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. The results in a series of break through is a frequent visitor to NCTS from Utah for in transcendence theory over function fields. several years. Papanikolas' first work in this series has been accepted by inventione mathematicae, Chang- Looking at the works reported by our Yu's first work in this series just appears in various topical programs this year, I would Advances in Mathematics. The preprint in like to comment particularly on results question is the 2nd in the series, which proves obtained by several international long term that for rational function field over finite collaborations. From the south of Taiwan, constant fields, all the algebraic relations Ching Hung Lam at NCKU is an expert on among the zeta values at positive integers Vertex Operator Algebras, this is in the frontier come from the Euler-Carlitz relations and the of algebra which is interwoven with Frobenius relations. mathematical physics. Lam and H. Yamauchi of Tsukuba made progress since 2005 on Non-linear partial differential equations is structures of framed operator algebras and traditionally a strong research area in Taiwan. their orbifolds, their preprints have been The focus group at NTU Chang-Shou Lin, accepted by important journals such as Chiun-Chuan Chen, Tai-Chia Lin among Communications in Mathematical Physics. others, have been very productive in recent Around the same time, Lam , with C. Dong years, with many first rate papers coming out. and R. L. Greiss from the US, also obtained an C.-S. Lin has long term collaboration with interesting characterization of the famous Max-Plank group at Leipzig, G. Wang and J. Moonshine vertex operator algebra. This work Yost in particular. Their recent important work has just been published by American Journal on analytic aspects of Toda's system has of Mathematics. appeared recently in Communications on Pure and Applied Mathematics. T.-C. Lin has been Calabi-Yau threefold has been at the central collaborating successfully with J.F. Wei of stage of mathematics since two decades ago. It CHUK in recent years on spike solution of involves algebraic geometry, string theory, and coupled nonlinear Schrödinger equations, with more recently arithmetic geometry. In 2004 results published by e.g. Annales de L'institut Yifang Yang of NCTU visited N. Yui of Henri Poincaré, Communications in Canada, under support of NCTS, they have a Mathematics Physics, Nonlinearity. Another successful collaboration ever since, on the important paper which appeared this year in monodromy of hypergeometric differential Journal of Functional Analysis, is by C.-S. equations which leads, among other things, to Lin, A. C. Ponce and Yisong Yang, in it is a a fascinating paper on Picard-Fuch differential proof of the very interesting existence of equations and Calabi-Yau threefolds. This topological vortices in a relativistic self-dual paper is now accepted by the Crelle Journal. Abelian Chern-Simons theory with two Higgs Another coauthor of this important work is particles and two gauge fields. Yang's Ph. D. student Yao-Han Chen who did most of the complicate but essential The above describes samples of the best calculations. works done at NCTS. There are certainly other Another important paper in 2007 NCTS important works at the center. Entering its preprint series is: Algebraic independence of second ten years, mathematicians at NCTS are Carlitz zeta values for different constant fields, ready to make further progress and to by Chieh-Yu Chang, M. A. Papanikolas and accomplish greater achievements in research. Jing Yu. Chang is currently a post doctor at

5 ‹‹- Report of the Division Head Executive Committee Members

Committees Affiliation Chiun-Chuan Chen National Taiwan University I-Liang Chen National Taiwan University Gerard J. Chang National Taiwan University Wen-Wei Lin National Tsing Hua University Chin-Lung Wang National Central University Soon-Yi Wu National Cheng Kung University Jing Yu National Tsing Hua University

Executive Committee Members -›› 6 Academic Committee Members

Committees Affiliation Gerard J. Chang National Taiwan University Jung-Kai Chen National Taiwan University Shun-Jen Cheng National Taiwan University Liang-Chung Hsia National Central University Sze-Bi Hsu National Tsing-Hua University Ming-Chih Lai National Chiao Tung University Yng-Ing Lee National Taiwan University Song-Sun Lin National Chiao Tung University Tai-Chia Lin National Taiwan University Yuen-Chung Sheu National Chiao Tung University Soon-Yi Wu National Cheng Kung University Wei-Cheng Wang National Tsing Hua University Jing Yu National Tsing Hua University

7 ‹‹- Academic Committee Members Highlights of the Programs

D.1 Algebraic Geometry at NCTS 2004-2007

Coordinator: Hui-Wen Lin (National Central University)

Part I: People and Activities remarkable work in the NCTS workshops or the NCTS summer school from various viewpoints during 2004-2007. Many domestic he goal of NCTS algebraic geometry researchers and students got the up-to-date program is to promote fundamental research information from these talks and had researches, to attract young talented students the chance to discuss the related problems with to study it and to bring up frontier research them. We believe that it will stimulate problems such that domestic researchers as fundamental research growth here in the well as foreign visitors can work together on following years. them through regular activities. To achieve this People involved in NCTS algebraic goal, we ran two types of activities during geometry program consist of local researchers, 2004-2007. The first type is for students, foreign visiting scholars, research assistants which includes weekly student's seminars, and visiting graduate students. winter courses and summer courses. The second type is purely for research purpose, Local Researchers which includes the weekly research seminar, • Jungkai A. Chen (NTU) advanced courses, summer schools and workshops. • Jiun-Cheng Chen (NCTS frequent visitor and Northwestern University (2004 - 2006), There were over 50 short term visitors NCTS center scientist and NTHU (2006-) joining in NCTS algebraic geometry program • Hui-Wen Lin (NCTS postdoctor (2000- during 2004-2007. Among them are either 2001), NCU(2001-) senior scholars of great renown such as H. Esnault, E. Getzler, Y. Kawamata, J. • Chin-Lung Wang (NCTS center scientist and McKernan, S.Mukai, . R. Pandharipande, M. NCU) Reid, Yum-Tong Siu, E.Viehweg, Kang Zuo or • Hung-Jen Chiang-Hsieh (NCTS postdoctor promising young algebraic geometers such as (2003-2004), CCU(2004-) C. Birkar, P. Cascini, C.D. Hacon, Yuan-Pin • Jyh-Haur Teh (NCTS postdoctor (2005- Lee, Xiaotao Sun, Sheng-Li Tan etc. We are 2006), NTHU(2006-) pleased to mention that C. Birkar, P. Cascini, • Yen-Lung Tsai (NCTS postdoctor (2004- C. D. Hacon and J. McKernan had a joint work 2005), NCCU(2005-) to make a very big break-through on higher dimensional Minimal Model Program (MMP) last year. All of them individually reported this

