COMMUTATIVE ALGEBRA AND NONCOMMUTATIVE ALGEBRAIC GEOMETRY VOL 1

In the 2012–13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs.

• High-quality articles survey the current state of knowledge in this extremely active field.
• Focuses on areas of common interest which emphasise the lively interaction between commutative algebra and noncommutative algebraic geometry.
• Valuable to researchers and graduate students studying algebra and algebraic geometry.

Authors
• David Eisenbud, University of California, Berkeley. Professor in the Department of Mathematics at the University of California, Berkeley.
• Srikanth B. Iyengar, University of Utah. Professor in the Department of Mathematics at the University of Utah.
• Anurag K. Singh, University of Utah. Professor in the Department of Mathematics at the University of Utah.
• J. Toby Stafford, University of Manchester. Professor in the Department of Mathematics at the University of Manchester.
• Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek (FWO), Belgium. Director of Research at the Research Foundation - Flanders (FWO) in Belgium.

Table of Contents
Preface.
1. Growth functions Syzygies, finite length modules, and random curves.
2. Vector bundles and ideal closure operations.
3. Hecke algebras and symplectic reflection algebras.
4. Limits in commutative algebra and algebraic geometry.
5. Introduction to uniformity in commutative algebra.
6. Noncommutative motives and their applications.
7. Infinite graded free resolutions.
8. Poincaré–Birkhoff–Witt theorems.
9. Frobenius splitting in commutative algebra.
10. From Briançon–Skoda to Scherk–Varchenko.
11. The interplay of algebra and geometry in the setting of regular algebras.
12. Survey on the D-module f s.
13. Introduction to derived categories.