based on large n chern-simons/topological string duality, in a series of papers, j.m.f. labastida, m. marino, h. ooguri and c. vafa conjectured certain remarkable new algebraic structure of link invariants and the existence of infinite series of new integer invariants. in this lecture, i will describe a proof of this conjecture. moreover, i will show that these new integer invariants vanish at large genera. in the end of the talk, some application in the knot theory and related problems (e.g., the famous volume conjecture), will also be discussed.