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October 2007 I October 2007 I. Words from the Director ----- 1 II. Mathematics Division--------- 3 Report of the Division Head ------------------- 4 Executive Committee Members -------------- 6 Academic Committee Members --------------- 7 Highlights of the Programs ---------------------- 8 Activities of Onsite Scientists------------------ 65 Preprints------------------------------------------- 75 Appendix------------------------------------------ 83 I. Visiting Scientists ---------------------------- 83 II. Conference, Workshop & School ---------- 97 III. Physics Division ------------------- 103 Report of the Division Head ------------------ 104 Highlights of Programs ------------------------- 110 Focus Group Complex System-------------------------------- 100 Condensed Matter Physics ------------------- 120 Particles and Fields----------------------------- 136 Interdisciplinary Fields ------------------------ 149 Working Group Plasma Science Program ---------------------- 157 Research Activities of Individuals ------------ 161 Introducing New Members --------------------- 192 Annual Report Publisher: Editors: National Center for Theoretical Sciences Jing Yu Mandy Chen(Mathematics Division) Sherry Pang (Physics Division) October 2007 Words from the Director ational Center for Besides the physical space Theoretical Sciences at their campus, they also started its operation in 1997. offer faculty positions for In the last 10 years, it grows Center Scientists which steadily under the strong constitute the major work support from the National force at the center. In the Science Council, the second phase of NCTS devotion of the Physics and operation since 2004, Mathematics community in National Taiwan University Taiwan, and the hard at Taipei and National workings of the Cheng Kung University at administrative staffs. During Tainan join in the form of these years, our Center was subprojects, providing also blessed and helped by facilities as well as research the international theoretical men powers into the NCTS scientists community, in particular by those project. Also National Central University at world scholars who originated from Taiwan. Chungli offers two faculties positions into the We just have a 10-th year anniversary main project of NCTS as center scientists. celebration at September 3, 2007, with the This development leads to more effective inauguration of new space at the fifth floor of implementations of NCTS activities, and the 3rd general building on the campus of the results in more large scale cooperation among National Tsing Hua University. Adding in this universities in Taiwan on researches of newly renovated office space, NCTS in the theoretical sciences. 3rd general building now occupies the major Promoting interdisciplinary researches in part of the fourth floor and a square wing at theoretical sciences is one of the major the fifth floor, and from now on the Physics objectives of NCTS. We had made great and the Mathematics Division shall work efforts at this in the past, and definitely will under one roof. We are greatly indebted to make more efforts in the future. One National Tsing Hua University for this interdiscipline is certainly the subject of beautifully designed and equipped space Mathematical Physics. We are happy to which, being adjacent to the mathematics report that data shows the number of papers library, makes it quite an ideal location for from Taiwan in important international NCTS. journals of mathematical physics is National Tsing Hua University and conspicuously increasing in the last decade. National Chiao Tung University at Hsinchu The increasing is more apparent in the best cohost NCTS from the very beginning. Communications in Mathematical Physics. 1 ‹‹- Words from the Director Research Works done at NCTS are in the agreed to serve as deputy head of the Physics direction of Conformal field theory, String Division. We are extremely grateful to Theory, Nonlinear Partial Differential Professor Hsian-nan Li for his excellent Equations from models in Physics, related services to NCTS in the year 2006/2007. Scientific Computations, etc. Another area Finally the mathematics Division has also which NCTS has made considerable endeavor appointed two deputy heads starting from is Mathematical Biology and Biological August 1, Professor Wen-Wei Lin from Physics and System Biology. Our major NTHU and Professor Yuan-Chung Sheu from directions in math biology is population NCTU. dynamics, and bioinformatics. We have built Another enlightening development at up interdisciplinary teams in both directions, NCTS is the establishment of Young interacting constantly with experts in related Theorists Awards. The aim is to encourage fields of biological sciences. They already young colleagues to pursue