Front Matter
 Volume IV
  杭州华人数学家会序
  Address of the Congress President
  Past Congresses of ICCM
  Past Morningside Medalists, Chern Prize Winners and
ICCM International Cooperation Award Winner
  Medal and Awards of ICCM and the Background
  The Committees of the Congress
  List of Sponsors, Donors and Contributors
  Morningside Medal of Mathematics Selection Committee
  Morningside Medalists, Chern Prize Winners and
ICCM International Cooperation Award Winner
 Part I The Work of the Morningside Medalists
 The Work of Xu-Jia Wang
  Fanghua Lin
 The Work of Jianqing Fan
  Zhiliang Ying
 The Work of Jianqing Fan
  Kefeng Liu
 The Work of Shi Jin
  Stanley Osher
 The Work of Chiun-Chuan Chen
  Chang-Shou Lin
 The Work of Ye Tian
  John Coates
 The Work of Lizhen Ji
  Gopal Prasad
 Part II
 Theory and Implementation of E cient Importance Sampling for
Monte Carlo Computation of Probabilities of Rare Events
  H. P. Chan and T. L. Lai
  1 Introduction
  2 Large deviations and importance sampling
  3 Mixtures of exponentially twisted measures and asymptotically
optimal importance sampling measures
  4 Sequential Importance Sampling with Resampling (SISR)
  References
 Fast Algorithms for Total Variation-Based Image Processing
  T. F. Chan and M. Zhu
  1 Introduction
  2 Primal and dual formulation
  3 Numerical methods
  4 Remarks and conclusions
  5 Acknowledgements
  References
 Sharp Isoperimetric Inequality for Minimal Surfaces in R3
  Jaigyoung Choe and Richard Schoen
  1 Introduction
  2 Minimal surfaces
  References
 Positive Quaternionic Kahler Manifolds with Symmetry
  Fuquan Fang
  1 Introduction
  2 A connectedness theorem
  3 Hyperkahler quotient and quaternionic Kahler quotient
  4 Symmetry rank
  References
 Linear Waves in the Kerr Geometry: Long-Time Dynamics,
Superradiance, and the Stability of Black Holes
  Felix Finster
  1 General relativity and black holes .
  2 Linear wave equations in the Kerr geometry and their separation .
  3 Dynamics of Dirac waves
  4 An integral representation and decay for scalar waves
  5 A rigorous treatment of superradiance for scalar waves
  6 The stability problem for Kerr black holes.
  References
 Loop Space and Holomorphic Disc: Summary
  Kenji Fukaya
  1 Introduction
  2 L1 algebra an its homotopy theory
  3 Corresponsdence parametrized by operad and string topology
  4 Pseudo-holomorphic disc and Maurer-Cartan equation
  References
 Reservoir Description by Using a Piecewise Constant Level Set Method
  Hongwei Li, Xue-Cheng Tai and Sigurd Ivar Aanonsen
  1 Introduction
  2 The inverse and minimization problem
  3 The Piecewise Constant Level Set Method for the inverse problem
  4 The numerical algorithm
  5 Implementation issues
  6 Numerical experiments
  7 Conclusion and remarks
  8 Acknowledgments
  References
 Center of Expansion and Isoperimetric Di erence for Expanding
Convex Closed Plane Curves
  Yu-Chu Lin and Dong-Ho Tsai
  1 Introduction; the decreasing of the isoperimetric dierence
  2 Preserving convexity
  3 The contracting
flow
  4 The expanding
flow
  References
 Predictive Modeling Approaches for Studying Protein-DNA Binding
  Jun S. Liu and Qing Zhou
  1 Introduction: Central dogma of molecular biology
  2 Statistical generative models for transcription regulation
  3 A Framework for predictive modeling
  4 RSIR and histone modication prediction
  5 A case study: Oct4 ChIP-chip data in human ESCs
  6 A simulation study
  7 Discussion
  References
 Intersections of Bruhat Cells and Steinberg Fibers
  Sam Evens and Jiang-Hua Lu
  1 Introduction
  2 The resolution t;w : Xt;w ! Ft;w
  3 The Poisson geometry of the resolution t;w : Xt;w ! Ft;w
  References
 Loops in the Hamiltonian Group
  Dusa McDuff
  1 Introduction
  2 Classical methods
  3 Quantum methods
  References
 String Duality and the Integrality Structure in Calabi-Yau Geometry
  Pan Peng
  1 Introduction
  2 Gopakumar-Vafa conjecture
  3 Labastida-Mari~no-Ooguri-Vafa conjecture
  4 Concluding remarks
  References
 Positively Curved Manifolds with Abelian Symmetry
  Xiaochun Rong
  0 Introduction
  1 Isometric tori actions and Synge-type arguments
  2 Critical point theory for distance functions and classi cation of
maximal rank
  3 A connectedness principle of positive curvature and classi cation
of one half maximal rank
  4 Classication of the almost maximal rank
  5 An equivariant Synge-type theorem and fundamental groups
  6 Euler Characteristics
  7 Discrete symmetry ranks
  8 Conjectures and open problems
  References
 Moduli Spaces of Torsion Free Sheaves on Nodal Curves and
Generalisations - II
  C. S. Seshadri
  1 Basic properties of the moduli spaces of torsion free sheaves
  2 Gieseker moduli spaces
  3 Understanding the moduli spaces of X through objects on the
normalisation of X
  References
 Harmonic Maps in Real and Complex Finsler Geometry
  Yi-Bing Shen
  1 Introduction
  2 Volume measures
  3 Energy functional
  4 Stable harmonic maps
  5 The stress-energy tensor
  6 Maps from complex Finsler manifolds
  7 Total energy and homotopy invariant
  References
 Evolvabilty
  Leslie G. Valiant
  1 Introduction
  2 The approach
  References
 Some Aspects of Fractal in China
  Zhi-Ying Wen
  1 Dimensions, measures and gauges
  2 Lipschitz equivalence on fractals
  3 Self-similar sequences and combinatorial on words
  4 Multifractal analysis
  5 Some applications
  References
 Rigorous Derivation of the Gross-Pitaevskii Equation
  Horng-Tzer Yau
  1 Introduction
  2 Main results
  References
 On the Global Existence and Uniqueness of Solutions to
Prandtl’s System
  Junning Zhao and Xu Xinying
  1 Introduction
  2 Main results
  3 Proof of Theorem 2.1
  4 Uniqueness and stability of weak solution
  5 Existence of global solution of (1.1){(1.2)
  References
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