Complex cobordism & stable homotopy

Homotopy groups are extremely dificult to compute, and even the homotopy groups of spheres are only understood through some small range of degrees. The aim of this project is to use complex cobordism and formal group laws to understand certain systematic phenomena in the stable homotopy groups of spheres. Here complex cobordism is a certain generalized cohomology theory, and a formal group law over a ring R is a power series F(x; y) € R[[x; y]] satisfying certain properties. As it turns out complex cobordism carries the universal formal group law in some precise sense.