Highlights of the Programs -›› 8 Frequent Visitors • Jen-Yuin Lin (NCTS RA (2004-2005), • The following scholars keep working Columbia U. (2005-)) together with some local researchers (Y.-P. • Kung-Zen Wu (NCTS RA (2004-2005) Lee with H.-W. Lin and C.-L.wang; H.- • Yu-Shen Lin (NCTS RA (2006-2007), H.Tseng with J.-C.Chen). Harvard U. (2007-)) • Yuan-Pin Lee (University of Utah) • Hsian-Hua Tseng (University of British Visiting Graduate Students Columbia) • Chen-Yu Chi (Harvard) • Yu-Chieh Chung (Utah) Short Term Visitors • Ming-Tao Chuan (Harvard) F. Ambro (RIMS), D. Andrea (Padova), C. Birkar (Cambridge), P. Cascini (UC Santa • C.-C. Liu (UCLA) Barbara), C.-L. Chai (U. of Penn and NCTS), • Yu-jong Tzeng (Stanford) M. Chen (Fudan U.), I. Ciocan-Fontanine (Minnesota), A.Corti (Cambridge), L. Ein Student's Program (Illinois), H. Esnault (Essen), E. Getzler There are three purposes for the student's (Northwestern), G. Farkas (Princeton), program during 2004-2007. The fist one is to Tommaso de Fernex (Utah), O. Fujino (IAS prepare the background for students who were and Nagoya), C. Hacon (Utah), J.-M. Hwang selected to participate in "Asia – Franco (KIAS), M. Kawakita (Tokyo), Y. Kawamata Summer School in Algebraic Geometry: (Tokyo), S. Kebekus (Bayreuth), J. Keum Motives and related topics", held by IHES (KIAS), B. KIM (KIAS), S. Kovacs from 2006 July 15 to 30. The second one is to (Washington), A. Kresch (Warwick), J.M. prepare the background of MMP for students Landsberg (Georgia Tech /Texas A.M.), W.-P. who were interested in the fruitful activities Li (HKU of S.T.), S. Lu (Essen), J. McKernan related to MMP at NCTS. The third one is to (UC Santa Barbara), M. Mella (Ferrara), N. provide students background for advanced Mok (HKU), S. Mukai (RIMS Kyoto), K. study in Mirror Symmetry and other related Oguiso (Toyko), R. Pignatelli (Trento), R. topics. Pandharipande (Princeton), M. Paun (Strasbourg), T. Peternell (Bayreuth), M. Popa For the First Purpose (Harvard), Z. Ran (California Riverside), M. • The winter course in basic projective Reid (Warwick), P. Schapira (dierre et marie geometry was organized by H.-W. Lin and Curie), S. Schroer (Bayreuth), B. Siebert held at NCU in 2005. (Freiburg), Y.-T. Siu (Harvard), X.-T. Sun The winter course in Lie Algebras was (Academia Sinica of China and HKU), S.-L. • organized by C.-L. Wang in 2005. Tan (Essen and East China Normal U.), Z. Tang (Suzhou U.), J. Tilouine (Paris-Nord), A. • The summer course in complex algebraic Todorov (UC Santa Cruz), Y.-L. Tong geometry was organized by H.-W. Lin in (Purdue), G.R. Vasant (Tata Institute), E. 2005. Viehweg (Essen), J. Wierzba (Energy • The weekly student seminar in etale Convergence Group), J. Wlodarczyk (Purdue), cohomology was organized by H.-W. Lin T. Yasuda (Kyoto), Stephen S.-T. Yau and C.-L. Wang from 2006 March to June at (Illinois), D.-Q. Zhang (Singapore), I. Zharkov NCU. (Harvard), J. Zhou (Beijin Tsing-Hua U.), K. Zuo (Mainz). For the Second Purpose • A regular student seminar was organized by Research Assistants J.A. Chen and held at NTU from 2005 to • Keng-Li Lin (NCTS RA (2003-2004), NCU 2007. . (2004-)) • NCTS summer lecture series on intersection

