Seminar Algebra and Geometry: Aldo Conca (University of Genova)

Koszul algebras and their syzygies

The goal of the talk is to explain recent results and conjectures regarding Koszul algebras and their syzygies. Koszul algebras are  graded K-algebras R such that the residue filed K has a linear R-free resolution. Koszul algebras are defined by quadrics.  But not all algebras defined by quadric are Koszul. However many classical algebras defined by quadrics  (e.g. the coordinate ring of the Grassmannian in its standard embedding)  are Koszul.
The main idea I will discuss is that  the syzygies of Koszul algebras have some properties in common with the syzygies of algebras defined by monomials
of degree two.

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