We report our recent progress on the Equivariant Minimal Model Program (EMMP), the MMP which preserves an endomorphism f of a projective variety with mild singularities.
We apply this EMMP to algebraic and arithmetic dynamics, especially to the Kawaguchi-Silverman conjecture (KSC) about the equality of dynamical degree and arithmetic degree of f, and the Zariski Dense Orbit conjecture (ZDO) of f.