Books & Videos
Analytic Number Theory; A Tribute to Gauss and Dirichlet; Editors: William Duke, Yuri Tschinkel. CMI/ AMS, 2007, 265 pp. www.claymath.org/publications/Gauss_Dirichlet. This volume contains the proceedings of the Gauss–Dirichlet Conference held in Göttingen from June 20–24 in 2005, commemorating the 150th anniversary of the death of Gauss and the 200th anniversary of Dirichlet’s birth. It begins with a definitive summary of the life and work of Dirichlet by J. Elstrodt and continues with thirteen papers by leading experts on research topics of current interest within number theory that were directly influenced by Gauss and Dirichlet.
Clay Mathematics Monographs Ricci Flow and the Poincaré Conjecture; Authors: John Morgan, Gang Tian. CMI/AMS, 3 Volume 3 Ricci Flow and the Poincaré Conjecture Poincaré the and Flow Ricci 2007, 521 pp., www.claymath.org/publications/ricciflow. This book presents a complete Ricci Flow and the and detailed proof of the Poincaré Conjecture. This conjecture was formulated by Henri
Publications Poincaré Conjecture Poincaré in 1904 and has remained open until the recent work of Grigory Perelman. The arguments given in the book are a detailed version of those that appear in Perelman’s three
The Millennium Prize Problems; Editors: James Carlson,$.* $MBZ.BUIFNBUJDT*OTUJUVUF ".4 "NFSJDBO.BUIFNBUJDBM4PDJFUZ Arthur Jaffe, Andrew Wiles. CMI/AMS,0O"VHVTU BUUIFTFDPOE*OUFSOBUJPOBM$POHSFTTPG.BUIFNBUJDJBOT 2006, 165 pp., JO1BSJT %BWJE)JMCFSUEFMJWFSFEIJTGBNPVTMFDUVSFJOXIJDIIFEFTDSJCFE UXFOUZUISFFQSPCMFNTUIBUXFSFUPQMBZBOJOnVFOUJBMSPMFJONBUIFNBUJDBM 5IF.JMMFOOJVN1SJ[F1SPCMFNT SFTFBSDI"DFOUVSZMBUFS PO.BZ BUBNFFUJOHBUUIF$PMMÒHFEF 'SBODF UIF$MBZ.BUIFNBUJDT*OTUJUVUF $.* BOOPVODFEUIFDSFBUJPOPGB
www.claymath.org/publications/Millennium_Problems. This Morgan and Tian and Morgan 64NJMMJPOQSJ[FGVOEGPSUIFTPMVUJPOPGTFWFOJNQPSUBOUDMBTTJDQSPCMFNT XIJDIIBWFSFTJTUFETPMVUJPO5IFQSJ[FGVOEJTEJWJEFEFRVBMMZBNPOHUIF volume gives the official descriptionTFWFOQSPCMFNT5IFSFJTOPUJNFMJNJUGPSUIFJSTPMVUJPO of each of the seven prob- JOHN MORGAN 5IF.JMMFOOJVN1SJ[F1SPCMFNTXFSFTFMFDUFECZUIFGPVOEJOH4DJFOUJmD "EWJTPSZ#PBSEPG$.*"MBJO$POOFT "SUIVS+BGGF "OESFX8JMFT BOE 5IF.JMMFOOJVN lems as well as the rules governing&EXBSE8JUUFOBGUFSDPOTVMUJOHXJUIPUIFSMFBEJOHNBUIFNBUJDJBOT the prizes. It also contains For additional information GANG TIAN 5IFJSBJNXBTTPNFXIBUEJGGFSFOUUIBOUIBUPG)JMCFSUOPUUPEFmOFOFX and updates on this book, visit DIBMMFOHFT CVUUPSFDPSETPNFPGUIFNPTUEJGmDVMUJTTVFTXJUIXIJDI www.ams.org/bookpages/cmim-3 NBUIFNBUJDJBOTXFSFTUSVHHMJOHBUUIFUVSOPGUIFTFDPOENJMMFOOJVN UP 1SJ[F1SPCMFNT an essay by Jeremy Gray on the SFDPHOJ[FBDIJFWFNFOUJONBUIFNBUJDTPGIJTUPSJDBMEJNFOTJPO UPFMFWBUFhistory of prize problems in