Jan-Erik Roos: On some unexpected rings that are close to Golod rings

In 2015 Lukas Katthän made a remarkable discovery: He found an example of a quotient Q of a polynomial ring in six variables with an ideal generated by monomials in the variables such that the Koszul homology of Q had trivial multiplication, but nevertheless Q was not a Golod ring. This was unexpected and contradicts assertions related to homotopy theory in the literature e.g. in Transactions American Mathematical society, vol. 368, issue 9, September 2016 page 6668. I was able to simplify Katthän's example and obtain more than 100 similar examples of similar cases for commutative local rings of embedding dimension four.

In the first part of the talk I will survey the general theory of Golod rings related to Serre's inequality that led to the definition of Golod rings. In the second part I will present my results (based on Katthän's preprint) and corresponding questions.