Santiago Zarzuela – författare

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it.

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: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (…). 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 M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (…) 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

Valla lecture: "… 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." - Mathematicalreviews

Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015.

Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.