TAGG seminar

This talk is based on joint work with Emily Berghofer, Peder Thompson, and Thomas Westerbäck.

A standard graded commutative algebra A is Koszul if its residue field has a linear free resolution over A. These resolutions are infinite, which makes proving Koszulness a challenging task. However, there are several tools one may use. The most common method is to prove that the algebra is G-quadratic, meaning that its defining ideal has a quadratic Gröbner basis, possibly after a change of coordinates. An alternative method is to find a Koszul filtration.

Both being G-quadratic and having a Koszul filtration are sufficient, but not necessary, conditions for being Koszul. In our recent work, we study the relationship between these two properties. It is known that there are algebras with Koszul filtrations that are not G-quadratic. But does every G-quadratic algebra have a Koszul filtration?