American Mathematical Society • International Press

Studies inAdvancedMathematicsS.-T. Yau, Series Editor

AMS/IP

Lizhen JiYat Sun PoonLo YangShing-Tung YauEditors

Fifth International Congress of Chinese MathematiciansPart 1

Fifth International Congress of Chinese Mathematicians

Fifth International Congress of Chinese Mathematicians

Lizhen Ji Yat Sun Poon Lo Yang Shing-Tung Yau Editors

Studies inAdvancedMathematics

AMS/IP

Volume 51, Part 1

American Mathematical Society • International Press

https://doi.org/10.1090/amsip/051.1

Shing-Tung Yau, General Editor

2000 Mathematics Subject Classification. Primary 05–XX, 08–XX, 11–XX, 14–XX,22–XX, 35–XX, 37–XX, 53–XX, 58–XX, 62–XX, 65–XX, 20–XX, 30–XX, 80–XX,

83–XX, 90–XX.

All photographs courtesy of International Press.

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International Congress of Chinese Mathematicians (5th : 2010 : Beijing, China)p. cm. (AMS/IP studies in advanced mathematics ; v. 51)

Includes bibliographical references.ISBN 978-0-8218-7555-1 (set : alk. paper)—ISBN 978-0-8218-7586-5 (pt. 1 : alk. paper)—

ISBN 978-0-8218-7587-2 (pt. 2 : alk. paper)1. Mathematics—Congresses. I. Ji, Lizhen, 1964– II. Title. III. Title: 5th International

Congress of Chinese Mathematicians.

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2011048032

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v

Contents

In Part One

Preface...........................................................................................................................ix

xi

Welcome Letter from the Congress President ...............................................................xii

Past Congresses of ICCM.............................................................................................xiii

Past Morningside Medalists, Chern Prize Recipients, and ICCM International Cooperation Award Recipients ..............................................xiii

On the Works of the 2010 Morningside Medalists ....................................................... xv

About the Medals and Awards of ICCM .................................................................... xviii

The Committees of the Congress.................................................................................xix

Sponsors, Donors and Contributors ............................................................................xxi

Photographs ...............................................................................................................xxii

Papers on Pure Mathematics

Gradient and oscillation estimates and their applications in geometric PDE ···················3 BEN ANDREWS

On canonical and explicit classification of algebraic threefolds·····································21 JUNGKAI A. CHEN AND MENG CHEN

Canonical pseudonorms on pluricanonical spaces························································33 CHEN-YU CHI

The enigmatic Tate-Shafarevich group ·········································································43 JOHN COATES

Eta invariants for even-dimensional manifolds ·····························································51 XIANZHE DAI

vi

Ricci flow on 4-manifolds and Seiberg-Witten equations ·············································61 FUQUAN FANG AND ZHENLEI ZHANG

Vector bundles and p-adic Galois representations ························································77 LAURENT FARGUES AND JEAN-MARC FONTAINE

Geometry of nilpotent orbits: results and conjectures·················································115 BAOHUA FU

Integrable connections and Galois representations ·····················································127 LEI FU

Asymptotic Chow polystability in Kähler geometry ····················································139 AKITO FUTAKI

Representations of metaplectic groups········································································155 WEE TECK GAN

Notes on partial conjugation ······················································································171 CHUYING FANG AND XUHUA HE

Geometric modular forms and the cohomology of torsion automorphic sheaves········183 KAI-WEN LAN

SYZ transformations for toric varieties ········································································209 NAICHUNG CONAN LEUNG

Some variational problems in conformal geometry·····················································221 BIN GUO AND HAIZHONG LI

Geometry of tamed almost complex structures on 4-dimensional manifolds ··············233 TEDI DRAGHICI, TIAN-JUN LI, AND WEIYI ZHANG

The arithmetic of noncongruence modular forms·······················································253 WEN-CHING WINNIE LI

Analytic continuations of quantum cohomology ························································269 YUAN-PIN LEE, HUI-WEN LIN, AND CHIN-LUNG WANG

Mathematical aspects of string duality ········································································283 KEFENG LIU AND PAN PENG

The tame kernels of number fields ·············································································293 XUEJUN GUO AND HOURONG QIN

Notes on MVW-extensions·························································································305 BINYONG SUN

Vertex operator representations for a class of BC�-graded Lie algebras ·······················315 FULIN CHEN AND SHAOBIN TAN

Notes on orbifold Gromov-Witten theory ··································································327 HSIAN-HUA TSENG

Cohomologies and elliptic operators on symplectic manifolds ···································341 LI-SHENG TSENG

Quasilocal mass from a mathematical perspective ······················································355 MU-TAO WANG

On dimension data and local vs. global conjugacy ·····················································365 SONG WANG

Variational problems of Monge-Ampère type ·····························································383 XU-JIA WANG AND BIN ZHOU

Wellposedness of the two and three dimensional full water wave problem ················397 SIJUE WU

CONTENTS

vii

Recent developments in differentiable sphere theorems ·············································415 HONG-WEI XU

New invariants for complex manifolds, singularities, and CR manifolds with applications·········································································································431 RONG DU AND STEPHEN YAU

Gross-Zagier formula and arithmetic fundamental lemma ··········································447 WEI ZHANG

Integrality properties of mirror maps··········································································461 JIAN ZHOU

Ohsawa-Takegoshi L² extension theorem: revisited ····················································475 XIANGYU ZHOU AND LANGFENG ZHU

In Part Two

Papers on Applied Mathematics

Regularity of Einstein spacetimes················································································493 BING-LONG CHEN

A survey on retrograde and prograde orbits of the three-body problem by variational methods·····························································································499 KUO-CHANG CHEN

