Math @ Duke

Books
 A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes
(Spring, 2017), Springer, in preparation
 A. O. Petters and X. Dong, An Introduction to Mathematical Finance: Understanding and Building Financial Intuition, SUMAT
(Winter, 2016), 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
 AB Aazami, CR Keeton and AO Petters, Lensing by Kerr black holes. II: Analytical study of quasiequatorial lensing observables,
Journal of Mathematical Physics, vol. 52 no. 10
(2011),
pp. 102501, ISSN 00222488 [doi] [abs]
 AB Aazami, AO Petters and JM Rabin, Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing,
Journal of Mathematical Physics, vol. 52 no. 2
(2011), ISSN 00222488 [doi] [abs]
 AB Aazami, CR Keeton and AO Petters, Lensing by Kerr black holes. I. General lens equation and magnification formula,
Journal of Mathematical Physics, vol. 52 no. 9
(2011),
pp. 092502, ISSN 00222488 [doi] [abs]
 AO Petters, Gravity's action on light,
Notices of the American Mathematical Society, vol. 57 no. 11
(2010),
pp. 13921409, ISSN 00029920
 AO Petters and MC Werner, Mathematics of gravitational lensing: Multiple imaging and magnification,
General Relativity and Gravitation, vol. 42 no. 9
(Fall, 2010),
pp. 20112046, ISSN 00017701 [doi] [abs]
 AB Aazami and AO Petters, A universal magnification theorem. III. Caustics beyond codimension 5,
Journal of Mathematical Physics, vol. 51 no. 2
(2010),
pp. 023503, ISSN 00222488 [DukeSpace], [doi] [abs]
 AO Petters, B Rider and AM Teguia, A mathematical theory of stochastic microlensing. II. Random images, shear, and the KacRice formula,
Journal of Mathematical Physics, vol. 50 no. 12
(2009),
pp. 122501, ISSN 00222488 [DukeSpace], [doi] [abs]
 AO Petters, B Rider and AM Teguia, A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps,
Journal of Mathematical Physics, vol. 50 no. 7
(June, 2009),
pp. 072503, ISSN 00222488 [doi] [abs]
 AB Aazami and AO Petters, A universal magnification theorem. II. Generic caustics up to codimension five,
Journal of Mathematical Physics, vol. 50 no. 8
(Summer, 2009),
pp. 082501, ISSN 00222488 [doi] [abs]
 AB Aazami and AO Petters, A universal magnification theorem for higherorder caustic singularities,
Journal of Mathematical Physics, vol. 50 no. 3
(Spring, 2009),
pp. 032501, ISSN 00222488 [3447], [doi] [abs]
 CR Keeton and AO Petters, Testing theories of gravity with black hole lensing,
11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories  Proc. of the MG11 Meeting on General Relativity
(December, 2008),
pp. 17191721 [abs]
 MC Werner and AO Petters, Magnification relations for Kerr lensing and testing cosmic censorship,
Physical Review D  Particles, Fields, Gravitation and Cosmology, vol. 76 no. 6
(September, 2007),
pp. 064024, ISSN 15507998 [0132], [doi] [abs]
 SV Iyer and AO Petters, Light's bending angle due to black holes: From the photon sphere to infinity,
General Relativity and Gravitation, vol. 39 no. 10
(2007),
pp. 15631582, ISSN 00017701 [0611086], [doi] [abs]
 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)
 CR Keeton and AO Petters, Formalism for testing theories of gravity using lensing by compact objects. III. Braneworld gravity,
Physical Review D  Particles, Fields, Gravitation and Cosmology, vol. 73 no. 10
(2006),
pp. 104032, ISSN 15507998 [0603061], [doi] [abs]
 CR Keeton and AO Petters, Formalism for testing theories of gravity using lensing by compact objects. II. Probing postpostNewtonian metrics,
Physical Review D  Particles, Fields, Gravitation and Cosmology, vol. 73 no. 4
(2006),
pp. 044024, ISSN 15507998 [0601053], [doi] [abs]
 C Keeton, S Gaudi and AO Petters, Identifying Lensing by Substructure II. Fold Lenses,
Astrophysical Journal, vol. 635 no. 1 I
(2005),
pp. 35, ISSN 0004637X [0503452], [doi] [abs]
 CR Keeton and AO Petters, Formalism for testing theories of gravity using lensing by compact objects: Static, spherically symmetric case,
Physical Review D  Particles, Fields, Gravitation and Cosmology, vol. 72 no. 10
(2005),
pp. 104006, ISSN 15507998 [0511019], [doi] [abs]
 CR Keeton, BS Gaudi and AO Petters, Identifying lenses with smallscale structure. II. Fold lenses,
Astrophysical Journal, vol. 635 no. 1 I
(2005),
pp. 3559, ISSN 0004637X [doi] [abs]
