Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 [electronic resource] /
Marta Sanz-Solé, Javier Soria, Juan Luis Varona, Joan Verdera
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2007
- 1 online resource (4392 pages)
The work of Andrei Okounkov / The work of Grigory Perelman / The work of Terence Tao / The work of Wendelin Werner / The work of Jon Kleinberg / On Kiyosi Itô's work and its impact / Universality for mathematical and physical systems / Kähler manifolds and transcendental techniques in algebraic geometry / Optimal computation / Symplectic field theory and its applications / Knots and dynamics / Prime numbers and L-functions / High dimensional statistical inference and random matrices / Iwasawa theory and generalizations / Energy-driven pattern formation / Moduli spaces from a topological viewpoint / Advances in convex optimization: conic programming / Deformation and rigidity for group actions and von Neumann algebras / Cardiovascular mathematics / Conformally invariant scaling limits: an overview and a collection of problems / Increasing and decreasing subsequences and their variants / The dichotomy between structure and randomness, arithmetic progressions, and the primes / Perspectives in nonlinear diffusion: between analysis, physics and geometry / Applications of equivariant cohomology / P, NP and mathematics – a computational complexity perspective / The Poincaré Conjecture / 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) / Algorithmic randomness and computability / Determinacy and large cardinals / The art of ordinal analysis / Analytic difference rings / Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rank / Quiver algebras, weighted projective lines, and the Deligne–Simpson problem / Zeta functions of groups and rings / On differential graded categories / Derived equivalences and finite dimensional algebras / Algorithmic and asymptotic properties of groups / A unified approach to computations with permutation and matrix groups / Some results in noncommutative ring theory / Higher composition laws and applications / Higher composition laws and applications / Heegner points, Stark–Heegner points, and values of L-series / Galois deformations and arithmetic geometry of Shimura varieties / Generalising the Hardy–Littlewood method for primes / Aspects géométriques du Lemme Fondamental de Langlands-Shelstad / Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik / p-adic motivic cohomology in arithmetic / Vanishing of L-functions and ranks of Selmer groups / Special values of L-functions modulo p / Higher-dimensional analogues of stable curves / Evaluation maps, slopes, and algebraicity criteria / Derived categories of coherent sheaves / Invariants of singularities of pairs / Rational curves and rational points / Rigidity of rational homogeneous spaces / Geometry of multiple zeta values / Geometry over nonclosed fields / Algebraic Morse theory and the weak factorization theorem / Manifolds with positive curvature operators are space forms / Elliptic and parabolic problems in conformal geometry / The topology and geometry of contact structures in dimension three / Generalized triangle inequalities and their applications / The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity / Lagrangian submanifolds: from the local model to the cluster complex / Gromov–Witten invariants and moduli spaces of curves / Extremal metrics and stabilities on polarized manifolds / Tropical geometry and its applications / Embedded minimal surfaces / Floer homology in symplectic geometry and in mirror symmetry / Properly embedded minimal surfaces with finite topology / Applications of loop group factorization to geometric soliton equations / Finiteness of arithmetic Kleinian reflection groups / Non-positive curvature and complexity for finitely presented groups / Link homology and categorification / Curve complexes, surfaces and 3-manifolds / A1-algebraic topology / Development in symplectic Floer theory / Heegaard diagrams and Floer homology / The cohomology of automorphism groups of free groups / Noncommutative counterparts of the Springer resolution / Spaces of quasi-maps into the flag varieties and their applications / On the local Langlands and Jacquet–Langlands correspondences / An invitation to bounded cohomology / Fibration de Hitchin et structure endoscopique de la formule des traces / Hecke algebras and harmonic analysis / Continuous representation theory of p-adic Lie groups / The algebraization of Kazhdan’s property (T) / Rankin–Selberg integrals, the descent method, and Langlands functoriality / Representation theory and the cohomology of arithmetic groups / Some results on compactifications of semisimple groups / Quasiconformal geometry of fractals / Local Tb theorems and applications in PDE / Almost everywhere convergence and divergence of Fourier series / Iterated Segre mappings of real submanifolds in complex space and applications / Towards conformal invariance of 2D lattice models / Aspects of the L2-Sobolev theory of the ∂-Neumann problem / Greedy approximations with regard to bases / Analytic capacity, rectifiability, and the Cauchy integral / The Brunn–Minkowski theorem and related geometric and functional inequalities / Isomorphic and almost-isometric problems in high-dimensional convex geometry / Amenable actions and applications / Structure and classification of C*-algebras / Convexity, complexity, and high dimensions / Higher index theory of elliptic operators and geometry of groups / On spectral invariants in modern ergodic theory / Giovanni Felder -- John Lott -- Charles Fefferman -- Charles M. Newman -- John Hopcroft -- Hans Föllmer -- Percy Deift -- Jean-Pierre Demailly -- Ronald A. DeVore -- Yasha Eliashberg -- Étienne Ghys -- Henryk Iwaniec -- Iain M. Johnstone -- Kazuya Kato -- Robert V. Kohn -- Jørgen Ellegaard Andersen -- Arkadi Nemirovski -- Sorin Popa -- Alfio Quarteroni -- Oded Schramm -- Richard P. Stanley -- Terence Tao -- Juan Luis Vázquez -- Michèle Vergne -- Avi Wigderson -- John W. Morgan -- José M. Sánchez-Ron -- Rodney G. Downey -- Itay Neeman -- Michael Rathjen -- Thomas Scanlon -- Simon Thomas -- William Crawley-Boevey -- Marcus J. du Sautoy, Fritz Grunewald -- Bernhard Keller -- Raphaël Rouquier -- Mark V. Sapir -- Ákos Seress -- Agata Smoktunowicz -- Manjul Bhargava -- Ching-Li Chai -- Henri Darmon -- Kazuhiro Fujiwara -- Ben J. Green -- Gérard Laumon -- Philippe Michel, Akshay Venkatesh -- Wiesława Nizioł -- Christopher Skinner, Eric Urban -- Vinayak Vatsal -- Valery Alexeev -- Jean-Benoît Bost -- Tom Bridgeland -- Lawrence Ein, Mircea Mustaţă -- Tom Graber -- Jun-Muk Hwang -- Tomohide Terasoma -- Yuri Tschinkel -- Jarosław Włodarczyk -- Christoph Böhm, Burkhard Wilking -- Simon Brendle -- Ko Honda -- Michael Kapovich -- Bruce Kleiner -- Philippe Charron -- Xiaobo Liu -- Toshiki Mabuchi -- Grigory Mikhalkin -- William P. Minicozzi II -- Yong-Geun Oh, Kenji Fukaya -- Antonio Ros -- Chuu-Lian Terng -- Ian Agol -- Martin R. Bridson -- Aaron D. Lauda -- Yair N. Minsky -- Fabien Morel -- Kaoru Ono -- Peter Ozsváth, Zoltán Szabó -- Karen Vogtmann -- Roman Bezrukavnikov -- Alexander Braverman -- Guy Henniart -- Nicolas Monod -- Bao-Châu Ngô -- Eric M. Opdam -- Peter Schneider -- Yehuda Shalom -- David Soudry -- Birgit Speh -- Tonny A. Springer -- Mario Bonk -- Dorina Mitrea -- Sergey V. Konyagin -- Linda Preiss Rothschild -- Stanislav Smirnov -- Emil J. Straube -- Vladimir N. Temlyakov -- Xavier Tolsa -- Franck Barthe -- Bo'az Klartag -- Narutaka Ozawa -- Mikael Rørdam -- Stanislaw J. Szarek -- Guoliang Yu -- Oleg N. Ageev -- Ergodic Ramsey theory: a dynamical approach to static theorems / Hyperbolic billiards and statistical physics / Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics / Diagonalizable flows on locally homogeneous spaces and number theory / Braids and differential equations / Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems / From combinatorics to ergodic theory and back again / From Brouwer theory to the study of homeomorphisms of surfaces / All, most, some differentiable dynamical systems / Geodesics on flat surfaces / Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximation / Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem / Vitaly Bergelson -- Nikolai Chernov, Dmitry Dolgopyat -- Rafael de la Llave -- Manfred Einsiedler, Elon Lindenstrauss -- Robert Ghrist -- Anton Gorodetski, Brian Hunt, Vadim Kaloshin -- Bryna Kra -- Patrice Le Calvez -- Michael Shub -- Anton Zorich -- Stefano Bianchini -- Patrick Gérard.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037195222
