Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006
Volume II. Invited Lectures
Editors
Marta Sanz-Solé
Universitat de Barcelona, SpainJavier Soria
Universitat de Barcelona, SpainJuan L. Varona
Universidad de La Rioja, Logroño, SpainJoan Verdera
Universitat Autónoma de Barcelona, Spain
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Note: The ICM2006 Proceedings are available only as a set, individual volumes cannot be ordered.
The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress.
The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject.
pp. i–iv Front matterpp. v–x Contentspp. 1–26 Algorithmic randomness and computabilityRodney G. Downey
pp. 27–43 Determinacy and large cardinalsItay Neeman
pp. 45–69 The art of ordinal analysisMichael Rathjen
pp. 71–92 Analytic difference ringsThomas Scanlon
pp. 93–116 Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rankSimon Thomas
pp. 117–129 Quiver algebras, weighted projective lines, and the Deligne–Simpson problemWilliam Crawley-Boevey
pp. 131–149 Zeta functions of groups and ringsMarcus J. du SautoyFritz Grunewald
pp. 151–190 On differential graded categoriesBernhard Keller
pp. 191–221 Derived equivalences and finite dimensional algebrasRaphaël Rouquier
pp. 223–244 Algorithmic and asymptotic properties of groupsMark V. Sapir
pp. 245–258 A unified approach to computations with permutation and matrix groupsÁkos Seress
pp. 259–269 Some results in noncommutative ring theoryAgata Smoktunowicz
pp. 271–294 Higher composition laws and applicationsManjul Bhargava
pp. 295–312 Higher composition laws and applicationsChing-Li Chai
pp. 313–345 Heegner points, Stark–Heegner points, and values of -seriesHenri Darmon
pp. 347–371 Galois deformations and arithmetic geometry of Shimura varietiesKazuhiro Fujiwara
pp. 373–399 Generalising the Hardy–Littlewood method for primesBen J. Green
pp. 401–419 Aspects géométriques du Lemme Fondamental de Langlands-ShelstadGérard Laumon
pp. 421–457 Equidistribution, -functions and ergodic theory: on some problems of Yu. LinnikPhilippe MichelAkshay Venkatesh
pp. 459–472 -adic motivic cohomology in arithmeticWiesława Nizioł
pp. 473–500 Vanishing of -functions and ranks of Selmer groupsChristopher SkinnerEric Urban
pp. 501–514 Special values of -functions moduloVinayak Vatsal
pp. 515–536 Higher-dimensional analogues of stable curvesValery Alexeev
pp. 537–562 Evaluation maps, slopes, and algebraicity criteriaJean-Benoît Bost
pp. 563–582 Derived categories of coherent sheavesTom Bridgeland
pp. 583–602 Invariants of singularities of pairsLawrence EinMircea Mustaţă
pp. 603–611 Rational curves and rational pointsTom Graber
pp. 613–626 Rigidity of rational homogeneous spacesJun-Muk Hwang
pp. 627–635 Geometry of multiple zeta valuesTomohide Terasoma
pp. 637–651 Geometry over nonclosed fieldsYuri Tschinkel
pp. 653–682 Algebraic Morse theory and the weak factorization theoremJarosław Włodarczyk
pp. 683–690 Manifolds with positive curvature operators are space formsChristoph BöhmBurkhard Wilking
pp. 691–704 Elliptic and parabolic problems in conformal geometrySimon Brendle
pp. 705–717 The topology and geometry of contact structures in dimension threeKo Honda
pp. 719–741 Generalized triangle inequalities and their applicationsMichael Kapovich
pp. 743–768 The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidityBruce Kleiner
pp. 769–789 Lagrangian submanifolds: from the local model to the cluster complexFrançois Lalonde
pp. 791–812 Gromov–Witten invariants and moduli spaces of curvesXiaobo Liu
pp. 813–826 Extremal metrics and stabilities on polarized manifoldsToshiki Mabuchi
