A n n u a l R e p o r t N a t i o n a l October 2008 C e n t e Annual Report r f o October 2008 r T h e Annual Report National Center for Theoretical Sciences o r e t i c a l S c i e n c National Center for Theoretical Sciences e s 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013 Mathematics Division Physics Division Tel: 886-3-5728263 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 O c t o b e r 2 0 0 8 I. Words from the Director ----- 1 II. Mathematics Division --------- 2 Report of the Division Head ------------------- 3 Executive Committee Members --------------- 5 Academic Committee Members --------------- 6 Highlights of the Programs --------------------- 7 Activities of Onsite Scientists ------------------ 50 Preprints ------------------------------------------- 61 Appendix ------------------------------------------ 69 I. Visiting Mathematicians -------------------- 69 II. Conference, Workshop & School ---------- 79 III. Physics Division ------------------- 85 Report of the Division Head ------------------ 86 Highlights of Programs ------------------------ 92 Focus Group Complex System ------------------------------- 92 Condensed Matter Physics ------------------- 95 Particles and Fields ---------------------------- 107 Interdisciplinary Fields ------------------------ 126 Working Group Plasma Science --------------------------------- 134 Softmatter and Nonlinear Physics ----------- 138 Research Activities of Individuals ------------ 144 Introducing New Members -------------------- 183 Annual Report Publisher: Editors: National Center for Theoretical Sciences Jing Yu Mandy Chen(Mathematics Division) October 2008 Sherry Pang(Physics Division) Words from the Director he second phase of interdisciplinary researches NCTS operation in theoretical sciences. starts from January 2004 till Besides Mathematical December 2008. This is the Biology, Bioinformatics, and last year. National Science Biological Physics in which Council (NSC) has focus programs are actively conducted an on-site review going on, a new initiative of NCTS this January. this year is in the direction Basing on the report of the of theoretical Statistics. In review committee, and the the subproject at NCKU, a suggestion of the steering program on Statistics committee of NCTS, the methods including NSC made the decision in Biostatistics has been July, to continue supporting implemented and well NCTS with a third phase received. In 2009, further operation, from January 2009 to December interdisciplinary program relating to 2014. The basic operating framework remains theoretical Statistics are expected to be the same, with main project at Hsinchu, incorporated into the main project. We cohosted by NTHU, NCTU, and NCU, one anticipate that new international research team subproject at Taipei hosted by NTU, and in this direction will also be formed in the near another subproject in southern Taiwan future. cohosted by NCKU and NSYSU. The detailed When NCTS started its operation 11 years proposal for the 3rd phase is being worked out ago, one of its mission in our mind is to by all participating parts at this moment. modify the landscape of theoretical sciences This year we enjoyed the newly expanded research in Taiwan. On the international and renovated space of the headquarter of stages, there were important research areas in NCTS at the campus of NTHU. Located on which Taiwanese scientists didn't take part. We the 4-th and 5-th floor of the 3rd general made efforts and we now see some changes. building, this expanded space puts the Physics Mathematical Physics is one such area. Division and the Mathematics Division under Dynamical Systems is another. In the direction one roof, working more closely together. The of interdisciplinary researches, theoretical new 1st guest house of NTHU, after one year sciences relating to Biology is also becoming running, also was highly acclaimed by all our an important trend in Taiwan. New research visitors. There is yet another new guest house groups started to form, existed research groups of TCTU nearby. Thus as far as hardware is become more established, as the on-site concerned, we are ready to enter into the 3rd review committee remarked in January. We phase of NCTS. look forward to another 10 years of NCTS with success. We continue our efforts of promoting 1 ‹‹- Words from the Director Mathematics Division Report of the Division Head his is the last year of the 2nd phase (Canada) and Arizona Arithmetic Geometry operation of NCTS. We are now Center this year, we also supported two planning a detailed proposal for the 3rd phase advanced students to do research abroad for of NCTS, 2009-2014, and looking forward to three months, one at Max-Planck Institute further develop the roles play by NCTS in the (Bonn), the other one at Fields Intitute (with global mathematics research. On the one hand, local expenses supported by Fields). Another we are searching for the new division head to initiative this year is a Taiwan-Tohoku