9 ‹‹- Highlights of the Programs theory and Riemann-Roch theorem was Kawamata at the end of 2005 at NTU and given by V. Maillot and held at NTU in NCU. 2005. Summer Schools For the Third Purpose • 2004 NCTS Summer School in Algebraic • A student seminar on basic algebraic Geometry (22-26 June; 5-9 July). geometry was organized by J.-C. Chen in • Organizers: J.A. Chen, Y.-P. Lee, E. Viehweg July 2006. and C.-L. Wang • C.-L. Wang organized some student seminars • Speakers: A. Corti, L. Ein, H. Esnault, S. regularly at NCTS or at NCU from 2004 to Kebekus, M. Paun, R. 2007. Pandharipande, Z. Ran, E. Viehweg Research Programs • Topics: Gromov-Witten theory, rational NCTS keeps running high standard curves and higher dimensional activities in algebraic geometry. We choose the birational geometry topics directly related to our research interest • 2005 NCTS Summer School in Algebraic including Geometry (8-18 August). • Birational Geometry, especially the new • Organizers: C.-L. Wang development in the Minimal Model Program • Speakers: A. Todorov, Kang Zuo, Jian Zhou, by Shokurov, Siu and Biakar-Cascini-Hacon- C.-L. Wang McKernan • Topics: the geometry of moduli spaces, • The theory of K-equivalence and related methods of localization in string theory on Quantum Cohomology dualities and birational geometry. • The theory of Calabi-Yau manifolds and • 2007 NCTS Mini-Course in Algebraic Mirror Symmetry Geometry (3-12 July). • Organizers: J.A. Chen, J.-C. Chen and C.-L. Seminars in Algebraic Geometry Wang • Many short courses in Gromov-Witten • Speakers: C. Birkar, J.A. Chen, P. Cascini, theory were given by Y.-P. Lee from 2004 to M. Kawakita 2006. • Topics: the latest development of higher • Regular research seminars were organized by dimensional MMP C.-L. Wang at NCTS and by J.A. Chen at NTU from 2004 to 2007. The main Workshops contributors included J.A. Chen, J.-C. Chen, • 2004 Workshop on Higher Dimensional H.-W. Lin, C.-L. Wang and some short term Algebraic Geometry (22-28 March) at NTU visitors. was organized by A. Corti, M. Reid and J.A. Chen. The purpose of this workshop is to Advanced Courses study the development of higher dimensional • The advanced course on Flips, Mori fiber MMP and related topics such as linear series, spaces and Mirror symmetry of Fano 3-folds K-equivalence and some analytic aspects. was given by A.Corti at NTU from 2004 • 2004 NCTS Workshop in Algebraic January to March. Geometry (28 June-2 July) was organized by • NCTS 2005 summer course in Homological J.A. Chen, Y.-P. Lee, E. Viehweg and C.-L. Algebra and D-modules was lectured by Wang. The main theme is on Gromov-Witten Andrea D'Agnolo and P. Schapira at NTU. theory, rational curves and higher dimensional birational geometry. • The Mini-Course in recent development of minimal model theory was given by Y. • 2006 NCTS Workshop in Algebraic

Highlights of the Programs -›› 10 Geometry (7-12 July) was organized by Y.-P. dimensional algebraic geometry. In 1988, Mori Lee. The main purpose is to study Deligne- solved the flip conjecture in dimension 3 and Mumford moduli spaces of stable curves and achieved the 3-dimensional MMP. He then Gromov-Witten theory. The main speaker is received the 1990 Fields Medal due to this E. Getzler. fundamental work. However, to get the • 2007 Workshop on Higher Dimensional existence of higher dimensional minimal Algebraic Geometry (27-31 March) at NTU models and to understand the non-uniqueness was organized by J.A. Chen, J.-C. Chen and issues of minimal models are still challenging C.-L. Wang. The purpose of this workshop is problems. C.-L. Wang in 1998 initiated the to study the development of higher notion of K-equivalence aiming at resolving dimensional algebraic geometry including the non-uniqueness problem. MMP, singularity theory, toric theory and C.-L. Wang in 1998 showed that K- flops. equivalent smooth varieties have the same Betti numbers. In 2006, Y.-P. Lee, H.-W. Lin and C.-L. Wang [7] showed that for ordinary Part II. Accomplishments and flops, the graph closure gives rise to the Anticipations canonical isomorphism of Chow motives in Selected works of local researchers: the sense that the Poincare pairing is preserved under the correspondence. Ordinary flops are [1] J.A. Chen, C.D. Hacon, Varieties with P3=4 not only the first examples of K-equivalent and q=dim X, Ann. Sc. norm. super. Pisa, maps, but also crucial to the general theory. V, vol. III. (2004), 399-425. However the cohomology ring structures are in [2] J.A. Chen, M. Chen, D.Q. Zhang, The 5- general different. They precisely determined canonical system on 3-folds of general the defect caused by the classical product type, J. Reine Angew. Math., 603, (2007), under simple ordinary flops and found this 165-181. defect is exactly remedied by adding the quantum corrections attached to the extremal [3] J.A. Chen, C.D. Hacon, Pluricanonical rays. For simple ordinary flops, they showed systems on irregular 3-folds of general that the big quantum cohomology ring is type, Math. Zeit, 255, (2007), 343-355. invariant after an analytic continuation over [4] D. Abramovich , J.-C. Chen, Flops, flips the extended Kahler moduli spaces. This and perverse point sheaves on threefold analytic continuation phenomenon is their stack, J. Algebra 290 (2005), no. 2, 372- major contribution to the study of higher 407. dimensional algebraic geometry. [5] J.C. Chen, H.H. Tseng, Cone theorem via In [4], D. Abramovich and J.-C. Chen made Deligne-Mumford stacks, Preprint some contribution in understanding flops and math.AG 0505043, submitted to J. flips in terms of derived categories and moduli Algebraic Geometry, 2005. spaces: they generalized Bridgeland's result to terminal Gorenstein threefolds flops and [6] J.-C. Chen, H.-H. Tseng, Note on proved similar results for threefold Francia characterizations of projective spaces, to flips. In [5], J.-C. Chen and H.-H. Tseng appear in Comm. Algebra. worked out important results in Cone theorm [7] Y.-P. Lee, H.-W. Lin, C.-L. Wang, Flops, in characteristic p as well as sharp estimate of motives and invariance of quantum rings, length of extremal rays for LCIQ (quotient of to appear in Annals of Mathematics. locally complete intersection singularities) For the passed twenty five years, the MMP varieties. They combine moduli of stacky developed by Mori in 1982 and by others stable maps with Mori's bend and break theory (Kawamata, Kollar, Shokurov etc) in the and open a research direction. An interesting sequel has been the core theory in higher application is their characterization results of projective spaces for possibly singular