Recent development of computational conformal geometry ·······································515 DAVID XIANFENG GU, WEI ZENG, LOK MING LUI, FENG LUO, AND SHING-TUNG YAU

Some developments in spectral methods ····································································561 BEN-YU GUO, CHAO ZHANG, AND TAO SUN

On the center of mass in general relativity··································································575 LAN-HSUAN HUANG

Tailored finite point method for numerical simulation of partial differential equations·············································································································593 ZHONGYI HUANG

Loop symmetric functions and factorizing matrix polynomials···································609 THOMAS LAM

Spectral inequalities for partial differential equations and their applications···············629 ARI LAPTEV

Structured doubling algorithms for solving g-palindromic quadratic eigenvalue problems ·············································································································645 ERIC KING-WAH CHU, TSUNG-MING HUANG, AND WEN-WEI LIN

Ricci curvature and functional inequalities on graphs·················································663 YONG LIN

Complexity dichotomies of counting problems ··························································677 PINYAN LU

A survey on recent development in computational quasi-conformal geometry and its applications ····································································································697 LOK MING LUI, TSZ WAI WONG, WEI ZENG, XIANFENG GU, PAUL M. THOMPSON, TONY F. CHAN, SHING-TUNG YAU

CONTENTS

viii

Dynamics of shock fronts for some hyperbolic systems ··············································719 TAO LUO

Time-stepping methods for linear complementarity systems ······································731 LANSHAN HAN AND JONG-SHI PANG

A brief survey of high order accurate maximum principle satisfying and positivity preserving discontinuous Galerkin and finite volume schemes for conservation laws ································································································747 CHIWANG SHU

A one parameter family of expanding wave solutions of the Einstein equations that induces an anomalous acceleration into the standard model of cosmology··········759 JOEL SMOLLER AND BLAKE TEMPLE

Banded matrices with banded inverses and A = LPU ··················································771 GILBERT STRANG

Dissimilarity data in statistical model building and machine learning·························785 GRACE WAHBA

Some progress on computational geometry ································································811 REN-HONG WANG

Geometrization program of semilinear elliptic equations············································831 JUNCHENG WEI

Fast and near-optimal matrix completion via randomized basis pursuit ·····················859 ZHISU ZHU, ANTHONY MAN-CHO SO, AND YINYU YE

Mathematical questions of quantum dilute gases························································883 JUN YIN

Algebraic dynamics, canonical heights and Arakelov geometry ··································893 XINYI YUAN

Well-posedness and control of the Korteweg-de Vries equation on a bounded domain················································································································931 BING-YU ZHANG

Statistical analysis in genetic association studies of mental illnesses····························957 YUAN JIANG, HEPING ZHANG, AND WENSHENG ZHU

Compressible Navier-Stokes equations with large density oscillation ·························971 HUIJIANG ZHAO

Some results on variational and topological methods ·················································987 WENMING ZOU

CONTENTS

ix

Preface

The International Congress of Chinese Mathematicians, or ICCM, is a major event in the mathematics community, especially among Chinese mathematicians. The First Con-gress was held in Beijing in 1998. Subsequent congresses were held in Taipei (2001), Hong Kong (2004), and Hangzhou (2007). In 2010, after twelve years, the Congress re-turned to Beijing.

The Fifth International Congress of Chinese Mathematicians was held on December 17 to 22, 2010. The opening ceremony was held in the Great Hall of the People, with two thousand in attendance, and the proceedings took place on the campus of Tsinghua University. ICCM 2010 was co-hosted by the Academy of Mathematics and Systems Sci-ence of the Chinese Academy of Sciences, and by Tsinghua University.

ICCM 2010 was specially dedicated to the 100th anniversary of the birth of Loo-Keng Hua, and to the 99th anniversary of the birth of Shiing-Shen Chern—two of the greatest Chinese mathematicians of the twentieth century. While teaching at Tsinghua University, Hua and Chern trained many outstanding mathematicians (among them H. C. Wang, H. Wang, and Z. X. Wan) who went on to become leading mathematicians in China. Hua was a dominating figure in the development of mathematics in modern China, and was instrumental in the formation of the Academy of Mathematics and Sys-tems Science.

The world-class applied mathematician C. C. Lin, and statistician P. L. Hsu, were also from Tsinghua. Lin, Hsu, Chern, and Hua represent four major areas of mathemati-cal sciences. It is therefore quite fitting that ICCM 2010 was co-organized by the Acad-emy of Mathematics and Systems Science and by Tsinghua University.

Several mathematic awards were given at the opening ceremony—including the Morningside Medal of Mathematics, the Chern Prize, and the International Cooperation Award

The Morningside Medal of Mathematics is awarded to exceptional mathematicians of Chinese descent under the age of forty-five, for seminal achievement in mathematics and applied mathematics. The 2010 Morningside Gold Medal of Mathematics was awarded to Mu-Tao Wang of Columbia University and to Sijue Wu of the University of Michigan. The 2010 Morningside Gold Medal of Applied Mathematics was awarded to Jun S. Liu, of Harvard University. The 2010 Morningside Silver Medal of Mathematics was awarded to Jixiang Fu of Fudan University, Juncheng Wei of the Chinese University of Hong Kong, Jungkai Alfred Chen of Taiwan University and Meng Chen of Fudan University, as a col-laborative team.

x

The Chern Prize in Mathematics was established in 2001 in honor of Shiing-Shen Chern, one of the greatest geometers and Chinese mathematicians of the twentieth cen-tury. It is presented to mathematicians of Chinese descent who have made exceptional contributions to mathematical research or to public service activities which support mathematics. The 2010 Chern Prize was awarded to Jiaxing Hong of Fudan University, Conan Nai-Chung Leung of the Chinese University of Hong Kong, and to Wen-Ching Winnie Li, of the National Center of Theoretical Sciences in Taiwan and Penn State Uni-versity.

