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The work of Andrei Okounkov / Giovanni Felder  The work of Grigory Perelman / John Lott  The work of Terence Tao / Charles Fefferman  The work of Wendelin Werner / Charles M. Newman  The work of Jon Kleinberg / John Hopcroft  On Kiyosi Itô's work and its impact / Hans Föllmer  Universality for mathematical and physical systems / Percy Deift  Kähler manifolds and transcendental techniques in algebraic geometry / JeanPierre Demailly  Optimal computation / Ronald A. DeVore  Symplectic field theory and its applications / Yasha Eliashberg  Knots and dynamics / Étienne Ghys  Prime numbers and Lfunctions / Henryk Iwaniec  High dimensional statistical inference and random matrices / Iain M. Johnstone  Iwasawa theory and generalizations / Kazuya Kato  Energydriven pattern formation / Robert V. Kohn  Moduli spaces from a topological viewpoint / Jørgen Ellegaard Andersen  Advances in convex optimization: conic programming / Arkadi Nemirovski  Deformation and rigidity for group actions and von Neumann algebras / Sorin Popa  Cardiovascular mathematics / Alfio Quarteroni  Conformally invariant scaling limits: an overview and a collection of problems / Oded Schramm  Increasing and decreasing subsequences and their variants / Richard P. Stanley  The dichotomy between structure and randomness, arithmetic progressions, and the primes / Terence Tao  Perspectives in nonlinear diffusion: between analysis, physics and geometry / Juan Luis Vázquez  Applications of equivariant cohomology / Michèle Vergne  P, NP and mathematics – a computational complexity perspective / Avi Wigderson  The Poincaré Conjecture / John W. Morgan  Panel discussion: Should mathematicians care about communicating to broad audiences? Theory and practice  ICM 2006 Closing round table: Are pure and applied mathematics drifting apart?  From the private to the public: The road from Zurich (1897) to Madrid (2006) / José M. SánchezRon  Algorithmic randomness and computability / Rodney G. Downey  Determinacy and large cardinals / Itay Neeman  The art of ordinal analysis / Michael Rathjen  Analytic difference rings / Thomas Scanlon  Borel superrigidity and the classification problem for the torsionfree abelian groups of finite rank / Simon Thomas  Quiver algebras, weighted projective lines, and the Deligne–Simpson problem / William CrawleyBoevey  Zeta functions of groups and rings / Marcus J. du Sautoy, Fritz Grunewald  On differential graded categories / Bernhard Keller  Derived equivalences and finite dimensional algebras / Raphaël Rouquier  Algorithmic and asymptotic properties of groups / Mark V. Sapir  A unified approach to computations with permutation and matrix groups / Ákos Seress  Some results in noncommutative ring theory / Agata Smoktunowicz  Higher composition laws and applications / Manjul Bhargava  Higher composition laws and applications / ChingLi Chai  Heegner points, Stark–Heegner points, and values of Lseries / Henri Darmon  Galois deformations and arithmetic geometry of Shimura varieties / Kazuhiro Fujiwara  Generalising the Hardy–Littlewood method for primes / Ben J. Green  Aspects géométriques du Lemme Fondamental de LanglandsShelstad / Gérard Laumon  Equidistribution, Lfunctions and ergodic theory: on some problems of Yu. Linnik / Philippe Michel, Akshay Venkatesh  padic motivic cohomology in arithmetic / Wiesława Nizioł  Vanishing of Lfunctions and ranks of Selmer groups / Christopher Skinner, Eric Urban  Special values of Lfunctions modulo p / Vinayak Vatsal  Higherdimensional analogues of stable curves / Valery Alexeev  Evaluation maps, slopes, and algebraicity criteria / JeanBenoît Bost  Derived categories of coherent sheaves / Tom Bridgeland  Invariants of singularities of pairs / Lawrence Ein, Mircea Mustaţă  Rational curves and rational points / Tom Graber  Rigidity of rational homogeneous spaces / JunMuk Hwang  Geometry of multiple zeta values / Tomohide Terasoma  Geometry over nonclosed fields / Yuri Tschinkel  Algebraic Morse theory and the weak factorization theorem / Jarosław Włodarczyk  Manifolds with positive curvature operators are space forms / Christoph Böhm, Burkhard Wilking  Elliptic and parabolic problems in conformal geometry / Simon Brendle  The topology and geometry of contact structures in dimension three / Ko Honda  Generalized triangle inequalities