Math @ Duke

Books
 A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes
(July, 2016), Springer, in preparation
 A. O. Petters and X. Dong, An Introduction to Mathematical Finance: Understanding and Building Financial Intuition, SUMAT
(July, 2015), Springer, in preparation
 A.O. Petters, Algebra, Geometry, and Trigonometry: Student and Teacher Editions
(August, 2007), BRC, BenqueBelize
 A.O. Petters, Scientific Reasoning: Student and Teacher Editions
(July, 2007), BRC, BenqueBelize
 A.O. Petters, PSE Mathematics: Student and Teacher Editions
(February, 2007), BRC, BenqueBelize
 A. O. Petters, H. Levine, and J. Wambsganss, Singularity Theory and Gravitational Lensing, Progress in Mathematical Physics, Volume 21
(June, 2001), Birkhauser [0021045375379126]
Papers Published
 A. Aazami, C. Keeton, and A.O. Petters, Lensing by Kerr Black Holes. II. Analytical Study of QuasiEquatorial Lensing Observables, vol. 52
(2011),
pp. 102501
 A. Aazami, C. Keeton, and A.O. Petters, Lensing by Kerr Black Holes. I. General Lens Equation and Magnification Formula,
J. Math. Phys., vol. 52
(2011),
pp. 092502
 A. B. Aazami, A. O. Petters, and J. M. Rabin, Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing,
J. Math. Physics, vol. 52
(2011)
 A.O. Petters and M. C. Werner, Mathematics of Gravitational Lensing: Multiple Imaging and Magnification,
Gen. Rel. and Grav., Special Issue on Gravitational Lensing, vol. 42
(Fall, 2010),
pp. 2011
 A. Aazami and A.O. Petters, A Universal Magnification Theorem III. Caustics Beyond Codimension Five,
J. Math. Physics no. 51
(2010),
pp. 023503
 A. B. Aazami and A.O. Petters, A Universal Magnification Theorem II. Generic Caustics up to Codimension Five,
J. Math. Physics, vol. 50
(Summer, 2009),
pp. 082501
 A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps,
J. Math. Physics, vol. 50
(June, 2009),
pp. 072503
 A. M. Aazami and A.O. Petters, A Universal Magnification Theorem for HigherOrder Caustic Singularities,
J. Math. Phys., vol. 50
(Spring, 2009),
pp. 032501 [3447]
 A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the KacRice Formula,
J. Math. Physics, vol. 50
(2009),
pp. 122501
 M. C. Werner and A.O. Petters, Magnification Relations for Kerr Lensing and Testing Cosmic Censorship,
Physical Review D, vol. 76
(September, 2007),
pp. 064024 [0132]
 S. Iyer and A.O. Petters, Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity,
General Relativity and Gravitation, vol. 39
(2007),
pp. 1563 [0611086]
 C. Keeton and A.O. Petters, Testing Theories of Gravity with Black Hole Lensing,
in Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity, ed. R. Ruffini
(Summer, 2006)
 C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. III. Braneworld Gravity,
Phys. Rev. D, vol. 73
(2006),
pp. 104032 [0603061]
 C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. II. Probing PostPostNewtonian Metrics,
Phys. Rev. D, vol. 73
(2006),
pp. 044024 [0601053]
 C. Keeton and A.O. Petters, Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I. Static, Spherically Symmetric Case,
Physical Review D, vol. 72
(2005),
pp. 104006 [0511019]
 C. Keeton, S. Gaudi, and A.O. Petters, Identifying Lensing by Substructure II. Fold Lenses,
Astrophysical Journal, vol. 635
(2005),
pp. 35 [0503452]
 C. Keeton, S. Gaudi, and A.O. Petters, Identifying Lensing by Substructure I. Cusp Lenses,
Astrophys. J., vol. 598
(2003),
pp. 138 [0210318]
 A. O. Petters, On Relativistic Corrections to Microlensing Effects: Applications to the Galactic Black Hole,
Monthly Notices of the Royal Astronomical Society, vol. 338
(2003),
pp. 457 [0208500]
 S. Frittelli and A. O. Petters, Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing,
J. Math. Phys., vol. 43
(2002),
pp. 5578 [0208135]
 S. Gaudi and A. O. Petters, Gravitational Microlensing Near Caustics II: Cusps,
The Astrophysical Journal, vol. 580 no. 468
(2002) [0206162]
 S. Gaudi and A. O. Petters, Gravitational Microlensing Near Caustics I: Folds,
The Astrophysical Journal, 574, 970 (2002), vol. 574 no. 970
(2002) [0112531]
