Arlie O Petters, Benjamin Powell Professor & Professor of Mathematics, Physics, and Business Administration

Contact Info:

Office Location:
Office Phone:	(919) 660-2812
Email Address:
Web Page:	http://www.math.duke.edu/~petters

Education:

Ph.D., MIT, 1991 (Mathematics)
B.A./M.A., Hunter College, CUNY, 1986 (Mathematics and Physics)

Specialties:

Mathematical Physics
Geometry
Probability

Research Interests:

• 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.
  

Curriculum Vitae

Current Ph.D. Students   (Former Students)

Postdocs Mentored

• Carla Cederbaum (2011/07-2014/06)
• Marcus Werner (2009/07-2011/06)
• Kumar Virbhadra (2000/09-2002/02)

Recent Publications   (More Publications)

1. A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes (December, 2012), Springer, in preparation.
2. X. Dong and A. O. Petters, Mathematical Finance with Applications (August, 2012), in preparation.
3. A. Aazami, C. Keeton, and A.O. Petters, Lensing by Kerr Black Holes. II. Analytical Study of Quasi-Equatorial Lensing Observables, vol. 52 (2011), pp. 102501.
4. A. Aazami, C. Keeton, and A.O. Petters, Lensing by Kerr Black Holes. I. General Lens Equation and Magnification Formula, J. Math. Phys., vol. 52 (2011), pp. 092502.
5. A. B. Aazami, A. O. Petters, and J. M. Rabin, Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing, J. Math. Physics, vol. 52 (2011).