A 1986 thesis on the mathematical theory of general relativity marked the beginning of Arlie Petters’s career, establishing a trajectory that led him from the rural community of Dangriga, Belize, to leadership roles at major research universities and institutions. He specializes in the intersection of physics and mathematics, focusing on how gravity and light interact.
Academic Foundation and Early Training
Born in 1964, Petters spent his early years in Dangriga before moving to Brooklyn, New York, at age 14. He pursued undergraduate studies at Hunter College, graduating in 1986. That same year, he commenced doctoral work at the Massachusetts Institute of Technology. During this period, he spent two years as an exchange scholar at Princeton University. He earned his Ph.D. in mathematics in 1991 under the guidance of advisors Bertram Kostant and David Spergel. Following graduation, he served as an instructor of pure mathematics at MIT for two years.
Advancing Gravitational Lensing Theory
Petters spent a decade, from 1991 to 2001, developing a rigorous mathematical framework for weak-deflection gravitational lensing. His research addressed complex theoretical challenges, including image counting, magnification, and the local geometry of caustics. This work culminated in the 2012 monograph, Singularity Theory and Gravitational Lensing, co-authored with Harold Levine and Joachim Wambganns. The volume provided a unified foundation for stability and genericity in k-plane gravitational lensing, drawing on singularity theory to clarify gravitational interactions.
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Between 2002 and 2007, his focus shifted toward practical astrophysical issues. Collaborating with astronomers, he developed diagnostic tests to detect dark substructures in galaxies and analyzed the curves produced by Galactic binary lenses. During this phase, he also investigated higher-order lensing effects to test Einstein’s general relativity against alternative gravitational theories within the PPN formalism. His research extended to hyperspace models, utilizing semi-classical wave theory to predict signatures of microscopic braneworld black holes.
Stochastic Models and Geometric Invariants
Starting in 2008, Petters moved into the study of stochastic gravitational lensing. Alongside colleagues including Rider and Teguia, he characterized probability densities for random time delay functions and lensing maps. His work produced a Kac-Rice type formula to estimate the expected number of images in random lens systems. Further studies with Aazami identified geometric universal magnification invariants for higher-order caustics, providing consistency checks for research involving random image magnifications.
Professional Appointments
Petters held an assistant professorship at Princeton University from 1993 to 1998 before joining the faculty at Duke University. During his tenure at Duke, he served as the dean of academic affairs for the Trinity College of Arts and Sciences and associate vice provost for undergraduate education from 2016 to 2019. In 2020, he was appointed provost at New York University Abu Dhabi. His professional recognitions include the 2002 Blackwell–Tapia prize and a fellowship from the American Mathematical Society in 2013.
Fast facts
- Born: 1964, Dangriga
- Ph.D.: Mathematics, 1991
- Alma Mater: Hunter College, MIT
- Citizenship: United States
- Blackwell–Tapia prize: 2002
- Fellow, American Mathematical Society: 2013
- Major Work: Singularity Theory and Gravitational Lensing
- Provost, NYU Abu Dhabi: Effective 2020
Questions readers ask
What is the primary focus of Arlie Petters's research?
His research centers on mathematical physics, specifically the interplay between gravity and light, including gravitational lensing, singularity theory, and stochastic models.
Where has Arlie Petters held academic appointments?
He has been a faculty member at Princeton University, MIT, and Duke University, and served as provost at New York University Abu Dhabi.
Achievements
- Blackwell–Tapia prize — 2002
- Held posts at Princeton University, Massachusetts Institute of Technology and Duke University
- Fields: mathematical physics, mathematics and physics
