Research Interests for Arlie O Petters

• 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.
  

Recent Publications

1. A. O. Petters, Gravitational Lensing and Black Holes (August, 2009), in preparation
2. X. Dong and A. O. Petters, Mathematical Finance II (April, 2009), in preparation
3. X. Dong and A.O. Petters, Mathematical Finance I (December, 2008), in preparation
4. A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula (Submitted, 2008)
5. A.O. Petters, B. Rider, and A. M. Teguia, A Mathematical Theory of Stochastic Microlensing I. Random Time Delay Functions and Lensing Maps (Submitted, 2008)