Math @ Duke
Research Interests for Arlie O. Petters
- 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
Singularity Theory and Gravitational Lensing
(A. O. Petters, H. Levine, and J. Wamsbganss).
Two layman articles about my research are at:
Prescription lens brings spinning black holes into focus
- Mathematical and Scientific Methods in Business Administration
Mathematical finance with applications
Entrepreneurship and business innovation in STEM fields (developing world)
My 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.
- Recent Publications
- 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
- 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
pp. 102501-102501, AIP Publishing, ISSN 0022-2488 [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
pp. 092502-092502, AIP Publishing, ISSN 0022-2488 [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
pp. 022501-022501, AIP Publishing, ISSN 0022-2488 [doi] [abs]
Duke University, Box 90320
Durham, NC 27708-0320