11 ‹‹- Highlights of the Programs varieties [6]. London Math., 75 (2007), 463-478. The research of J.A. Chen was mainly [3] J.-H. Teh, Harnack-Thom theorem for around the birational classification problem. higher cycle groups and Picard varieties, to For varieties of general type, mK defines a appear in the Transaction of AMS. birational map for m sufficiently large. It's [4] Y. L. Tsai and E. Z. Xia. Non-abelian local natural to ask whether one can determine m invariant cycles. Proc. Amer. Math. effectively. For dim X =1, 2, these bounds are Soc.135 (2007), No.8, 2365-2367. known to be 3 and 5 respectively. There is a recent work by Hacon and McKernan asserts Anticipations that there is a theoretical bound m(n) which depends on dim X = n. However, the number In the future, we will keep on organizing m(n) is far from being optimal in any way. On high standard activities for cultivating students his joint work with Meng Chen and De-Qi as well as stimulating research works, and try Zhang [2], they obtained that 5K is birational to open up more channels to collaborate with for minimal Gorenstein threefolds with at reputable foreign visitors. Meanwhile, we are worst canonical singularities. This bound is still focusing on promoting researches related optimal. In [1], they could completely describe to birational geometry including MMP, Calabi- Yau manifolds and Mirror symmetry, as well varieties with P3 ≤ 4 and q = dim X. In [3], they proved that if X is an irregular 3-fold with as motivic or quantum-theoretic aspects of some positivity, then |mK| is birational for all algebraic geometry. In particular, the current m bigger than or equal to 5. remaining step to complete the MMP in higher dimensions is the termination conjecture of NCTS Post-doctors in Algebraic flips. To resolve this conjecture may require Geometry new invariants for singular varieties. We will be interested in studying it by combining the We would like to mention that since 1997, classic minimal model theory with other all NCTS post-doctors working on algebraic techniques from orbifold theory, arc spaces, geometry got the teaching positions in national quantum cohomology as well as the theory of research universities one after another. We list motives. their works (for people after 2004) as follows. Since 2000, there have been many [1] H.-J., Chiang-Hsieh and J. Lipman, A numerical criterion for simultaneous outstanding students from NCTS studying normalization, Duke Math. J. 133 (2006), algebraic geometry in the top ranking no. 2, 347-390. universities of U.S.A. We expect that they will [2] J.-H. Teh, Complexification of real cycles join our research group to enhance the and Lawson suspension theorem, J. research works in a few years.

Highlights of the Programs -›› 12 D.2 Discrete Mathematics at NCTS 2004-2007

Coordinator: Gerard Jennhwa Chang (National Taiwan University) and Xuding Zhu (National Sun Yat-sen University)

Part I: Background and Activities in month. However, we made efforts to make the Program short time visits fruitful. Instead of having short time visitors come-talk-leave, we try to initiate collaboration before visitors start their iscrete mathematics has seen rapid visits. Select visitors who share common development in recent decades, both interests with member of local group, and abroad and in Taiwan, in width and in depth. prepare ourselves and students for coming As a focus group of NCTS, the discrete visitors, and make the best use of visitor's time mathematics group has been focused on during their stay in Taiwan. There are many research in graph coloring, graph labeling, joint papers of members of the group and our combinatorial optimization, algorithms, visitors are finished or under preparation, enumerative combinatorics, cluster resulting from their visits to our group. Some combinatorics, combinatorial number theory. visits initiated long term collaborations. A visit In the past four years, through seminars, of Professor Andre Raspaud from Bordeaux workshops and hosting visitors, the project has France initiated a two year collaboration helped local focus group, especially young project supported by NSC and CNRS, and a researchers in the group, to establish joint supervising program between NSYSU collaborations with researchers abroad, and Bordeaux University. develop links with experts abroad, and start Each semester, the discrete mathematics their research in the frontier of related fields. group in north and south has series of Discrete mathematics program in NCTS seminars. Some of the seminar talks are given has two teams, one in north which is organized by visitors and some talks from group by by Gerad Jennhwa Chang at National members, post doctors and students. Taiwan University, the other in south which is The discrete mathematics group organized organized by Xuding Zhu at National Sun Yat- four local workshops and two international sen University. conferences. Speakers of the workshops are During the past four years, the discrete from Taiwan. Each workshop focuses on mathematics group in north has invited 6 problems in a special topic. Our purposes are visitors. As we do not have budge for post to get students involved in our program and doctors, we use personal NSC projects of also enhance collaborations among local Gerard Jennhwa Chang to hire post doctors researchers. The two conferences aim to joining the program. They are Changhong Lu, bridge local researches with experts aboard. J. Qian, Fei-Huang Chang, Yongqiang Zhao, One Conference has 49 speakers and the other Jiaojiao Wu. 61 speakers. Since 2004, the discrete mathematics group As NCTS aims to train talented students in south has invited 13 visitors from abroad. and promote young researchers, we design the The financial support of our group is limited student summer research program for students (with NT$300,000 per year, which includes who have strong interest in mathematics support for visitors and local activities), we are research. In 2005, we have the topic "Graph unable to support long term visitors. The stays Coloring and Related Topics" (2005.7.11- of our visitors are from one week to one 2005.8.19) with 9 selected students. There is a

