Mathematics in the 21st Century 6th World Conference, Lahore, March
Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra,
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Pierre Cartier A.D.R. Choudary Michel Waldschmidt Editors
Mathematics in the 21st Century 6th World Conference, Lahore, March 2013
Springer Proceedings in Mathematics & Statistics Volume 98
This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today.
More information about this series at http://www.springer.com/series/10533
Pierre Cartier • A.D.R. Choudary Michel Waldschmidt Editors
Mathematics in the 21st Century 6th World Conference, Lahore, March 2013
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Editors Pierre Cartier Institut des Hautes Études Scientifiques (IHÉS) Bures-sur-Yvette, France
A.D.R. Choudary Abdus Salam School of Mathematical Sciences Lahore, Pakistan
Michel Waldschmidt Université Pierre et Marie Curie (Paris VI) Paris Cedex 05, France
ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-3-0348-0858-3 ISBN 978-3-0348-0859-0 (eBook) DOI 10.1007/978-3-0348-0859-0 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2014950900 © Springer Basel 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the a
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