Mathematical Sciences 2010 press.princeton.edu 1 Annals of Mathematics Studies 3 Princeton Mathematical Series 3 Princeton Landmarks in Mathematics & Physics 4 London Mathematical Society Monographs 5 Princeton Series in Applied Mathematics 8 Princeton Graduate & Undergraduate Textbooks 14 Mathematical Sciences 16 Mathematics & Social Sciences 18 History & Philosophy of Science 20 General Interest 28 Albert Einstein 29 Index/Order Form Cover images courtesy of Shutterstock and Dimitri Karetnikov Annals of Mathematics Studies Phillip A. Griffiths, John N. Mather & Elias M. Stein, series editors Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century. To mark the continued success of the series, all books are avail- able again in paperback. For a complete listing of all books in this series, please check our Web site: press.princeton.edu/math. Forthcoming Introduction to Ramsey Spaces Stevo Todorcevic Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate ac- cessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. Stevo Todorcevic is professor of mathematics at the University of Toronto and holds senior research positions at the CNRS in Paris and SANU in Belgrade. July 2010. 296 pages. 12 line illus. Pa: 978-0-691-14542-6 $45.00 | £30.95 Cl: 978-0-691-14541-9 $89.50 | £62.00 Many of the books in this catalog are now being made available as ebook editions that can be pur- chased from online booksellers. For more information, please visit our Web site at press.princeton.edu. Annals of Mathematics Studies Forthcoming New On the Cohomology of The Ergodic Theory of Certain Non-Compact Lattice Subgroups Shimura Varieties Alexander Gorodnik & Amos Nevo Sophie Morel The results established in this book constitute a new departure in ergodic theory and a signifi- This book studies the intersection cohomology cant expansion of its scope. Alexander Gorodnik of the Shimura varieties associated to unitary and Amos Nevo develop a systematic general groups of any rank over Q. In general, these approach to the proof of ergodic theorems for varieties are not compact. The intersection a large class of non-amenable locally compact cohomology of the Shimura variety associated to groups and their lattice subgroups. Simple a reductive group G carries commuting actions general conditions on the spectral theory of of the absolute Galois group of the reflex field the group and the regularity of the averaging and of the group G(A ) of finite adelic points f sets are formulated, which suffice to guarantee of G. The second action can be studied on the convergence to the ergodic mean. set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois Alexander Gorodnik is senior research fellow in action—at good places—on the G(Af)-isotypical mathematics at the University of Bristol. Amos components of the cohomology. Nevo is professor of mathematics at the Tech- nion, Israel Institute for Technology. Sophie Morel is a member in the School of Mathematics at the Institute for Advanced Study 2010. 136 pages. 2 line illus. in Princeton and a research fellow at the Clay Pa: 978-0-691-14185-5 $29.95 | £20.95 Cl: 978-0-691-14184-8 $60.00 | £41.95 Mathematics Institute. March 2010. 256 pages. New Pa: 978-0-691-14293-7 $39.50 | £27.95 Cl: 978-0-691-14292-0 $75.00 | £52.00 Outer Billiards on Kites Richard Evan Schwartz New In Outer Billiards on Kites, Richard Schwartz Higher Topos Theory presents his affirmative solution to the Moser- Jacob Lurie Neumann problem. He shows that an outer billiards system can have an unbounded orbit Higher category theory is generally regarded as when defined relative to any irrational kite. In technical and forbidding, but part of it is con- addition to solving the basic problem, Schwartz siderably more tractable: the theory of infinity- relates outer billiards on kites to such topics categories, higher categories in which all higher as Diophantine approximation, the modular morphisms are assumed to be invertible. In group, self-similar sets, polytope exchange Higher Topos Theory, Jacob Lurie presents the maps, profinite completions of the integers, and foundations of this theory, using the language of solenoids—connections that together allow for a weak Kan complexes introduced by Boardman fairly complete analysis of the dynamical system. and Vogt, and shows how existing theorems in algebraic topology can be reformulated and Richard Evan Schwartz is professor of mathemat- generalized in the theory’s new language. The ics at Brown University. result is a powerful theory with applications in 2009. 