First presented in 2004, the ICCM International Cooperation Award is given to an individual who has promoted the development of mathematics in China, Hong Kong, and Taiwan through collaboration, teaching, and support of Chinese mathematicians. The 2010 ICCM International Cooperation Award was presented to Richard M. Schoen, of Stanford University.

Seven outstanding mathematicians were invited to give Morningside Lectures. Also presented were thirty-one hour-long talks and nearly two hundred 45-minute talks, by some of the outstanding mathematicians in the world today. The talks covered a broad spectrum of subjects in mathematical sciences—including algebra, number theory, ge-ometry, analysis, dynamical systems, functional analysis, partial differential equations, numerical analysis, bio-mathematics, probability, and statistics.

For the present volume, we solicited sixty distinguished speakers from the 2010 Congress, to write papers which explain their topics in a manner both accessible and comprehensive. The result is the book in your hand. The sixty papers presented herein do justice to the high quality and mathematical innovation of the lectures and talks given at the Congress. They are interesting and useful to both experts and general mathemati-cians.

Preparation of this book entailed much work, and it could not have been finished in such a timely fashion without generous help from many people. Firstly, we would like to thank all the contributors for their hard work in writing such high-quality papers, and the referees for reviewing the papers. Secondly, we would like to thank Ms. Yan Zhang and Prof. Yunbo Zeng for their efforts in collecting and putting the papers into the proper format.

Finally, we wish to take this opportunity to thank the Morningside Group, the Acad-emy of Mathematics and Systems Science in the Chinese Academy of Sciences, and the staff and faculty of both the Department of Mathematical Sciences and the Mathematical Sciences Center of Tsinghua University, for making ICCM 2010 such a success.

The Editors: Lizhen Ji Yat Sun Poon Lo Yang Shing-Tung Yau September 2, 2011

PREFACE

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xii

Welcome Letter from the Congress President

December 17, 2010 Distinguished guests, fellow mathematicians and friends: It gives me honor and great pleasure to welcome you to the Fifth International Con-

gress of Chinese Mathematicians (ICCM 2010) held in Beijing, China this year. Twelve years ago, the First International Congress of Chinese Mathematicians (ICCM 1998) was inaugurated here in the same city, and it is gratifying to see that ICCM has grown from strength to strength since its inception, and has today attained international acclaim. It is an internationally highly-regarded conference. More than a thousand mathematicians, university presidents, heads of leading scientific bodies, and students will gather at this special event. Mathematicians will present their research and discuss the latest develop-ments, with a view to promoting and stimulating research in mathematics as a thriving science, both in China and around the globe.

On the morning of the first day of the conference, there will be an opening ceremony at which we will announce and recognize the winners of the Morningside Medal of Mathematics for their outstanding attainments in pure and applied mathematics. These medalists have demonstrated exceptional achievement in their fields of study, and I am confident that their relentless effort and dedication will further inspire young Chinese tal-ents to explore the world of mathematics through research and publications. At the cere-mony, we will also present the Chern Prize and the ICCM International Cooperation Award to individuals for their long-term commitments and contributions to mathematics and for their promotion of international exchanges.

This year marks the one-hundredth birthday of the late Hua Loo-Keng and the ninety-ninth birthday of the late Shiing-Shen Chern, both world-renowned Chinese mathematicians of the twentieth century. We will have special sessions in the afternoon to pay tribute to these two great scientists, which kick off the celebration of the 100th Anniversary of Tsinghua University forthcoming in 2011. After that, we will have a panel discussion featuring business leaders who will share their views on the increasingly im-portant application of mathematics in internet technology and business development, and explore the role played by mathematics education in the technology evolution of the twenty-first century.

Last but not least, my deepest appreciation goes to brothers Ronnie and Gerald Chan, founders of Morningside, who have been most supportive of the Morningside Medal of Mathematics and the ICCM since their inception. It goes without saying that the generosity and continuous support of the Chan brothers have contributed much to the success of the ICCM. Apart from the tremendous support given by Morningside, this year’s conference could not have been made possible without the sponsorship of the Mathematical Sciences Center of Tsinghua University, the Morningside Center of Mathe-matics, and the School of Mathematics of the Academy of Sciences. I would like to ac-knowledge the leadership of Professor Yat Sun Poon and Professor Jie Xiao at Tsinghua University, and of Professors Lo Yang, Guo Lei, and Wang Yuefei, at the Chinese Acad-emy of Sciences, in the organizing of this triennial event. My heart-felt thanks also go to the members of the various ICCM 2010 committees, to the staff at the Mathematical Sci-ences Center of Tsinghua University, to the Morningside Center of Mathematics at the Chinese Academy of Sciences, and to Morningside and Hang Lung Properties, for their hard work and commitment to making this Congress a success.

As we enter the Fifth ICCM, I am delighted to see that the Congress has helped strengthen the cooperation among Chinese and non-Chinese mathematicians, which is of

xiii

vital importance for the enhancement of the development of mathematics in China as well in other parts of the world. It is hoped that the Congress will continue to thrive and to be a stimulant which inspires more young people to be interested in mathematical re-search, as this will have a profound impact on the future development of the study of mathematics as a living science. I am sure that everyone will enjoy ICCM 2010 and find it to be a rewarding experience.

