Tuesday, December 3, 2019 1:30 pm
-
1:30 pm
EST (GMT -05:00)
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