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
DOI 10.4171/022-2/1pp. 27–43 Determinacy and large cardinalsItay Neeman
DOI 10.4171/022-2/2pp. 45–69 The art of ordinal analysisMichael Rathjen
DOI 10.4171/022-2/3pp. 71–92 Analytic difference ringsThomas Scanlon
DOI 10.4171/022-2/4pp. 93–116 Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rankSimon Thomas
DOI 10.4171/022-2/5pp. 117–129 Quiver algebras, weighted projective lines, and the Deligne–Simpson problemWilliam Crawley-Boevey
DOI 10.4171/022-2/6pp. 131–149 Zeta functions of groups and ringsMarcus J. du SautoyFritz Grunewald
DOI 10.4171/022-2/7pp. 151–190 On differential graded categoriesBernhard Keller
DOI 10.4171/022-2/8pp. 191–221 Derived equivalences and finite dimensional algebrasRaphaël Rouquier
DOI 10.4171/022-2/9pp. 223–244 Algorithmic and asymptotic properties of groupsMark V. Sapir
DOI 10.4171/022-2/10pp. 245–258 A unified approach to computations with permutation and matrix groupsÁkos Seress
DOI 10.4171/022-2/11pp. 259–269 Some results in noncommutative ring theoryAgata Smoktunowicz
DOI 10.4171/022-2/12pp. 271–294 Higher composition laws and applicationsManjul Bhargava
DOI 10.4171/022-2/13pp. 295–312 Higher composition laws and applicationsChing-Li Chai
DOI 10.4171/022-2/14pp. 313–345 Heegner points, Stark–Heegner points, and values of -seriesHenri Darmon
DOI 10.4171/022-2/15pp. 347–371 Galois deformations and arithmetic geometry of Shimura varietiesKazuhiro Fujiwara
DOI 10.4171/022-2/16pp. 373–399 Generalising the Hardy–Littlewood method for primesBen J. Green
DOI 10.4171/022-2/17pp. 401–419 Aspects géométriques du Lemme Fondamental de Langlands-ShelstadGérard Laumon
DOI 10.4171/022-2/18pp. 421–457 Equidistribution, -functions and ergodic theory: on some problems of Yu. LinnikPhilippe MichelAkshay Venkatesh
DOI 10.4171/022-2/19pp. 459–472 -adic motivic cohomology in arithmeticWiesława Nizioł
DOI 10.4171/022-2/20pp. 473–500 Vanishing of -functions and ranks of Selmer groupsChristopher SkinnerEric Urban
DOI 10.4171/022-2/21pp. 501–514 Special values of -functions moduloVinayak Vatsal
DOI 10.4171/022-2/22pp. 515–536 Higher-dimensional analogues of stable curvesValery Alexeev
DOI 10.4171/022-2/23pp. 537–562 Evaluation maps, slopes, and algebraicity criteriaJean-Benoît Bost
DOI 10.4171/022-2/24pp. 563–582 Derived categories of coherent sheavesTom Bridgeland
DOI 10.4171/022-2/25pp. 583–602 Invariants of singularities of pairsLawrence EinMircea Mustaţă
DOI 10.4171/022-2/26pp. 603–611 Rational curves and rational pointsTom Graber
DOI 10.4171/022-2/27pp. 613–626 Rigidity of rational homogeneous spacesJun-Muk Hwang
DOI 10.4171/022-2/28pp. 627–635 Geometry of multiple zeta valuesTomohide Terasoma
DOI 10.4171/022-2/29pp. 637–651 Geometry over nonclosed fieldsYuri Tschinkel
DOI 10.4171/022-2/30pp. 653–682 Algebraic Morse theory and the weak factorization theoremJarosław Włodarczyk
DOI 10.4171/022-2/31pp. 683–690 Manifolds with positive curvature operators are space formsChristoph BöhmBurkhard Wilking
DOI 10.4171/022-2/32pp. 691–704 Elliptic and parabolic problems in conformal geometrySimon Brendle
DOI 10.4171/022-2/33pp. 705–717 The topology and geometry of contact structures in dimension threeKo Honda
DOI 10.4171/022-2/34pp. 719–741 Generalized triangle inequalities and their applicationsMichael Kapovich
DOI 10.4171/022-2/35pp. 743–768 The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidityBruce Kleiner
DOI 10.4171/022-2/36pp. 769–789 Lagrangian submanifolds: from the local model to the cluster complexFrançois Lalonde
DOI 10.4171/022-2/37pp. 791–812 Gromov–Witten invariants and moduli spaces of curvesXiaobo Liu
DOI 10.4171/022-2/38pp. 813–826 Extremal metrics and stabilities on polarized manifoldsToshiki Mabuchi
DOI 10.4171/022-2/39pp. 827–852 Tropical geometry and its applicationsGrigory Mikhalkin
DOI 10.4171/022-2/40pp. 853–877 Embedded minimal surfacesWilliam P. Minicozzi II
DOI 10.4171/022-2/41pp. 879–905 Floer homology in symplectic geometry and in mirror symmetryKenji FukayaYong-Geun Oh
DOI 10.4171/022-2/42pp. 907–926 Properly embedded minimal surfaces with finite topologyAntonio Ros