With best regards, Shing-Tung Yau President International Congress of Chinese Mathematicians

Past Congresses of ICCM

1998 Beijing

2001 Taipei

2004 Hong Kong

2007 Hangzhou

2010 Beijing

Past Morningside Medalists, Chern Prize Recipients, and ICCM International Cooperation Award Recipients

Morningside Medalists 2010

Gold Medalists Mu-Tao Wang Columbia University Sijue Wu University of Michigan at Ann Arbor Jun S. Liu Harvard University

Silver Medalists Jungkai Alfred Chen, Meng Chen (jointly) National Taiwan University &

Fudan University Jixiang Fu Fudan University Juncheng Wei The Chinese University of Hong Kong

PAST AWARD RECIPIENTS

xiv

Morningside Medalists 2007

Gold Medalists Xu-Jia Wang Australian National University Jianqing Fan Princeton University

Silver Medalists Melissa Chiu-Chu Liu Columbia University Lizhen Ji University of Michigan at Ann Arbor Shi Jin University of Wisconsin at Madison Chiun-Chuan Chen National Taiwan University Ye Tian Chinese Academy of Science

Morningside Medalists 2004

Gold Medalists Yizhao Hou California Institute of Technology Kefeng Liu Zhejiang University Zhouping Xin The Chinese University of Hong Kong Ziliang Ying Columbia University

Silver Medalists Jinyi Cai University of Wisconsin at Madison Aiko Liu University of California at Berkeley Xiping Zhu Zhongshan University

Morningside Medalists 2001

Gold Medalists Jun Li Stanford University Horng-Tzer Yau New York University

Silver Medalists Daqing Wan University of California at Irvine Chin-Lung Wang Tsing Hua University (Taiwan) Sijue Wu University of Maryland, College Park Nanhua Xi The Chinese Academy of Sciences

Morningside Medalists 1998

Gold Medalists Chang-Shou Lin Chung Cheng University (Taiwan) Shouwu Zhang Columbia University

Silver Medalists Raymond Chan The Chinese University of Hong Kong Chong-Qing Cheng Nanjing University Kefeng Liu University of California at Los Angeles Tong Yang City University of Hong Kong

PAST AWARD RECIPIENTS

xv

Chern Prize Recipients

2010 Jiaxing Hong Fudan University Conan Nai-Chung Leung The Chinese University of Hong Kong Wen-Ching Winnie Li National Tsing Hua University &

Pennsylvania State University

2007 Shiu-Yuen Cheng Hong Kong University of Science and

Technology Mu-Tao Wang Columbia University

2004 Fanghua Lin New York University Lo Yang The Chinese Academy of Sciences

2001 Song-Sun Lin Chiao Tung University (Taiwan) Jiu-Kang Yu Purdue University

ICCM International Cooperation Award Recipients

2010 Richard M. Schoen Stanford University

2007 Stanley J. Osher University of California at Los Angeles

2004 John Coates University of Cambridge

On the Works of the 2010 Morningside Medalists

2010 Morningside Gold Medal of Mathematics

Mu-Tao Wang

Professor Wang is awarded the 2010 Morningside Gold Medal of Mathematics for his profound work in differential geometry and geometric PDE. Wang’s work on higher co-dimension mean curvature flow established sharp criteria for the long time existence, regularity, and convergence of the flow. His work on quasilocal mass in General Relativ-ity has produced a remarkably successful definition for arbitrary two surfaces in space-time. Both of these contributions are groundbreaking, and will be of lasting importance in the field. Professor Wang is a Professor of Mathematics at Columbia University. His re-search interests include differential geometry, discrete groups, partial differential equa-tions and general relativity. He received his B.S. and M.S. in mathematics from Taiwan

ON THE WORKS OF THE 2010 MORNINGSIDE MEDALISTS

xvi

University and his Ph.D. in mathematics from Harvard University. Prior to joining Co-lumbia University, Professor Wang has taught at Stanford University. Among his awards and honors are the Chern Prize, awarded at ICCM 2007, a Kavli Fellowship in 2007, a Sloan Research Fellowship for 2003-2005, the Harold M. Bacon Memorial Teaching Award from Stanford University in 2000, and a U.S. National Science Foundation Grant since 2001.

Sijue Wu

Professor Wu is awarded the 2010 Morningside Gold Medal of Mathematics for her outstanding contributions to the global well-posedness of small amplitude solutions to the water wave problems in both 2-D and 3-D.

She is the Robert W. and Lynne H. Browne Professor of Mathematics at the Univer-sity of Michigan. Professor Wu received her B.S. and M.S. from Peking University and her Ph.D. from Yale University. Prior to joining the University of Michigan, Professor Wu held appointments at the Courant Institute, the Institute for Advanced Study at Prince-ton, Northwestern University, the University of Iowa and the University of Maryland at College Park. In 2001 she was awarded a Morningside Silver Medal of Mathematics and a Ruth Lyttle Satter Prize by the American Mathematics Society. The prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. Other academic honors include a Radcliffe Institute for Ad-vanced Study Fellowship at Harvard University for 2002-2003, and a U.S. National Sci-ence Foundation Grant, for 2004-2009.

2010 Morningside Gold Medal of Applied Mathematics

Jun S. Liu

Professor Liu is awarded the 2010 Morningside Gold Medal of Applied Mathematics for his fundamental contributions to Monte Carlo inference. He has clarified the proper-ties of Rao-Blackwellization and the collapsed Gibbs sampler, and co-introduced sequen-tial importance sampling into general Bayesian computation. By developing the Gibbs motif sampler, his work also has a profound influence on computational biology. Profes-sor Liu is a Professor of Statistics at Harvard University and a Professor of Biostatistics at the Harvard School of Public Health. He received his B.S. in mathematics from Peking University, continued his studies at Rutgers University and received his Ph.D. in statistics from the University of Chicago. Prior to re-joining Harvard, Professor Liu has held ap-pointments at the National Center for Biotechnology Information, Harvard University, the National University of Singapore, the University of California at Los Angeles, Stanford University, and Peking University. His honors include being a Bernoulli Lecturer and an Institute of Mathematical Statistics (IMS) Fellow in 2004, being a IMS Medallion Lecturer and receiving the COPSS President’s Award in 2002, the Mitchell Prize in 2000, and a Terman Fellowship, for 1995-1998.

