Annual Report National Center for Theoretical Sciences Theoretical for National Center December 2009 Annual Report December 2009 Annual Report National Center for Theoretical Sciences National Center for Theoretical Sciences No. 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013 Mathematics Division Physics Division Tel: 886-3-5728263/5745253~5 Tel: 886-3-5734969 Fax: 886-3-5728161 Fax: 886-3-5735086 e-mail: [email protected] e-mail: [email protected] http://www.math.cts.nthu.edu.twl http://phys.cts.nthu.edu.tw December 2009 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 Focus Programs ------------- 8 Highlights of the Regional Programs --------- 56 Activities of Onsite Scientists ------------------ 77 Preprints ------------------------------------------- 90 Appendix ------------------------------------------100 I. Visiting Mathematicians --------------------100 II. Conference, Workshop, School & Special Lecture -------------------------------120 III. Physics Division --------------------129 Report of the Division Head -------------------130 Highlights of Programs ------------------------- 134 Focus Group & Working Group Complex Systems and Soft Matter ----------- 134 Condensed Matter Physics --------------------142 Particles and Fields -----------------------------153 Interdisciplinary Fields ------------------------171 Topic Program ------------------------------------182 Initiative -------------------------------------------186 Research Activities of Individuals ------------196 Introducing New Members --------------------225 Annual Report Publisher: Editors: National Center for Theoretical Sciences Wen-Ching Winnie L Mandy Chen(Mathematics Division) December 2009 Sherry Pang(Physics Division) Words from the Director any changes took research in theoretical sciences in p l a c e t h i s y e a r. Taiwan have improved remarkably, Fiscally, it is the beginning international cooperation and of the third phase of NCTS, collaborations were established, a six year project, funded by and many young scientists were the National Science trained and some are shining stars Council. The overall today. We salute him for his organization of the center outstanding achievements and and the programs within each division remain the thank him for his enduring same as before, except for contributions to the NCTS. the addition to the main Beginning September 1, the PI project in mathematics of a of the Subproject I in Taipei is r e g i o n a l p r o g r a m i n Professor Wei-Shu Hou from the theoretical statistics this Physics Department of National July. The new program is off Taiwan University (NTU), with to a good start, and the continuing programs are progressing and Professor Chuin-Chuan Chen from the improving steadily with several stellar Mathematics Department of NTU serving as the achievements in mathematics and theoretical co-PI in mathematics. For the Subproject II in physics. We welcome National Central University Tainan, the lead PI is Professor Yung-Guei Fu (NCU), which joined National Tsing Hua from the Physics Department of National Cheng University (NTHU) and National Chiao Tung Kung University (NCKU); his colleague University (NCTU) as a hosting institution of the Professor Yan-Tien Lu is the co-PI in physics. main project headquartered in NTHU. The co-PI in mathematics was Professor King-Fai There have been leadership changes in all Lai from the Mathematics Department of NCKU locations. Professor Jing Yu completed his term as from Feb. 1 to July 31; after Professor Lai moved the Director of NCTS on June 1 and the Head of to National Sun Yet-Sen University (NSYSU) this the Mathematics Division on May 14; his summer, his post was resumed by his former successor, Professor Wen-Ching Winnie Li, is colleague Professor Soon-Yi Wu as of August 1. from the Pennsylvania State University. Professor The Head of the Physics Division has been Yu has played a pivotal role at NCTS since its Professor Chung-Yu Mou from the Physics inauguration, serving as an acting director twice Department of NTHU since 2007. In 2010, and the director since 2006 on top of being the Professor Ling-Fong Li of Carnegie Mellon head of the mathematics division from 1997 to University will succeed him. We express our 2009 except for a four-year interruption. Under hearty thanks to the former PI's and co-PI's for his leadership, NCTS expanded steadily with their seless devotion to the development of the more research programs, more space and more center and welcome the new comers to work sponsoring institutions, the quantity and quality of jointly for the future well-being of the center. 