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
 Petters, AO; Dong, X, An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition
(June, 2016),
pp. 483 pages, SPRINGER, ISBN 1493937812 [abs]
 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
 Petters, A, PSE Mathematics
(2007), BRC Publishing
 Petters, A, Algebra, Geometry, and Trignonometry
(2007), BRC Publishing
 Petters, A, Scientific Reasoning
(2007), BRC Publishing
 Petters, AO; Levine, H; Wambsganss, J, Singularity Theory and Gravitational Lensing, Progress in Mathematical Physics, Volume 21
(June, 2001),
pp. 603 pages, Springer Science & Business Media, ISBN 0817636684 [0021045375379126] [abs]
 Kayser, R; Schramm, T; Nieser, L, Gravitational lenses proceedings of a conference held in Hamburg, Germany, 913 September 1991
(1992),
pp. 399 pages, SpringerVerlag
Papers Published
 Aazami, AB; Keeton, CR; Petters, AO, Magnification cross sections for the elliptic umbilic caustic surface,
Universe, vol. 5 no. 7
(July, 2019) [doi] [abs]
 Aazami, AB; Keeton, CR; Petters, AO, Lensing by Kerr black holes. II: Analytical study of quasiequatorial lensing observables,
Journal of Mathematical Physics, vol. 52 no. 10
(October, 2011),
pp. 102501102501, AIP Publishing, ISSN 00222488 [doi] [abs]
 Aazami, AB; Keeton, CR; Petters, AO, Lensing by Kerr black holes. I. General lens equation and magnification formula,
Journal of Mathematical Physics, vol. 52 no. 9
(September, 2011),
pp. 092502092502, AIP Publishing, ISSN 00222488 [doi] [abs]
 Aazami, AB; Petters, AO; Rabin, JM, Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing,
Journal of Mathematical Physics, vol. 52 no. 2
(February, 2011),
pp. 022501022501, AIP Publishing, ISSN 00222488 [doi] [abs]
 Petters, AO, Gravity's action on light,
Notices of the American Mathematical Society, vol. 57 no. 11
(December, 2010),
pp. 13921409, ISSN 00029920
 Petters, AO; Werner, MC, Mathematics of gravitational lensing: Multiple imaging and magnification,
General Relativity and Gravitation, vol. 42 no. 9
(Fall, 2010),
pp. 20112046, Springer Nature, ISSN 00017701 [doi] [abs]
 Aazami, AB; Petters, AO, A universal magnification theorem. III. Caustics beyond codimension 5,
Journal of Mathematical Physics, vol. 51 no. 2
(Summer, 2010),
pp. 082501, ISSN 00222488 [doi] [abs]
 Petters, AO; Rider, B; Teguia, AM, A mathematical theory of stochastic microlensing. II. Random images, shear, and the KacRice formula,
Journal of Mathematical Physics, vol. 50 no. 12
(December, 2009),
pp. 122501122501, AIP Publishing, ISSN 00222488 [repository], [doi] [abs]
 Aazami, AB; Petters, AO, A universal magnification theorem. II. Generic caustics up to codimension five,
Journal of Mathematical Physics, vol. 50 no. 8
(September, 2009),
pp. 023503, ISSN 00222488 [repository], [doi] [abs]
 Petters, AO; Rider, B; Teguia, AM, A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps,
Journal of Mathematical Physics, vol. 50 no. 7
(August, 2009),
pp. 072503072503, AIP Publishing, ISSN 00222488 [doi] [abs]
 Aazami, AB; Petters, AO, A universal magnification theorem for higherorder caustic singularities,
Journal of Mathematical Physics, vol. 50 no. 3
(Spring, 2009),
pp. 032501032501, AIP Publishing, ISSN 00222488 [3447], [doi] [abs]
 Keeton, CR; Petters, AO, 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
(January, 2008),
pp. 17191721 [doi] [abs]
 Iyer, SV; Petters, AO, Light's bending angle due to black holes: From the photon sphere to infinity,
General Relativity and Gravitation, vol. 39 no. 10
(October, 2007),
pp. 15631582, Springer Nature, ISSN 00017701 [0611086], [doi] [abs]
 Werner, MC; Petters, AO, Magnification relations for Kerr lensing and testing cosmic censorship,
Physical Review D, vol. 76 no. 6
(September, 2007),
pp. 064024, American Physical Society (APS), ISSN 15507998 [0132], [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)
 Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects. III. Braneworld gravity,
Physical Review D, vol. 73 no. 10
(May, 2006),
pp. 104032, American Physical Society (APS), ISSN 15507998 [0603061], [doi] [abs]
 Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects. II. Probing postpostNewtonian metrics,
Physical Review D, vol. 73 no. 4
(March, 2006),
pp. 044024, American Physical Society (APS), ISSN 15507998 [0601053], [doi] [abs]
 Keeton, CR; Gaudi, BS; Petters, AO, Identifying lenses with smallscale structure. II. Fold lenses,
The Astrophysical Journal, vol. 635 no. 1 I
(December, 2005),
pp. 3559, IOP Publishing, ISSN 0004637X [doi] [abs]
 Keeton, CR; Petters, AO, Formalism for testing theories of gravity using lensing by compact objects: Static, spherically symmetric case,
Physical Review D, vol. 72 no. 10
(November, 2005),
pp. 104006, American Physical Society (APS), ISSN 15507998 [0511019], [doi] [abs]
 Keeton, C; Gaudi, S; Petters, AO, Identifying Lensing by SmallScale Structure. II. Fold Lenses,
Astrophysical Journal, vol. 635 no. 1 I
(November, 2005),