2010 Morningside Silver Medal of Mathematics

Jungkai Alfred Chen and Meng Chen

Professor Jungkai Alfred Chen and Professor Meng Chen are jointly awarded the 2010 Morningside Silver Medal of Mathematics for their breakthrough in the explicit bi-rational classification of algebraic threefolds. In particular, they determined the effective optimal bound for the pluri-canonical system to give rise to birational maps for threefolds of general type. This is the best and in fact the only complete result after Bombieri’s fa-mous similar work for surfaces. They also successfully applied their theory to the study of

ON THE WORKS OF THE 2010 MORNINGSIDE MEDALISTS

xvii

Fano threefolds to get optimal boundedness. Professor Jungkai Alfred Chen is a Professor of Mathematics at Taiwan University. He

previously taught at Chung Cheng University in Taiwan. He serves as a member of the Taida Institute for Mathematical Sciences and the Center for Theoretic Sciences in Tai-wan.

Professor Meng Chen is the Chang Jiang Scholars Program Chair Professor at the School of Mathematical Sciences at Fudan University. He received his B.S., M.S. and D.S. degrees from East China Normal University. Prior to joining the Fudan faculty, Professor Chen taught at Tonji University.

Jixiang Fu

Professor Fu is awarded the 2010 Morningside Silver Medal of Mathematics for his pioneering work on the existence of Strominger’s system on a non-Kähler Calabi-Yau threefolds; and for his proof of the existence of balance metrics on Calabi-Yau threefolds under conifold transition. Professor Fu’s works are significant contributions to the study of non-Kähler Calabi-Yau manifolds. Professor Fu is a Professor at the School of Mathe-matical Sciences at Fudan University. He was an invited speaker at the 2010 International Congress of Mathematicians in Hyderabad, India.

Juncheng Wei

Professor Wei is awarded the 2010 Morningside Silver Medal of Mathematics for his achievements in semi-linear elliptic equations. An outstanding one is the counter-example to the De Giorgi conjecture when the space dimension is larger than eight. An-other significant one is the existence of multiple peak solutions for a singularly perturbed Neumann problem. He also obtained the existence of infinitely many solutions to the prescribing scalar curvature equation on the unit sphere. Professor Wei is a Professor of Mathematics at The Chinese University of Hong Kong. He obtained his B.S. in mathemat-ics from Wuhan University and his Ph.D. from the University of Minnesota. Professor Wei was a 2005 Croucher Senior Research Fellow, and has published more than 120 pa-pers and has spoken at more than 40 international conferences.

The Chern Prize

Jiaxing Hong

Professor Hong is awarded the 2010 Chern Prize for his systematic study of the iso-metric embedding of surfaces into Euclidean three-space and his proof of a series of exis-tence and regularity that have far reaching consequences. He is widely recognized for his contribution to non-linear PDE. Professor Hong cares deeply about the young generation, making every effort to help and nurture young mathematicians in China. Professor Hong is a Professor at the School of Mathematical Sciences at Fudan University and the Super-intendent of the University’s Institute of Mathematics. He is also the Director of the Labo-ratory of Nonlinear Mathematical Models and Methods under the Ministry of Education, and serves as an editor for the Chinese Annals of Mathematics and the Asian Journal of Mathematics. He is a member of the Chinese Academy of Sciences.

Conan Nai-Chung Leung

Professor Leung is awarded the 2010 Chern Prize for his significant research contri-butions in the study of mirror symmetry and quantum cohomology, in particular for his proof of the Yau-Zaslow conjecture, for introducing new methods in studying various geometric invariants and the geometry of manifolds with different holonomy. Professor Leung has helped organize many international mathematics conferences, including the

ON THE WORKS OF THE 2010 MORNINGSIDE MEDALISTS

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2007 International conference on Geometric Analysis held at Taiwan University and the fourth Yamabe Symposium held at the University of Minnesota in 2008. He is an editor of the New York Journal of Mathematics and The Asian Journal of Mathematics. Professor Leung is a Professor of Mathematics at The Chinese University of Hong Kong. He re-ceived his M.S. in mathematics from the University of California at San Diego, and his Ph.D. in mathematics from the Massachusetts Institute of Technology.

Wen-Ching Winnie Li

The career of Dr. Wen-Ching Winnie Li began with a brilliant 1974 dissertation ex-tending the seminal 1970 paper by Atkin and Lehner on new forms, and a 1976 sequel of these two fundamental papers with Atkin. The trio had a lasting impact on the arithmetic of modular forms.

Her subsequent work covered a wide range of topics in number theory, including Eisenstein series, Rankin-Selberg L-functions, local constants, Jacquet-Langlands corre-spondence, the converse theorem, class groups, and exponential sums. Her contribution extends to graph theory and coding theory, including the construction of Ramanujan graphs by arithmetic methods and the distribution of eigenvalues for regular graphs. In recent years Dr. Li revitalized the area of the arithmetic of non-congruence arithmetic subgroups and lead a group of young researchers in an adventure in an area that has been dormant for many years.

