### Arlie O Petters, Benjamin Powell Professor of Mathematics, secondary appt: Fuqua and Physics

**Office Phone:** (919) 660-2812

**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.

**Teaching (Fall 2014):**

- Math 581.01,
*Mathematical finance*
Synopsis
- Physics 150, MW 08:30 AM-09:45 AM

- Math 581.02,
*Mathematical finance*
Synopsis
- Physics 259, MW 10:05 AM-11:20 AM

- Math 790-90.07,
*Minicourse in advanced topics*
Synopsis
- Gross hall 318, MW 11:45 AM-01:00 PM

**Recent Publications**
(More Publications)

- A. O. Petters and M. C. Werner,
*Gravitational Lensing and Black Holes*
(July, 2015), Springer, in preparation .
- A. O. Petters and X. Dong,
*Mathematical Finance with Applications: Understanding and Buiding Financial Intuition*, SUMAT
(July, 2014), Springer, in preparation .
- 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 .
- 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 .
- 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) .

**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)