13 ‹‹- Highlights of the Programs regular lecture from 9:00 to 11:00 every week Ching Yeh (Feng-Chia), David Kuo day. Problems for discussion are assigned (NDHU), post doctors and graduated during the lectures, and the posted on the web. students. From 11:00 to 14:00, students have free time South: Xuding Zhu (NSYSU), Meng-Na Lo to do the assigned problems by themselves. (NSYSU), Tsai-Lien Wong (NSYSU), There is then a discussion time for all students Li-Da Tong (NSYSU), Mei-Hui Guo and the lecturer from 14:00 to 16:00. Some (NSYSU), Zhishi Pan (NSYSU), Sen- problems may be solved at the same day they Peng Eu (NUK), Szu-En Cheng assigned, but some may be solved the other (NUK), Hong-Gwa Yeh (NCU), plus 5 days. During this period, totally about 100 Ph.D. students. problems are assigned, some of them are typical exercises while some are research Visitors problems. Among them, about 70% are solved completely by the students and some are • Wen-Ling Huang, University of Hamburg, solved partially. As the organizer needs to (2004.9.19-2009.10.17), attain the Pacific Rim Conference, Xuding • Yuan Hong, East Chia Normal University, Zhu chipped in for the rest of the program. In, (2004.9.29-2004.10.4), 2006 we have "Graph Ramsey Theory" • Jerrold R. Griggs, University of South (2006.7.10-2006.8.18) with 5 selected Carolina (2005.5.22-2005.5.24), students. The running method is the same as • Jae-Hoon Kwon, University of Seoul, the previous one. During this period, totally (2006.8.6-2006.8.19), about 70 problems are assigned, some of them are typical exercises while some are research • Khee Meng Koh, National University of problems. Among them, about 70% are solved Singapore, (2007.6.16-2007.6.29), completely by the students and some are • Frank Kwang-Ming Hwang, (2007.6.21- solved partially. 2007.6.30), As the probabilistic method becomes more • Sandi Klavzar, University of Maribor, and more important in the study of discrete Slovenia, (2004.9.22-2004.10.1), mathematics, we invited Professor Hong-Gwa • Zhidong Bai, National Singapore University, Yeh (NCU) offering a regular course Singapore, (2004.9.19-204.9.23), "Probabilistic Method" on Tuesday mornings • Daniel Kral, Charles Unviersity, Czech from September 2006 to January 2007. To Republic, (2004.12.5-2004.12.21), make it formal, we do cooperate with the • Andre Raspaud, Universite Bordeaux, Department of Mathematics of National France, (2005.1.8-2005.1.28), Taiwan University to make it as a regular • Pavol Hell, Simon Fraser Univerity, Canada, course offering credits to students attaining the (2005.12.8-205.12.13), classes. Professor Yeh's lecture is based on the book "Probabilistic Method" by Alon and • Mike Albertson, Smith college, USA, Spencer, plus many personal notes and (2005.12.9-2005.12.13), materials posted on his web page. Besides the • Claude Tardif, Royal Military College, students and I, we also have faculties of Canada, (2005.12.19-2005.12.28), Academia Sinca and probability people of my • Douglas West, University of Illinois at department attaining the classes. Urbana-Champaign, USA, (2005.12.19- 2005.12.23), Local Focus Group • Daqing Yang, Fuzhou University, PRC, North: Gerard Jennhwa Chang (NTU), Ko-Wei (2006.1.19-2006.2.19 and 2007.6.30- Lih (AS), Jing-Ho Yan (Aletheia), 2007.7.22), Hsun-Wen Chang (Tatung), Chiang Lin • Wensong Lin, South-East University, (NCU), Hong-Gwa Yeh (NCU), Sheng- Nanjing, PRC, (2006.1.20-2006.2.20, Chyang Liaw (NCU), Roger Kwan- 2007.6.30-2007.7.22),

Highlights of the Programs -›› 14 • Alexandr Kostochka, University of Illinois at Part II: The Accomplishment Urbana-Champaign, USA, (2007.1.5- In the north, selected publications are listed 2007.1.15), below with their descriptions follow. • Serguei Norine, Georgia Institute of Technology, USA, (2007.3.5-2007.3.15), [175] F.-H. Chang, G. J. Chang and C. Lu, Distance-two labelings of graphs, • Peter Horak, University of Washington, preparing. Tacoma, USA, (2007.3.12-2007.3.25). [174] G. J. Chang and C. Lu, Full Color of Workshops and Conferences graphs with small numbers of edges, preparing. • Workshop on Graph Coloring, (2004.7.24- 7.26). Speakers: X. Zhu, G. Chang, B. Chen, [145] Y.-Y. Chien and G. J. Chang, The upper H. Yeh. domination of Cartesian products of • CTS Conference on Combinatorics and Its graphs, preparing. Applications, in Honor of Frank K. Hwang's [168] J.-J. Chen and G. J. Chang, Distance 65th Birthday, (2005.5.19-2005.5.21). Invited graphs on Rn with 1-norm, J. Combin. Speakers: G. J. Chang, C.-S. Chang, C. J. Optimization (accepted). Colboum, D.-Z. Du, G. Fan, J. R. Groggs, C. Rodgers, U. Rothblum, J. H. Spencer, R. M. [161] R.-Y. Wu, G.-H. Chen, Y.-L. Kuo and Wilson. There are 39 contribution talks. G. J. Chang, Node-disjoint paths on hierarchical hypercube networks, • Workshop on Edge Coloring and Graph Inform. Sciences (accepted). Decomposition, (2005.8.5-2005.8.6). Speakers: H. Fu, C. Fu, W. Hu, K. Huang, Q. [151] B.-J. Li and G. J. Chang, Clique Lin, S. Wu. coverings and partitions of line graphs, Discrete Math. (accepted). • Workshop on Quantum Algorithms, (2005.8.23). Speakers: D. Guan, Y. Wong, S. [137] J. S.-T. Juan and G. J. Chang, Adaptive Zhuan. group testing for consecutive positives, • Workshop on Graph Theory and Network, Discrete Math. (accepted). (2007.6.20). Speakers: W. Wang, Y. Bu, L. [135] Y.-P. Tsao and G. J. Chang, Profile Xiong, S. Zhou. minimization of compositions of • 2007 International Conference on Graph graphs, J. Combin. Optimization Theory and Combinatorics & Fourth Corss- (accepted). strait Conference on Graph Theory and [129] J. S.-T. Juan and G. J. Chang, Group Combinatorics. (2007.6.24-2007.6.29). testing in graphs, J. Combin. Plenary speakers: G. Fan, F. K. Hwang, Y.- Optimization (accepted). N. Yeh, X. Yu, X. Zhu. There are 56 contribution talks. [169] G. J. Chang, S.-P. Eu and C.-H. Yeh, On the (n,t)-antipodal Gray codes, Theore. International Cooperation Comput. Sci. 374 (2007) 82-90. Initiated during Professor Andre Raspaud's [162] G.-Y. Chang, G.-H. Chen and G. J. visit in 2005, which was supported by NCTS, Chang, (t,k)-Diagnosis for matching the focus group started a 2 year joint project composition networks under MM* with LaBRI, Universite de Bordeaux I, model, IEEE Trans. Computers 56 supported by NSC and CNRS. Under the joint (2007) 73-79. project, X. Zhu and a graduate student visited [146] J.-J. Pan and G. J. Chang, Induced-path Universite de Bordeaux, and A. Raspaud and partition on graphs with special blocks, A. Pecher visited National Sun Yat-sen Theore. Comput. Sci. 370 (2007) 121- University. L. Tong is planning a visit to 130. Bordeaux in August, 2007. [144] C.-C. Lin, G. J. Chang and G.-H. Chen,