Through her courses and lectures in the last twenty five years she has inspired gen-erations of Chinese mathematicians. Since May 2009 Dr. Li has been the Director of the National Center of Theoretical Sciences in Hsinchu, succeeding Dr. Jing Yu as the Direc-tor of the NCTS as well as the head of the Mathematical Division at the NCTS. The NCTS continues to flourish under her energetic leadership, as an institution with high esteem in the international mathematical community. The contribution of the NCTS to the devel-opment of mathematics in Taiwan is universally acknowledged.

ICCM International Cooperation Award

Richard M. Schoen

Professor Schoen is awarded the third ICCM International Cooperation Award for his steadfast contribution to the training of Chinese mathematicians. Professor Schoen has cultivated close relations with Chinese mathematicians throughout his career. Professor Schoen’s own doctoral supervisor at Stanford University was Professor Shing-Tung Yau and now, as the Bass Professor of Humanities and Sciences at Stanford University, more than one third of Professor Schoen’s 34 Ph.D. students and many of his post doctoral re-searchers hail from mainland China, Hong Kong, and Taiwan. Professor Schoen is also recognized for his efforts in continually fostering the Chinese mathematics community, not only in the United States, but also worldwide. This year, Professor Schoen joined the Selection Committee of the Morningside Medal of Mathematics.

About the Medals and Awards of ICCM

At each International Congress of Chinese Mathematicians (ICCM), the winners of several prestigious awards are announced at the opening ceremony. These awards include the Morningside Medal of Mathematics, the Chern Prize in Mathematics, and the ICCM International Cooperation Award.

ABOUT THE MEDALS AND AWARDS OF ICCM

xix

Morningside Medal of Mathematics The Morningside Medal of Mathematics is awarded to exceptional mathematicians of

Chinese descent under the age of forty-five for their seminal achievements in mathemat-ics and applied mathematics. The winners of the Morningside Medal of Mathematics are traditionally announced at the opening ceremony of the triennial International Congress of Chinese Mathematicians. The inaugural medals were presented in 1998. Each Morn-ingside Medalist receives a certificate, a medal, and cash award of US$25,000 for a gold medal, or US$10,000 for a silver medal.

Chern Prize in Mathematics The Chern Prize in Mathematics was established in 2001 in honor of Professor

Shing-Shen Chern, one of the greatest geometers and Chinese mathematicians of the twentieth century. The Chern Prize is presented every three years at the International Congress of Chinese Mathematicians to mathematicians of Chinese descent who have made exceptional contributions to mathematical research or to public service activities in support of mathematics.

ICCM International Cooperation Award The ICCM International Cooperation Award is presented to an individual who has

promoted the development of mathematics in the Chinese mainland, Hong Kong, and Taiwan through collaboration, teaching, and support of Chinese mathematicians. The in-augural award was presented at the Third International Congress of Chinese Mathemati-cians in 2004.

The Committees of the 2010 Congress

Congress Chairman Shing-Tung Yau ( ) Harvard University

2010 Morningside Medal of Mathematics Selection Committee

John H. Coates. Sadleirian Professor of Pure Mathematics at the University of Cambridge and a Fellow of Emmanuel College, Cambridge.

Simon K. Donaldson. Royal Society Research Professor in Pure Mathematics at Imperial College London.

Gerd Faltings. Director of the Max Planck Institute for Mathematics in Germany.

Jean-Marc Fontaine. Professor Emeritus of Mathematics at the University of Paris-Sud.

Benedict H. Gross. George Vasmer Leverett Professor of Mathematics at Harvard University.

Nigel Hitchin. Savilian Professor of Geometry at Oxford University.

Stanley J. Osher. Professor of Mathematics, Computer Science, Electrical Engineering at the University of California at Los Angeles.

Richard M. Schoen. Bass Professor of Humanities and Sciences at Stanford University.

Joel A. Smoller. Lamberto Cesari Chair of Mathematics at the University of Michigan, Ann Arbor.

THE COMMITTEES OF THE 2010 CONGRESS

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Grace Wahba. I.J. Schoenberg-Hilldale Professor of Statistics at the University of Wisconsin at Madison.

Shing-Tung Yau. William Casper Graustein Professor of Mathematics at Harvard University.

