AbstractAfter reviewing the notion of Castelnuovo-Mumford regularity of a finitely generated graded moduleover a polynomial ring with coefficients in a field, some history and known results wil be discussedregarding the regularity of ideals associated to subspace arrangements and the connections with theilHilbert functions. in the sequel, recent results obtained together with Aldo Conca wil be ...
AbstractIn the second of two lectures,l am going to draw people's attention to the`geometry of syzygies". We begin with a research problem from geometry: Findingall Gorenstein Calabi-Yau varieties. In dimension 3 cases, their coordinate rings have regularity 4.There are 16 Betti diagrams for such graded Gorenstein algebras with projective dimension 4. Byapolarity, they correspond to degree 4 fo...