Algebraic Geometry Working Seminar

Wednesday, March 8, 2023 2:00 pm - 2:00 pm EST

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Dynamical Cancellation of Polynomials"

In this talk we introduce the problem of dynamical cancellations and prove a version for finitely generated semigroup of polynomials. Plainly, we consider a finite set of polynomials $S$ over a number field $K$ and give a necessary and sufficient condition for the existence of a positive integer $N$ and a finite set $Z \subset \P^1_K \times \P^1_K$ such that for any $(a,b)\in (\P^1_K \times \P^1_K)\setminus Z$ we have the cancellation result: if $k>N$ and $f_1,…,f_k$ are maps in the semigroup generated by $S$ such that $f_k \circ ... \circ f_1(a)=f_k\circ ... \circ f_1(b)$, then in fact $f_N \circ ... \circ f_1(a)=f_N \circ ... \circ f_1(b)$. The talk is based on the preprint (arXiv:2302.01208).

This seminar will be held both online and in person: