Let Q be a regular local ring. An ideal I in 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.

This is the first of a series of three talks on the spectral sequence of a filtered complex.
This material is by now classical and is an important part of homological algebra.
The main difficulty in dealing with spectral sequences is that there are a lot of indexes involved and this is a considerable obstacle to understanding what is going on. The goal of these talks is to present this material, including most proofs, in an accessible manner.