Oana Veliche
Northeastern University, Boston, MA, USA

In a paper from 1968, Golod proved that the Betti sequence of the residue field of a local ring attains the upper bound given by Serre if and only if the homology algebra of the Koszul complex of the ring has trivial multiplications and trivial Massey operations. This is the origin of the notion of Golod ring. Using the Koszul complex components as building blocks Golod also constructed a minimal free resolution of the residue field of a Golod ring.

With Van Nguyen, we extend this construction for an arbitrary local ring, up to the degree five, and explicitly show how the multiplicative structure of the homology of the Koszul algebra is involved, including the triple Massey products. The talk will illustrate: first, various consequences of this construction, and second, using a further analysis of the homology of the Koszul algebra, a construction of the minimal free resolution of a complete intersection local ring.