The Mathematical Elephant

A presentation from 2021–2022 Sally Starling Seaver Fellow Holly Krieger

Holly Krieger is the Corfield Lecturer at the University of Cambridge and a fellow at Murray Edwards College.

While at Radcliffe, Krieger is exploring an emerging aspect of the connection between two fundamental fields of pure mathematics: complex dynamics and arithmetic geometry. Complex dynamics is the study of iteration of self-maps of functions of a complex variable, with connections to a wide variety of fields in mathematics, biology, physics, and more. Arithmetic geometry is based in the classical study of integer solutions to polynomial equations, such as the famous Fermat’s Last Theorem. Recently, arithmetic height functions have provided a new insight into the study of complex dynamical systems, although even the simplest families of examples exhibit features not yet understood. This project will improve and greatly expand these recently developed mathematical tools, which allow us to study the arithmetic and geometry of special points for families of dynamical systems, with applications to the structure of torsion points on elliptic curves, an example of substantial interest in number theory and geometry.

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