杭州華人數學家大會序
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 IThe Work of the Morningside Medalists
  The Work of Xu-Jia Wang Fanghua Lin
  The Work of Jianqing Fan Zhiliang Ying
  The Work of Chiu-Chu Liu Kefeng Liu
  The Work of Lizhen Ji Gopal Prasad
  The Work of Shi Jin Stanley Osher
  The Work of Chiun-Chuan Chen Chang-Shou Lin
  The Work of Ye Tian John Coates
Part II
Theory and Implementation of Efficient 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 R Jaigyoung
Choe and Richard Schoen
  1 Introduction
  2 Minimal surfaces
  References
Positive Quaternionic Kaihler 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 L algebra and 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 LiXue-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 Difference for Expanding
  Convex Closed Plane Curves
  Yu一Chu Lin and Dong-Ho Tsai
  1  Introduction：the decreasing of the isoperimetric difierence
  2 Preserving convexity
  3 The contracting flow
  4 The expanding flow
  References
Predictive Modeling Approaches for Studying ProteinDNA Binding
  Jun SLiu 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 modification 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 Even8 and Jiang—Hua Lu
  1 Introduction
  2 The resolution μt.w：Xt.w—Ft.w
  3 The Poisson geometry of the resolution μt.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 Penq
  1 Introduction
  2 Gopakumar—Vafa conjecture
  3 Labastida—Marino—Ooguri—Vafa CO njecture
  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 classification
of maximal rank
  3 A connectedness principle of positive curvature and
classification of one half maximal rank
  4 Classification 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
  CSSeshadri
  0 Introduction
  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 GValiant
  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