季理真等编著的《第4届华人数学家大会文集(英文版)(精)》是第4届华人数学家大会论文的英文结集，本次数学家大会的议题围绕着“数学”与“教育”展开。本书所集论文显示了华人数学研究的最新成果，汇聚了众家之言，可供数学研究者和从事数学教育的读者参考阅读。

杭州华人数学家大会序

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 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