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Fifth International Congress of Chinese Mathematicians Part 1 AMS/IP Studies in Advanced Mathematics S.-T. Yau, Series Editor Fifth International Congress of Chinese Mathematicians Part 1 Lizhen Ji Yat Sun Poon Lo Yang Shing-Tung Yau Editors American Mathematical Society • International Press Fifth International Congress of Chinese Mathematicians https://doi.org/10.1090/amsip/051.1 AMS/IP Studies in Advanced Mathematics Volume 51, Part 1 Fifth International Congress of Chinese Mathematicians Lizhen Ji Yat Sun Poon Lo Yang Shing-Tung Yau Editors American Mathematical Society • International Press 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. Library of Congress Cataloging-in-Publication Data 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. QA1.I746 2010 510—dc23 2011048032 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Math- ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) c 2012 by the American Mathematical Society and International Press. All rights reserved. The American Mathematical Society and International Press retain all rights except those granted to the United States Government. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ Visit the International Press home page at URL: http://www.intlpress.com/ 10987654321 171615141312 Contents In Part One Preface...........................................................................................................................ix 噾ⅉ㠇⸇⮶㦒ⓜ岏 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 v vi CONTENTS 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
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