
Preface  Introduction  Preview Material  Table of Contents  Supplementary Material 
CBMS Regional Conference Series in Mathematics 2011; 317 pp; softcover Number: 114 ISBN10: 0821852329 ISBN13: 9780821852323 List Price: US$57 Member Price: US$45.60 All Individuals: US$45.60 Order Code: CBMS/114 See also: Mirror Symmetry and Tropical Geometry  Ricardo CastanoBernard, Yan Soibelman and Ilia Zharkov Mirror Symmetry and Algebraic Geometry  David A Cox and Sheldon Katz Dirichlet Branes and Mirror Symmetry  Paul S Aspinwall, Tom Bridgeland, Alastair Craw, Michael R Douglas, Mark Gross, Anton Kapustin, Gregory W Moore, Graeme Segal, Balazs Szendroi and PMH Wilson  Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A and Bmodels in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of FontaineIllusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, Bmodel side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for "integral tropical manifolds." A complete version of the argument is given in two dimensions. A copublication of the AMS and CBMS. Readership Graduate students and research mathematicians interested in mirror symmetry and tropical geometry. 


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