Transcendental values of power series and dynamical degrees

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.

Speaker Biography

Holly Krieger is a leader in the area of arithmetic dynamics. She received a Ph.D. from the University of Illinois at Chicago, and was a postdoc at MIT before starting her present position in Cambridge. She was the Australian Mathematical Society's Mahler Lecturer in 2019, and received a Whitehead Prize from the London Mathematical Society in 2020.