# PIMS Network-Wide Colloquium

**
Thu., Mar. 24, 2022 2:30 p.m.
**

**Speaker:** Holly Krieger (University of Cambridge)

**Title:** Transcendental values of power series and dynamical degrees

**Registration in advance and details at:** https://www.pims.math.ca/scientific-event/220324-pnwchk

**Abstract:**

In the study of a discrete dynamical system defined by polynomials, we hope as a starting point to understand the growth of the degrees of the iterates of the map. This growth is measured by the dynamical degree, an invariant which controls the topological, arithmetic, and algebraic complexity of the system. I will discuss the history of this question and the recent surprising construction, joint with Bell, Diller, and Jonsson, of a transcendental dynamical degree for an invertible map of this type, and how our work fits into the general phenomenon of power series taking transcendental values at algebraic inputs.