Valuative Tree Seminar

Fei Hu, Department of Pure Mathematics, University of Waterloo

Building on previous preliminary results on the valuative tree at infinity (e.g., classification of valuations), I will describe the proof of Medvedev-Scanlon-Zhang conjecture for polynomial endomorphisms of the affine plane given by Junyi Xie in 2017.

More precisely, he proved that for a dominant polynomial endomorphism f of the affine plane A^2, both defined over an algebraically closed field k of characteristic zero, if f does not preserve any nonconstant rational function g of X, then there exists a k-rational point x in A^2 such that its forward f-orbit O_f(x) is Zariski dense in A^2.

M3 3103