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This book presents four lectures on Rees rings and blow-ups, Koszul
modules with applications to syzygies, Groebner bases and
degenerations, and applications of Adams operations. Commutative
Algebra has witnessed a number of spectacular developments in
recent years, including the resolution of long-standing problems;
the new techniques and perspectives are leading to an extraordinary
transformation in the field. The material contained in this volume,
based on lectures given at a workshop held in Levico Terme, Trento,
in July 2019, highlights some of these developments. The text will
be a valuable asset to graduate students and researchers in
commutative algebra and related fields.
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.
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.
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