Clay Mathematics Monographs
The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas.
Editors in Chief: Simon Donaldson and Andrew Wiles
Managing Editor: James Carlson
Assoicate Editors: Brian Conrad, Ingrid Daubechies, Charles Fefferman, János Kollár, David Morrison, Andrei Okounkov, Peter Ozsváth, Karen Smith, and Cliff Taubes
Editorial Manager: Vida Salahi
The fourth volume in the series has just appeared: "Ricci Flow and the Poincaré Conjecture", by John Morgan and Gang Tian.
Vida Salahi manages the reviewing, editing, technical preparation, and submission of manuscripts. All manuscripts are carefully copy edited to ensure an end result of which the authors will be proud. CMI also works with the AMS to ensure a suitable cover design.
To submit a manuscript or inquire about submission, please contact Vida Salahi (salahi@claymath.org).
Published Monographs
Ricci Flow and the Poincaré Conjecture
Authors: John Morgan and Gang Tian
For over 100 years the Poincaré Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the seven Clay Millennium Problems in Mathematics. In 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincaré Conjecture in the affirmative.
Lecture notes on Motivic Cohomology
Authors: Carlo Mazza, Vladimir Voevodsky and Charles Weibel
This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, develop its main properties and, finally, to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology and Chow groups.
The Millennium Prize Problems
Editors: James Carlson, Arthur Jaffe and Andrew Wiles
On August 8, 1900, at the second International Congress of Mathematicians in Paris, David Hilbert delivered the famous lecture in which he described twenty-three problems that were to play an influential role in future mathematical research. A century later, on May 24, 2000, at a meeting at the Collge de France, the Clay Mathematics Institute announced the creation of a US$7 million prize fund for the solution of seven important classic problems that have resisted solution. The prize fund is divided equally among the seven problems. There is no time limit for their solution.
Mirror Symmetry
Editors: Cumrun Vafa and Eric Zaslow
This book is a product of a month-long school on mirror symmetry that CMI held at Pine Manor College in Brookline, Massachusetts in the Spring of 2000. The aim of the book is to provide a pedagogical introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the main part of the monograph is devoted to the proof of mirror symmetry from various viewpoints. More advanced topics are also discussed. In particular, topological strings at higher genera and the notion of holomorphic anomaly.
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