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 2 focuses on the most recent research.

About the Authors

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 a 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) in Belgium.

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