Smith The principal investigator will study finitely presented, noetherian graded algebras, particularly the Sklyanin algebras. The study of these algebras has been significant in the development of noncommutative algebraic geometry. A key problem is to classify the fat point modules over the Sklyanin algebras. The principal investigator will also extend to higher dimensions the results he has obtained on the 4-dimensional Sklyanin algebras. In addition, noncommutative surfaces of Gelfand-Kirillov dimension 3 will be studied. This will provide a clearer understanding of the general outline of noncommutative algebraic geometry. This research is in the general area of noncommutative ring theory. The rings considered in the project are of interest in many areas of mathematics including algebraic geometry. Given a curve, one of these rings can be associated with certain points on the curve. A better understanding of these rings and this association will be useful in determine the geometry of a given curve. ***
