Scientific activities
All the topics and the open problems were related to “Local cohomology and syzygies of affine algebras". During the courses the teachers introduced all basic facts on local cohomology and syzygies. One of the topics was the study of the local cohomology of polynomial rings with respect to arbitrary ideals and, in particular, how these may be regarded as modules over rings of differential operators. Many applications of local cohomology were done related to questions on the minimal number of defining equations of algebraic sets. Another topic deal with therecent developments concerning the degrees of syzygies of affine algebras and their Koszul homology, with special regard to Koszul algebras, as Veronese subrings of polynomial rings. Moreover were discussed strong versions of Koszulness and comparison among them.