Arlie O. Petters

  • Benjamin Powell Professor of Mathematics in Trinity College of Arts and Sciences
  • Dean of Academic Affairs of Trinity College of Arts and Sciences
  • Associate Vice Provost for Undergraduate Education
  • Professor of Mathematics
  • Professor of Economics (Secondary)
  • Professor of Physics (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
geometric lensing, black holes, extra dimensions, singularities
Mathematical Physics
gravity, light, geometric lensing, stochastic lensing, black holes, extra dimensions, singularities
PDE & Dynamical Systems
gravity, light, mathematical finance
Physical Modeling
gravity, light, geometric lensing, stochastic lensing, black holes, extra dimensions
Probability
stochastic lensing, mathematical finance
Signals, Images & Data
stochastic lensing, mathematical finance
Topology
geometric lensing, black holes, singularities
  • 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.

Education & Training
  • Ph.D., Massachusetts Institute of Technology 1991

  • M.A., CUNY Hunter College 1986

  • B.A., CUNY Hunter College 1986

Aazami, AB, Keeton, CR, and Petters, AO. "Lensing by Kerr black holes. I. General lens equation and magnification formula." Journal of Mathematical Physics 52.9 (2011). Full Text

Aazami, AB, Petters, AO, and Rabin, JM. "Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing." Journal of Mathematical Physics 52.2 (2011). Full Text

Aazami, AB, Keeton, CR, and Petters, AO. "Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables." Journal of Mathematical Physics 52.10 (2011). Full Text

Aazami, AB, and Petters, AO. "A universal magnification theorem. III. Caustics beyond codimension 5." Journal of Mathematical Physics 51.2 (2010). Full Text Open Access Copy

Petters, AO, and Werner, MC. "Mathematics of gravitational lensing: Multiple imaging and magnification." General Relativity and Gravitation 42.9 (2010): 2011-2046. Full Text

Petters, AO. "Gravity's action on light." Notices of the American Mathematical Society 57.11 (2010): 1392-1409.

Aazami, AB, and Petters, AO. "A universal magnification theorem for higher-order caustic singularities." Journal of Mathematical Physics 50.3 (2009). Full Text

Aazami, AB, and Petters, AO. "A universal magnification theorem. II. Generic caustics up to codimension five." Journal of Mathematical Physics 50.8 (2009). Full Text

Petters, AO, Rider, B, and Teguia, AM. "A mathematical theory of stochastic microlensing. I. Random time delay functions and lensing maps." Journal of Mathematical Physics 50.7 (2009). Full Text

Petters, AO, Rider, B, and Teguia, AM. "A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula." Journal of Mathematical Physics 50.12 (2009). Full Text Open Access Copy

Pages

Mathematical physicist Arlie Petters has been appointed Dean of Academic Affairs and Associate Vice Provost for Undergraduate Education, effective July 1. He will serve through June 2020. In the words of Valerie S. Ashby, Dean of Trinity College of... read more »