Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006
Volume III. 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 Braids and differential equationsRobert Ghrist
DOI 10.4171/022-3/1pp. 27–55 Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systemsAnton GorodetskiBrian HuntVadim Kaloshin
DOI 10.4171/022-3/2pp. 57–76 From combinatorics to ergodic theory and back againBryna Kra
DOI 10.4171/022-3/3pp. 77–98 From Brouwer theory to the study of homeomorphisms of surfacesPatrice Le Calvez
DOI 10.4171/022-3/4pp. 99–120 All, most, some differentiable dynamical systemsMichael Shub
DOI 10.4171/022-3/5pp. 121–146 Geodesics on flat surfacesAnton Zorich
DOI 10.4171/022-3/6pp. 147–155 Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximationStefano Bianchini
DOI 10.4171/022-3/7pp. 156–182 Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problemPatrick Gérard
DOI 10.4171/022-3/8pp. 183–201 The periodic Lorentz gas in the Boltzmann-Grad limitFrançois Golse
DOI 10.4171/022-3/9pp. 203–212 Conformal invariants and nonlinear elliptic equationsMatthew J. Gursky
DOI 10.4171/022-3/10pp. 213–227 Asymptotic solutions for large time of Hamilton–Jacobi equationsKenji Nishihara
DOI 10.4171/022-3/11pp. 229–256 The weak-coupling limit of large classical and quantum systemsMario Pulvirenti
DOI 10.4171/022-3/12pp. 257–265 Symmetry of entire solutions for a class of semilinear elliptic equationsOvidiu Savin
DOI 10.4171/022-3/13pp. 267–290 Vortices in the Ginzburg–Landau model of superconductivitySylvia Serfaty
DOI 10.4171/022-3/14pp. 291–301 Recent developments in elliptic partial differential equations of Monge–Ampère typeNeil S. Trudinger
DOI 10.4171/022-3/15pp. 303–319 The initial value problem for nonlinear Schrödinger equationsLuis Vega
DOI 10.4171/022-3/16pp. 321–338 Singular solutions of partial differential equations modelling chemotactic aggregationJuan José L. Velazques
DOI 10.4171/022-3/17pp. 339–365 From topological field theory to deformation quantization and reductionAlberto S. Cattaneo
DOI 10.4171/022-3/18pp. 367–382 Matrix ansatz and large deviations of the density in exclusion processesBernard Derrida
DOI 10.4171/022-3/19pp. 383–408 Correlation functions of the Heisenberg spin chain: Bethe ansatz approachJean Michel Maillet
DOI 10.4171/022-3/20pp. 409–419 Gromov–Witten invariants and topological strings: a progress reportMarcos Mariño
DOI 10.4171/022-3/21pp. 421–442 The Cauchy problem in General RelativityIgor Rodnianski
DOI 10.4171/022-3/22pp. 443–458 Categorification and correlation functions in conformal field theoryJürgen FuchsChristoph Schweigert
DOI 10.4171/022-3/23pp. 459–471 Soliton dynamics and scatteringAvy Soffer
DOI 10.4171/022-3/24pp. 473–498 Hypocoercive diffusion operatorsCédric Villani
DOI 10.4171/022-3/25pp. 499–518 Metastability: a potential theoretic approachAnton Bovier
DOI 10.4171/022-3/26pp. 519–533 On Ising dropletsRaphaël Cerf
DOI 10.4171/022-3/27pp. 535–558 Simple random covering, disconnection, late and favorite pointsAmir Dembo
DOI 10.4171/022-3/28pp. 559–574 Modelling genes: mathematical and statistical challenges in genomicsPeter Donnelly
DOI 10.4171/022-3/29pp. 575–594 Geometric stochastic analysis on path spacesK. David ElworthyXue-Mei Li
DOI 10.4171/022-3/30pp. 595–622 Statistical challenges with high dimensionality: feature selection in knowledge discoveryJianqing FanRunze Li
DOI 10.4171/022-3/31pp. 623–636 Random matrices and enumeration of mapsAlice Guionnet
DOI 10.4171/022-3/32pp. 637–647 The weak/strong survival transition on trees and nonamenable graphsSteven P. Lalley
DOI 10.4171/022-3/33pp. 649–667 New developments in stochastic dynamicsYves Le Jan
DOI 10.4171/022-3/34pp. 669–686 Stochastic classification modelsPeter McCullaghJie Yang
DOI 10.4171/022-3/35pp. 687–711 Random partitions and instanton countingAndrei Okounkov
DOI 10.4171/022-3/36pp. 713–739 Estimation in inverse problems and second-generation waveletsGérard KerkyacharianDominique Picard
DOI 10.4171/022-3/37pp. 741–762 Conformal restriction propertiesWendelin Werner
DOI 10.4171/022-3/38pp. 763–787 The complexity of generating functions for integer points in polyhedra and beyondAlexander Barvinok
DOI 10.4171/022-3/39pp. 789–826 Rational and algebraic series in combinatorial enumerationMireille Bousquet-Mélou
DOI 10.4171/022-3/40pp. 827–842 Towards a structure theory for matrices and matroidsJim GeelenBert GerardsGeoff Whittle
DOI 10.4171/022-3/41pp. 843–872 Cherednik algebras, Macdonald polynomials and combinatoricsMark Haiman
DOI 10.4171/022-3/42pp. 873–897 Poisson cloning model for random graphsJeong Han Kim
DOI 10.4171/022-3/43pp. 899–909 Randomness and regularityTomasz Łuczak
DOI 10.4171/022-3/44pp. 911–930 Additive combinatorics and geometry of numbersImre Z. Ruzsa
DOI 10.4171/022-3/45pp. 931–962 Geometric bistellar flips: the setting, the context and a constructionDomingo Gómez-Pérez
DOI 10.4171/022-3/46pp. 963–984 A survey of Pfaffian orientations of graphsRobin Thomas
DOI 10.4171/022-3/47pp. 985–997 Determinant versus permanentManindra Agrawal
DOI 10.4171/022-3/48pp. 999–1018 The additivity problem in quantum information theoryAlexander S. Holevo
DOI 10.4171/022-3/49pp. 1019–1044 Complex networks and decentralized search algorithmsJon Kleinberg
DOI 10.4171/022-3/50pp. 1045–1069 On expander graphs and connectivity in small spaceOmer Reingold
DOI 10.4171/022-3/51pp. 1071–1094 Potential functions and the inefficiency of equilibriaTim Roughgarden
DOI 10.4171/022-3/52pp. 1095–1110 Sublinear time algorithmsRonitt Rubinfeld
DOI 10.4171/022-3/53pp. 1111–1136 Pseudorandomness and combinatorial constructionsLuca Trevisan
DOI 10.4171/022-3/54pp. 1137–1162 Least-squares finite element methodsPavel BochevMax Gunzburger
DOI 10.4171/022-3/55pp. 1163–1180 A posteriori error analysis and adaptive methods for partial differential equationsZhiming Chen
DOI 10.4171/022-3/56pp. 1181–1200 Error estimates for anisotropic finite elements and applicationsRicardo G. Durán
DOI 10.4171/022-3/57pp. 1201–1226 Linear subdivision schemes for the refinement of geometric objectsNira Dyn
DOI 10.4171/022-3/58pp. 1227–1253 Wave propagation software, computational science, and reproducible researchIdo Bright
DOI 10.4171/022-3/59pp. 1255–1270 Reduced basis method for the rapid and reliable solution of partial differential equationsYvon Maday
DOI 10.4171/022-3/60pp. 1271–1297 Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractabilityEndre Süli
DOI 10.4171/022-3/61pp. 1299–1309 Ergodic control of diffusion processesVivek S. Borkar
DOI 10.4171/022-3/62pp. 1311–1319 Convex optimization of graph Laplacian eigenvaluesStephen Boyd
DOI 10.4171/022-3/63pp. 1321–1338 Controllability of evolution equations of fluid dynamicsOleg Yu. Emanouilov (Imanuvilov)
DOI 10.4171/022-3/64pp. 1339–1365 Port-Hamiltonian systems: an introductory surveyArjan van der Schaft
DOI 10.4171/022-3/65pp. 1367–1388 Passive linear discrete time-invariant systemsOlof J. Staffans
DOI 10.4171/022-3/66pp. 1389–1417 Control and numerical approximation of the wave and heat equationsEnrique Zuazua
DOI 10.4171/022-3/67pp. 1419–1432 Multiscale modeling for epitaxial growthRussel E. Caflisch
DOI 10.4171/022-3/68pp. 1433–1452 Compressive samplingEmmanuel J. Candès
DOI 10.4171/022-3/69pp. 1453–1472 Total variation based image denoising and restorationVicent Caselles
DOI 10.4171/022-3/70pp. 1473–1506 A wavelet based sparse grid method for the electronic Schrödinger equationMichael GriebelJan Hamaekers
DOI 10.4171/022-3/71pp. 1507–1522 Mathematical and numerical analysis for molecular simulation: accomplishments and challengesClaude Le Bris
DOI 10.4171/022-3/72pp. 1523–1540 Evolutionary dynamics of cooperationMartin A. Nowak
DOI 10.4171/022-3/73pp. 1541–1562 Fractional Brownian motion: stochastic calculus and applicationsDavid Nualart
DOI 10.4171/022-3/74pp. 1563–1582 Atomistic and continuum models for phase change dynamicsAnders Szepessy
DOI 10.4171/022-3/75pp. 1583–1598 Competitions and mathematics educationPetar S. Kenderov
DOI 10.4171/022-3/76pp. 1631–1644 Mathematics, the media, and the publicIan Stewart
DOI 10.4171/022-3/78pp. 1645–1661 DOI 10.4171/022-3/79Panel A — Controversial issues in K-12 mathematical educationpp. 1663–1672 DOI 10.4171/022-3/80Panel B — What are PISA and TIMSS? What do they tell us?pp. 1673–1696 DOI 10.4171/022-3/81Panel C — The role of mathematicians in K-12 mathematics educationpp. 1697–1718 On the origins of Hilbert’s sixth problem: physics and the empiricist approach to axiomatizationLeo Corry
DOI 10.4171/022-3/82pp. 1719–1742 Method versus calculus in Newton’s criticisms of Descartes and LeibnizNiccolo Guicciardini
DOI 10.4171/022-3/83pp. 1743–1768 DOI 10.4171/022-3/84e-learning mathematicspp. 1599–1630 Understanding and misunderstanding the Third International Mathematics and Science Study: what is at stake and why K-12 education studies matterAlan Siegel
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