Applied Math

Duke Applied Mathematics



Arlie O. Petters, Benjamin Powell Professor of Mathematics and Dean of Academic Affairs of Trinity College of Arts and Sciences and Associate Vice Provost for Undergraduate Education of Trinity College of Arts & Sciences and Professor of Physics and Economics and Bass Fellow of Mathematics

Arlie O. Petters

  • 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.

Contact Info:
Office Location:  
Office Phone:  (919) 684-3465
Email Address: send me a message
Web Page:  http://www.math.duke.edu/~petters

Education:

Ph.D.Massachusetts Institute of Technology1991
B.A.CUNY Hunter College1986
M.A.CUNY Hunter College1986
Specialties:

Mathematical Physics
Geometry
Probability
Research Interests:

  • Mathematical Physics:
    Mathematics - Differential Geometry, Singularities, Probability Theory
    Physics - Gravitational Lensing, General Relativity, Astrophysics, Cosmology

    My current research in mathematical physics 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, 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).

  • Business Administration:
    Mathematical Finance
    Entrepreneurship and Innovation

    I am co-authoring a two-volume text on Mathematical Finance. In addition, I am involved with Entrepreneurship and Innovation in Science and Technology for the Developing World. These efforts are being piloted in Belize in collaboration with the Petters Research Institute and through my joint appointment with Duke's Fuqua School of Business. The overall goal is to research and implement innovative ways to drive national development through high-tech industries.

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)  
    Recent Publications   (More Publications)

    1. A. O. Petters and M. C. Werner, Gravitational Lensing and Black Holes (Spring, 2017), Springer, in preparation
    2. A. O. Petters and X. Dong, An Introduction to Mathematical Finance: Understanding and Building Financial Intuition, SUMAT (Winter, 2016), Springer, in preparation
    3. 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 (2011), pp. 102501, ISSN 0022-2488 [doi]  [abs]
    4. Aazami, AB; Petters, AO; Rabin, JM, Orbifolds, the A, D, E family of caustic singularities, and gravitational lensing, Journal of Mathematical Physics, vol. 52 no. 2 (2011), ISSN 0022-2488 [doi]  [abs]
    5. Aazami, AB; Keeton, CR; Petters, AO, Lensing by Kerr black holes. I. General lens equation and magnification formula, Journal of Mathematical Physics, vol. 52 no. 9 (2011), pp. 092502, ISSN 0022-2488 [doi]  [abs]


    Duke University * Arts & Sciences * Mathematics * December 17, 2017

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