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**PREFACE : **

In 2002, an introductory workshop was held at the Mathematical Sciences
Research Institute in Berkeley to survey some of the many directions of
the commutative algebra field. Six principal speakers each gave three
lectures, accompanied by a help session, describing the interaction of
commutative algebra with other areas of mathematics for a broad audience
of graduate students and researchers. This book is based on those
lectures, together with papers from contributing researchers. David
Benson and Srikanth Iyengar present an introduction to the uses and
concepts of commutative algebra in the cohomology of groups. Mark Haiman
considers the commutative algebra of n points in the plane. Ezra Miller
presents an introduction to the Hilbert scheme of points to complement
Professor Haiman's paper. Further contributors include David Eisenbud
and Jessica Sidman; Melvin Hochster; Graham Leuschke; Rob Lazarsfeld and
Manuel Blickle; Bernard Teissier; and Ana Bravo.

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