theoretical produced series of very significant research researches, to maintain active and to do results in important international journals of excellent works. The selection of recipients is related subjects. In particular, the development based on evaluations from international of bioinformatics at NCTS is greatly helped experts. There are four recipients in 2007, by Academician Wen-Hsiung Li from the Chih-Tin Shih of Tung-Hai University, and University of Chicago. Daw-Wei Wang of NTHU in Physics, Kuo- Due to eye pressure problem, the Head of Chang Chen of NTHU and Cheng-Hsiung Physics Division, Professor Hsiang-nan Li Hsu of NCU in mathematics. The two had to resign in July 2007. We have asked recipients in mathematics later on have also Professor Chung-Yu Mou from National been awarded 2007 Ta-You Wu Fellowship of Tsing-Hua University to serve as the new head NSC. NCTS is promised to be a breeding of Physics Division starting from August 1, ground for next generation theoretical 2007. Also Professor Chon-Saar Chu from scientists in Taiwan, we shall keep this National Chiao-Tung University has kindly promise. Words from the Director -›› 2 Mathematics Division Report of the Division Head CTS started its operation on August 1, Ho Tsai (NTHU) in Differential Geometry, 1997. It is already ten years old. We Chin-Lung Wang (NCU) in Algebraic are very happy to have our 10-th year Geometry, Jing Yu (NTHU) in Number anniversary celebration this summer, with Theory. To make the operations at Hsinchu Academician Shing-Tung Yau from Harvard more effective, the Mathematics Division also University visited us at August 1 2007, for one appointed two Deputy Heads at August 1: week. Professor Yau has been chairman of our Professor Wen-Wei Lin from NTHU and international advisory committee in Professor Yuan-Chung Sheu from NCTU. mathematics since 10 years ago. Also joining We are also continuing our commitment to us this summer at NCTS are the academicians, supporting younger generation as much as we Professor Horng-Tzer Yau, Professor Yum- can. This year we have partially supported 6 Tong Siu, both from Harvard University, and Ph.D. students, to ICTP summer school in Professor Wen-Hsiung Li from the University Italy, Arizona winter school in USA, MSRI of Chicago. Professors H.-T. Yau and W.-H. Li workshop in USA, and presenting paper at have also been on our advisory committee, and journees arithmetiques in Britain. We also made constant advices to us during these supported 4 post doctors and junior faculties to years. There are many other old friends in international conferences/workshops. We grant mathematics coming to see us this summer, CTS fellowships to one junior faculty visiting and we are grateful to all of them for their long Cornell University/Georgia Tech, and one term enthusiastic and devoted efforts to help Ph.D. student doing research at Queens and support NCTS growing up. University, both for period of three months. Starting from the second phase of operation There are more than 50 students enrolled in (January 2004), the hosting universities of the out summer internship program. main project of NCTS, i.e. NTHU and NCTU, As before, the NCTS 2007 Math Preprint promised to raise the offer of center scientists Series is divided into three subseries I, II, and positions, from 4 positions to 10 positions in III, collected from the main project and the Mathematics. The center scientists are very two subprojects respectively. Works from important to the actual operation of the center, NCTS preprint series of past years have they reside at NCTS leading the researches of appeared in various important international the various topical programs. We are satisfying mathematical journals, including the most to report that from August 1 this very year, we influential ones. For example, the paper by get ten Center Scientists in Mathematics for Yuan-Pin Lee, Hui-Wen Lin (NCU), and Chin- the first time. They are: Guan-Yu Chen Lung Wang (NCU), entitled : Flops, (NCTU) in Probability, Jiun-Cheng Chen Correspondences and Quantum Corrections (NTHU) in Algebraic Geometry, Kuo-Chang has now been accepted by the Annals of Chen (NTHU) in Dynamical System, Ment- Mathematics. We have reported this important Kiat Chuah (NTHU) in Representation Theory, progress of algebraic geometry last year Ming-Chia Li (NCTU) in Dynamical system, already in the NCTS 2006 Annual Report. Song-Sun Lin (NCTU) in Dynamical System, This annals paper is just the beginning of a Wen-Hsiung Lin (NTHU) in Topology, Dong- Report of the Division Head -›› 4 beak through in higher-dimensional geometry NCTS. This collaboration started in summer made by these authors after years of study and 2004 when Papanikolas visited NCTS from collaborations supported by NCTS. Y.-P. Lee Texas.
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