李思辰,华东理工大学

The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. When there exist such a rational point P, Prof. Kawaguchi and Prof. Silverman conjecture defined the arithmetic degree at P and claimed that its arithmetic degree is equal to the first dynamical degree of f, i.e., Kawaguchi-Silverman conjecture of the arithmetic dynamic. In this talk, I will explain my recent progress towards on the Zariski dense orbit conjecture and Kawaguchi-Silverman conjecture on automorphisms of projective threefolds from the viewpoint of the explicit birational geometry.