Scientific Committee Zhi-Ming Chen ( ), Chinese Academy of Sciences

Shiu-Yuen Cheng ( ), Hong Kong University of Science and Technology

Fan Chung Graham ( ), University of California at San Diego

Jiaxing Hong ( ), Fudan University

Tze-Leung Lai ( ), Stanford University

Jun Li ( ), Stanford University

Peter Li ( ), University of California, Irvine Bong Lian ( Brandeis University

Chang-Shou Lin ( ), National Chung Cheng University

Kefeng Liu ( ), Zhejiang University and University of California at Los Angeles

Ngaiming Mok ( ), The University of Hong Kong

Yum-Tong Siu ( ), Harvard University

Shengli Tan ( ), East China Normal University

Chuu-lian Terng ( ), University of California at Irvine

Xujia Wang ( ), National University of Australia

Jie Xiao ( ), Tsinghua University

Ling Xiao ( ), Chinese Academy of Science

Zhouping Xin ( ), The Chinese University of Hong Kong

Lo Yang ( ), Chinese Academy of Sciences

Andrew Chi-Chih Yao ( ), Tsinghua University

Shouwu Zhang ( ), Columbia University

Weiping Zhang ( ), Nankai University

Xiping Zhu ( ), Sun Yat-Sen University

Executive Committee Huai-Dong Cao ( ), Lehigh University

Gerard J. Chang ( ), National Taiwan University

Chiun-Chuan Chen ( ), National Taiwan University

Louis Chen ( ), National University of Singapore

Chongqing Cheng ( ), Nanjing University

Jih-Hsin, Cheng ( ), Institute of Mathematics, Academia Sinica, Taipei

Xiaqi Ding ( ), Chinese Academy of Sciences

Weinan E ( ), Princeton University

Ka-Sing Lau ( ), The Chinese University of Hong Kong

Daqian Li ( ), Fudan University

Qikeng Lu ( ), Chinese Academy of Sciences

Zhongci Shi ( ), Chinese Academy of Sciences

THE COMMITTEES OF THE 2010 CONGRESS

xxi

Chiwang Shu ( ), Brown University

Zhexian Wan ( ), Chinese Academy of Sciences

Yuan Wang ( ), Chinese Academy of Sciences

Jeff Wu ( ), Georgia Institute of Technology

Jia-An Yan ( ), Chinese Academy of Sciences

Horng-Tzer Yau ( ), New York University

Stephen S. T. Yau ( ), University of Illinois at Chicago

Jing Yu ( ), National Tsing Hua University

Liqun Zhang ( ), Chinese Academy of Sciences

Organizing Committee Keqin Feng ( ), Tsinghua University

Qi Feng ( ), Chinese Academy of Sciences

Kefeng Liu ( ), University of California at Los Angeles

Yat Sun Poon ( ), University of California at Riverside

Yuefei Wang ( ), Chinese Academy of Sciences

Jie Xiao ( ), Tsinghua University

Jian Zhou ( ), Tsinghua University

Sponsors, Donors and Contributors

Sponsors Morningside Group Academy of Mathematics and Systems Science, Chinese Academy of Sciences Tsinghua University

Co-Sponsors Department of Mathematics, Chinese University of Hong Kong School of Mathematical Sciences, Fudan University Department of Mathematics, Hong Kong University of Science & Technology Department of Mathematics, National Central University Department of Mathematics, National Taiwan University National Center for Theoretical Sciences, National Tsing Hua University Department of Mathematical Sciences, Renmin University of China Department of Mathematics, Capital Normal University Department of Mathematical Sciences, Beijing Institute of Technology Department of Mathematics, Beijing Normal University College of Applied Science, Beijing University of Technology School of Mathematics and Computational Science, Sun Yat-Sen University Department of Mathematics, Tongji University Department of Mathematics, University of Science and Technology of China Center of Mathematical Sciences, Zhejiang University National Natural Science Foundation of China

SPONSORS, DONORS AND CONTRIBUTORS

Photographs

PHOTOGRAPHS xxiii

The Opening Ceremony of ICCM 2010

Awardees and members of the selection committee at the opening ceremony of ICCM 2010

Prof. S.-T. Yau (Chairman of ICCM 2010) delivers the opening address.

PHOTOGRAPHSxxiv

Mu-Tao Wang (center) is awarded the 2010 Morningside Gold Medal of Mathematics. WithS.-T. Yau (left) and Yongxiang Lu (right, President of the Chinese Academy of Sciences).

Sijue Wu (center) is awarded the 2010 Morningside Gold Medal of Mathematics. With S.-T. Yau(left) and Ping Hao (right, Vice Minister of the Ministry of Education of the P. R. of China).

Jun S. Liu (center) is awarded the 2010 Morningside Gold Medal of Applied Mathematics. WithS.-T. Yau (left) and Binglin Gu (right, President of Tsinghua University).

PHOTOGRAPHS xxv

Jungkai Alfred Chen (second from right) and Meng Chen (second from left) are jointly awarded the2010 Morningside Silver Medal of Mathematics. With S.-T. Yau (left) and Benedict H. Gross (right,

Harvard University).

Jixiang Fu (center) is awarded the 2010 Morningside Silver Medal of Mathematics. With S.-T. Yau(left) and Stanislaw Janeczko (right, Polish Academy of Sciences, Warsaw Univ. of Technology).

Juncheng Wei (center) is awarded the 2010 Morningside Silver Medal of Mathematics. With S.-T.Yau (left) and Ari Laptev (right, Imperial College London).

PHOTOGRAPHSxxvi

Wen-Ching Winnie Li (center) is awarded the2010 Chern Prize. With S.-T. Yau (left) and Lo

Yang (right, member of the Chinese Academy ofSciences).

Conan Nai-Chung Leung (left) is awarded the2010 Chern Prize. With S.-T. Yau (right).

Jiaxing Hong (center) isawarded the 2010 Chern

Prize. With S.-T. Yau (left)and John Coates (right,

University of Cambridge).

Richard M. Schoen(center) is awarded the2010 ICCM InternationalCooperation Award. WithS.-T. Yau (left) andRonnie C. Chan (right,President of Hang LungProperties).

Titles in This Series

51.2 Lizhen Ji, Yat Sun Poon, Lo Yang, and Shing-Tung Yau, Editors, FifthInternational Congress of Chinese Mathematicians, 2012

51.1 Lizhen Ji, Yat Sun Poon, Lo Yang, and Shing-Tung Yau, Editors, FifthInternational Congress of Chinese Mathematicians, 2012

50 Jørgen E. Andersen, Hans U. Boden, Atle Hahn, and Benjamin Himpel,Chern-Simons Gauge Theory: 20 Years After, 2011

49 Matthias Plaue, Alan Rendall, and Mike Scherfner, Advances in LorentzianGeometry, 2011

48 Lizhen Ji, Kefeng Liu, Lo Yang, and Shing-Tung Yau, Fourth InternationalCongress of Chinese Mathematicians, 2010

47 Alexander Grigor’yan, Heat Kernel and Analysis on Manifolds, 2009

46.2 Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono, Editors,Lagrangian Intersection Floer Theory, 2009

46.1 Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono, LagrangianIntersection Floer Theory, 2009

