# Algebra/Number Theory Seminar

## A transcendental dynamical degree

Jason Bell, U Waterloo

Wednesday, February 19th, 2020
12:00 PM - 1:00 PM
Hylan 1106A

Given a complex variety $X$ and a rational self-map $f: X\to X$, one of the most important quantities in understanding the corresponding dynamical system is the dynamical degree, which is a nonnegative real number that gives some measure of how complex the system is. The dynamical degree is often a nonnegative integer and in many settings has been proved to be an algebraic number, including the case of endomorphisms of the plane. This naturally leads to the question: can the dynamical be transcendental? We show that the answer to this question is `yes’, by giving a rational self-map $f$ of the projective plane and using techniques from Diophantine approximation to exhibit the transcendence of the dynamical degree $f$.

This is joint work with Jeff Diller and Mattias Jonsson.

Event contact: dinesh dot thakur at rochester dot edu