John R. Doyle

John R. Doyle serves as Associate Professor in the Department of Mathematics at Oklahoma State University, specializing in arithmetic dynamics with complementary work in arithmetic geometry and algebraic number theory. His research investigates rational functions over fields of arithmetic interest including rational numbers, number fields, p-adic fields, and function fields, with particular focus on dynamical moduli spaces and their applications to the dynamical uniform boundedness conjecture of Morton and Silverman.

Dr. Doyle earned his bachelor's, master's, and doctoral degrees in mathematics from the University of Georgia, the first state-chartered university in the United States. Following graduate studies, he completed a three-year postdoctoral appointment at the University of Rochester before joining Louisiana Tech University as an assistant professor in 2017. His academic journey reflects progression through major research institutions with increasing responsibility in both teaching and research.

His research program centers on the intersection of dynamical systems and number theory, examining preperiodic structures in polynomial dynamics. Doyle's work frequently involves constructing and analyzing dynamical moduli spaces that parametrize rational maps with specified preperiodic behavior. This research contributes significantly to addressing fundamental questions about uniform boundedness of preperiodic points across number fields, connecting Galois theory with dynamical systems in innovative ways.

Dr. Doyle maintains an active publication record with numerous articles in top-tier mathematics journals including Transactions of the American Mathematical Society, Compositio Mathematica, and Mathematische Annalen. His recent publications demonstrate consistent advancement in understanding preperiodic points, dynamical modular curves, and Galois-theoretic aspects of arithmetic dynamics, with several 2024-2025 publications indicating ongoing productive research.

As an educator, Doyle teaches across the mathematics curriculum at Oklahoma State University, from foundational calculus courses to advanced graduate seminars in algebraic curves and arithmetic dynamics. His teaching portfolio reflects deep expertise in algebra and number theory, with current Spring 2025 offerings including Abstract Algebra II and specialized graduate coursework. His pedagogical approach connects advanced research topics with undergraduate and graduate instruction, enriching the mathematical education experience for students at all levels.