pp. 827–852 Tropical geometry and its applicationsGrigory Mikhalkin
pp. 853–877 Embedded minimal surfacesWilliam P. Minicozzi II
pp. 879–905 Floer homology in symplectic geometry and in mirror symmetryKenji FukayaYong-Geun Oh
pp. 907–926 Properly embedded minimal surfaces with finite topologyAntonio Ros
pp. 927–950 Applications of loop group factorization to geometric soliton equationsChuu-Lian Terng
pp. 951–960 Finiteness of arithmetic Kleinian reflection groupsIan Agol
pp. 961–987 Non-positive curvature and complexity for finitely presented groupsMartin R. Bridson
pp. 989–999 Link homology and categorificationMikhail Khovanov
pp. 1001–1033 Curve complexes, surfaces and 3-manifoldsYair N. Minsky
pp. 1035–1059 -algebraic topologyFabien Morel
pp. 1061–1082 Development in symplectic Floer theoryKaoru Ono
pp. 1083–1099 Heegaard diagrams and Floer homologyPeter S. OzsváthZoltán Szabó
pp. 1101–1117 The cohomology of automorphism groups of free groupsKaren Vogtmann
pp. 1119–1144 Noncommutative counterparts of the Springer resolutionRoman Bezrukavnikov
pp. 1145–1170 Spaces of quasi-maps into the flag varieties and their applicationsAlexander Braverman
pp. 1171–1182 On the local Langlands and Jacquet–Langlands correspondencesGuy Henniart
pp. 1183–1211 An invitation to bounded cohomologyNicolas Monod
pp. 1213–1225 Fibration de Hitchin et structure endoscopique de la formule des tracesBao-Châu Ngô
pp. 1227–1259 Hecke algebras and harmonic analysisEric M. Opdam
pp. 1261–1282 Continuous representation theory of -adic Lie groupsPeter Schneider
pp. 1283–1310 The algebraization of Kazhdan’s property (T)Yehuda Shalom
pp. 1311–1325 Rankin–Selberg integrals, the descent method, and Langlands functorialityDavid Soudry
pp. 1327–1335 Representation theory and the cohomology of arithmetic groupsBirgit Speh
pp. 1337–1348 Some results on compactifications of semisimple groupsTonny A. Springer
pp. 1349–1373 Quasiconformal geometry of fractalsMario Bonk
pp. 1375–1392 Local theorems and applications in PDESteve Hofmann
pp. 1393–1403 Almost everywhere convergence and divergence of Fourier seriesSergey Konyagin
pp. 1405–1419 Iterated Segre mappings of real submanifolds in complex space and applicationsLinda Preiss Rothschild
pp. 1421–1451 Towards conformal invariance of 2D lattice modelsStanislav Smirnov
pp. 1453–1478 Aspects of the -Sobolev theory of the -Neumann problemEmil J. Straube
pp. 1479–1504 Greedy approximations with regard to basesVladimir N. Temlyakov
pp. 1505–1527 Analytic capacity, rectifiability, and the Cauchy integralXavier Tolsa
pp. 1529–1546 The Brunn–Minkowski theorem and related geometric and functional inequalitiesFranck Barthe
pp. 1547–1562 Isomorphic and almost-isometric problems in high-dimensional convex geometryBo'az Klartag
pp. 1563–1580 Amenable actions and applicationsNarutaka Ozawa
pp. 1581–1598 Structure and classification of -algebrasMikael Rørdam
pp. 1599–1621 Convexity, complexity, and high dimensionsStanislaw J. Szarek
pp. 1623–1639 Higher index theory of elliptic operators and geometry of groupsGuoliang Yu
pp. 1641–1653 On spectral invariants in modern ergodic theoryOleg N. Ageev
pp. 1655–1678 Ergodic Ramsey theory: a dynamical approach to static theoremsVitaly Bergelson
pp. 1679–1704 Hyperbolic billiards and statistical physicsNikolai ChernovDmitry Dolgopyat
pp. 1705–1729 Some recent progress in geometric methods in the instability problem in Hamiltonian mechanicsRafael de la Llave
pp. 1731–1759 Diagonalizable flows on locally homogeneous spaces and number theoryManfred EinsiedlerElon Lindenstrauss