
Fields Institute Communications 2003; 367 pp; hardcover Volume: 38 ISBN10: 0821833553 ISBN13: 9780821833551 List Price: US$122 Member Price: US$97.60 Order Code: FIC/38 See also: Strings 2001  Atish Dabholkar, Sunil Mukhi and Spenta R Wadia Mirror Symmetry  Claire Voisin  The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinitedimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in CalabiYau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on CalabiYau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for CalabiYau threefolds defined over the rationals, the BlochBeilinson conjectures, regulator maps of higher algebraic cycles, PicardFuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zetafunctions and Lseries of mirror pairs of CalabiYau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory. Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in mirror symmetry and string theory. Table of Contents



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