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

Please note: Arlie has left the "Finance" group at Duke University; some info here might not be up to date.

Contact Info:

Office Location:
Email Address:
Web Page:	http://www.math.duke.edu/%7Epetters/

Specialties:

Mathematical Physics
Geometry
Probability

Research Interests: Mathematical Finance, Entrepreneurship and Innovation in Science and Technology (Developing World), Mathematical Physics, Applied Mathematics

• 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.
  

Areas of Interest:

Geometry, Singularities
Probability with applications to Mathematical Finance
Gravitational Lensing
General Relativity

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. Aazami, AB; Keeton, CR; Petters, AO, Magnification cross sections for the elliptic umbilic caustic surface, Universe, vol. 5 no. 7 (July, 2019) [doi]  [abs]
2. A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes (Spring, 2017), Springer, in preparation
3. A. O. Petters and X. Dong, An Introduction to Mathematical Finance: Understanding and Building Financial Intuition, SUMAT (Winter, 2016), Springer, in preparation
4. Petters, AO; Dong, X, An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition (June, 2016), pp. 483 pages, SPRINGER, ISBN 1493937812  [abs]
5. 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 (October, 2011), pp. 102501-102501, AIP Publishing, ISSN 0022-2488 [doi]  [abs]