**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, Benque-Belize - A.O. Petters,
*Scientific Reasoning: Student and Teacher Editions*(July, 2007), BRC, Benque-Belize - A.O. Petters,
*PSE Mathematics: Student and Teacher Editions*(February, 2007), BRC, Benque-Belize - A. O. Petters, H. Levine, and J. Wambsganss,
*Singularity Theory and Gravitational Lensing*, Progress in Mathematical Physics, Volume 21 (June, 2001), Birkhauser

**Papers Published**

- Aazami, AB; Keeton, CR; Petters, AO,
*Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables*, Journal of Mathematical Physics, vol. 52 no. 10 (October, 2011), pp. 102501-102501, AIP Publishing, ISSN 0022-2488 - 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. 092502-092502, AIP Publishing, ISSN 0022-2488 - 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. 022501-022501, AIP Publishing, ISSN 0022-2488 - Petters, AO; Werner, MC,
*Mathematics of gravitational lensing: Multiple imaging and magnification*, General Relativity and Gravitation, vol. 42 no. 9 (Fall, 2010), pp. 2011-2046, Springer Nature, ISSN 0001-7701 - 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 0022-2488 - Petters, AO,
*Gravity's action on light*, Notices of the American Mathematical Society, vol. 57 no. 11 (2010), pp. 1392-1409, ISSN 0002-9920 - Petters, AO; Rider, B; Teguia, AM,
*A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula*, Journal of Mathematical Physics, vol. 50 no. 12 (December, 2009), pp. 122501-122501, AIP Publishing, ISSN 0022-2488 - 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 0022-2488 - 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. 072503-072503, AIP Publishing, ISSN 0022-2488 - Aazami, AB; Petters, AO,
*A universal magnification theorem for higher-order caustic singularities*, Journal of Mathematical Physics, vol. 50 no. 3 (Spring, 2009), pp. 032501-032501, AIP Publishing, ISSN 0022-2488 - 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 (December, 2008), pp. 1719-1721 - 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. 1563-1582, Springer Nature, ISSN 0001-7701 - 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 1550-7998 - 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 1550-7998 - Keeton, CR; Petters, AO,
*Formalism for testing theories of gravity using lensing by compact objects. II. Probing post-post-Newtonian metrics*, Physical Review D, vol. 73 no. 4 (March, 2006), pp. 044024, American Physical Society (APS), ISSN 1550-7998 - Keeton, CR; Gaudi, BS; Petters, AO,
*Identifying lenses with small-scale structure. II. Fold lenses*, The Astrophysical Journal, vol. 635 no. 1 I (December, 2005), pp. 35-59, IOP Publishing, ISSN 0004-637X - 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 1550-7998 - Keeton, C; Gaudi, S; Petters, AO,
*Identifying Lensing by Substructure II. Fold Lenses*, Astrophysical Journal, vol. 635 no. 1 I (November, 2005), pp. 35, ISSN 0004-637X - 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. 457-464, Oxford University Press (OUP) - Keeton, C; Gaudi, S; Petters, AO,
*Identifying Lensing by Substructure I. Cusp Lenses*, Astrophys. J., vol. 598 no. 1 I (2003), pp. 138, ISSN 0004-637X - Keeton, CR; Gaudi, BS; Petters, AO,
*Identifying lenses with small-scale structure. I. Cusp lenses*, The Astrophysical Journal, vol. 598 no. 1 I (2003), pp. 138-161, IOP Publishing, ISSN 0004-637X - Frittelli, S; Petters, AO,
*Wavefronts, caustic sheets, and caustic surfing in gravitational lensing*, Journal of Mathematical Physics, vol. 43 no. 11 (November, 2002), pp. 5578-5611, AIP Publishing, ISSN 0022-2488 - Gaudi, BS; Petters, AO,
*Gravitational microlensing near caustics. I. Folds*, The Astrophysical Journal, vol. 574 no. 2 I (August, 2002), pp. 970-984, IOP Publishing, ISSN 0004-637X - Gaudi, BS; Petters, AO,
*Gravitational microlensing near caustics. II. Cusps*, The Astrophysical Journal, vol. 580 no. 1 I (2002), pp. 468-489, IOP Publishing, ISSN 0004-637X - 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) - Petters, AO; Wicklin, FJ,
*Fixed points due to gravitational lenses*, Journal of Mathematical Physics, vol. 39 no. 2 (January, 1998), pp. 1011-1023, AIP Publishing - A. O. Petters, 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) (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. 627-634, Elsevier BV, ISSN 0362-546X - Petters, AO,
*Multiplane gravitational lensing. III. Upper bound on number of images*, Journal of Mathematical Physics, vol. 38 no. 3 (January, 1997), pp. 1605-1613, AIP Publishing - 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. 2920-2933, AIP Publishing - Fetters, AO,
*Lower bounds on image magnification in gravitational lensing*, Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 452 no. 1949 (January, 1996), pp. 1475-1490, The Royal Society, ISSN 1364-5021 - 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. 2920-2933 - Petters, AO; Wicklin, FJ,
*New Caustic Phenomena In Double-Plane Lensing*, Symposium International Astronomical Union, vol. 173 (1996), pp. 283-284, Cambridge University Press (CUP) - Petters, AO,
*A cusp - Counting formula for caustics due to multiplane gravitational lensing*, Symposium International Astronomical Union no. 173 (1996), pp. 281-282, ISSN 0074-1809 - Petters, AO; Wicklin, FJ,
*Caustics of the double-plane two-point-mass gravitational lens with continuous matter and shear*, Monthly Notices of the Royal Astronomical Society, vol. 277 no. 4 (Summer, 1995), pp. 1399-1403, Oxford University Press (OUP), ISSN 0035-8711 - Petters, AO,
*Multiplane gravitational lensing. II. Global geometry of caustics*, Journal of Mathematical Physics, vol. 36 no. 8 (January, 1995), pp. 4276-4295, AIP Publishing, ISSN 0022-2488 - Petters, AO,
*Multiplane gravitational lensing. I. Morse theory and image counting*, Journal of Mathematical Physics, vol. 36 no. 8 (January, 1995), pp. 4263-4275, AIP Publishing, ISSN 0022-2488 - 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, Fontenany-St Cloud (1994) - Witt, HJ; Petters, AO,
*Singularities of the one‐ and two‐point mass gravitational lens*, Journal of Mathematical Physics, vol. 34 no. 9 (September, 1993), pp. 4093-4111, AIP Publishing, ISSN 0022-2488 - Petters, AO,
*Arnold's singularity theory and gravitational lensing*, Journal of Mathematical Physics, vol. 34 no. 8 (January, 1993), pp. 3555-3581, AIP Publishing, ISSN 0022-2488 - 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. 4781-4808, AIP Publishing, ISSN 0022-2488 - Levine, H; Petters, AO,
*New Caustic Singularities in Multiple Lens Plane Gravitational Lensing*, Astron. Astrophys., vol. 272 no. L17 (1993) - Levine, H; Petters, AO; Wambsganss, J,
*Applications of Singularity Theory to Gravitational Lensing*, J. Math. Phys., vol. 34 no. 10 (1993), pp. 4781, ISSN 0022-2488 - Petters, AO,
*Morse theory and gravitational microlensing*, Journal of Mathematical Physics, vol. 33 no. 5 (January, 1992), pp. 1915-1931, AIP Publishing, ISSN 0022-2488 - 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)