# Professor Arlie O. Petters

Benjamin Powell Professor### Current Research:

Mathematical Physics

Mathematics- tools from differential geometry, singularities, and probability theory

Physics- problems connected to the interplay of gravity and light (gravitational lensing, general relativity, astrophysics, cosmology)My current mathematical physics research 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, singularity theory, and probability theory). This research is supported in part by the NSF.

A mathematical theory of gravitational lensing is given in the following book:

Singularity Theory and Gravitational Lensing

A. O. Petters, H. Levine,andJ. Wambsganss

(Birkhäuser-Springer, Boston, 2001). 603 pages. 184 illus. ISBN: 978-0-8176-3668-5.My publications also contain recent research work on the mathematical and physical aspects of gravitational lensing. Related popular articles on gravitational lensing:

- Prescription lens brings spinning black holes into focus
- Tiny Black Holes

- Scientists Predict How to Detect a Fourth Dimension of Space

- Astrophysical Introduction to Gravitational Lensing

- Examples of gravitational lenses

- Database of gravitational lensing papers

Mathematical and Scientific Methods in Business Administration

Mathematical Finance with Applications, Entrepreneurship and Innovation in STEM Fields (Developing World Context)By current business administration activities are three-fold. First, I am co-authoring a text on

Mathematical Finance with Applications: Securities, Portfolios, Derivatives.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 joint appointment with Fuqua. The overall goal is to research innovative ways to help drive national development through applications of STEM tools.