Arlie O. Petters
Professor of Economics
- Mathematical Physics
Mathematics - tools form differential geometry, singularities, and probability theory
Physics - problems connected to the interplay of gravity and light (gravitational lensing, general relativity, astrophysics, cosmology)
My current research in mathematical physics is on gravitational lensing, which is the study of how gravity acts on light. In particular, I utilizing weak and strong deflection gravitational lensing to characterize the geometry of spacetime around black holes, test theories of gravity, and probe the nature of dark matter on galactic scales. I employ tools from astrophysics, cosmology, general relativity, high energy physics, and a variety of mathematical fields (e.g., differential geometry, singularities, and probability theory).
A mathematical theory of gravitational lensing is presented in the monograph:
Singularity Theory and Gravitational Lensing (A. O. Petters, H. Levine, and J. Wamsbganss).
Two layman articles about my research are at:
Ripple Effect (Scott Huler).
Prescription lens brings spinning black holes into focus (Ashley Yeager).
- Mathematical and Scientific Methods in Business Administration
Mathematical finance with applications
Entrepreneurship and business innovation in STEM fields (developing world)
By current business administration activities are three-fold. First, I am co-authoring a text on Mathematical Finance with Xiaoying Dong, who is an Adjunct Assistant Professor in our department and a trader for over 20 years. This book is aimed at first year graduate students from mathematics, economics, physics, computer science, and engineering. Second, at Duke's Fuqua School of Business I supervise the finance concentration research projects of Executive M.B.A. students. These projects cover a variety of topics: company valuations, derivatives, portfolio theory, mergers and acquisitions, etc. Third, I am involved with sustainable business and environmentally friendly applications of Science, Technology, Engineering, and Mathematics (STEM) in a developing-world setting that integrates education and entrepreneurship. These efforts are being piloted in Belize in collaboration with the Petters Research Institute and through my appointment with Fuqua. The overall goal is to research innovative ways to help drive national development through applications of STEM tools.
- Ph.D., Massachusetts Institute of Technology 1991
- B.A., CUNY Hunter College 1986
- M.A., CUNY Hunter College 1986
Aazami, A. B., C. R. Keeton, and A. O. Petters. “Magnification cross sections for the elliptic umbilic caustic surface.” Universe 5, no. 7 (July 2, 2019). https://doi.org/10.3390/universe5070161. Full Text
Aazami, A. B., C. R. Keeton, and A. O. Petters. “Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables.” Journal of Mathematical Physics 52, no. 10 (October 5, 2011). https://doi.org/10.1063/1.3642616. Full Text
Aazami, A. B., C. R. Keeton, and A. O. Petters. “Lensing by Kerr black holes. I. General lens equation and magnification formula.” Journal of Mathematical Physics 52, no. 9 (September 23, 2011). https://doi.org/10.1063/1.3642614. Full Text
Aazami, A. B., A. O. Petters, and J. M. Rabin. “Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing.” Journal of Mathematical Physics 52, no. 2 (February 3, 2011). https://doi.org/10.1063/1.3545578. Full Text
Petters, A. O. “Gravity's action on light.” Notices of the American Mathematical Society 57, no. 11 (December 1, 2010): 1392–1409.
Petters, A. O., and M. C. Werner. “Mathematics of gravitational lensing: Multiple imaging and magnification.” General Relativity and Gravitation 42, no. 9 (March 30, 2010): 2011–46. https://doi.org/10.1007/s10714-010-0968-6. Full Text
Aazami, A. B., and A. O. Petters. “A universal magnification theorem. III. Caustics beyond codimension 5.” Journal of Mathematical Physics 51, no. 2 (February 1, 2010). https://doi.org/10.1063/1.3271043. Full Text Open Access Copy
Petters, A. O., B. Rider, and A. M. Teguia. “A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula.” Journal of Mathematical Physics 50, no. 12 (December 1, 2009). https://doi.org/10.1063/1.3267859. Full Text Open Access Copy
Aazami, A. B., and A. O. Petters. “A universal magnification theorem. II. Generic caustics up to codimension five.” Journal of Mathematical Physics 50, no. 8 (September 9, 2009). https://doi.org/10.1063/1.3179163. Full Text
Petters, A. O., B. Rider, and A. M. Teguia. “A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps.” Journal of Mathematical Physics 50, no. 7 (August 20, 2009). https://doi.org/10.1063/1.3158854. Full Text
Petters, Arlie O., and Xiaoying Dong. An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition. Springer, 2016.
Petters, Arlie. PSE Mathematics. Belize: BRC Publishing, 2007.
Petters, Arlie. Algebra, Geometry, and Trignonometry. Belize: BRC Publishing, 2007.
Petters, Arlie. Scientific Reasoning. Belize: BRC Publishing, 2007.
Petters, Arlie O., Harold Levine, and Joachim Wambsganss. Singularity Theory and Gravitational Lensing. Springer Science & Business Media, 2001.
Kayser, Rainer, Thomas Schramm, and Lars Nieser. Gravitational lenses proceedings of a conference held in Hamburg, Germany, 9-13 September 1991. Springer Verlag, 1992.