Hodge theory, algebraic cycles of hyper-Kähler manifolds

Abstract: This thesis is devoted to the study of algebraic cycles in projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It also studies some birational invariants of projective hyper-K\"ahler manifolds.