320 pages. 64 halftones. 35 line illus. many areas of mathematics. Pa: 978-0-691-14249-4 $45.00 | £30.95 Cl: 978-0-691-14248-7 $99.50 | £69.95 Jacob Lurie is associate professor of mathematics at Massachusetts Institute of Technology. 2009. 944 pages. Pa: 978-0-691-14049-0 $55.00 | £37.95 Cl: 978-0-691-14048-3 $95.00 | £65.00 Annals of Mathematics Studies • 1 The Structure of Affine Classifying Spaces of Buildings Degenerating Polarized Richard M. Weiss Hodge Structures In The Structure of Affine Buildings, Richard Weiss Kazuya Kato & Sampei Usui gives a detailed presentation of the complete In 1970, Phillip Griffiths envisioned that points at proof of the classification of Bruhat-Tits buildings infinity could be added to the classifying space first completed by Jacques Tits in 1986. The D of polarized Hodge structures. In this book, book includes numerous results about auto- Kazuya Kato and Sampei Usui realize this dream morphisms, completions, and residues of these by creating a logarithmic Hodge theory. They use buildings. It also includes tables correlating the the logarithmic structures begun by Fontaine- results in the locally finite case with the results of Illusie to revive nilpotent orbits as a logarithmic Tits’s classification of absolutely simple algebraic Hodge structure. groups defined over a local field. 2008. 352 pages. 58 line illus. 2009. 384 pages. 8 line illus. 8 tables. Pa: 978-0-691-13822-0 $55.00 | £37.95 Pa: 978-0-691-13881-7 $49.95 | £34.95 Cl: 978-0-691-13821-3 $80.00 | £55.00 Cl: 978-0-691-13659-2 $99.50 | £69.95 Lectures on Resolution of The Hypoelliptic Laplacian Singularities and Ray-Singer Metrics János Kollár Jean-Michel Bismut & Gilles Lebeau “The book will be an invaluable tool not only for This book presents the analytic foundations to graduate students, but also for algebraic geom- the theory of the hypoelliptic Laplacian. The eters. Mathematicians working in different fields hypoelliptic Laplacian, a second-order operator will also enjoy the clarity of the exposition and acting on the cotangent bundle of a compact the wealth of ideas included. This will become, I’m manifold, is supposed to interpolate between the sure, as it happened to most books in this series, classical Laplacian and the geodesic flow. Jean- one of the classics of modern mathematics.” Michel Bismut and Gilles Lebeau establish the —Paul Blaga, Mathematica basic functional analytic properties of this opera- tor, which is also studied from the perspective of 2007. 208 pages. 2 line illus. Pa: 978-0-691-12923-5 $42.00 | £28.95 local index theory and analytic torsion. Cl: 978-0-691-12922-8 $87.00 | £60.00 2008. 376 pages. 4 line illus. Pa: 978-0-691-13732-2 $45.00 | £30.95 Cl: 978-0-691-13731-5 $70.00 | £48.95 Spherical CR Geometry and Dehn Surgery Modular Forms and Special Richard Evan Schwartz Cycles on Shimura Curves This book proves an analogue of William Stephen S. Kudla, Michael Thurston’s celebrated hyperbolic Dehn surgery Rapoport & Tonghai Yang theorem in the context of complex hyperbolic discrete groups, and then derives two main “This book represents a major milestone for re- geometric consequences from it. In an acces- search at the intersection of arithmetic geometry sible and straightforward manner, Richard Evan and automorphic forms. The results will shape Schwartz also presents a large amount of useful the research in this area for some time to come.” information on complex hyperbolic geometry —Jens Funke, Mathematical Reviews and discrete groups. 2006. 384 pages. 1 line illus. 3 tables. 2007. 200 pages. 15 halftones. 9 line illus. Pa: 978-0-691-12551-0 $59.00 | £40.95 Pa: 978-0-691-12810-8 $45.00 | £30.95 Cl: 978-0-691-12809-2 $80.00 | £55.00 2 • Annals of Mathematics Studies Princeton Mathematical Series Phillip A. Griffiths, John N. Mather & Elias M. Stein, series editors Princeton University Press is proud to have published the Princeton Mathematical Series since 1946. The first book published in the series was the Classical Groups by Hermann Weyl. The books in the series consist of introductions to a particular area of math that has attained a level of stability and complete- ness.