Arlie O. Petters
Benjamin Powell Professor of Mathematics
- 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.
Aazami, AB, Keeton, CR, and Petters, AO. "Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables." Journal of Mathematical Physics 52.10 (October 5, 2011). Full Text
Aazami, AB, Keeton, CR, and Petters, AO. "Lensing by Kerr black holes. I. General lens equation and magnification formula." Journal of Mathematical Physics 52.9 (September 23, 2011). Full Text
Aazami, AB, Petters, AO, and Rabin, JM. "Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing." Journal of Mathematical Physics 52.2 (February 3, 2011). Full Text
Petters, AO, and Werner, MC. "Mathematics of gravitational lensing: Multiple imaging and magnification." General Relativity and Gravitation 42.9 (March 30, 2010): 2011-2046. Full Text
Aazami, AB, and Petters, AO. "A universal magnification theorem. III. Caustics beyond codimension 5." Journal of Mathematical Physics 51.2 (February 1, 2010). Full Text Open Access Copy
Petters, AO. "Gravity's action on light." Notices of the American Mathematical Society 57.11 (2010): 1392-1409.
Petters, AO, Rider, B, and Teguia, AM. "A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula." Journal of Mathematical Physics 50.12 (December 1, 2009). Full Text Open Access Copy
"A universal magnification theorem. II. Generic caustics up to codimension five." Journal of Mathematical Physics 50.8 (September 9, 2009). Full Text
Petters, AO, Rider, B, and Teguia, AM. "A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps." Journal of Mathematical Physics 50.7 (August 20, 2009). Full Text
Aazami, AB, and Petters, AO. "A universal magnification theorem for higher-order caustic singularities." Journal of Mathematical Physics 50.3 (April 13, 2009). Full Text