Product Description
Since its discovery in the early 1990s, mirror symmetry, or more generally, string theory, has exploded onto the mathematical landscape. This topic touches upon many branches of mathematics and mathematical physics, and has revealed deep connections between subjects previously considered unrelated. The papers in this volume treat mirror symmetry from the perspectives of both mathematics and physics. The articles can be roughly grouped into four sub-categories within the topic of mirror symmetry: arithmetic aspects, geometric aspects, differential geometric and mathematical physics aspects, and geometric analytic aspects. In these works, the reader will find mathematics addressing, and in some cases solving, problems inspired and influenced by string theory.Titles in this series are co-published with International Press, Cambridge, MA. ... Read more

Book Description
The collection of articles in this volume are based on lecturespresented during the Winter School on Mirror Symmetry held atHarvard University. There are many new directions suggested bymirror symmetry which could potentially have very richconnections in physics and mathematics.

This book brings together the latest research in a major area ofmathematical physics, including the recent progress in mirrormanifolds and Lagrangian submanifolds. In particular, severalarticles describing homological approach and related topics areincluded.

Other AMS titles edited by S.-T Yau published in the AMS/IPStudies in Advanced Mathematics series include, Mirror SymmetryIII, Volume 10, Mirror symmetry II, Volume 1, and MirrorSymmetry I, Volume 9. ... Read more

Book Description
Mirror symmetry has undergone dramatic progress during the lastfive years. Tremendous insight has been gained on a number ofkey issues. This volume surveys these results. Some of thecontributions in this work have appeared elsewhere, while otherswere written specifically for this collection. The areas coveredare organized into 4 sections, and each presents papers by bothphysicists and mathematicians.

This volume collects the most important developments that havetaken place in mathematical physics since 1991. It is anessential reference tool for both mathematics and physicslibraries and for students of physics and mathematics. ... Read more

Customer Reviews (1)

Excellent
This book is somewhat dated since Mirror Symmetry III has recently appeared. However, this volume is now being reprinted and so a review is appropriate. The topic of mirror symmetry has to rank as the most fascinating one in all of modern mathematics. It has its origins in high energy physics, and as such to understand it fully, one must have a background in both quantum field theory and in some fairly esoteric mathematics, such as algebraic geometry, algebraic topology, and complex manifolds. A mathematician familiar with these areas will also have to get used to the sometimes hand-waving arguments used by physicists to discuss some of the concepts in mirror symmetry. The book is a collection of articles written by well-known experts in the field, and each article has varying degrees of physics/mathematics interplay. The literature on mirror symmetry has been dubbed "physical mathematics" by some mathematicians because of the physical constructions employed that are not based on rigorous mathematics. The powerful connections between quantum field theory and algebraic geometry are brought out in the first article of the book by B.R. Greene and H.Oogurt. Correlation functions in quantum field theory are related to the collection of holomorphic maps to rational curves on a complex compact 3-dimensional Kahler manifold. This theme of relating correlation functions in quantum field theory and superstring theory to various structures in algebraic geometry and complex manifolds is played out in the rest of the book.Most fascinating is the construction of the mirror manifolds themselves, for these look the same from a physical string-theory standpoint but are different as complex manifolds. The properties needed by physics imply the relevant manifolds are Calabi-Yau, many having been found by computer. The challenge of defining mirror symmetry rigorously is brought out in many articles in the book, with toric varieties showing the most promise: the enlarged Kahler moduli space of a given manifold is isomorphic to the complex structure moduli space of its mirror. Interestingly, some of the authors show that topology change can occur intrinsically in string theories; this is to be contrasted with "effective" changes in topology that occur in quantum field theory (and even in quantum mechanics). Again, toric varieties play the predominant role in showing this behavior. Some of the authors discuss the connection between mirror symmetry and enumerative geometry. This connection has stimulated much research, and the book serves as an introduction to the fascinating area of quantum cohomology.I think it would be fair to classify the results in this book as a kind of "quantization of mathematics". The reasonable effectiveness of physics in mathematics, to rephrase the statement by Eugene Wigner, is brought out brilliantly by the authors in this book. ... Read more