Golod rings are the rings over which Betti numbers achieve the maximum possible growth. Because of their extremal homological behaviour, Golod rings are also of interest in combinatorial topology, in particular through their connection with moment-angle complexes. In this talk, we consider rings defined by subsets of 2×2 minors of generic matrices, and characterize the Golod ones among them. These rings can also be realized as generalized binomial edge ideals of graphs. Our main result is clean: such rings are Golod if and only if the ideal is generated by all minors of a 2×n generic matrix.
We will also see that in our setup, Golodness is equivalent to the triviality of the product on the Koszul homology. Towards the end, we will also mention potential directions for further study. This talk is based on the following recent work: https://arxiv.org/abs/2601.18153
