**Email Address:** arlie.petters@duke.edu**Web Page:** http://www.math.duke.edu/~petters

**Specialties:**

Mathematical Physics

Geometry

Probability

**Research Categories:** *Gravitational Lensing, General Relativity, and Cosmology*

**Research Description:** I develop physically based mathematical theories of
gravitational lensing (light deflection by gravitational
fields) in a variety of astrophysical contexts and
investigate the observational consequences of the
associated theorems. I am currently researching flux
ratio anomalies with applications to the nature of dark
matter and exploring relativistic gravitational lensing
with applications to supermassive black holes. One of
my goals is to emphasize the stable and generic
features of lensing, drawing conclusions essentially
independent of the oversimplifying approximations of a
chosen lens system model. At the same time, I also
analyze in depth specific physically realistic models
having predictive power. The mathematical tools
employed draw upon the theory of singularities,
differential geometry, and probability theory. My
research involves collaborations with astrophysicists,
mathematicians, and physicists.

**Recent Publications**
(More Publications)

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

**Highlight:**

**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.

**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)