 C Keeton, S Gaudi and AO Petters, Identifying Lensing by Substructure I. Cusp Lenses,
Astrophys. J., vol. 598 no. 1 I
(2003),
pp. 138, ISSN 0004637X [0210318], [doi] [abs]
 AO Petters, On relativistic corrections to microlensing effects: Applications to the Galactic black hole,
Monthly Notices of the Royal Astronomical Society, vol. 338 no. 2
(2003),
pp. 457464 [0208500], [doi] [abs]
 CR Keeton, BS Gaudi and AO Petters, Identifying lenses with smallscale structure. I. Cusp lenses,
Astrophysical Journal, vol. 598 no. 1 I
(2003),
pp. 138161, ISSN 0004637X [doi] [abs]
 BS Gaudi and AO Petters, Gravitational Microlensing Near Caustics II: Cusps,
Astrophys.J., vol. 580 no. 1 I
(June, 2002),
pp. 468489, ISSN 0004637X [0206162v2], [doi] [abs]
 BS Gaudi and AO Petters, Gravitational microlensing near caustics. I. Folds,
Astrophysical Journal, vol. 574 no. 2 I
(2002),
pp. 970984, ISSN 0004637X [0112531], [doi] [abs]
 S Frittelli and AO Petters, Wavefronts, caustic sheets, and caustic surfing in gravitational lensing,
Journal of Mathematical Physics, vol. 43 no. 11
(2002),
pp. 55785611, ISSN 00222488 [0208135], [doi] [abs]
 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)
 AO Petters and FJ Wicklin, Fixed points due to gravitational lenses,
Journal of Mathematical Physics, vol. 39 no. 2
(1998),
pp. 10111023 [abs]
 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)
 AO Petters, Curvature of caustics and singularities of gravitational lenses,
Nonlinear Analysis, Theory, Methods and Applications, vol. 30 no. 1
(1997),
pp. 627634, ISSN 0362546X
 AO Petters, Multiplane gravitational lensing. III. Upper bound on number of images,
Journal of Mathematical Physics, vol. 38 no. 3
(1997),
pp. 16051613 [abs]
 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)
 AO 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),
pp. 29202933 [doi] [abs]
 AO Petters and FJ 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)
 AO Petters, A cusp  Counting formula for caustics due to multiplane gravitational lensing,
ASTROPHYSICAL APPLICATIONS OF GRAVITATIONAL LENSING no. 173
(1996),
pp. 281282, ISSN 00741809 [Gateway.cgi]
 AO Fetters, Lower bounds on image magnification in gravitational lensing,
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 452 no. 1949
(1996),
pp. 14751490, ISSN 13645021 [abs]
 AO Petters and HJ Witt, Bounds on number of cusps due to point mass gravitational lenses,
Journal of Mathematical Physics, vol. 37 no. 6
(1996),
pp. 29202933 [doi] [abs]
 AO Petters and FJ Wicklin, Caustics of the doubleplane twopointmass gravitational lens with continuous matter and shear,
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, vol. 277 no. 4
(Summer, 1995),
pp. 13991403, ISSN 00358711 [Gateway.cgi]
 AO Petters, Multiplane gravitational lensing. II. Global geometry of caustics,
Journal of Mathematical Physics, vol. 36 no. 8
(April, 1995),
pp. 42764295, ISSN 00222488 [abs]
 AO Petters, Multiplane gravitational lensing. I. Morse theory and image counting,
Journal of Mathematical Physics, vol. 36 no. 8
(March, 1995),
pp. 42634275, ISSN 00222488 [abs]
 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)
 HJ Witt and AO Petters, Singularities of the one and twopoint mass gravitational lens,
Journal of Mathematical Physics, vol. 34 no. 9
(1993),
pp. 40934111, ISSN 00222488 [abs]
 AO Petters, Arnold's singularity theory and gravitational lensing,
Journal of Mathematical Physics, vol. 34 no. 8
(1993),
pp. 35553581, ISSN 00222488 [abs]
 H Levine and AO Petters, New Caustic Singularities in Multiple Lens Plane Gravitational Lensing,
Astron. Astrophys., vol. 272 no. L17
(1993)
 H Levine, AO Petters and J Wambsganss, Applications of Singularity Theory to Gravitational Lensing,
J. Math. Phys., vol. 34 no. 10
(1993),
pp. 4781, ISSN 00222488 [abs]
 HI Levine, AO Petters and J Wambsganss, Applications of singularity theory to gravitational lensing. I. Multiple lens planes,
Journal of Mathematical Physics, vol. 34 no. 10
(1993),
pp. 47814808, ISSN 00222488 [abs]
 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)
 AO Petters, Morse theory and gravitational microlensing,
Journal of Mathematical Physics, vol. 33 no. 5
(1992),
pp. 19151931, ISSN 00222488 [abs]
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

