Arlie O. Petters

 

Birthplace: Dangriga, Belize
citizen. U.S. A.

B.A./M.A. (Mathematics and Physics) Hunter College 1986

Ph.D. (Mathematics) Massachusettes Institute of Technology 1991.

Area of Research Interests: Mathematical Physics

Read articles on Petters:

  1. A Journey to Bridge Math and the Cosmos
  2. Star Professor

Full Professor of Physics and of Mathematics Departments of Duke University and a Bass Fellow.

Petters's book on Gravitational Lensing is considered a tour de force in mathematical physics and he has been called a founder of mathematical astronomy.

Arlie Petters emigrated to the U.S. in 1979 and he has been a U.S. citizen since 1990. He earned his B.A./M.A. Hunter College - CUNY, 1986 (Mathematics, with additional major in Physics). During the summers, 1986-90 he was a Member of Technical Staff at Bell Laboratories (Lucent Technologies). He earned his Ph.D. in Mathematics from M.I.T (Massachusettes Institute of Technology-1991). From 1991-93, he was an Instructor of Pure Math at M.I.T. Dr. Arlie Petters has been a Visiting Mathematician at Oxford University Mathematical Institute, the Max-Planck-Instute für Astrophsik, and the Geometry Center of The University of Minnesota. From 1993-1998, Dr. Petters was an Assistant Professor in Mathematics at Princeton University and during 1996 to 1998 he served as co-Director of Graduate Studies in Mathematics.

In 1998, Petters was awarded Mathematics most prestigious Sloan Research Fellowship as well as a 5 year National Science Foundation Career Grant. In the fall of 1998, Dr. Arlie Petters joined Duke University, where he holds the William & Sue Gross Chair in the Mathematics Department where he is the first African American tenured faculty in the sciences/mathematics.

In 2003, he became a Full Professor at Duke University and is the first black elected
to Duke's prestigious Bass Society of Fellows..

In November 2002, he became the first recipient of the Blackwell-Tapia Prize (acceptance speech).

His personal home page: http://www.math.duke.edu/~petters/
Email: petters@math.duke.edu

AWARDS

William and Sue Gross Endowed Chair (1998-2003)
CAREER Grant Award - National Science Foundation (1998-2003)
Alfred P. Sloan Research Fellowship (1998-2002)
Belizeans in Solidarity Award for Outstanding Academic Achievement (1996)
Sigma Xi (Elected 1992, MIT Chapter)
Bell Labs Cooperative Research Fellowship Award (1986-1991)
Hall of Fame of Hunter College (CUNY) for his research work in mathematical physics
Blackwell-Tapia Prize (2002)

RESEARCH NOTES

Dr. Petters is chiefly interested in the Mathematical Theory of Gravitational Lensing and related areas (Singularity Theory, General Relativity, Theoretical Astrophysics). He has published 30 papers and one book, chiefly in the area Gravitational Lensing. It has been said that he founded the field of Mathematical Astronomy. DBelow is his research statement.

"Currently, I am working on developing a general mathematical theory of light deflection in weak gravitational fields, and investigating the observational consequences of the theorems in such a theory. This is done by addressing a series of problems touching on several aspects of gravitational lensing: multiple imaging, magnification, critical curves and caustics, and mass reconstruction. These issues are treated not only for the single lens plane case, but for any finite number of lens planes. My goal is to emphasize the stable and generic features of lensing, drawing conclusions essentially independent of the details (especially, the oversimplifying approximations and assumptions) of a chosen lens system model. To obtain such "universal'' results, one must employ tools from singularity theory. At the same time, I also analyze in-depth specific models that are physically realistic. My research involves collorations with mathematicians, astrophysicists, and computer scientists."

A first step towards the aforementioned mathematical theory appears in the book: Singularity Theory and Gravitational Lensing.

BOOKS

A. O. Petters, H. I. Levine, and J. Wambsganss Singularity Theory and Gravitational Lensing, BirkhSuser, Boston, 2000.

SELECTED PUBLICATIONS

In Press:

1. C. Keeton, S. Gaudi, and A. O. Petters, Identifying Lensing by Substructure I. Cusp Lenses, submitted (2002). See astro-ph/0210318 .
2. A. O. Petters, On Relativistic Corrections to Microlensing Effects: Applications to the Galactic Black Hole, MNRAS (2002). In press. See astro-ph/0208500 .

