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 com- Ricci Flow and the plete 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 argu- ments given in the book are a detailed version of those that appear in Perelman’s three preprints.
The Millennium Prize Problems; Editors: James Carlson,$.* $MBZ.BUIFNBUJDT*OTUJUVUF ".4 "NFSJDBO.BUIFNBUJDBM4PDJFUZ 0O"VHVTU BUUIFTFDPOE*OUFSOBUJPOBM$POHSFTTPG.BUIFNBUJDJBOT Arthur Jaffe, Andrew Wiles. CMI/AMS,JO1BSJT %BWJE)JMCFSUEFMJWFSFEIJTGBNPVTMFDUVSFJOXIJDIIFEFTDSJCFE 2006, 165 pp., UXFOUZUISFFQSPCMFNTUIBUXFSFUPQMBZBOJOnVFOUJBMSPMFJONBUIFNBUJDBM 5IF.JMMFOOJVN1SJ[F1SPCMFNT SFTFBSDI"DFOUVSZMBUFS PO.BZ BUBNFFUJOHBUUIF$PMMÒHFEF 'SBODF UIF$MBZ.BUIFNBUJDT*OTUJUVUF $.* BOOPVODFEUIFDSFBUJPOPGB
Morgan and Tian and Morgan www.claymath.org/publications/Millennium_Problems. This 64NJMMJPOQSJ[FGVOEGPSUIFTPMVUJPOPGTFWFOJNQPSUBOUDMBTTJDQSPCMFNT XIJDIIBWFSFTJTUFETPMVUJPO5IFQSJ[FGVOEJTEJWJEFEFRVBMMZBNPOHUIF volume gives the official descriptionTFWFOQSPCMFNT5IFSFJTOPUJNFMJNJUGPSUIFJSTPMVUJPO of each of the seven prob- JOHN MORGAN 5IF.JMMFOOJVN1SJ[F1SPCMFNTXFSFTFMFDUFECZUIFGPVOEJOH4DJFOUJmD "EWJTPSZ#PBSEPG$.*"MBJO$POOFT "SUIVS+BGGF "OESFX8JMFT BOE 5IF.JMMFOOJVN &EXBSE8JUUFOBGUFSDPOTVMUJOHXJUIPUIFSMFBEJOHNBUIFNBUJDJBOT For additional information GANG TIAN lems as well as the rules governing5IFJSBJNXBTTPNFXIBUEJGGFSFOUUIBOUIBUPG)JMCFSUOPUUPEFmOFOFX the prizes. It also contains and updates on this book, visit DIBMMFOHFT CVUUPSFDPSETPNFPGUIFNPTUEJGmDVMUJTTVFTXJUIXIJDI www.ams.org/bookpages/cmim-3 NBUIFNBUJDJBOTXFSFTUSVHHMJOHBUUIFUVSOPGUIFTFDPOENJMMFOOJVN UP 1SJ[F1SPCMFNT SFDPHOJ[FBDIJFWFNFOUJONBUIFNBUJDTPGIJTUPSJDBMEJNFOTJPO UPFMFWBUF an essay by Jeremy Gray on the JOUIFDPOTDJPVTOFTTPGUIFHFOFSBMQVCMJDUIFGBDUUIBUJONBUIFNBUJDT UIFhistory of prize problems in AMS GSPOUJFSJTTUJMMPQFOBOEBCPVOETJOJNQPSUBOUVOTPMWFEQSPCMFNT BOEUP +$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 +$BSMTPO "+BGGF BOE"8JMFT &EJUPST
4 color process ??? pages pages on 50 lb stock • 1 3/16 spine Floer Homology, Gauge Theory, and Low-Dimensional ")JTUPSZPG1SJ[FTJO.BUIFNBUJDT +FSFNZ(SBZ Topology; Proceedings of the CMI 2004 Summer School #JSDIBOE4XJOOFSUPO%ZFS$POKFDUVSF "OESFX8JMFT )PEHF$POKFDUVSF 1JFSSF%FMJHOF at Rényi Institute of Mathematics, Budapest. Editors: David /BWJFSo4UPLFT&RVBUJPO $IBSMFT-'FGGFSNBO 1PJODBSÏ$POKFDUVSF +PIO.JMOPS 1WFSTVT/11SPCMFN 4UFQIFO$PPL XXXDMBZNBUIPSH >ÞÊ >Ì i>ÌVÃÊ*ÀVii`}Ã 3JFNBOO)ZQPUIFTJT &OSJDP#PNCJFSJ x Ellwood, Peter Ozsváth, András Stipsicz,XXXBNTPSH Zoltán Szábo. 6ÕiÊx 2VBOUVN:BOHo.JMMT5IFPSZ "SUIVS+BGGFBOE&EXBSE8JUUFO CMI/AMS, 2006, 297 pp., www.claymath.org/publications/ -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 .13*;& MATHEMATICAL PHYSICS AND PLAY AN IMPORTANT ROLE IN THE DESCRIPTION OF Floer_Homology. This volume grew out of the summer 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 school that took place in June of 2004 at the Alfréd 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 Rényi Institute of MathematicsDPMPSQSPDFTT in Budapest, Hungary. It provides QBHFTPOMCTUPDLt#BDLTQBDF a state-of-the-artJODIFT -ORSE THEORY WHICH APPLIES IN TWO A PRIORI DIFFERENT CONTEXTS EITHER 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 FOR SMOOTH FOUR MANIFOLDS h(EEGAARD &LOER HOMOLOGY THE RECENTLY introduction to current research, covering material from Heegaard Floer homology, 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 contact geometry, smooth four-manifold topology, and symplectic four-manifolds. 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 SOME OF THESE EXCITING DEVELOPMENTS WITH A SPECIAL EMPHASIS ON THE ÕiÊxqÓÈ]ÊÓää{ VERY FRUITFUL INTERPLAY BETWEEN DISCIPLINES Lecture Notes on Motivic Cohomology; Authors: Carlo Mazza, Vladimir Voevodsky, 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 Charles Weibel. CMI/AMS, 2006, 210 pp., www.claymath.org/publications/Motivic_ 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 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, and finally to relate it to other known invariants of algebraic varieties and rings such as ÜÜÜ°>ðÀ} !MERICAN -ATHEMATICAL 3OCIETY #-)0 !-3 ÜÜÜ°V>Þ>Ì °À} #-) #LAY -ATHEMATICS )NSTITUTE Milnor K-theory, étale cohomology and Chow groups.