15 ‹‹- Highlights of the Programs Locally connected spanning trees of and Rall states that (G H) ≥ (G) (H), proper circular-arc graphs, Discrete where (G) and (H) are the upper Math. 307 (2007) 208-215. domination numbers of G and H respectively. [131] G. J. Chang, C. Lu, and S. Zhou, No- Clark and Suen recently establish a stronger hole 2-distance colorings for Cayley result that (G H) ≥ (G) (H) + 1 for graphs on finitely generated abelian any graphs G and H. They then ask for a groups, Discrete Math. 307 (2007) stronger bound that (G H) ≥ (G) (H) 1808-1817. + min{|V(G)| (G), |V(H)| (H)} for any graphs G and H. We have just settled this [119] G. J. Chang, J.-J. Chen, D. Kuo, and S.- question, please see [145] in the publication C. Liaw, Distance-two labelings of list. digraphs, Discrete Applied Math. 155 (2007) 1007-1013. [174] It is proved that a graph G = (V, E) with |V| 1 |E| |V| is full colorable except [157] G. Y. Chang, G. H. Chen and G. J. when G is one of some particular graphs, Chang, (t,k)-Diagnosis for matching where the graph G is called full colorable if it composition networks, IEEE Trans. has a no-hole (G)-L(2,1)-labeling. Computers 55 (2006) 88-92. [168] Degrees of vertices, connectivity and [150] M. Zhao, L. Kang and G. J. Chang, chromatic numbers of various distance graphs Power domination in graphs, Discrete in the n-dimensional spaces using 1-norm and Math. 306 (2006) 1812-1816. the subsets of all lattice points of the n-spaces [148] Y.-P. Tsao and G. J. Chang, Profile are obtained. minimization on product of graphs, [161] The concept of wide-diameter, Discrete Math. 306 (2006) 792-800. introduced by Frank Hsu, unifies connectivity [139] J.-J. Pan and G. J. Chang, Isometric- and diameter. This paper gives node-disjoint path numbers of graphs, Discrete Math. paths for hierarchical hypercube networks 306 (2006) 2091-2096. better than previous constructions. [175] In the study of the distance-two [151] A unified and simple proof for labeling problem, graphs G with distance-two previous results on clique coverings and clique labeling number (G) = 2 (G) and hall partitions is given. Using the same proof number (G) = (G) play a critical role, technique, we also give a simple proof for the where (G) is the maximum degree of G. De Bruijn-Erdos Theorem Previous results show that many such kind of [137] Combinatorial group testing has wide graphs have numbers of vertices polynomial in applications in the real world. In this paper, we (G). People believe that the desired give bounds on the adaptive group testing for properties should constrain the graphs in some consecutive positives which is better than special shapes and so the numbers of vertices previous constructions. can only be polynomial in terms of (G). Our recent study show that there are much more [135] Profile numbers for graphs obtained freedom on these kind of graphs. In particular from various operations are determined, where such kind of graphs with numbers of vertices the graph operations include Cartesian exponential in (G) are plentiful, please see product, join, composition, tenser product and [175] in the publication list. strong product …etc. [145] The well known conjecture proposed [131] The study of colorings with by Vizing for the domination problem states conditions at distance two arise from the that (G H) ≥ (G) (H) for any graphs channel assignment problem. In this paper, we G and H, where (G) and (H) are the give no-hole 2-distnace colorings of some domination numbers of G and H respectively. Cayley graphs by using a group-theoretic A related conjecture proposed by Nowakowski approach.

