A-infinity resolutions and the Golod property for monomial rings Seminar

Event details

A classic result by Serre tells us that the Poincaré series of a monomial ring R is bounded above by a rational function involving the Betti numbers of the Koszul homology of R. A ring is called Golod if the two expressions are equal. One can show that R is Golod if and only if all Massey products on Koszul homology vanish. However, in general it is hard to determine when Massey products vanish. In this talk we will discuss a new approach to determine Golodness using A-infinity algebras. We will show that Golodness is equivalent to having a minimal A-infinity structure on a free resolution. Using this description we show that for a large class of monomial rings Golodness is equivalent to the vanishing of the product on Koszul homology. If time permits, we give a combinatorial description of Golodness for monomial rings whose Lyubeznik resolution is minimal.