1 ‹‹- Words from the Director The climax of the numerous lectures/courses at To further international cooperation, the NCTS this year is the one week lecture series in Subproject II in Tainan signed an agreement with July given by Professor Jean-Pierre Serre of Hong Kong University of Science and Technology Collège de France. His 4 lectures on "Variation in April of 2009. This is a welcome addition to the with p of the number of solutions modulo p of a existing formal cooperation agreements with system of polynomial equations" left a long- IHES, lasting impressive memory to a huge crowd KIAS, APCTP, and KEK. We wish them many coming from all over the country and abroad. years of fruitful collaborations ahead. Another very important event was the one week visit in October to all locations of NCTS by four Looking forward, we anticipate a new year of French delegates, two mathematicians and two vigorous, high quality activities aimed to elevate theoretical physicists, whose primary purpose was research quality, nurture young scientists, promote to seek further cooperation between Taiwan and international cooperation and collaborations, and France. The highlight of their visit was the develop new international and interdisciplinary bilateral cross-disciplinary "Taiwan-France programs. workshop on theoretical sciences" held at the headquarter of NCTS. This was the first joint scientific conference between the two divisions. Their initiative has led to planned cooperative Wen-Ching Winnie Li (李文卿) activities to be carried out next year. November 2009 Words from the Director -›› 2 Mathematics Division Report of the Division Head his year marks the beginning of the third from NCU, seven from NCTU, five from NTHU, phase of NCTS, a six year project, funded one from NSYSU, and one from NCTS. Their by the National Science Council. Since its specialties are diverse: two in algebraic geometry, inauguration, the headquarter of NCTS has been three in analysis, five in dynamical systems, one housed in the National Tsing Hua University in geometry and mathematical physics, four in (NTHU). Starting this year, National Central number theory, one in partial differential University joined NTHU and National Chiao equations, one in probability, one in topology, and Tung University (NCTU) as one of the hosting one in scientific computation. institutions of the main project. The new regional program on theoretical statistics added to the main The new recipient of the Young Theorists project this July is off to a good start. Award of NCTS this year is Professor Nan-Kuo Professor Jing Yu completed his term as the Ho of NTHU. Professor Ho received her Ph.D. Head of the Mathematics Division on May 14, from University of Toronto. Her research area is 2009. His successor, Professor Wen-Ching Winnie symplectic geometry and mathematical physics. Li, is from the Penn State University. We are The continuing recipients are Professor Kuo- indebted to Professor Yu for his devotion and Chang Chen (NTHU) in dynamical systems, invaluable services to NCTS for so many years. Guan-Yu Chen (NCTU) in probability theory, We thank him for his leadership and enduring Cheng-Hsiung Hsu (NCU) in dynamical systems, contributions. Ming-Yee Lee (NCTU) in dynamical systems, and Jyh-Haur Teh (NTHU) in algebraic geometry and There are also leadership changes in the two topology. These recipients were selected from all Subprojects. The co-PI in mathematics of the applicants by the Executive Committee based on Subproject I in Taipei is Professor Chuin-Chuan the evaluations by international experts. Chen from the Mathematics Department of National Taiwan University (NTU). For the On the research front, this is a fruitful and Subproject II in Tainan, the co-PI in mathematics productive year. Compared to previous years, the was Professor King-Fai Lai from the Mathematics number of publications is increasing steadily, and Department of NCKU from Feb. 1 to July 31; the overall qualityis improving. There are after Professor Lai moved to National Sun Yet- outstanding results published in leading Sen University (NSYSU) this summer, his post international journals. We mention a few was resumed by his former colleague Professor highlights below. Soon-Yi Wu as of August 1. We deeply appreciate (a) In the area of arithmetic over function fields, the efforts made by the former co-PI's, and look great progresses have been made in recent forward to working together with the new comers years. In particular, in transcendence theory of for the well-being of the center. positive characteristic, all algebraic relations among special zeta values and gamma values In this year nineteen mathematicians either are determined. In fact, the motivic have completed