JOUIFDPOTDJPVTOFTTPGUIFHFOFSBMQVCMJDUIFGBDUUIBUJONBUIFNBUJDT UIF AMS GSPOUJFSJTTUJMMPQFOBOEBCPVOETJOJNQPSUBOUVOTPMWFEQSPCMFNT BOEUP +$BSMTPO "+BGGF BOE"8JMFT &EJUPST CMIM/3 American Mathematical Society www.ams.org CMI FNQIBTJ[FUIFJNQPSUBODFPGXPSLJOHUPXBSETBTPMVUJPOPGUIFEFFQFTU www.claymath.org Clay Mathematics Institute mathematics. NPTUEJGmDVMUQSPCMFNT 5IFQSFTFOUWPMVNFTFUTGPSUIUIFPGmDJBMEFTDSJQUJPOPGFBDIPGUIFTFWFO QSPCMFNTBOEUIFSVMFTHPWFSOJOHUIFQSJ[FT*UBMTPDPOUBJOTBOFTTBZCZ +FSFNZ(SBZPOUIFIJTUPSZPGQSJ[FQSPCMFNTJONBUIFNBUJDT +$BSMTPO "+BGGF BOE"8JMFT &EJUPST
4 color process ??? pages pages on 50 lb stock • 1 3/16 spine Floer Homology, Gauge Theory, and Low-Dimensional
")JTUPSZPG1SJ[FTJO.BUIFNBUJDT +FSFNZ(SBZ Topology; Proceedings of the 2004 CMI Summer #JSDIBOE4XJOOFSUPO%ZFS$POKFDUVSF "OESFX8JMFT )PEHF$POKFDUVSF 1JFSSF%FMJHOF School at Rényi Institute of Mathematics, Budapest. /BWJFSo4UPLFT&RVBUJPO $IBSMFT-'FGGFSNBO 1PJODBSÏ$POKFDUVSF +PIO.JMOPS 1WFSTVT/11SPCMFN 4UFQIFO$PPL XXXDMBZNBUIPSH >ÞÊ >Ì i>ÌVÃÊ*ÀVii`}Ã Editors: David Ellwood, Peter Ozsváth, András Stipsicz, 3JFNBOO)ZQPUIFTJT &OSJDP#PNCJFSJ x XXXBNTPSH 6ÕiÊx Zoltán Szábo. CMI/AMS, 2006, 297 pp., 2VBOUVN:BOHo.JMMT5IFPSZ "SUIVS+BGGFBOE&EXBSE8JUUFO -ATHEMATICAL GAUGE THEORY STUDIES CONNECTIONS ON PRINCIPAL BUNDLES OR >`Ê ÜÊ iÃ>Ê/«}Þ iÀÊ}Þ]Ê>Õ}iÊ/ iÀÞ] MORE PRECISELY THE SOLUTION SPACES OF CERTAIN PARTIAL DIFFERENTIAL EQUATIONS FOR SUCH CONNECTIONS (ISTORICALLY THESE EQUATIONS HAVE COME FROM www.claymath.org/publications/Floer_Homology..13*;& This MATHEMATICAL PHYSICS AND PLAY AN IMPORTANT ROLE IN THE DESCRIPTION OF THE ELECTO WEAK AND STRONG NUCLEAR FORCES 'AUGE THEORY AS A TOOL FOR STUDYING TOPOLOGICAL PROPERTIES OF FOUR MANIFOLDS WAS PIONEERED BY THE FUNDAMENTAL WORK OF 3IMON $ONALDSON IN THE EARLY S AND WAS REVOLUTIONIZED BY THE INTRODUCTION OF THE 3EIBERG 7ITTEN volume grew out of the summer school that took place in June of EQUATIONS IN THE MID S 3INCE THE BIRTH OF THE SUBJECT IT HAS RETAINED ITS CLOSE CONNECTION WITH SYMPLECTIC TOPOLOGY 4HE ANALOGY BETWEEN THESE TWO lELDS OF STUDY WAS FURTHER UNDERSCORED BY !NDREAS &LOERS CONSTRUCTION OF AN INlNITE DIMENSIONAL VARIANT OF 2004 at the Alfréd Rényi Institute of Mathematics in Budapest, -ORSE THEORY WHICH APPLIES IN TWO A PRIORI DIFFERENT CONTEXTS EITHER DPMPSQSPDFTT QBHFTPOMCTUPDLt#BDLTQBDFJODIFT TO DElNE SYMPLECTIC INVARIANTS FOR PAIRS OF ,AGRANGIAN SUBMANIFOLDS OF A SYMPLECTIC MANIFOLD OR TO DElNE TOPOLOGICAL INVARIANTS FOR THREE MANIFOLDS WHICH lT INTO A FRAMEWORK FOR CALCULATING INVARIANTS Hungary. It provides a state-of-the-art introduction to current research, covering material FOR SMOOTH FOUR MANIFOLDS h(EEGAARD &LOER HOMOLOGY THE RECENTLY DISCOVERED INVARIANT FOR THREE AND FOUR MANIFOLDS COMES FROM AN *ÀVii`}ÃÊvÊÌ iÊ APPLICATION OF ,AGRANGIAN &LOER HOMOLOGY TO SPACES ASSOCIATED TO (EEGAARD >ÞÊ >Ì i>ÌVÃÊÃÌÌÕÌiÊ DIAGRAMS !LTHOUGH THIS THEORY IS CONJECTURALLY ISOMORPHIC TO 3EIBERG 7ITTEN THEORY IT IS MORE TOPOLOGICAL AND COMBINATORIAL IN ITS mAVOR AND THUS EASIER TO Óää{Ê-ÕiÀÊ-V from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and WORK WITH IN CERTAIN CONTEXTS 4HE INTERACTION BETWEEN GAUGE THEORY