Highlights of the Programs -›› 16 [129] The bipartite graph conjecture for Combinatorics, accepted. group testing says that every bipartite graph of [9] D. West, X. Zhu, Circular chromatic index 2n edges always has an induced sub-graph of of product of graphs, Journal of Graph the half number of edges. Toward to the study Theory, accepted. of the conjecture, we give a bound for the optimal numbers of testing that is better than [10] A. Raspaud, X. Zhu, List circular coloring previous ones. of trees and cycles, Journal of Graph Theory, accepted. As for the south, activities organized by the focus group and exchange of visits have [11] A. Pecher, X. Zhu, On the circular stimulated collaborations between local group chromatic number of circular partitionable members and visitors from abroad. There are graphs, Journal of Graph Theory, 13 joint papers that are closely related to the accepted. visits to the group, either initiated during their [12] D, Kral, L. Tong, X. Zhu, Upper visits or initiated before the visits and made Hamiltonian number and Hamiltonian progress during the visits. Selected spectra of graphs, Australasian Journal of publications of the local group since 2004: Combiantorics, 35 (2006), 329-340. [1] T. Kaiser, D. Kral, R. Skrekovski, X. Zhu, [13] G. J. Chang, S. Eu, C. Yeh, On the The circular chromatic index of graphs of antipodal Gray codes, Theoretical high girth, Journal of Combinatorial Computer Science, 374 (2007), 82-90. Theory Series B, 97 (2007) 1-13. A. Graph coloring. Graph coloring is a [2] S. Eu, T. Fu, The Cyclic Sieving central topic in graph theory. Circular coloring Phenomenon for Faces of Generalized of graphs is a concept that are most studied in Cluster Complexes, Advances in Applied this group. The circular chromatic index of Mathematics, accepted. graphs (i.e., the circular chromatic number of [3] S. Eu, T. Fu, Y. Yeh, Refined Chung-Feller line graphs) is a difficult topic, with many Theorem, Journal of Combinatorics Theory open problems and few results. A surprising series A, accepted. result is obtained in [5], where it is proved that the circular chromatic index of a graph of [4] S. Eu, S. Liu, Y. Yeh, On the Congruences maximum degree at most 3 is either 4, or of Some Combinatorial Numbers, Studies bounded by 11/3. In particular, it is shown that in Applied Mathematics, 116 (2006), 135- 2-edge connected cubic graphs have circular 144. chromatic index at most 11/3. This result [5] P. Afshani, M. Ghandehari, M. Ghandehari, stimulated further research in this direction. H. Hatami, R. Tusserkani, X. Zhu, Circular Kaiser, Kral and Skrekovski showed that cubic chromatic index of graphs of maximum graphs of large girth have circular chromatic degree 3, Journal of Graph Theory, 49 number close to 3. This result is greatly (2005), 325-335. improved in [1], where it is proved that graphs with maximum degree k and large girth has [6] S. Klavzar, T. Wong, X. Zhu, circular chromatic index close to k. West and Distinguishing group actions on vector Zhu [9] investigated the circular chromatic spaces and graphs, Journal of Algebra, 303 index of the Cartesian product of graphs and (2006), 626-641. determined the value of χ'c (C2k+1 C2m+1)for [7] S. Klavzar, X. Zhu, Cartesian powers of m≥3k+1. Another fast developing area graphs can be distinguished by two labels, concerning circular coloring of graphs is the European Journal of Combinatorics, circular choosability of graphs. The joint work accepted. of Raspaud and Zhu [10] gives a complete [8] Z. Pan, X. Zhu, Minimal circular-imperfect characterization of color-size list assignments graphs of large clique number and large l for which a tree is circular l -choosable. independence number, European Journal of Tight bounds for cycles are obtained there.

17 ‹‹- Highlights of the Programs Before and during the visits of Serguei Norine Dyck paths on the check board and its relation from Georgia Institute of Technology, T. Wong with pattern-avoid permutations, the and X. Zhu have worked together with him to computing of the generalized Wiener index, successfully apply algebraic methods to solve the new simple proof of the Aztec diamond problems concerning circular choosability. A theorem, the enumeration of the k-leading few joint papers (by W. Lin, C. Yang, D. Yang, functions for generalized parking functions, X. Zhu, S. Norine, Z. Pan) on consecutive and a refinement for classic Chung-Feller circular choosabilities of graphs are initiated theorem and a characterization for the Chung- during our visitors' stay in Taiwan, and are Feller type theorem. either submitted or under revision. D. Distinguishing labeling of graphs and B. Cluster combinatorics. The notion of group actions. This is a research topic that cyclic sieving phenomenon was introduced by was initiated during S. Klavzar's visit to our Reiner, Stanton, and White as a generalization group, and have been fruitfully carried out of Stembridge's q = 1 phenomenon. The later on. The question started with finding generalized cluster complexes associated to labeling of a graph with minimumlabels so root systems are given by Fomin and Reading that identity is the only automorphism of the as a generalization of the cluster complexes graph which preserves the labels. The found by Fomin and Zelevinsky. S. Eu and T. minimum number of labels used in such a Fu have shown that the faces of various labeling is called the distinguishing number of dimensions of the generalized cluster the graph. To answer this question, it is important to understand the structure of the complexes in type An, Bn, Dn, and I2(a) are shown to exhibit the cyclic sieving automorphism group of the graph. One phenomenon under a cyclic group action. For specific question studied first by Albertson and the cluster complexes of exceptional type E , Collins is this: what are the possible values of 6 the distinguishing number of a graph with E7, E8, F4, H3, and H4, a verification for such a phenomenon on the facets is given. automorphism group isomorphic to the symmetric group Sn? This question is now C. Enumerative Combinatorics. Various completely solved (in a paper by problems and applications on Enumerative T.Wong and X. Zhu under revision). Combinatorics, centered on lattice paths and Moreover, a complete answer is also given to tree structures, are considered. Including the the question as what are the possible values of characterization of the (n, t) antipodal Gray the distinguishing number of actions of Sn and codes when n is odd, the area counting under An.

