Duke Applied Mathematics

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

Teaching (Summer1 2012):

• MATH 288.01, TOPICS IN PROBABILITY Synopsis

  French Sci 2231, MTuTh 12:30 PM-02:35 PM

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 - Differential Geometry, Singularities, Probability Theory
  Physics - Gravitational Lensing, General Relativity, Astrophysics, Cosmology

  My current research in mathematical physics deals with employing weak and strong deflection gravitational lensing to test theories of gravity, explore the geometry of spacetime around black holes, and probe the nature of dark matter on galactic scales. I utilize 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).
  

• Business Administration:
  Mathematical Finance
  Entrepreneurship and Innovation

  I am co-authoring a two-volume text on Mathematical Finance. In addition, I am involved with Entrepreneurship and Innovation in Science and Technology for the Developing World. These efforts are being piloted in Belize in collaboration with the Petters Research Institute and through my joint appointment with Duke's Fuqua School of Business. The overall goal is to research and implement innovative ways to drive national development through high-tech industries.
  

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)