Arlie O. Petters

Benjamin Powell Professor

Bass Fellow of Mathematics

(919) 660-2812
(919) 660-2821


Gravitational Lensing and Black Holes

An Introduction to Mathematical Finance: Understanding and Building Financial Intuition

Lensing by Kerr Black Holes. I. General Lens Equation and Magnification Formula
J. Math. Phys. (2011)

Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing
J. Math. Physics (2011)

Lensing by Kerr Black Holes. II. Analytical Study of Quasi-Equatorial Lensing Observables

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification
Gen. Rel. and Grav., Special Issue on Gravitational Lensing (2010)

A Universal Magnification Theorem III. Caustics Beyond Codimension Five
J. Math. Physics (2010)

A Universal Magnification Theorem II. Generic Caustics up to Codimension Five
J. Math. Physics (2009)

A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps
J. Math. Physics (2009)

  • Mathematical Physics

    Mathematics - tools form differential geometry, singularities, and probability theory

    Physics - problems connected to the interplay of gravity and light (gravitational lensing, general relativity, astrophysics, cosmology)

    My current research in mathematical physics is on gravitational lensing, which is the study of how gravity acts on light. In particular, I utilizing weak and strong deflection gravitational lensing to characterize the geometry of spacetime around black holes, test theories of gravity, and probe
    the nature of dark matter on galactic scales.
    I employ tools from astrophysics, cosmology, general relativity, high energy physics, and a variety of mathematical fields
    (e.g., differential geometry, singularities, and probability theory).

    A mathematical theory of gravitational lensing is presented in the

    Singularity Theory and Gravitational Lensing

    (A. O. Petters, H. Levine, and J. Wamsbganss).

    Two layman articles about my research are at:

    Ripple Effect

    (Scott Huler).

    Prescription lens brings spinning black holes into focus

    (Ashley Yeager).

  • Mathematical and Scientific Methods in Business Administration

    Mathematical finance with applications

    Entrepreneurship and business innovation in STEM fields (developing world)

    By current business administration activities are three-fold. First, I am co-authoring a text on Mathematical Finance with Xiaoying Dong, who is an Adjunct Assistant Professor in our department and a trader for over 20 years. This book is aimed at first year graduate students from mathematics, economics, physics, computer science, and engineering. Second, at Duke's Fuqua School of Business I supervise the finance concentration research projects of Executive M.B.A. students. These projects cover a variety of topics: company valuations, derivatives, portfolio theory, mergers and acquisitions, etc.
    Third, I am involved with sustainable business and environmentally friendly applications of Science, Technology, Engineering, and Mathematics (STEM) in a developing-world setting that integrates education and entrepreneurship. These efforts are being piloted in Belize in collaboration with the Petters Research Institute and through my appointment with Fuqua. The overall goal is to research innovative ways to help drive national development through applications of STEM tools.

Ph.D. - Massachusetts Institute of Technology
B.A. - CUNY Hunter College
M.A. - CUNY Hunter College

Testing Theories of Gravity with Black Hole Lensing
In Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini edited by . Summer, 2006; : .

2012 Grand Marshall, Central American Parade in L.A., COFECA
2012 Grand Marshal, 2012 Central American Parade in L.A., received certificate of recognition from the mayor of L.A.
2011 Caribbean American Heritage Award for Excellence in Science and Technology, The Institute of Caribbean Studies
2011 Robert L. Clark Award for Scientific Achievement, Bronx Community College of the City University of New York
2010 Chairman, Belize Prime Minister's Council of Science Advisers
2008 Honorary Doctor of Science, Hunter College of the City University of New York
2008 Honorary Doctor of Science, Hunter College of City University of New York
2008 Member of the Most Excellent Order of the British Empire, The Queen of England
2008 Named by the Queen of England to Membership in the Most Excellent Order of the British Empire
2007 Award for Service to the Educational Development of Belize, Belizean organization, Friends in Support of the Diocese of Belize, New York
2006 Portrait Inductee, National Academy of Sciences' Portrait Gallery of Distinguished African-American Scientists, National Academy of Sciences
2004 Mathematical Innovations Grant Award, National Science Foundation
2003 Martin Luther King, Jr. Visiting Professor of Physics, MIT
2002 Blackwell-Tapia Prize in Mathematics, Cornell University and the Mathematical Sciences Research Institute
2002 Blackwell-Tapia Prize in the Mathematical Sciences, Cornell University and the Mathematical Sciences Research Institute
1999 Hall of Fame inductee - Hunter College, C.U.N.Y., Hunter College, CUNY
1998 Alfred P. Sloan Research Fellowship Award, Alfred P. Sloan Foundation
1998 Bass Fellow, Society of Bass Fellows, Duke University
1998 Faculty Early Career Grant Award, Nation Science Foundation
1998 CAREER Grant Award, National Science Foundation
1998 Sloan Research Fellowship-Mathematics, Alfred P. Sloan Foundation
1996 Belizeans in Solidarity Award for Outstanding Academic Achievement, Belizean Organization, New York
1992 Sigma Xi, MIT
1986 Bell Laboratories Cooperative Fellowship Award, Bell Laboratories