Dynkin diagrams and the licci conjecture

An ideal I in a regular local ring Q is said to be licci if it is in the linkage class of a complete intersection. Christensen, Veliche and Weyman conjectured that a perfect ideal of grade 3 in Q is licci if and only if its free resolution corresponds to Dynkin diagrams. After introducing the theory of linkage, I will talk about the conjecture, how Dynkin diagrams are involved, and their approach in showing one direction of the conjecture in arXiv:1712.04016.