Research summary
Numbers, fractals and dynamical systems are essential to many aspects of modern life, from coding theory to natural patterns like snowflakes. Dynamical systems, which involve the repeated transformation of elements by an outside force, often exhibit randomness that is crucial in cryptographic algorithms (used for coding information). Despite this randomness, key algebraic structures, like the canonical height function and the Artin-Mazur zeta function, reveal underlying patterns.
Dr. Dang Khoa Nguyen, Canada Research Chair in Number Theory and Arithmetic Geometry, aims to better understand these functions by establishing effective lower bounds on linear combinations of canonical height values, akin to Baker’s theory of logarithmic forms, and developing new criteria for the Pólya-Carlson dichotomy in dynamical systems. He and his research team are addressing open problems in the dynamics of compact abelian groups, and their work has potential applications in solving Diophantine equations. The research promises to advance knowledge in number theory, algebraic dynamics, and their applications in cryptography and information theory.