Speaker: Yohsuke Matsuzawa (Brown University)
Join Zoom Meeting:
https://zoom.us/j/94787937855?pwd=c2FiS3VGaGowUGRpcTVoenJqZW8rQT09
Meeting ID: 947 8793 7855
Passcode: 323472
Time: 9h15, Friday, January 8, 2021
Abstract: I will discuss applications of Vojta's conjecture to some problems in arithmetic dynamics, concerning the growth of sizes of coordinates of orbits, greatest common divisors among coordinates, and prime factors of coordinates. These problems can be restated and generalized in terms of (local/global) height functions, and I proved estimates on asymptotic behavior of height functions along orbits assuming Vojta's conjecture.
One of the key inputs is an asymptotic estimate of log canonical thresholds of (X, f^{-n}(Y)), where f : X->X is a self-morphism and Y is a closed subscheme of X.
As corollaries, I showed that Vojta's conjecture implies Dynamical Lang-Siegel conjecture for projective spaces (the sizes of coordinates grow in the same speed),and existence of primitive prime divisors in higher dimensional setting.
For general information of the AGEA seminar, please check out
https://sites.google.com/ncts.ntu.edu.tw/agea-seminar
or the mirror site
http://www.math.ntu.edu.tw/~jkchen/agea-seminar.html | 
