# Arlie O. Petters

- Benjamin Powell Professor of Mathematics in Trinity College of Arts and Sciences
- Professor of Mathematics
- Dean of Academic Affairs of Trinity College of Arts and Sciences
- Associate Vice Provost for Undergraduate Education
- Professor of Physics (Secondary)
- Professor of Economics (Secondary)
- Bass Fellow

**External address:**114 Allen Bldg, Durham, NC 27708

**Internal office address:**Box 90042, Durham, NC 27708-0320

**Phone:**(919) 684-3465

### Research Areas and Keywords

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

##### Signals, Images & Data

##### Topology

**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.

Keeton, CR, Gaudi, BS, and Petters, AO. "Identifying lenses with small-scale structure. I. Cusp lenses." *Astrophysical Journal* 598.1 I (2003): 138-161.
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Frittelli, S, and Petters, AO. "Wavefronts, caustic sheets, and caustic surfing in gravitational lensing." *Journal of Mathematical Physics* 43.11 (2002): 5578-5611.
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Gaudi, BS, and Petters, AO. "Gravitational microlensing near caustics. II. Cusps." *Astrophysical Journal* 580.1 I (2002): 468-489.
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Gaudi, BS, and Petters, AO. "Gravitational microlensing near caustics. I. Folds." *Astrophysical Journal* 574.2 I (2002): 970-984.
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Petters, AO, and Wicklin, FJ. "Fixed points due to gravitational lenses." *Journal of Mathematical Physics* 39.2 (1998): 1011-1023.

Petters, AO. "Multiplane gravitational lensing. III. Upper bound on number of images." *Journal of Mathematical Physics* 38.3 (1997): 1605-1613.

Petters, AO. "Curvature of caustics and singularities of gravitational lenses." *Nonlinear Analysis, Theory, Methods and Applications* 30.1 (1997): 627-634.

Fetters, AO. "Lower bounds on image magnification in gravitational lensing." *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences* 452.1949 (1996): 1475-1490.

Petters, AO. "A cusp - Counting formula for caustics due to multiplane gravitational lensing." *ASTROPHYSICAL APPLICATIONS OF GRAVITATIONAL LENSING* 173 (1996): 281-282.

Petters, AO, and Wicklin, FJ. "New Caustic Phenomena for Caustics in Double-Plane Lensing." *Astrophysical Applications of Gravitational Lensing, eds. C.S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht)* (1996). (Academic Article)