E-Book Overview
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.
The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
E-Book Content
The IMA Volumes in Mathematics and its Applications Volume 149
Series Editors Douglas N. Arnold Arnd Scheel
For other titles published in this series, go to www.springer.com/series/811
Mihai Putinar
Seth Sullivant Editors
Emerging Applications of Algebraic Geometry
~ Springer
Editors Mihai Putinar Department of Mathematics University of California Santa Barbara, CA 93106 USA http://www.math.ucsb.edu/~mputinar/
Seth Sullivant Department of Mathematics North Carolina State University Raleigh, North Carolina 27695 USA http://www4.ncsu.edu/~smsulli2/
Series Editors Douglas N. Arnold Arnd Scheel Institute for Mathematics and its Applications University of Minnesota Minneapolis, MN 55455 USA
ISSN: 0940-6573 e-ISBN: 978-0-387-09686-5 ISBN: 978-0-387-09685-8 DOI: 10.1007/978-0-387-09686-5 Library of Congress Control Number: 2008932579 Mathematics Subject Classification (2000): 13P10, 14P10, 44A60, 52B12, 52C45, 62-09, 62H17, 90C22, 90C26, 92-08, 92D20, 93B25, 93B28 © 2009 Springer Science + Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science + Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Camera-ready copy provided by the IMA. 9 8 7 6 5 4 3 2 1 springer.com
FOREWORD
This IMA Volume in Mathematics and its Applications EMERGING APPLICATIONS OF ALGEBRAIC GEOMETRY contains papers presented at two highly successful workshops, Optimization and Control, held January 16–20, 2007, and Applications in Biology, Dynamics, and Statistics, held March 5–9, 2007. Both events were integral parts of the 2006-2007 IMA Thematic Year on “Applications of Algebraic Geometry.” We are grateful to all the participants for making these workshops a very productive and stimulating events. The organizing committee for the first workshop are Dimitris Bertsimas (Sloan School of Management, Massachusetts Institute of Technology), J. William Helton (Mathematics, University of California - San Diego), Jean Bernard Lasserre (LAAS-CNRS, France), and Mihai Putina