Highlights of the Programs -›› 18 D.3 Dynamical Systems at NCTS 2004-2007

Coordinator: Song-Sun Lin (National Chiao Tung University)

Part I: Background and Activities in Short Term Visitors the Program Zin Arai (Kyoto Univ.), Yong Moo Chung (Hiroshima Univ.), Jin Hatomoto (Tokyo Metropolitan Univ.), Shin Kiriki (Kyoto ynamical System is one of the major University of Education), Hiroshi Kokubu and classical research areas in (Kyoto Univ.), Masashi Kisaka (Kyoto Univ.), mathematical science. In the sequence of Eiko Kin (Kyoto Univ.), Toshikazu Ito dynamical systems programs, we emphasize (Ryukoku Univ.), Hiroe Oka (Ryukoku Univ.), the theory and the applications of dynamical Toshiyuki Ogawa (Osaka Univ.), Mitsuhiro systems. We also cooperate with the people in Shishikura (Kyoto Univ.), Naoya Sumi (Tokyo the topical program of scientific computation Institute of Technology), Masato Tsujii to study the computation of chaotic dynamical (Hokkaido Univ.), Valentin Afraimovich systems. (Investigator of San Luis Potosi University, During the period, we also organize a Mexico), Anatoli Babin (UC Irvine ), Kening student's seminar so that the graduates can be Lu (Brigham Young University), Alica Miller well trained. The activities and visiting (University of California, Irvine), Roger scholars are listed in the following. Nussbaum ( Rutgers University ), Marcelo Viana (IMPA Rio de Janeiro), Xiangdong Ye Local Focus Group (USTC), James Yorke (University of S.-S. Lin (NCTS Center Scientist and Maryland), Leon Glass (McGill University), NCTU), J. Juang (NCTU), C.-W. Shih Henk Broer (University of Groningen), Walter (NCTU), M.-C. Li (NCTU), K.-C. Chen Craig (McMaster University), Luigi Chierchia (NTHU) (Univerità Roma 3 ), Rafael Ortega (Universidad de Granada), Zhihong Jeff Xia Post Doctors (Northwestern University), Luca Dieci (Georgia Tech), Russell Johnson (Università di C.-T. Wu (NCTS 2004-05), T.-H. Yang Firenze ), Peter Kloeden (Johann Wolfgang (NCTS 2003-04), J.-C. Ban (NCTS 2003-06) Goethe University), Weishi Liu (University of Kansas), Mason Porter (Georgia Institute of Frequent Participants Technology), Hildebrando Munhoz Rodrigues B.-S. Du (Academia Sinica), Y.-C. Chen (Universidade de São Paulo), Huiping Zhu (Academia Sinica), K.J. Palmer (NTU), T.-Y. (York University), Yingfei Yi (Georgia Yang (Tamkang Univ.), C.-H. Hsu (NCU), S.- Institute of Technology), Rick Moeckel B. Hsu (NTHU), W.-W. Lin (NTHU), C.-J. Yu (University of Minnesota), Eusebius Doedel (NCTU), T.-S. Yang (Tung-Hai Univ.), C.-N. (Concordia University), Piotr Zgliczynski Chen (NCUE), C.-Y. Cheng (NPUE), J.-C. (Jagiellonian University), Hal Smith (Arizona Ban (NHLUE) State University), Jinqiao Duan (Illinois Institute of Technology), Xiao-Qiang Zhao Long Term Visiting Scientist (Memorial University of Newfoundland), Goong Chen (Texas A&M University), Gareth Roberts (College of the Holy Cross), 2006 Fall, at NTHU Pawel Pilarczyk (Kyoto University)

19 ‹‹- Highlights of the Programs Special Courses in 2004-2007 • NCTS Joint Seminar in Math. Biology & • Theory and Applications of Dynamical Dynamical Systems 2006 System (IV), 2007 spring. • Monotone Dynamical Systems and Its • Speaker : S.-S. Lin (NCTU) Application to Population Biology 2006 • Theory and Applications of Dynamical • This intensive course will basically System (III), 2006 fall. follows the book "Monotone Dynamical Systems" of Hal Smith (1995) and his recent Speaker : S.-S. Lin (NCTU) • survey paper with Hirsch "Monotone • Theory and Applications of Dynamical Dynamical Systems" (2004). We shall first System (II), 2006 spring. introduce the ODE of cooperative systems as • Speaker : S.-S. Lin (NCTU) the first example of Monotone Flow. Then • Theory and Applications of Dynamical we present the monotone flow in abstract System (I), 2005 fall. space and its basic properties. The application of the theory to 3-dimension • Speaker : S.-S. Lin (NCTU) competitive system and several biological Conferences and Workshops models will be discussed. Then we apply the theory to reaction-diffusion equations , delay • 2007 CTS Workshop on Dynamical Systems, differential equations and maps. May 14-18, • Topical Program in Dynamical Systems 2006 • 2007 at NCTS. Organizers : K.-C. Chen Fall (NTHU), J. Juang (NCTU), M.-C. Li (NCTU) and C.-W. Shih (NCTU). • We will begin with many concrete models of ODEs and PDEs in dynamical system • International Conference on Chaos and theory and quantum mechanics. From the Dynamical Complexity, May 24-30, 2006 at given models, we examine their invariant NCTS. Organizers : S.-N. Chow (Georgia transformations, Lie groups and invariants. Inst. Of Tech.), S.-S. Lin (NCTU). Using invariants corresponding to the Lie • International Conference on Chaos and algebra structure, we seek ways to reduce the Dynamical Complexity, May 16-20, 2005 at ODEs and PDEs to lower order systems and NCTS. Organizers : S.-N. Chow (Georgia sometimes even Explicit solutions of the Inst. Of Tech.), S.-S. Lin (NCTU), W.-W. physical model, and the physical Lin (NTHU), Y.-F. