Proceedings, Vol. 2 PDF
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Volume II Invited Lectures Editor Rajendra Bhatia ~HINDUSTAN U LQJ UB OOK AGENCY Proceedings of the International Congress of Mathematicians Hyderabad, August 19–27, 2010 This page is intentionally left blank Proceedings of the International Congress of Mathematicians Hyderabad, August 19–27, 2010 Volume II Invited Lectures Editor Rajendra Bhatia Co-Editors Arup Pal G. Rangarajan V. Srinivas M. Vanninathan Technical Editor Pablo Gastesi Editor RajendraBhatia,IndianStatisticalInstitute,Delhi Co-editors ArupPal,IndianStatisticalInstitute,Delhi G.Rangarajan,IndianInstituteofScience,Bangalore V.Srinivas,TataInstituteofFundamentalResearch,Mumbai M.Vanninathan,TataInstituteofFundamentalResearch,Bangalore Technicaleditor PabloGastesi,TataInstituteofFundamentalResearch,Mumbai Publishedby HindustanBookAgency(India) P19,GreenParkExtension NewDelhi110016 India email:[email protected] http://www.hindbook.com Copyright©2010,Authorsofindividualarticles. Nopartofthematerialprotectedbythiscopyrightnoticemaybereproducedorutilizedinany formorbyanymeans,electronicormechanical,includingphotocopying,recordingorbyany informationstorageandretrievalsystem,withoutwrittenpermissionfromthecopyrightowner, whohasalsothesolerighttograntlicencesfortranslationintootherlanguagesandpublication thereof. ISBN978-81-85931-08-3 ExclusivedistributionworldwideexceptIndia WorldScientificPublishingCo.Pte.Ltd. 5TohTuckLink,Singapore596224 Contents 1 Logic and Foundations Justin Tatch Moore The Proper Forcing Axiom.............................................. 3 Andr´e Nies Interactions of Computability and Randomness.......................... 30 Ya’acov Peterzil∗ and Sergei Starchenko∗ Tame Complex Analysis and o-minimality............................... 58 2 Algebra Paul Balmer Tensor Triangular Geometry............................................ 85 David J. Benson Modules for Elementary Abelian p-groups............................... 113 Sergey Fomin Total Positivity and Cluster Algebras................................... 125 Nikita A. Karpenko Canonical Dimension.................................................... 146 Zinovy Reichstein Essential Dimension..................................................... 162 V. Suresh Quadratic Forms, Galois Cohomology and Function Fields of p-adic Curves............................................................... 189 In case of papers with several authors, invited speakers at the Congress are marked with anasterisk. vi Contents 3 Number Theory Christophe Breuil The Emerging p-adic Langlands Programme............................. 203 Ralph Greenberg Selmer Groups and Congruences........................................ 231 D.R. Heath-Brown Artin’s Conjecture on Zeros of p-adic Forms............................. 249 Kiran Sridhara Kedlaya Relative p-adic Hodge Theory and Rapoport-Zink Period Domains...... 258 Chandrashekhar Khare∗ and Jean-Pierre Wintenberger∗ Serre’s Modularity Conjecture........................................... 280 Mark Kisin The Structure of Potentially Semi-stable Deformation Rings............. 294 Sophie Morel The Intersection Complex as a Weight Truncation and an Application to Shimura Varieties..................................... 312 Takeshi Saito Wild Ramification of Schemes and Sheaves.............................. 335 K. Soundararajan Quantum Unique Ergodicity and Number Theory....................... 357 Akshay Venkatesh∗ and Jordan S. Ellenberg Statistics of Number Fields and Function Fields......................... 383 4 Algebraic and Complex Geometry Prakash Belkale The Tangent Space to an Enumerative Problem......................... 405 Christopher D. Hacon∗ and James McKernan∗ Boundedness Results in Birational Geometry............................ 427 Daniel Huybrechts Hyperk¨ahler Manifolds and Sheaves..................................... 450 D. Kaledin Motivic Structures in Non-commutative Geometry...................... 461 Chiu-Chu Melissa Liu Gromov-Witten Theory of Calabi-Yau 3-folds........................... 497 Christopher D. Hacon∗ and James McKernan∗ Flips and Flops......................................................... 513 Contents vii Mihai P˘aun Quantitative Extensions of Twisted Pluricanonical Forms and Non-vanishing........................................................ 540 Shuji Saito Cohomological Hasse Principle and Motivic Cohomology of Arithmetic Schemes.................................................. 558 Frank-Olaf Schreyer∗ and David Eisenbud Betti Numbers of Syzygies and Cohomology of Coherent Sheaves........ 586 Vasudevan Srinivas Algebraic Cycles on Singular Varieties................................... 603 Richard P. Thomas An Exercise in Mirror Symmetry........................................ 624 Jean-Yves Welschinger Invariants Entiers en G´eom´etrie E´num´erative R´eelle..................... 652 5 Geometry Anna Erschler Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups.................................................... 681 Jixiang Fu On non-K¨ahler Calabi-Yau Threefolds with Balanced Metrics............ 705 William M. Goldman Locally Homogeneous Geometric Manifolds.............................. 717 Larry Guth Metaphors in Systolic Geometry........................................ 745 Sergei Ivanov Volume Comparison via Boundary Distances............................ 769 Xiaonan Ma Geometric Quantization on K¨ahler and Symplectic Manifolds............ 785 Fernando Cod´a Marques Scalar Curvature, Conformal Geometry, and the Ricci Flow with Surgery......................................................... 811 Isabel Fern´andez∗ and Pablo Mira∗ Constant Mean Curvature Surfaces in 3-dimensional Thurston Geometries........................................................... 830 Alexander Nabutovsky Morse Landscapes of Riemannian Functionals and Related Problems............................................................. 862 viii Contents Frank Pacard Constant Scalar Curvature and Extremal K¨ahler Metrics on Blow ups............................................................. 882 Takao Yamaguchi Reconstruction of Collapsed Manifolds.................................. 899 6 Topology Denis Auroux Fukaya Categories and Bordered Heegaard-Floer Homology.............. 917 Kevin Costello A Geometric Construction of the Witten Genus, I....................... 942 David Gabai Hyperbolic 3-manifolds in the 2000’s.................................... 960 Jesper Grodal The Classification of p–compact Groups and Homotopical Group Theory........................................................ 973 Ursula Hamenst¨adt Actions of the Mapping Class Group....................................1002 Michael Hutchings Embedded Contact Homology and Its Applications......................1022 Marc Lackenby Finite Covering Spaces of 3-manifolds...................................1042 Wolfgang Lu¨ck K- and L-theory of Group Rings........................................1071 Jacob Lurie Moduli Problems for Ring Spectra...................................... 1099 Maryam Mirzakhani On Weil-Petersson Volumes and Geometry of Random Hyperbolic Surfaces..............................................................1126 Jongil Park A New Family of Complex Surfaces of General Type with p =0........1146 g Andr´as I. Stipsicz Ozsv´ath-Szab´o Invariants and 3-dimensional Contact Topology..........1159 Author Index.........................................................1179 Section 1 Logic and Foundations
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