Table Of ContentVolume 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
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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