and their applications / Michael Kapovich  The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity / Bruce Kleiner  Lagrangian submanifolds: from the local model to the cluster complex / Philippe Charron  Gromov–Witten invariants and moduli spaces of curves / Xiaobo Liu  Extremal metrics and stabilities on polarized manifolds / Toshiki Mabuchi  Tropical geometry and its applications / Grigory Mikhalkin  Embedded minimal surfaces / William P. Minicozzi II  Floer homology in symplectic geometry and in mirror symmetry / YongGeun Oh, Kenji Fukaya  Properly embedded minimal surfaces with finite topology / Antonio Ros  Applications of loop group factorization to geometric soliton equations / ChuuLian Terng  Finiteness of arithmetic Kleinian reflection groups / Ian Agol  Nonpositive curvature and complexity for finitely presented groups / Martin R. Bridson  Link homology and categorification / Aaron D. Lauda  Curve complexes, surfaces and 3manifolds / Yair N. Minsky  A1algebraic topology / Fabien Morel  Development in symplectic Floer theory / Kaoru Ono  Heegaard diagrams and Floer homology / Peter Ozsváth, Zoltán Szabó  The cohomology of automorphism groups of free groups / Karen Vogtmann  Noncommutative counterparts of the Springer resolution / Roman Bezrukavnikov  Spaces of quasimaps into the flag varieties and their applications / Alexander Braverman  On the local Langlands and Jacquet–Langlands correspondences / Guy Henniart  An invitation to bounded cohomology / Nicolas Monod  Fibration de Hitchin et structure endoscopique de la formule des traces / BaoChâu Ngô  Hecke algebras and harmonic analysis / Eric M. Opdam  Continuous representation theory of padic Lie groups / Peter Schneider  The algebraization of Kazhdan’s property (T) / Yehuda Shalom  Rankin–Selberg integrals, the descent method, and Langlands functoriality / David Soudry  Representation theory and the cohomology of arithmetic groups / Birgit Speh  Some results on compactifications of semisimple groups / Tonny A. Springer  Quasiconformal geometry of fractals / Mario Bonk  Local Tb theorems and applications in PDE / Dorina Mitrea  Almost everywhere convergence and divergence of Fourier series / Sergey V. Konyagin  Iterated Segre mappings of real submanifolds in complex space and applications / Linda Preiss Rothschild  Towards conformal invariance of 2D lattice models / Stanislav Smirnov  Aspects of the L2Sobolev theory of the ∂Neumann problem / Emil J. Straube  Greedy approximations with regard to bases / Vladimir N. Temlyakov  Analytic capacity, rectifiability, and the Cauchy integral / Xavier Tolsa  The Brunn–Minkowski theorem and related geometric and functional inequalities / Franck Barthe  Isomorphic and almostisometric problems in highdimensional convex geometry / Bo'az Klartag  Amenable actions and applications / Narutaka Ozawa  Structure and classification of C*algebras / Mikael Rørdam  Convexity, complexity, and high dimensions / Stanislaw J. Szarek  Higher index theory of elliptic operators and geometry of groups / Guoliang Yu  On spectral invariants in modern ergodic theory / Oleg N. Ageev  Ergodic Ramsey theory: a dynamical approach to static theorems / Vitaly Bergelson  Hyperbolic billiards and statistical physics / Nikolai Chernov, Dmitry Dolgopyat  Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics / Rafael de la Llave  Diagonalizable flows on locally homogeneous spaces and number theory / Manfred Einsiedler, Elon Lindenstrauss  Braids and differential equations / Robert Ghrist  Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems / Anton Gorodetski, Brian Hunt, Vadim Kaloshin  From combinatorics to ergodic theory and back again / Bryna Kra  From Brouwer theory to the study of homeomorphisms of surfaces / Patrice Le Calvez  All, most, some differentiable dynamical systems / Michael Shub  Geodesics on ﬂat surfaces / Anton Zorich  Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximation / Stefano Bianchini  Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem / Patrick Gérard 

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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 threevolume 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 
Subject 
Mathematics bicssc


General msc

Alt Author 
SanzSolé, Marta, editor


Soria, Javier, editor


Varona, Juan Luis, editor


Verdera, Joan, editor

