutions of Einstein's equations are typical ...
observationally using the realistic case of lensing by a
Kerr black hole The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...
. 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 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.


Social outreach

Petters has served as director of the Reginaldo Howard Memorial Scholarship program at
Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...
. 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.Duke Magazine, "Star Professor"
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
Fuqua School of Business The Duke University Fuqua School of Business (pronounced ) is the business school of Duke University, a Private university, private research university in Durham, North Carolina. It enrolls more than 1,300 students in degree-seeking programs. Du ...
(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 has received numerous awards and honors. He was won an
Alfred P. Sloan Alfred Pritchard Sloan Jr. ( ; May 23, 1875February 17, 1966) was an American business executive in the automotive industry. He was a longtime president, chairman and CEO of General Motors Corporation. First as a senior executive and later as ...
Research Fellowship in Mathematics (1998), and a CAREER award from the
National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...
(1998), and was the first winner of the 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,"going back to the eighteenth century. He received an honorary Doctor of Science from his alma mater,
Hunter College Hunter College is a public university in New York City, United States. It is one of the constituent colleges of the City University of New York and offers studies in more than one hundred undergraduate and postgraduate fields across five schools ...
, 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—
Dangriga Dangriga, formerly known as Stann Creek Town, is a town in southern Belize, located on the Caribbean Sea, Caribbean coast at the mouth of the North Stann Creek River. It is the capital of Belize's Stann Creek District. Dangriga is served by the ...
, Belize—honored him in 2009 by naming a road ''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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
and the first Belizean American to be Grand Marshal of the Central American Day Parade in
Los Angeles Los Angeles, often referred to by its initials L.A., is the List of municipalities in California, most populous city in the U.S. state of California, and the commercial, Financial District, Los Angeles, financial, and Culture of Los Angeles, ...
, where he received honors from the mayor and from the Confederation Centroamericana (COFECA). Petters was recognized by Mathematically Gifted & Black as a Black History Month 2017 Honoree.


References


External links

* '' NOVA scienceNOW'
Profile: Arlie Petters
* New York Time

* National Academy of Science
National Academy of Sciences:
* Mathematicians of the African Diaspor

{{DEFAULTSORT:Petters, Arlie 1964 births 20th-century American mathematicians 21st-century American mathematicians African-American mathematicians 21st-century African-American scientists Scientists from New York (state) 21st-century American physicists Belizean academics Belizean emigrants to the United States Duke University faculty Fellows of the American Mathematical Society Hunter College alumni Living people Massachusetts Institute of Technology School of Science alumni Massachusetts Institute of Technology School of Science faculty People from Dangriga Princeton University faculty 20th-century African-American academics 20th-century American academics 21st-century African-American academics 21st-century American academics African-American physicists Members_of_the_Order_of_the_British_Empire