Uniformity in arithmetic dynamics

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• Holly Krieger (Cambridge)
• Thursday 09 October 2025, 16:00-17:00
• CMS MR2.

If you have a question about this talk, please contact HoD Secretary, DPMMS.

The periodic points of a discrete algebraic dynamical system control its local and global dynamical behaviour. When we impose an arithmetic structure on such a system, we do not generally expect periodic points to be rational. The central open conjecture in arithmetic dynamics asks whether this arithmetic structure imposes uniform constraints on the possible periods of points for families of algebraic dynamical systems. In this talk, we will discuss this conjecture, how it generalizes the torsion conjecture—in particular, the celebrated theorems of Mazur and Merel on rational torsion of elliptic curves—and survey some recent progress on and strategies for attacking this problem.

A wine reception will follow the talk in Pavilion D common room.

This talk is part of the DPMMS Departmental Colloquia series.

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