PUBLISHED

  1. (with S. Frittelli), Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing, J. Math. Phys., 43 , November (2002).
  2. (with B. S. Gaudi), Gravitational Microlensing Near Caustics I: Folds, Astrophys. J., 574 , 970 (2002).
  3. Stable Lens Systems, Lensed Image Magnification, and Magnification Cross Sections, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  4. (with S. Frittelli), Wavefront Singularities due to an Elliptical Potential, Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  5. (with B. S. Gaudi), Center of Light Curves for Whitney Fold and Cusp , Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).
  6. (with H. I. Levine and J. Wambsganss), Singularity Theory and Gravitational Lensing, Birkhauser, Boston, 2000.
  7. (with F. J. Wicklin) Fixed Points Due to Gravitational Lenses, J. Math. Phys., 39, 1011 (1998).
  8. Some Global Results on Gravitational Lensing, Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore, 1997).
  9. (with S. Mao, and H. Witt), Properties of Point Mass Lenses on a Regular Polygon and the Problem of Maximum Number of Lensed Images, Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity , ed. R. Ruffini (World Scientific, Singapore, 1997). See astro-ph/0708111.
  10. (with F.J. Wicklin), Counting Formulas and Bounds on Number of Fixed Points Due to Point-Mass Lenses, Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity 1997, ed. R. Ruffini (World Scientific, Singapore).
  11. Multiplane gravitational lensing: III. Upper bound on number of images, J. Math. Phys. 38 (1997), 1605--1613.
  12. Curvature of Caustics and Singularities of Gravitational Lenses, Proceedings of the Second World Congress of Nonlinear Analysts ed. V. Lakshmikantham (Elsevier Science Ltd., Oxford, 1997).
  13. (with F.J. Wicklin), New Caustic Phenomena for Caustics in Double-Plane Lensing, Astrophysical Applications of Gravitational Lensing , ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  14. Mathematical Aspects of Gravitational Lensing, 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).
  15. A Cusp-Counting Formula for Caustics due to Multiplane Gravitational Lensing, in Astrophysical Applications of Gravitational Lensing , ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).
  16. (with H. J. Witt) Bounds on number of cusps due to point mass gravitational lenses, J. Math. Phys. 37 (1996), 2920--2933.
  17. Lower Bounds on Image Magnification in Gravitational Lensing, Proc. R. Soc. Lond. A, 452 , 1 (1996).
  18. (with F.J. Wicklin), Caustics of the Double-Plane Two Point-Mass Gravitational Lens with Continuous Matter and Shear, Mon. Not. R. Astron. Soc., 277 , 1399 (1995).
  19. Multiplane gravitational lensing: II. Global geometry of caustics, J. Math. Phys. 36 (1995), 4276--4295.
  20. Multiplane gravitational lensing: I. Morse theory and image counting, J. Math. Phys. 36 (1995), 4263--4275.
  21. (with H. Levine), Singularities and Gravitational Lensing, in Passion des Formes: Hommage a' Rene' Thom , vol. 1, ed. M. Porte (E.N.S. Edition, Fontenay-St Cloud, 1994).
  22. (with H. Levine and J. Wambsganss) Applications of singularity theory to gravitational lensing: I. Multiple lens planes, J. Math. Phys. 34 (1993), 4781--4808.
  23. (with H. Levine), New Caustic Singularities in Multiple Lens Plane Gravitational Lensing, Astron. Astrophys., 272 , L17 (1993).
  24. Arnold's Singularity Theory and Gravitational Lensing, J. Math. Phys., 34 , 3555 (1993).
  25. (with Hans J. Witt) Singularities of the one- and two-point mass gravitational lens, J. Math. Phys. 34 (1993), 4093--4111.
  26. (with D. Spergel) An Analytical Approach to Quasar Variability due to Microlensing in Gravitational Lenses , , in Gravitational Lenses , eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Berlin, 1992).
  27. Morse theory and gravitational microlensing, J. Math. Phys. 33 (1992), 1915--1931. ALSO in , Gravitational Lenses , eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Berlin, 1992).

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