Koszul algebras and regularity
  This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras. We discuss variants of the Koszul property such as strongly Koszul, absolutely Koszul and universally Koszul. We present several open problems related with these notions and their local variants. 
Aldo Conca, Emanuela De Negri, Maria Evelina Rossi
math.AC