LOW DIMENSIONAL TOPOLOGY AND SYMPLECTIC GEOMETRY HAS LED TO A NUMBER *Ài>ÀÞÊV«Þ]ÊvÀÊ«ÃÌÊÞ° Ü`]Ê"âÃÛ?Ì ]Ê-Ì«ÃVâ]Ê>`Ê-â>L ]Ê `ÌÀà vÀj`Ê,jÞÊÃÌÌÕÌiÊvÊ >Ì i>ÌVÃÊ OF STRIKING NEW DEVELOPMENTS IN THESE lELDS 4HE AIM OF THIS VOLUME Õ`>«iÃÌ]ÊÕ}>ÀÞ IS TO INTRODUCE GRADUATE STUDENTS AND RESEARCHERS IN OTHER lELDS TO symplectic four-manifolds. SOME OF THESE EXCITING DEVELOPMENTS WITH A SPECIAL EMPHASIS ON THE ÕiÊxqÓÈ]ÊÓää{ VERY FRUITFUL INTERPLAY BETWEEN DISCIPLINES
4HIS VOLUME GREW OUT OF AN INTENSE SUMMER SCHOOL OF THE SAME TITLE THAT TOOK PLACE IN *UNE OF AT THE !LFRÏD 2ÏNYI )NSTITUTE >Û`Ê°Ê Ü`Ê OF -ATHEMATICS IN "UDAPEST (UNGARY 4HE TEXT IS BASED ON *iÌiÀÊ"âÃÛ?Ì Ê EXPANDED VERSIONS OF THE LECTURE COURSES FROM THE SCHOOL AS WELL `À?ÃÊ°Ê-Ì«ÃVâÊ Lecture Notes on Motivic Cohomology; Authors: Carlo Mazza, Vladimir Voevodsky, AS MORE ADVANCED RESEARCH LEVEL TALKS GIVEN DURING THIS PROGRAM 4HE RESULTING VOLUME PROVIDES A STATE OF THE ART INTRODUCTION TO <Ì?Ê-â>LÊ CURRENT RESEARCH COVERING MATERIAL FROM (EEGAARD &LOER HOMOLOGY `ÌÀà CONTACT GEOMETRY SMOOTH FOUR MANIFOLD TOPOLOGY AND SYMPLECTIC Charles Weibel. CMI/AMS, 2006, 210 pp., www.claymath.org/publications/Motivic_ FOUR MANIFOLDS Cohomology. This book provides an account of the triangulated theory of motives. Its purpose is to introduce the reader to Motivic Cohomology, to develop its main properties,
ÜÜÜ°>ðÀ} !MERICAN -ATHEMATICAL 3OCIETY #-)0 !-3 ÜÜÜ°V>Þ>Ì °À} #-) #LAY -ATHEMATICS )NSTITUTE and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology and Chow groups.
Clay Mathematics Proceedings The modern theory of automorphic forms, embodied in 4 Volume 4 what has come to be known as the Langlands program, is an extraordinary unifying force in mathematics. It proposes fundamental relations that tie arithmetic Surveys in Noncommutative Geometry; Editors: Nigel Higson, Johninformation Roe. from number theory and algebraic CMI/AMS, geometry with analytic information from harmonic analysis and group representations. These “reciprocity laws”, and Shimura VarietiesShimura and
conjectured by Langlands, are still largely unproved. Analysis, Harmonic 2006, 189 pp., www.claymath.org/publications/Noncommutative_Geometry.However, their capacity to unite large Inareas of June Formula, ofTrace the mathematics insures that they will be a central area of study for years to come.