 A. O. Petters, 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
(2001), World Scientific, Singapore
 S. Frittelli and A. O. Petters, 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
(2001), World Scientific, Singapore
 B. S. Gaudi and A. O. Petters, 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)
 A. O. Petters, F. Wicklin, Fixed Points Due to Gravitational Lenses,
J. Math. Phys., 39, 1011
(1998)
 A. O. Petters, F.J. Wicklin, Counting Formulas and Bounds on Number of Fixed Points Due to PointMass Lenses,
Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity 1997, ed. R. Ruffini (World Scientific, Singapore)
(Summer, 1997)
 S. Mao, A. O. Petters, and H. Witt, Properties of Point Mass Lenses on a Regular Polygon and the Problem of Maximum Number of Lensed Images,
in Proceedings of the Eighth Marcel Grossman Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore)
(Summer, 1997)
 A. O. Petters, Some Global Results on Gravitational Lensing,
Proceedings of the Eight Marcel Grossman Meeting on General Relativity, ed. R. Ruffini (World Scientific, Singapore)
(Summer, 1997)
 A. O. Petters, 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)
 A. O. Petters, Multiplane Gravitational Lensing III. Upper Bound on Number of Images,
J. Math. Phys., vol. 38
(1997),
pp. 1605
 A. O. Petters, Lower Bounds on Image Magnification in Gravitational Lensing,
Proc. R. Soc. Lond. A, vol. 452
(1996),
pp. 1475
 A. O. Petters, A CuspCounting Formula for Caustics Due to Multiplane Gravitational Lensing,
Astrophysical Applications of Gravitational Lensing, eds. C.S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht)
(1996)
 A. O. Petters, Mathematical Aspects of Gravitational Lensing,
Proceedings of the Seventh Marcel Grossman Meeting on General Relativity, Vol. B, eds. R.T. Jantzen and G.M. Keiser (World Scientific, Singapore)
(1996)
 A. O. Petters and F.J. Wicklin, New Caustic Phenomena for Caustics in DoublePlane Lensing,
Astrophysical Applications of Gravitational Lensing, eds. C.S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht)
(1996)
 A. O. Petters and H. Witt, Bounds on Number of Cusps Due to Point Mass Gravitional Lenses with Continuous Matter and Shear,
J. Math. Phys., vol. 37 no. 2920
(1996)
 A. O. Petters, F.J. Wicklin, Caustics of the DoublePlane Two PointMass Gravitational Lens with Continuous Matter and Shear,
Mon. Not. R. Astron. Soc., vol. 277
(Summer, 1995),
pp. 1399
 A. O. Petters, Multiplane Gravitational Lensing II: Global Geometry of Caustics,
J. Math. Phys., vol. 36
(April, 1995),
pp. 4276
 A. O. Petters, Multiplane Gravitational Lensing I: Morse Theory and Image Counting,
J. Math. Phys., vol. 36
(March, 1995),
pp. 4263
 H. Levine and A. O. Petters, Singularities and Gravitational Lensing,
Passion des Formes: Hommage a Rene Thom,Vol. 1 (M. Porte, ed.) E.N.S. Edition, FontenanySt Cloud
(1994)
 H. Levine, A. O. Petters, and J. Wambsganss, Applications of Singularity Theory to Gravitational Lensing,
J. Math. Phys., vol. 34
(1993),
pp. 4781
 H. Witt and A. O. Petters, Singularities of the One and Two Point Mass Gravitational Lens,
J. Math. Phys., 34, 4781
(1993)
 H. Levine and A. O. Petters, New Caustic Singularities in Multiple Lens Plane Gravitational Lensing,
Astron. Astrophys., vol. 272 no. L17
(1993)
 A. O. Petters, Arnold's Singularity Theory and Gravitational Lensing,
J. Math. Phys., vol. 34
(1993),
pp. 3555
 A. O. Petters, Morse Theory and Gravitational Microlensing,
J. Math. Phys., vol. 33
(1992),
pp. 1915
 A. O. Petters and D. Spergel, An Analytical Approach to Quasar Variability due to Microlensing,
Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics, 406, Springer, Ber1in)
(1992)
 A. O. Petters, Morse Theory and Gravitational Microlensing,
Gravitational Lenses, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics 406, Springer, Ber1in)
(1992)
Other
 A.O. Petters, Singularities in Gravitational Microlensing, Ph.D. Thesis,
MIT, Department of Mathematics
(1991)


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