pp. 3535, ISSN 0004637X [0503452], [doi] [abs]
 Keeton, CR; Gaudi, BS; Petters, AO, Identifying lenses with smallscale structure. I. Cusp lenses,
The Astrophysical Journal, vol. 598 no. 1 I
(November, 2003),
pp. 138161, IOP Publishing, ISSN 0004637X [doi] [abs]
 Petters, AO, On relativistic corrections to microlensing effects: Applications to the Galactic black hole,
Monthly Notices of the Royal Astronomical Society, vol. 338 no. 2
(January, 2003),
pp. 457464, Oxford University Press (OUP) [0208500], [doi] [abs]
 Keeton, C; Gaudi, S; Petters, AO, Identifying Lensing by Substructure I. Cusp Lenses,
Astrophys. J., vol. 598 no. 1 I
(2003),
pp. 138, ISSN 0004637X [0210318], [doi] [abs]
 GAUDI, BS; PETTERS, AO, CENTER OF LIGHT CURVES FOR WHITNEY FOLD AND CUSP
(December, 2002),
pp. 21032104, World Scientific Publishing Company [doi]
 Gaudi, BS; Petters, AO, Gravitational microlensing near caustics. II. Cusps,
The Astrophysical Journal, vol. 580 no. 1 I
(November, 2002),
pp. 468489, IOP Publishing, ISSN 0004637X [0206162v2], [doi] [abs]
 Frittelli, S; Petters, AO, Wavefronts, caustic sheets, and caustic surfing in gravitational lensing,
Journal of Mathematical Physics, vol. 43 no. 11
(November, 2002),
pp. 55785611, AIP Publishing, ISSN 00222488 [0208135], [doi] [abs]
 Gaudi, BS; Petters, AO, Gravitational microlensing near caustics. I. Folds,
The Astrophysical Journal, vol. 574 no. 2 I
(August, 2002),
pp. 970984, IOP Publishing, ISSN 0004637X [0112531], [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
 Petters, AO; Wicklin, FJ, Fixed points due to gravitational lenses,
Journal of Mathematical Physics, vol. 39 no. 2
(January, 1998),
pp. 10111023, AIP Publishing [doi] [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)
 Petters, AO, Curvature of caustics and singularities of gravitational lenses,
Nonlinear Analysis: Theory, Methods & Applications, vol. 30 no. 1
(January, 1997),
pp. 627634, Elsevier BV, ISSN 0362546X [doi]
 Petters, AO, Multiplane gravitational lensing. III. Upper bound on number of images,
Journal of Mathematical Physics, vol. 38 no. 3
(January, 1997),
pp. 16051613, AIP Publishing [doi] [abs]
 Petters, AO; Witt, HJ, Bounds on number of cusps due to point mass gravitational lenses,
Journal of Mathematical Physics, vol. 37 no. 6
(June, 1996),
pp. 29202933, AIP Publishing [doi] [abs]
 Fetters, AO, Lower bounds on image magnification in gravitational lensing,
Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 452 no. 1949
(January, 1996),
pp. 14751490, The Royal Society, ISSN 13645021 [doi] [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)
 Petters, AO; Witt, H, 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]
 Petters, AO; Wicklin, FJ, New Caustic Phenomena In DoublePlane Lensing,
Symposium International Astronomical Union, vol. 173
(1996),
pp. 283284, Cambridge University Press (CUP) [doi] [abs]
 Petters, AO, A Cuspâ€”Counting Formula For Caustics Due To Multiplane Gravitational Lensing,
Symposium International Astronomical Union, vol. 173 no. 173
(1996),
pp. 281282, Cambridge University Press (CUP), ISSN 00741809 [Gateway.cgi], [doi] [abs]
 Petters, AO; Wicklin, FJ, 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, Oxford University Press (OUP), ISSN 00358711 [Gateway.cgi], [doi]
 Petters, AO, Multiplane gravitational lensing. II. Global geometry of caustics,
Journal of Mathematical Physics, vol. 36 no. 8
(January, 1995),
pp. 42764295, AIP Publishing, ISSN 00222488 [doi] [abs]
 Petters, AO, Multiplane gravitational lensing. I. Morse theory and image counting,
Journal of Mathematical Physics, vol. 36 no. 8
(January, 1995),
pp. 42634275, AIP Publishing, ISSN 00222488 [doi] [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)
 Witt, HJ; Petters, AO, Singularities of the one and twopoint mass gravitational lens,
Journal of Mathematical Physics, vol. 34 no. 9
(January, 1993),
pp. 40934111, AIP Publishing, ISSN 00222488 [doi] [abs]
 Petters, AO, Arnold's singularity theory and gravitational lensing,
Journal of Mathematical Physics, vol. 34 no. 8
(January, 1993),
pp. 35553581, AIP Publishing, ISSN 00222488 [doi] [abs]
 Levine, HI; Petters, AO; Wambsganss, J, Applications of singularity theory to gravitational lensing. I. Multiple lens planes,
Journal of Mathematical Physics, vol. 34 no. 10
(January, 1993),
pp. 47814808, AIP Publishing, ISSN 00222488 [doi] [abs]
 Levine, H; Petters, AO, New Caustic Singularities in Multiple Lens Plane Gravitational Lensing,
Astron. Astrophys., vol. 272 no. L17
(1993),
pp. L17L19, EDP SCIENCES S A
 Levine, H; Petters, AO; Wambsganss, J, Applications of Singularity Theory to Gravitational Lensing,
J. Math. Phys., vol. 34 no. 10
(1993),
pp. 4781, ISSN 00222488 [abs]
 Petters, AO, Morse theory and gravitational microlensing,
Journal of Mathematical Physics, vol. 33 no. 5
(January, 1992),
pp. 19151931, AIP Publishing, ISSN 00222488 [doi] [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)
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

