Jerzy Weyman (Jagiellonian University)

I will discuss the new approach to Gorenstein ideals of codimension 4, with n generators.

This allows us to construct (by a single calculation, starting from scratch.) the examples of such ideals with 4\le n\le 8 generators. For n=4,5,6 they give generic models of resolutions of ideals of that type (in the sense that each such resolution comens from the generic model).

We conjecture that for n=7,8 these resolutions are also generic models.

The main idea is a construction of a certain generic ring which has unexpected symmetry of the type $E_n$.

For $n\ge 9$ such construction is not possible which indicates that the classification is much more difficult.