Table of Contents

Infinite Free Resolutions.- Generic Initial Ideals.- Tight Closure, Parameter Ideals, and Geometry.- On the Use of Local Cohomology in Algebra and Geometry.- Problems and Results on Hilbert Functions of Graded Algebras.- Cohomological Degrees of Graded Modules.

Reviews

From reviews: "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "Although this text is not presented as a textbook, it contains all the major results in its area, it explains carefully all the different techniques that apply, it provides complete—albeit short— proofs (some new, some with a new twist) of most of the results and references for the rest, and it presents numerous relevant questions. This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: The topic is tight closure, a theory developed by Melvin Hochster and the author which has in a short time proved to be a useful and powerful tool. This paper is intended to be an introduction to the theory, and it is also a good source of examples and insight into the more recent developments that can be of interest to the more experienced.(…) The paper is extremely well organized, written, and motivated. - Zentralblatt MATH Schenzel lecture: "… this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH   "This interesting survey would be useful for both the novice and the expert." - Mathematical reviews Valla lecture: "But since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory. (…) It will serve as a useful reference source for people interested in Hilbert functions." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relationsbetween them, and how to compute them." - Zentralblatt MATH