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.
Petters, A. O. “On relativistic corrections to microlensing effects: Applications to the Galactic black hole.” Monthly Notices of the Royal Astronomical Society, vol. 338, no. 2, Jan. 2003, pp. 457–64. Scopus, doi:10.1046/j.1365-8711.2003.06065.x. Full Text
Keeton, C., et al. “Identifying Lensing by Substructure I. Cusp Lenses.” Astrophys. J., vol. 598, 2003.
Gaudi, B. S., and A. O. Petters. “Gravitational microlensing near caustics. II. Cusps.” Astrophysical Journal, vol. 580, no. 1 I, Nov. 2002, pp. 468–89. Scopus, doi:10.1086/343114. Full Text
Frittelli, S., and A. O. Petters. “Wavefronts, caustic sheets, and caustic surfing in gravitational lensing.” Journal of Mathematical Physics, vol. 43, no. 11, Nov. 2002, pp. 5578–611. Scopus, doi:10.1063/1.1511790. Full Text
Gaudi, B. S., and A. O. Petters. “Gravitational microlensing near caustics. I. Folds.” Astrophysical Journal, vol. 574, no. 2 I, Aug. 2002, pp. 970–84. Scopus, doi:10.1086/341063. Full Text
Petters, A. O. “Multiplane gravitational lensing. III. Upper bound on number of images.” Journal of Mathematical Physics, vol. 38, no. 3, Jan. 1997, pp. 1605–13. Scopus, doi:10.1063/1.531818. Full Text
Petters, A. O. “Curvature of caustics and singularities of gravitational lenses.” Nonlinear Analysis, Theory, Methods and Applications, vol. 30, no. 1, Jan. 1997, pp. 627–34. Scopus, doi:10.1016/S0362-546X(97)00068-0. Full Text
Petters, A. O., and H. J. Witt. “Bounds on number of cusps due to point mass gravitational lenses.” Journal of Mathematical Physics, vol. 37, no. 6, June 1996, pp. 2920–33. Scopus, doi:10.1063/1.531630. Full Text
Petters, A. O. “A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing.” Symposium International Astronomical Union, vol. 173, Cambridge University Press (CUP), 1996, pp. 281–82. Crossref, doi:10.1017/s0074180900231550. Full Text