Clay Mathematics Proceedings Surveys in Noncommutative Geometry; Editors: Nigel Higson, John Roe.The modern theoryCMI/AMS, of automorphic forms, embodied in 2006,4 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 189 pp., www.claymath.org/publications/Noncommutative_Geometry. In Juneinformation from of number 2000, theory and algebraic ageometry summer 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 school on Noncommutative Geometry, organized jointly by the American However,Mathematical their capacity to unite large areas of Society Formula, Trace 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 and the Clay Mathematics Institute, was held at Mount Holyoke College inthis exciting Massachusetts. and challenging field. It is directed on the 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 meeting centered around several series of expository lectures that were enableintended a reader to master some of theto more difficultintroduce 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 key topics in noncommutative geometry to mathematicians unfamiliar withto consult the theexpository portionssubject. of the various articles. Those 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 expository lectures have been edited and are reproduced in this volume. subject, but they have been especially difficult 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 School. However, 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 Harmonic Analysis, the Trace Formula and Shimura Varieties; Proceedingstwo areas. of the 2003 CMI
James Arthur Summer School at Fields Institute, Toronto. Editors: James Arthur, David Ellwood, Robert David Ellwood Robert Kottwitz Kottwitz. CMI/AMS, 2005, 689 pp., www.claymath.org/publications/Harmonic_Analysis. Editors The subject of this volume is the trace formula and Shimura varieties. These areasCMIP/4 haveEditors
www.ams.org American Mathematical Society been especially difficult to learn because of a lack of expository material. This volume aimsAMS www.claymath.org CMI Clay Mathematics Institute to rectify that problem. It is based on the courses given at the 2003 Clay Mathematics 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 publication ordered.
Institute Summer School. Many of the articles have been expanded into comprehensive introductions, either to the trace formula or to 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 publications/Minimal_Surfaces. This book is the product of the 2001hosted the Clay Mathematics CMI Institute Summer Surfaces Minimal of Theory Global Summer School on the Global Theory of Minimal Surfaces, during which 150 mathematicians—undergraduates, post- School held at MSRI. The subjects covered include minimal and constant-mean-curvaturedoctoral students, young researchers, and the world's experts—participated in GLOBAL the most extensive meeting ever held on submanifolds, geometric measure theory and the double-bubble conjecture,the subject in its 250-year history. Lagrangian The unusual nature of the meeting has made THEORY OF it possible to assemble a volume of expository lectures, together with some MINIMAL geometry, numerical simulation of geometric phenomena, applicationsspecialized of reportsmean that give a curvature panoramic picture of a vital subject, presented with care by the best people SURFACES to general relativity and Riemannian geometry, the isoperimetric problem,in the field. the geometry The subjects covered include minimal Proceedings of the and constant-mean-curvature submanifolds, geometric measure theory Clay Mathematics Institute of fully nonlinear elliptic equations, and applications to the topology of andthree-manifolds. the double-bubble conjecture, 2001 Summer School Lagrangian 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. Strings and Geometry; Proceedings of the 2002 CMI Summer Editor School held at the Isaac Newton Institute for MathematicalEditor Hoffman , Sciences, UK. Editors: Michael Douglas, Jerome Gauntlett, Mark Gross. CMI/AMS publication, 376CMIP/2 pp., paperback, www.ams.org American Mathematical Society AMS ISBN 0-8218-3715-X. List: $69. AMS Members:www.claymath.org $55. OrderCMI Clay Mathematics Institute
code: CMIP/3. To order, visit www.ams.org/bookstore.4-color process 816 pages • 1 9/16" spine
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 manifoldsEric give rise to equivalentZaslow. 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 inclusion of D-brane states in the equivalence has led to further conjectures 929 pp., hardcover, ISBN 0-8218-2955-6.involving calibrated submanifolds of the mirror List: pairs and new (conjectural) $124. AMS invariants of complex manifolds: the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry Members: $99. Order code: CMIM/1.from both the mathematical To and physical order,viewpoint. Parts I and II develop visit www. 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 ams.org/bookstore. are given. From the physics side, this means demonstrating that two MIRROR SYMMETRY 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 Chern-Simons theory; geometric engineering; mirror symmetry at higher Ravi Vakil
Fundamental Research. Editor: American Mathematical Society (AMS), 2002, 489 pp., Editors Zaslov , Eric genus; Gopakumar-Vafa invariants; and Kontsevich's formulation of the 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 by thecode: Clay Mathematics Institute.CMIP/1. The several lecturers have tried to summarize this course in a coherent, To 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 Fran- çois Tisseyre; The Importance of Mathematics, a lecture by Timothy Gowers; The Millen- nium 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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