The goal of this volume is to provide an entry point into 2000, a summer school on Noncom- mutative Geometry, organized jointlythis exciting and challengingby field.the It is directed American on the one hand at graduate students and professional mathematicians who would like to work in the area. The longer articles in particular represent an attempt to Mathematical Society and the Clay Mathematics Institute, was held at Mountenable a reader toHolyoke master some of the more difficult College techniques. On the other hand, the book will also be useful to mathematicians who would like simply to Proceedings of the Clay Mathematics Institute understand something of the subject. They will be able 2003 Summer School, The Fields Institute in Massachusetts. The meeting centered around several series of expositoryto consult the expositorylectures portions of the various that articles. were Toronto, Canada, June 2–27, 2003 The volume is centered around the trace formula and Shimura varieties. These areas are at the heart of the intended to introduce key topics in noncommutative geometry to mathematicianssubject, but they have been especially difficult unfamiliar to learn because of a lack of expository material. The volume aims to rectify the problem. It is based on the courses
given at the 2003 Clay Mathematics Institute Summer Kottwitz, Arthur,and Ellwood with the subject. Those expository lectures have been edited and are reproducedSchool. However, many ofin the articles this have been volume. expanded into comprehensive introductions, either to the trace formula or the theory of Shimura varieties, or to some aspect of the interplay and application of the two areas.
James Arthur Harmonic Analysis, the Trace Formula and Shimura Varieties; Proceedings of the 2003 CMI David Ellwood Robert Kottwitz Summer School at Fields Institute, Toronto. Editors: James Arthur, David Ellwood, Robert Editors Kottwitz. CMI/AMS, 2005, 689 pp., www.claymath.org/publications/Harmonic_Analysis.CMIP/4 Editors
www.ams.org American Mathematical Society The subject of this volume is the trace formula and Shimura varieties. These areas haveAMS www.claymath.org CMI Clay Mathematics Institute been especially difficult to learn because of a lack of expository material. This volume aims 4-color process 704 pages • 31 5/16” spine 30 CMI ANNUAL REPORT The AMS will provide a discount of 20% to students purchasing Clay publications. Publications To receive the discount, students should provide the reference code CLAY MATH. Online Orders: enter “CLAY MATH” in the comments field for each Clay publication ordered. Phone Orders: give Customer Service the reference code and they will extend a 20% discount on each Clay publiction ordered. to rectify that problem. It is based on the courses given at the 2003 Clay Mathematics Institute Summer School. Many of the articles have been expanded into comprehensive introductions, either to the trace formula or the theory of Shimura varieties, or to some aspect of the interplay and application of the two areas.
Global Theory of Minimal Surfaces; Proceedings of the 2001 CMI Summer School Clay Mathematics Proceedings at MSRI. Editor: David Hoffman. CMI/AMS, 2005, 800 pp., www.claymath.org/2 Volume 2 During the Summer of 2001, MSRI
hosted the Clay Mathematics Institute Surfaces Minimal of Theory Global publications/Minimal_Surfaces. This book is the product of the 2001Summer School onCMI the Global Theory of Summer Minimal Surfaces, during which 150 mathematicians—undergraduates, post- doctoral students, young researchers, School held at MSRI. The subjects covered include minimal and constant-mean-curvatureand the world's experts—participated in GLOBAL the most extensive meeting ever held on the subject in its 250-year history. The unusual nature of the meeting has made THEORY OF submanifolds, geometric measure theory and the double-bubble conjecture,it possible to assemble a volume Lagrangian of expository lectures, together with some specialized reports that give a MINIMAL geometry, numerical simulation of geometric phenomena, applicationspanoramic of picture mean of a vital subject, curvature presented with care by the best people in the field. SURFACES
The subjects covered include minimal Proceedings of the to general relativity and Riemannian geometry, the isoperimetric problem,and constant-mean-curvature the geometry submanifolds, geometric measure theory Clay Mathematics Institute and the double-bubble conjecture, 2001 Summer School of fully nonlinear elliptic equations, and applications to the topology of Lagrangianthree-manifolds. geometry, numerical Mathematical Sciences Research Institute simulation of geometric phenomena, applications of mean curvature to Berkeley, California general relativity and Riemannian June 25 – July 27, 2001 geometry, the isoperimetric problem, the geometry of fully nonlinear elliptic equations, and applications to the David Hoffman topology of three manifolds. Editor , Editor Hoffman , Strings and Geometry; Proceedings of the 2002 CMI Summer
School held at the Isaac Newton Institute forCMIP/2 Mathematical
www.ams.org American Mathematical Society Sciences, UK. Editors: Michael Douglas, Jerome Gauntlett,AMS www.claymath.org CMI Clay Mathematics Institute Mark Gross. CMI/AMS publication, 376 pp., Paperback, ISBN 0-8218-3715-X. List: $69. AMS 4-colorMembers: process $55. Order 816 pages • 1 9/16" spine code: CMIP/3. To order, visit www.ams.org/bookstore.