DOI 10.4171/022-2/43pp. 927–950 Applications of loop group factorization to geometric soliton equationsChuu-Lian Terng
DOI 10.4171/022-2/44pp. 951–960 Finiteness of arithmetic Kleinian reflection groupsIan Agol
DOI 10.4171/022-2/45pp. 961–987 Non-positive curvature and complexity for finitely presented groupsMartin R. Bridson
DOI 10.4171/022-2/46pp. 989–999 Link homology and categorificationMikhail Khovanov
DOI 10.4171/022-2/47pp. 1001–1033 Curve complexes, surfaces and 3-manifoldsYair N. Minsky
DOI 10.4171/022-2/48pp. 1035–1059 -algebraic topologyFabien Morel
DOI 10.4171/022-2/49pp. 1061–1082 Development in symplectic Floer theoryKaoru Ono
DOI 10.4171/022-2/50pp. 1083–1099 Heegaard diagrams and Floer homologyPeter S. OzsváthZoltán Szabó
DOI 10.4171/022-2/51pp. 1101–1117 The cohomology of automorphism groups of free groupsKaren Vogtmann
DOI 10.4171/022-2/52pp. 1119–1144 Noncommutative counterparts of the Springer resolutionRoman Bezrukavnikov
DOI 10.4171/022-2/53pp. 1145–1170 Spaces of quasi-maps into the flag varieties and their applicationsAlexander Braverman
DOI 10.4171/022-2/54pp. 1171–1182 On the local Langlands and Jacquet–Langlands correspondencesGuy Henniart
DOI 10.4171/022-2/55pp. 1183–1211 An invitation to bounded cohomologyNicolas Monod
DOI 10.4171/022-2/56pp. 1213–1225 Fibration de Hitchin et structure endoscopique de la formule des tracesBao-Châu Ngô
DOI 10.4171/022-2/57pp. 1227–1259 Hecke algebras and harmonic analysisEric M. Opdam
DOI 10.4171/022-2/58pp. 1261–1282 Continuous representation theory of -adic Lie groupsPeter Schneider
DOI 10.4171/022-2/59pp. 1283–1310 The algebraization of Kazhdan’s property (T)Yehuda Shalom
DOI 10.4171/022-2/60pp. 1311–1325 Rankin–Selberg integrals, the descent method, and Langlands functorialityDavid Soudry
DOI 10.4171/022-2/61pp. 1327–1335 Representation theory and the cohomology of arithmetic groupsBirgit Speh
DOI 10.4171/022-2/62pp. 1337–1348 Some results on compactifications of semisimple groupsTonny A. Springer
DOI 10.4171/022-2/63pp. 1349–1373 Quasiconformal geometry of fractalsMario Bonk
DOI 10.4171/022-2/64pp. 1375–1392 Local theorems and applications in PDESteve Hofmann
DOI 10.4171/022-2/65pp. 1393–1403 Almost everywhere convergence and divergence of Fourier seriesSergey Konyagin
DOI 10.4171/022-2/66pp. 1405–1419 Iterated Segre mappings of real submanifolds in complex space and applicationsLinda Preiss Rothschild
DOI 10.4171/022-2/67pp. 1421–1451 Towards conformal invariance of 2D lattice modelsStanislav Smirnov
DOI 10.4171/022-2/68pp. 1453–1478 Aspects of the -Sobolev theory of the -Neumann problemEmil J. Straube
DOI 10.4171/022-2/69pp. 1479–1504 Greedy approximations with regard to basesVladimir N. Temlyakov
DOI 10.4171/022-2/70pp. 1505–1527 Analytic capacity, rectifiability, and the Cauchy integralXavier Tolsa
DOI 10.4171/022-2/71pp. 1529–1546 The Brunn–Minkowski theorem and related geometric and functional inequalitiesFranck Barthe
DOI 10.4171/022-2/72pp. 1547–1562 Isomorphic and almost-isometric problems in high-dimensional convex geometryBo'az Klartag
DOI 10.4171/022-2/73pp. 1563–1580 Amenable actions and applicationsNarutaka Ozawa
DOI 10.4171/022-2/74pp. 1581–1598 Structure and classification of -algebrasMikael Rørdam
DOI 10.4171/022-2/75pp. 1599–1621 Convexity, complexity, and high dimensionsStanislaw J. Szarek
DOI 10.4171/022-2/76pp. 1623–1639 Higher index theory of elliptic operators and geometry of groupsGuoliang Yu
DOI 10.4171/022-2/77pp. 1641–1653 On spectral invariants in modern ergodic theoryOleg N. Ageev
DOI 10.4171/022-2/78pp. 1655–1678 Ergodic Ramsey theory: a dynamical approach to static theoremsVitaly Bergelson
DOI 10.4171/022-2/79pp. 1679–1704 Hyperbolic billiards and statistical physicsNikolai ChernovDmitry Dolgopyat
DOI 10.4171/022-2/80pp. 1705–1729 Some recent progress in geometric methods in the instability problem in Hamiltonian mechanicsRafael de la Llave
DOI 10.4171/022-2/81pp. 1731–1759 Diagonalizable flows on locally homogeneous spaces and number theoryManfred EinsiedlerElon Lindenstrauss
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