lead NCTS. On the other hand, we are workshop supported by NCTS in April, considering new strategies and initiatives which can bring us to new grounds. organized by E. Yanagida (Tohoku U.), and Jann-Long Chen (NCU), with two Ph.D. There was an on-site review of NCTS students from Taiwan visiting Tohoku, conducted by an international committee in interacting with Ph.D. students on differential January 2008. The report of this committee on equations in Tohoku U. The second round will the mathematics division is very positive and be in Jan. 2009, to be held at NCTS, with 6 encouraging. Japanese Ph.D. students coming interacting In the main project, the three hosting with our Ph.D. students of differential universities now offers 15 center scientists equations. These are a bilateral activities, each positions for the mathematics division. In side pays their own air tickets. 2008, we have five from NCTU, three from Papers from NCTS Math Preprint Series NTHU, and two from NCU. Among them, one of previous years continue to appear in in Algebraic Geometry, one in Algebraic important international journals. We are happy Topology, one in Classical Analysis, three in to report, in particular, the paper: Elliptic Dynamical Systems, two in Number Theory, Functions, Green Function, and the Mean Field and one in Scientific Computation. Equation on Tori, by Chang-Shou Lin and We have committed firmly to the Chin-Lung Wang had recently been accepted cultivation and support of young generations. by Annals of Math. This paper was singled out In last decade the summer internship program in 2006 NCTS report as important at NCTS grows steadily, those undergraduate breakthrough. It is also the third paper from interns of past years now studies in top NCTS in two years accepted by the prestigious graduate schools of the States, Europe, as well Ann. Math. Mathematics papers usually take a as in Taiwan. Past research assistants (one year longer period for refereeing than papers from position at NCTS) are becoming post doctors other fields, for a preprint to appear in print or young faculties in Taiwan after getting their one may need more than two years after it is Ph. D. degrees from great universities abroad. submitted. Submitting to top journals usually Besides (partially) supporting graduate take more time. On the other hand, students to attend important international mathematics works also need more years to summer/winter schools, e.g. Fields Institute have its impact fully come out. The AMS 3 ‹‹- Report of the Division Head Math SciNet therefore keeps track a record of range of pure and applied mathematics. NCTS all the important math journals, counting is happily cooperating with all these university citations of five years, as contrast to the SCI institutions, working together for the common impact factors which count citations only in goal of developing theoretical sciences in two years. Taiwan. However, the role of NCTS is also distinct from and complement to these In the on-site review report this year, the university institutions. The population of following research contributions were mathematicians in Taiwan as compared to the highlighted : total population, is still far below the (a) A sharp bound for the pluri-canonical map developed countries, such as Japan, France, to be rational for threefolds which are U.S. etc. As a result, we dont have enough either of general type or Fano. critical mass in any theoretical science (b) Invariance of the quantum cohomology research field. In order to have research man ring after analytic continuation on the power in a particular field comparable to, say Kähler moduli. Tokyo University which has 60 permanent (c) An important result on the three body faculties in mathematical science, we actually problem by the variational method. have to group all the work forces of several (d) Determined all algebraic relations among universities. NCTS is for such a purpose. special zeta values and gamma values in Under topical program of NCTS, local positive characteristic. mathematicians in the same field are pulled together for going out to various international Since the five year five million project of stages. We can win together. the Ministry of Education started two years ago, the leading research universities in Finally, the Young Theorists Award of Taiwan have put more resources into basic NCTS enters its 2nd year, with three theoretical sciences. This is very encouraging. mathematicians receiving this award : Guan- At National Taiwan University, the Taida Yu Chen (NCTU), Ming-Yi Lee (NCU), and Institute of Mathematical Sciences TIMS was Jyh-Haur Teh (NCTU). G.-Y. Chen specializes established, with Chang-Shou Lin, previous in probability theory and related topics, with director of NCTS, as director. At National degrees from both Cornell U. and NCTU. M.- Tsing Hua University, CMS, a Center for Y. Li is analyst graduated from NCU, and now Mathematical Sciences founded with Sze-Bi works also on certain PDE.