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 / Jean-Pierre Demailly -- Optimal computation / Ronald A. DeVore -- Symplectic field theory and its applications / Yasha Eliashberg -- Knots and dynamics / Étienne Ghys -- Prime numbers and L-functions / Henryk Iwaniec -- High dimensional statistical inference and random matrices / Iain M. Johnstone -- Iwasawa theory and generalizations / Kazuya Kato -- Energy-driven 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. Sánchez-Ron -- 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 torsion-free abelian groups of finite rank / Simon Thomas -- Quiver algebras, weighted projective lines, and the Deligne–Simpson problem / William Crawley-Boevey -- 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 / Ching-Li Chai -- Heegner points, Stark–Heegner points, and values of L-series / 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 Langlands-Shelstad / Gérard Laumon -- Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik / Philippe Michel, Akshay Venkatesh -- p-adic motivic cohomology in arithmetic / Wiesława Nizioł -- Vanishing of L-functions and ranks of Selmer groups / Christopher Skinner, Eric Urban -- Special values of L-functions modulo p / Vinayak Vatsal -- Higher-dimensional analogues of stable curves / Valery Alexeev -- Evaluation maps, slopes, and algebraicity criteria / Jean-Benoît 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 / Jun-Muk 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 / Yong-Geun Oh, Kenji Fukaya -- Properly embedded minimal surfaces with finite topology / Antonio Ros -- Applications of loop group factorization to geometric soliton equations / Chuu-Lian Terng -- Finiteness of arithmetic Kleinian reflection groups / Ian Agol -- Non-positive curvature and complexity for finitely presented groups / Martin R. Bridson -- Link homology and categorification / Aaron D. Lauda -- Curve complexes, surfaces and 3-manifolds / Yair N. Minsky -- A1-algebraic 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 quasi-maps 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 / Bao-Châu Ngô -- Hecke algebras and harmonic analysis / Eric M. Opdam -- Continuous representation theory of p-adic 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 L2-Sobolev 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 almost-isometric problems in high-dimensional 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 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.