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

This volume explores key topics in commutative algebra and noncommutative algebraic geometry, highlighting their interaction. It features accessible expository papers and research articles, making it suitable for newcomers to the field.

Commutative Algebra and Noncommutative Algebraic Geometry: Volume 1, Expository Articles provides a comprehensive overview of essential contemporary topics within the realms of commutative algebra and noncommutative algebraic geometry. The book highlights the dynamic interplay between these two areas, illustrating how their boundaries have become increasingly intertwined. This volume is particularly aimed at newcomers to the field, offering accessible expository papers that lay the groundwork for deeper understanding.

The content of the book is informed by the programs hosted by the Mathematical Sciences Research Institute (MSRI) during the 2012–13 academic year, which focused on both commutative algebra and noncommutative algebraic geometry. These programs featured a series of joint seminars that explored shared themes such as birational geometry, D-modules, and invariant theory, among others. The collaborative nature of these discussions reflects the significant advancements made in the fields and demonstrates the rich dialogue occurring at the intersection of these mathematical disciplines.

In addition to the expository articles, the volume includes research papers and survey articles derived from lectures presented during the Introductory Workshops and Connections for Women Workshops. These contributions from experts in the field not only enrich the content but also serve to inspire and guide those who are just beginning their journey in these complex areas of study. Overall, this book serves as a valuable resource for anyone looking to engage with the latest developments in commutative and noncommutative algebraic geometry.