10.4171/022 doi
Mathematics
General
The work of Andrei Okounkov / The work of Grigory Perelman / The work of Terence Tao / The work of Wendelin Werner / The work of Jon Kleinberg / On Kiyosi Itô's work and its impact / Universality for mathematical and physical systems / Kähler manifolds and transcendental techniques in algebraic geometry / Optimal computation / Symplectic field theory and its applications / Knots and dynamics / Prime numbers and L-functions / High dimensional statistical inference and random matrices / Iwasawa theory and generalizations / Energy-driven pattern formation / Moduli spaces from a topological viewpoint / Advances in convex optimization: conic programming / Deformation and rigidity for group actions and von Neumann algebras / Cardiovascular mathematics / Conformally invariant scaling limits: an overview and a collection of problems / Increasing and decreasing subsequences and their variants / The dichotomy between structure and randomness, arithmetic progressions, and the primes / Perspectives in nonlinear diffusion: between analysis, physics and geometry / Applications of equivariant cohomology / P, NP and mathematics – a computational complexity perspective / The Poincaré Conjecture / 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) / Algorithmic randomness and computability / Determinacy and large cardinals / The art of ordinal analysis / Analytic difference rings / Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rank / Quiver algebras, weighted projective lines, and the Deligne–Simpson problem / Zeta functions of groups and rings / On differential graded categories / Derived equivalences and finite dimensional algebras / Algorithmic and asymptotic properties of groups / A unified approach to computations with permutation and matrix groups / Some results in noncommutative ring theory / Higher composition laws and applications / Higher composition laws and applications / Heegner points, Stark–Heegner points, and values of L-series / Galois deformations and arithmetic geometry of Shimura varieties / Generalising the Hardy–Littlewood method for primes / Aspects géométriques du Lemme Fondamental de Langlands-Shelstad / Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik / p-adic motivic cohomology in arithmetic / Vanishing of L-functions and ranks of Selmer groups / Special values of L-functions modulo p / Higher-dimensional analogues of stable curves / Evaluation maps, slopes, and algebraicity criteria / Derived categories of coherent sheaves / Invariants of singularities of pairs / Rational curves and rational points / Rigidity of rational homogeneous spaces / Geometry of multiple zeta values / Geometry over nonclosed fields / Algebraic Morse theory and the weak factorization theorem / Manifolds with positive curvature operators are space forms / Elliptic and parabolic problems in conformal geometry / The topology and geometry of contact structures in dimension three / Generalized triangle inequalities and their applications / The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity / Lagrangian submanifolds: from the local model to the cluster complex / Gromov–Witten invariants and moduli spaces of curves / Extremal metrics and stabilities on polarized manifolds / Tropical geometry and its applications / Embedded minimal surfaces / Floer homology in symplectic geometry and in mirror symmetry / Properly embedded minimal surfaces with finite topology / Applications of loop group factorization to geometric soliton equations / Finiteness of arithmetic Kleinian reflection groups / Non-positive curvature and complexity for finitely presented groups / Link homology and categorification / Curve complexes, surfaces and 3-manifolds / A1-algebraic topology / Development in symplectic Floer theory / Heegaard diagrams and Floer homology / The cohomology of automorphism groups of free groups / Noncommutative counterparts of the Springer resolution / Spaces of quasi-maps into the flag varieties and their applications / On the local Langlands and Jacquet–Langlands correspondences / An invitation to bounded cohomology / Fibration de Hitchin et structure endoscopique de la formule des traces / Hecke algebras and harmonic analysis / Continuous representation theory of p-adic Lie groups / The algebraization of Kazhdan’s property (T) / Rankin–Selberg integrals, the descent method, and Langlands functoriality / Representation theory and the cohomology of arithmetic groups / Some results on compactifications of semisimple groups / Quasiconformal geometry of fractals / Local Tb theorems and applications in PDE / Almost everywhere convergence and divergence of Fourier series / Iterated Segre mappings of real submanifolds in complex space and applications / Towards conformal invariance of 2D lattice models / Aspects of the L2-Sobolev theory of the ∂-Neumann problem / Greedy approximations with regard to bases / Analytic capacity, rectifiability, and the Cauchy integral / The Brunn–Minkowski theorem and related geometric and functional inequalities / Isomorphic and almost-isometric problems in high-dimensional convex geometry / Amenable actions and applications / Structure and classification of C*-algebras / Convexity, complexity, and high dimensions / Higher index theory of elliptic operators and geometry of groups / On spectral invariants in modern ergodic theory / Giovanni Felder -- John Lott -- Charles Fefferman -- Charles M. Newman -- John Hopcroft -- Hans Föllmer -- Percy Deift -- Jean-Pierre Demailly -- Ronald A. DeVore -- Yasha Eliashberg -- Étienne Ghys -- Henryk Iwaniec -- Iain M. Johnstone -- Kazuya Kato -- Robert V. Kohn -- Jørgen Ellegaard Andersen -- Arkadi Nemirovski -- Sorin Popa -- Alfio Quarteroni -- Oded Schramm -- Richard P. Stanley -- Terence Tao -- Juan Luis Vázquez -- Michèle Vergne -- Avi Wigderson -- John W. Morgan -- José M. Sánchez-Ron -- Rodney G. Downey -- Itay Neeman -- Michael Rathjen -- Thomas Scanlon -- Simon Thomas -- William Crawley-Boevey -- Marcus J. du Sautoy, Fritz Grunewald -- Bernhard Keller -- Raphaël Rouquier -- Mark V. Sapir -- Ákos Seress -- Agata Smoktunowicz -- Manjul Bhargava -- Ching-Li Chai -- Henri Darmon -- Kazuhiro Fujiwara -- Ben J. Green -- Gérard Laumon -- Philippe Michel, Akshay Venkatesh -- Wiesława Nizioł -- Christopher Skinner, Eric Urban -- Vinayak Vatsal -- Valery Alexeev -- Jean-Benoît Bost -- Tom Bridgeland -- Lawrence Ein, Mircea Mustaţă -- Tom Graber -- Jun-Muk Hwang -- Tomohide Terasoma -- Yuri Tschinkel -- Jarosław Włodarczyk -- Christoph Böhm, Burkhard Wilking -- Simon Brendle -- Ko Honda -- Michael Kapovich -- Bruce Kleiner -- Philippe Charron -- Xiaobo Liu -- Toshiki Mabuchi -- Grigory Mikhalkin -- William P. Minicozzi II -- Yong-Geun Oh, Kenji Fukaya -- Antonio Ros -- Chuu-Lian Terng -- Ian Agol -- Martin R. Bridson -- Aaron D. Lauda -- Yair N. Minsky -- Fabien Morel -- Kaoru Ono -- Peter Ozsváth, Zoltán Szabó -- Karen Vogtmann -- Roman Bezrukavnikov -- Alexander Braverman -- Guy Henniart -- Nicolas Monod -- Bao-Châu Ngô -- Eric M. Opdam -- Peter Schneider -- Yehuda Shalom -- David Soudry -- Birgit Speh -- Tonny A. Springer -- Mario Bonk -- Dorina Mitrea -- Sergey V. Konyagin -- Linda Preiss Rothschild -- Stanislav Smirnov -- Emil J. Straube -- Vladimir N. Temlyakov -- Xavier Tolsa -- Franck Barthe -- Bo'az Klartag -- Narutaka Ozawa -- Mikael Rørdam -- Stanislaw J. Szarek -- Guoliang Yu -- Oleg N. Ageev -- Ergodic Ramsey theory: a dynamical approach to static theorems / Hyperbolic billiards and statistical physics / Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics / Diagonalizable flows on locally homogeneous spaces and number theory / Braids and differential equations / Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems / From combinatorics to ergodic theory and back again / From Brouwer theory to the study of homeomorphisms of surfaces / All, most, some differentiable dynamical systems / Geodesics on flat surfaces / Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximation / Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem / Vitaly Bergelson -- Nikolai Chernov, Dmitry Dolgopyat -- Rafael de la Llave -- Manfred Einsiedler, Elon Lindenstrauss -- Robert Ghrist -- Anton Gorodetski, Brian Hunt, Vadim Kaloshin -- Bryna Kra -- Patrice Le Calvez -- Michael Shub -- Anton Zorich -- Stefano Bianchini -- Patrick Gérard.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037195222
10.4171/022 doi
Mathematics
General