Links, homology cobordism, and Milnor’s invariants. Lecture 1

In these two talks I will discuss an old and fundamental sequence of invariants due to John Milnor, and efforts to extend this sequence of invariants transfinitely. One can define a natural extension of Milnor's invariants to study homology cobordism invariants classes of 3-manifolds, and we will discuss new results in this direction as well.