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. Petters will become the Provost at New York University Abu Dhabi effective September 1, 2020. Petters is a founder of mathematical astronomy, focusing on problems connected to the interplay of gravity and light and employing tools from astrophysics,

cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

high energy physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standa ...

, differential geometry, singularities, and

probability theory Probability theory 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 expressing it through a set ...

. His monograph "Singularity Theory and Gravitational Lensing" developed a mathematical theory of

gravitational lensing A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer. This effect is known ...

. 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 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 Dangriga Airpo ...

Belize Belize (; bzj, Bileez) is a Caribbean and Central American country on the northeastern 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 wate ...

(formerly Stann Creek Town,

British Honduras British Honduras was a British Crown colony on the east coast of Central America, south of Mexico, from 1783 to 1964, then a self-governing colony, renamed Belize in 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'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid d ...

'', May 27, 2003. Petters earned a B.A./M.A. in Mathematics and

Physics Physics is the natural science that studies matter, its 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 which r ...

from Hunter College, CUNY in 1986 with a thesis on "The Mathematical Theory of General Relativity", and began his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

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 research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

Department of Physics ''in absentia'' from MIT. Petters earned his Ph.D. in mathematics in 1991 under advisors

Bertram Kostant Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics. Early life and education Kostant grew up in New York City, where he gradua ...

(MIT) and

David Spergel David Nathaniel Spergel is an American theoretical astrophysicist and the Emeritus Charles A. Young Professor of Astronomy on the Class of 1897 Foundation at Princeton University. Since 2021, he has been the President of the Simons Foundation ...

(Princeton University). He remained at MIT for two years as an instructor of pure mathematics (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 ''

'', NOVA, The HistoryMakers (a digital archive of oral histories featuring African-Americans and preserved at the

Library of Congress The Library of Congress (LOC) is the research library that officially serves the United States Congress and is the ''de facto'' national library of the United States. It is the oldest federal cultural institution in the country. The library ...

), Big Think, and Duke University's news outlet, ''The Chronicle''.

Research

Petters is known for his work in the mathematical theory of

. 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. His ...

(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, binary pulsars, and

gravitational microlensing Gravitational microlensing is an astronomical phenomenon due to 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, astronomers ...

scenarios to make testable predictions about lensed images and their time delays. Another paper took on the difficult issue of how to test

hyperspace In science fiction, hyperspace (also known as nulspace, subspace, overspace, jumpspace and similar terms) is a concept relating to higher dimensions as well as parallel universes and a faster-than-light (FTL) method of interstellar travel. ...

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 typically ...

observationally using the realistic case of lensing by a Kerr black hole. 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. 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 (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 Research Fellowship in Mathematics (1998), and a CAREER award from the

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National ...

(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, 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—

, 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 ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the List of municipalities in California, largest city in the U.S. state, state of California and the List of United States cities by population, sec ...

, where he received honors from the mayor and from the Confederation Centroamericana (COFECA). Petters was recognized by

Mathematically Gifted & Black Mathematically Gifted & Black (MGB) is a website that features the accomplishments of black scholars in mathematical sciences. In addition to highlighting the work and lives of established mathematicians in the African Diaspora, the platform aims ...

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 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 people 21st-century African-American people African-American physicists