Mirror Symmetry; Authors: Kentaro Hori, Sheldon Katz, Clay Mathematics Monographs MIRROR SYMMETRY 1 Volume 1 Kentaro Hori, Sheldon Katz, Albrecht Klemm, Albrecht Klemm, Rahul Pandharipande,Rahul Pandharipande, Richard Richard Thomas, Thomas, Cumrun Vafa, Ravi Vakil, Eric Zaslow Mirror Symmetry Mirror
Mirror symmetry is a phenomenon arising in string theory in which two very Ravi Vakil. Editors: Cumrun Vafa,different manifolds Eric give rise to equivalent Zaslow. physics. Such a correspondence CMI/AMS has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a “mirror” geometry. The publication, 929 pp., Hardcover. inclusionISBN of D-brane states in 0-8218-2955-6.the equivalence has led to further conjectures List: involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry $124. AMS Members: $99. Orderfrom both code:the mathematical and physicalCMIM/1. viewpoint. Parts I and II develop To order, the necessary mathematical and physical background “from scratch,” and are intended for readers trying to learn across disciplines. The treatment
is focussed, developing only the material most necessary for the task. In
Parts III and IV the physical and mathematical proofs of mirror symmetry visit www.ams.org/bookstore. MIRROR SYMMETRY are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory MIRROR SYMMETRY can be described geometrically,
and thus mirror symmetry gives rise to a “pairing” of geometries. The VafaCumrun R 1/R proof involves applying ↔ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Kentaro Hori Gromov-Witten theory in the algebraic setting, beginning with the moduli Sheldon Katz spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invari- Albrecht Klemm Strings 2001; Authors: Atish Dabholkar, Sunil Mukhi, Spenta R.ants in genus Wadia. zero, as is predicted by mirrorTata symmetry. PartInstitute V is devoted of Rahul Pandharipande to advanced topics in mirror symmetry, including the role of D-branes in Richard Thomas the context of mirror symmetry, and some of their applications in physics and mathematics. and mathematics; topological strings and large N and Cumrun Vafa Fundamental Research. Editor: American Mathematical SocietyChern-Simons (AMS), theory; geometric engineering; 2002, mirror symmetry at489 higher pp., Ravi Vakil
genus; Gopakumar-Vafa invariants; and Kontsevich's formulation of the Editors Zaslov , Eric mirror phenomenon as an equivalence of categories. Eric Zaslow This book grew out of an intense, month-long course on mirror symmetry Paperback, ISBN 0-8218-2981-5, List $74. AMS Members: $59.at Pine Manor Order College, sponsored bycode: the Clay Mathematics Institute.CMIP/1. The To several lecturers have tried to summarize this course in a coherent, order, visit www.ams.org/bookstore unified text.
Box for ISBN, Barcode and Itemcode www.ams.org American Mathematical Society AMS www.claymath.org CMI Clay Mathematics Institute Video Cassettes
The CMI Millennium Meeting Collection; Authors: Michael Atiyah, Timothy Gowers, John Tate, François Tisseyre. Editors: Tom Apostol, Jean-Pierre Bourguignon, Michele Emmer, Hans-Christian Hege, Konrad Polthier. Springer VideoMATH, © Clay Mathematics Institute, 2002. Box set consists of four video cassettes: The CMI Millennium Meeting, a film by François Tisseyre; The Importance of Mathematics, a lecture by Timothy Gowers; The Mil- lennium Prize Problems, a lecture by Michael Atiyah; and The Millennium Prize Problems, a lecture by John Tate. VHS/NTSC or PAL. ISBN 3-540-92657-7. List: $119, EUR 104.95. To order, visit www.springer-ny.com (in the United States) or www.springer.de (in Europe). These videos document the Paris meeting at the Collège de France where CMI announced the Millennium Prize Problems. The videos are for anyone who wants to learn more about these seven grand challenges in mathematics.
Videos of the 2000 Millennium event are available online and in VHS format from Springer-Verlag. To order the box set or individual tapes visit www.springer.com.
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