Holly Krieger: A transcendental birational dynamical degree (NTWS 182)
Channel: Number Theory Web Seminar
Date: 2023-09-29

Abstract: In the study of a discrete dynamical system defined by polynomials, we wish to understand the integer sequence formed by the degrees of the iterates of the map: examples of such a sequence include the Fibonacci and other integer linear recurrence sequences, but not all examples satisfy a finite recurrence.  The growth of this sequence is measured by the dynamical degree, an invariant which controls the topological, arithmetic, and algebraic complexity of the system. I will discuss the surprising construction, joint with Bell, Diller, and Jonsson, of a transcendental dynamical degree for a birational map of projective space, and how our work fits into the general phenomenon of power series taking transcendental values at algebraic inputs.

Link to slides: https://drive.google.com/file/d/1eNHN8xUFrZbgfowtNdKwjikT0bBAdRgY

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, September 28, 2023 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, September 29, 2023 (1am AEST, 4am NZDT)