Preface. Commutative Algebra, Proceedings of the Introductory Workshop in Commutative Algebra, MSRI Cambridge Univ. Press, 2004.

Size: px

Start display at page:

Download "Preface. Commutative Algebra, Proceedings of the Introductory Workshop in Commutative Algebra, MSRI Cambridge Univ. Press, 2004."

Josephine Dennis
6 years ago
Views:

1 Preface Commutative Algebra is an extremely vibrant field of mathematical research, with connections to many other disciplines. It began with work of David Hilbert in the 1890s and developed with the work of Emmy Noether in the 1920s and Oscar Zariski in the 1930s. Its roots in Algebraic Geometry continue to supply problems and intuition for research on commutative rings. For example, Paul Roberts proof of the New Intersection Theorem using sophisticated geometric techniques from intersection theory illustrates this beautifully. Currently, the field of Commutative Algebra is in a period of profound transformation: Over the last fifteen years commutative algebra has experienced a striking evolution. During that period the outlook of the subject has been altered, new connections to other areas have been established, and powerful techniques have been developed. 1 Today, Commutative Algebraists are involved in intense interaction with researchers in areas as diverse as Algebraic Geometry, Biology, Coding Theory, Combinatorics, Homotopy Theory, K-theory, Representation Theory, and Statistics. This volume grew from three mathematics research meetings focusing on the interactions between Algebra, Combinatorics, and Geometry: Workshop on Connections Between Algebra and Geometry, University of Regina, May 29 June 1, Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, Canadian Mathematical Society Summer Meeting, University of Regina, June 2 3, Conference on Further Connections Between Algebra and Geometry, North Dakota State University, February 2 3, By L. Avramov, M. Green, C. Huneke, K. Smith, B. Sturmfels, editors, in the Preface to Trends in Commutative Algebra, Proceedings of the Introductory Workshop in Commutative Algebra, MSRI Cambridge Univ. Press, vii

2 viii Preface However, this volume is not a conference proceedings. Instead, it is a collection of notes and papers documenting a few manifestations of the connections on which the meetings focused. The first part of this volume contains lecture notes (including exercises and solutions) from the three courses given at the first meeting listed above. These notes were prepared by the course instructors in collaboration with the problem session assistants and (in one case) one of the workshop participants. These notes provide introductions to three specific areas of interaction: DG homological algebra, fat points, and secant varieties. Each set of notes should be accessible to graduate students and some advanced undergraduate students. The second part of this volume consists of papers (part survey, part new research) written by some of the speakers from the special session and the conference, and their collaborators. Each paper focuses on interactions between Algebra, Combinatorics, and Geometry. Each one should be accessible to researchers and graduate students with a reasonable background in Commutative Algebra, say, at the level of the texts of Atiyah and MacDonald, Eisenbud, or Matsumura. Conference Personnel Workshop on Connections Between Algebra and Geometry, University of Regina, May 29 June 1, Organizers: Donald Stanley, University of Regina Course instructors: Brian Harbourne, University of Nebraska Lincoln Enrico Carlini, Politecnico di Torino Problem session assistants: Kristen A. Beck, University of Arizona Luke Oeding, University of California, Berkeley Participants: Seyedruhallah Ahmadi, University of Regina Ali Alilooee, Dalhousie University Hannah Altmann, North Dakota State University Marzieh Bayeh, University of Regina Ashwini Bhat, Lakehead University 2 We include affiliations given at the times of the meetings.

