REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring R attains an upper bound given by Serre if and only if the homology algebra A of the Koszul complex of R has trivial multiplications and trivial Massey operations. This is the origin of the notion of Golod rings. In joint work with Oana Veliche, using the Koszul complex as building blocks, we construct a minimal free resolution for any local ring. We describe how the multiplicative structure and the triple Massey products of the homology algebra A are involved in the construction. As a result, we provide explicit formulas for the first six terms of a sequence that measures how far the ring R is from being Golod, and discuss other consequences of this construction.