Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006
Volume I. Plenary Lectures and Ceremonies
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 Frontmatterp. v Prefacepp. vii–ix Contentspp. 1–24 Past conferences and organisational datapp. 25–43 Opening ceremonypp. 45–52 Closing ceremonyp. 53 The work of the Fields Medalists, the Rolf Nevanlinna Prize Winner and the Gauss Prize Winner – Contentspp. 54–64 The work of Andrei OkounkovGiovanni Felder
pp. 65–76 The work of Grigory PerelmanJohn Lott
pp. 77–86 The work of Terence TaoCharles Fefferman
pp. 87–95 The work of Wendelin WernerCharles M. Newman
pp. 96–108 The work of Jon KleinbergJohn Hopcroft
pp. 108–123 On Kiyosi Itô's work and its impactHans Föllmer
pp. 125–152 Universality for mathematical and physical systemsPercy Deift
pp. 153–186 Kähler manifolds and transcendental techniques in algebraic geometryJean-Pierre Demailly
pp. 187–215 Optimal computationRonald A. DeVore
pp. 217–246 Symplectic field theory and its applicationsYasha Eliashberg
pp. 247–277 Knots and dynamicsÉtienne Ghys
pp. 279–306 Prime numbers and -functionsHenryk Iwaniec
pp. 307–333 High dimensional statistical inference and random matricesIain M. Johnstone
pp. 335–357 Iwasawa theory and generalizationsKazuya Kato
pp. 359–383 Energy-driven pattern formationRobert V. Kohn
pp. 385–411 Moduli spaces from a topological viewpointJørgen Ellegaard Andersen
pp. 413–444 Advances in convex optimization: conic programmingArkadi Nemirovski
pp. 445–477 Deformation and rigidity for group actions and von Neumann algebrasSorin Popa
pp. 479–512 Cardiovascular mathematicsAlfio Quarteroni
pp. 513–543 Conformally invariant scaling limits: an overview and a collection of problemsOded Schramm
pp. 545–579 Increasing and decreasing subsequences and their variantsRichard P. Stanley
pp. 581–608 The dichotomy between structure and randomness, arithmetic progressions, and the primesTerence Tao
pp. 609–634 Perspectives in nonlinear diffusion: between analysis, physics and geometryJuan Luis Vázquez
pp. 635–664 Applications of equivariant cohomologyMichèle Vergne
pp. 665–712 and mathematics – a computational complexity perspectiveAvi Wigderson
pp. 713–736 The Poincaré ConjectureJohn W. Morgan
pp. 737–756 Panel discussion: Should mathematicians care about communicating to broad audiences? Theory and practicepp. 757–776 ICM 2006 Closing round table: Are pure and applied mathematics drifting apart?pp. 777–793 From the private to the public: The road from Zurich (1897) to Madrid (2006)José M. Sánchez-Ron