3 Preface ix Jennifer Biermann, Lakehead University Yuri Delanghe, University of Alberta Annika Denkert, University of Nebraska Lincoln Aaron Feickert, North Dakota State University Brandon Goodell, North Dakota State University Nathan Grieve, Queen s University Ryan Hines, Central Michigan University Andrew Hoefel, Queen s University Mike Janssen, University of Nebraska Lincoln Maryam Ehya Jahromi, Dalhousie University Jeremy Lane, University of Regina Melissa Lindsey, Indiana Wesleyan University Sarah Mayes, University of Michigan Augustine O Keefe, Tulane University Alessandro Oneto, Università di Genova Jared Painter, University of Texas at Arlington Megan Patnott, University of Notre Dame Alexandra Seceleanu, University of Nebraska Lincoln Stephen Sturgeon, University of Kentucky Jonathan Totushek, North Dakota State University Richard Wicklein, North Dakota State University Mark Wong, Syracuse University Liu Yong, University of Regina Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, Canadian Mathematical Society Summer Meeting, University of Regina, June 2 3, 2012 Organizers: Speakers: Kristen Beck, University of Arizona Jennifer Bierman, Lakehead University Enrico Carlini, Politecnico di Torino Annika Denkert, University of Nebraska Lincoln Sara Faridi, Dalhousie University Chris Francisco, Oklahoma State University Nathan Grieve, Queen s University Brian Harbourne, University of Nebraska Lincoln Andrew Hoefel, Queen s University Mike Janssen, University of Nebraska Lincoln Melissa Lindsey, Indiana Wesleyan University Uwe Nagel, University of Kentucky Luke Oeding, University of California, Berkeley Megan Patnott, University of Notre Dame

4 x Preface Chris Peterson, Colorado State University Sandra Spiroff, University of Mississippi Stephen Sturgeon, University of Kentucky Conference on Further Connections Between Algebra and Geometry, North Dakota State University, February 2 3, 2013 Organizers: Speakers: Kristen Beck, University of Arizona Jim Coykendall, North Dakota State University Chris Francisco, Oklahoma State University Tài Huy Hà, Tulane University Brian Harbourne, University of Nebraska Lincoln Augustine O Keefe, University of Kentucky Jared Painter, Houston Baptist University Branden Stone, Bard College/Bard Prison Initiative Mark Walker, University of Nebraska Lincoln Poster presenters: Brandon Goodell, North Dakota State University Sema Gunturkun, University of Kentucky Sara Malec, Georgia State University Saeed Nasseh, North Dakota State University Denise Rangle, University of Texas at Arlington Richard Wicklein, North Dakota State University Participants: Nitin Aggarwal, University of Kansas Saba Al-Kaseasbeh, North Dakota State University Hannah Altmann, North Dakota State University Pye Aung, North Dakota State University Robert Bradford, University of Kansas Cătălin Ciupercă, North Dakota State University Annika Denkert, University of Nebraska Lincoln Josef Dorfmeister, North Dakota State University Aaron Feickert, North Dakota State University Zachary Flores, University of Kansas Jeffrey Fujioka, Central Michigan University Mike Janssen, University of Nebraska Lincoln Pin-Hung Kao, Central Michigan University Bethany Kubik, United States Military Academy Kuei-Nuan Lin, University of California, Riverside Haydee Lindo, University of Nebraska Lincoln Chelsey Morrow, North Dakota State University Megan Patnott, University of Notre Dame

5 Preface xi Jason Pode, Central Michigan University William Robinson, University of Kentucky William Sanders, University of Kansas Piyush Shroff, Texas State University San Marcos Jonathan Totushek, North Dakota State University Mark Wong, Syracuse University Acknowledgments We gratefully acknowledge the following: The Department of Mathematics and Statistics at the University of Regina for its hospitality during the Workshop on Connections Between Algebra and Geometry, in particular, from Allen Herman, Chair. Donald Stanley (University of Regina) for co-organizing the Workshop on Connections Between Algebra and Geometry. The Canadian Mathematical Society for organizational support during the Special Session on Interactions Between Algebraic Geometry and Commutative Algebra. The Mathematics Department at North Dakota State University for its hospitality during the Conference on Further Connections Between Algebra and Geometry. Jacalyn Benson (North Dakota State University), Amy Hunter (University of Regina), Teresa Judge (Central Michigan University), and Karen Manders (Pacific Institute for the Mathematical Sciences) for administrative support with the Workshop and the Conference. The following funding agencies without which these meetings would not have been possible for us: Central Michigan University, Department of Mathematics National Science Foundation (Award #DMS ) National Security Agency North Dakota State University, Department of Mathematics North Dakota State University, College of Science and Mathematics Pacific Institute for the Mathematical Sciences University of Regina, Faculty of Science University of Regina, Department of Mathematics and Statistics. Mount Pleasant, MI Fargo, ND November 2013 Susan M. Cooper Sean Sather-Wagstaff

Springer Proceedings in Mathematics & Statistics

Springer Proceedings in Mathematics & Statistics Volume 76 For further volumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics This book series features volumes composed