45 Lydia Bieri and Nina Zipser, Extensions of the Stability Theorem of the MinkowskiSpace in General Relativity, 2009

44 Eric Sharpe and Arthur Greenspoon, Editors, Advances in String Theory, 2008

43 Lizhen Ji, Editor, Arithmetic Groups and Their Generalizations, 2008

42.1 Ka-Sing Lau, Zhou-Ping Xin, and Shing-Tung Yau, Editors, Third InternationalCongress of Chinese Mathematicians, 2008

41 Wen-Ching Winnie Li, Editor, Recent Trends in Coding Theory and its Applications,2007

40 Ovidiu Caliin, Der-Chen Chang, and Peter Greiner, Editors, Geometric Analysison the Heisenberg Group and Its Generalizations, 2007

39 Zhijie Chen, Sheng-Li Tan, Jianpan Wang, and Stephen S.-T. Yau, Editors,Proceedings of the International Conference on Complex Geometry and Related Fields, 2007

38 Noriko Yui, Shing-Tung Yau, and James D. Lewis, Editors, Mirror Symmetry V,2006

37 Lizhen Ji, Jian-Shu Li, H. W. Xu, and Shing-Tung Yau, Editors, Lie Groups andAutomorphic Forms, 2006

36 Chuu-Lian Terng, Editor, Integrable Systems, Geometry, and Topology, 2006

35 Felix Finster, The Principle of the Fermionic Projector, 2006

34 Ren-Hong Wong, Editor, Computational Geometry, 2003

33 Eric D’Hoker, Duong Phong, and Shing-Tung Yau, Mirror Symmetry IV, 2002

32 Xi-Ping Zhu, Lectures on Mean Curvature Flows, 2002

31 Kiyoshi Igusa, Higher Franz-Reidemeister Torsion, 2002

30 Weiman Han and Mircea Sofonea, Quasistatic Contact Problems in Viscoelasticityand Viscoplasticity, 2002

29 S. T. Yau and Shuxing Chen, Editors, Geometry and Nonlinear Partial Differential

Equations, 2002

28 Valentin Afraimovich and Sze-Bi Hsu, Lectures on Chaotic dynamical Systems, 2002

27 M. Ram Murty, Introduction to p-adic Analytic Number Theory, 2002

26 Raymond Chan, Yue-Kuen Kwok, David Yao, and Qiang Zhang, Editors,Applied Probability, 2002

25 Donggao Deng, Daren Huang, Rong-Qing Jia, Wei Lin, and Jian Zhong Wong,Editors, Wavelet Analysis and Applications, 2002

24 Jane Gilman, William W. Menasco, and Xiao-Song Lin, Editors, Knots, Braids,and Mapping Class Groups—Papers Dedicated to Joan S. Birman, 2001

23 Cumrun Vafa and S.-T. Yau, Editors, Winter School on Mirror Symmetry, VectorBundles and Lagrangian Submanifolds, 2001

TITLES IN THIS SERIES

22 Carlos Berenstein, Der-Chen Chang, and Jingzhi Tie, Laguerre Calculus and ItsApplications on the Heisenberg Group, 2001

21 Jurgen Jost, Bosonic Strings: A Mathematical Treatment, 2001

20 Lo Yang and S.-T. Yau, Editors, First International Congress of ChineseMathematicians, 2001

19 So-Chin Chen and Mei-Chi Shaw, Partial Differential Equations in Several Complex

Variables, 2001

18 Fangyang Zheng, Complex Differential Geometry, 2000

17 Lei Guo and Stephen S.-T. Yau, Editors, Lectures on Systems, Control, andInformation, 2000

16 Rudi Weikard and Gilbert Weinstein, Editors, Differential Equations andMathematical Physics, 2000

15 Ling Hsiao and Zhouping Xin, Editors, Some Current Topics on NonlinearConservation Laws, 2000

14 Jun-ichi Igusa, An Introduction to the Theory of Local Zeta Functions, 2000

13 Vasilios Alexiades and George Siopsis, Editors, Trends in Mathematical Physics,1999

12 Sheng Gong, The Bieberbach Conjecture, 1999

11 Shinichi Mochizuki, Foundations of p-adic Teichmuller Theory, 1999

10 Duong H. Phong, Luc Vinet, and Shing-Tung Yau, Editors, Mirror Symmetry III,1999

9 Shing-Tung Yau, Editor, Mirror Symmetry I, 1998

8 Jurgen Jost, Wilfrid Kendall, Umberto Mosco, Michael Rockner,and Karl-Theodor Sturm, New Directions in Dirichlet Forms, 1998

7 D. A. Buell and J. T. Teitelbaum, Editors, Computational Perspectives on NumberTheory, 1998

6 Harold Levine, Partial Differential Equations, 1997

5 Qi-keng Lu, Stephen S.-T. Yau, and Anatoly Libgober, Editors, Singularities andComplex Geometry, 1997

4 Vyjayanthi Chari and Ivan B. Penkov, Editors, Modular Interfaces: Modular LieAlgebras, Quantum Groups, and Lie Superalgebras, 1997

3 Xia-Xi Ding and Tai-Ping Liu, Editors, Nonlinear Evolutionary Partial DifferentialEquations, 1997

2.2 William H. Kazez, Editor, Geometric Topology, 1997

2.1 William H. Kazez, Editor, Geometric Topology, 1997

1 B. Greene and S.-T. Yau, Editors, Mirror Symmetry II, 1997

AmericanMathematical

Societywww.ams.org

InternationalPress

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AMSIP/51.1

This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest develop-ments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.

978-0-8218-7586-5 (Part 1)978-0-8218-7555-1 (Set)