Commutative Algebra and Noncommutative Algebraic Geometry: Volume 1, Expository Articles

by David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh

Overview

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. Volume 1 contains expository papers ideal for those entering the field.

Product Details

ISBN-13:	9781107065628
Publisher:	Cambridge University Press
Publication date:	11/19/2015
Series:	Mathematical Sciences Research Institute Publications , #67
Pages:	462
Product dimensions:	6.14(w) x 9.21(h) x 0.98(d)

About the Author

David Eisenbud is a Professor in the Department of Mathematics at the University of California, Berkeley.

Srikanth B. Iyengar is a Professor in the Department of Mathematics at the University of Utah.

Anurag K. Singh is a Professor in the Department of Mathematics at the University of Utah.

J. Toby Stafford is Professor in the Department of Mathematics at the University of Manchester.

Michel Van den Bergh is Director of Research at the Research Foundation - Flanders (FWO), Belgium.

Table of Contents

Preface David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford and Michel Van den Bergh; 1. Growth functions Jason P. Bell; Syzygies, finite length modules, and random curves Christine Berkesch and Frank-Olaf Schreyer; 2. Vector bundles and ideal closure operations Holger Brenner; 3. Hecke algebras and symplectic reflection algebras Maria Chlouveraki; 4. Limits in commutative algebra and algebraic geometry Steven Dale Cutkosky; 5. Introduction to uniformity in commutative algebra Craig Huneke and Claudiu Raicu; 6. Noncommutative motives and their applications Matilde Marcolli and Gonçalo Tabuada; 7. Infinite graded free resolutions Jason McCullough and Irena Peeva; 8. Poincaré–Birkhoff–Witt theorems Anne V. Shepler and Sarah Witherspoon; 9. Frobenius splitting in commutative algebra Karen E. Smith and Wenliang Zhang; 10. From Briançon–Skoda to Scherk–Varchenko Duco van Straten; 11. The interplay of algebra and geometry in the setting of regular algebras Michaela Vancliff; 12. Survey on the D-module f s Uli Walther, with an appendix by Anton Leykin; 13. Introduction to derived categories Amnon Yekutieli.