Algebraic Geometry Seminar
A local or graded ring is called Koszul if its residue field has a linear resolution. Roughly speaking, if a quadratic ideal defines a nice algebraic variety, then the coordinate ring should be Koszul. However, there is in general no finite test for Koszulness and there are many interesting conjectures about this property. In this talk I'll discuss some recent work with Hamid Hassanzadeh and Srikanth Iyengar using ideas from DG Algebras that shed light on these conjectures.