The Department of Mathematics is hosting a series of colloquia, open for all to attend. On 5 December 2025, Holly Krieger from the University of Cambridge will give a talk on 'Uniformity in Arithmetic Dynamics.'

Registration:

This talk will take place in person at King's College London in the Strand Building S-2.23. A reception will follow afterwards. The talk will also be streamed online via Microsoft Teams. Please click 'Get tickets' to sign up for either an In-Person Ticket or an Online Ticket. If you wish to attend the in-person event, you must select the correct ticket type.

Abstract

Uniformity in Arithmetic Dynamics

The periodic points of a discrete dynamical system control its local and global dynamical behaviour. When the system is defined over the rational numbers, one can ask about the arithmetic properties of periodic points. The central open conjecture in arithmetic dynamics asks whether there are uniform constraints on the possible periods of points for families of algebraic dynamical systems. In this talk, we will discuss this conjecture, how it generalises 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.

About the Speaker: 

Holly Krieger is a Professor of Mathematics at the University of Cambridge, specialising in arithmetic dynamics, the interplay between number theory and dynamical systems. She earned her PhD from the University of Illinois Chicago and was later a Fellow at MIT. In 2020, she received the prestigious Whitehead Prize of the London Mathematical Society. Holly Krieger is also known for her clear and engaging explanations of advanced mathematics, and she has appeared regularly on the popular YouTube channel Numberphile.

Learn more about Holly Krieger on her webpage and also on Wikipedia.

Future colloquia

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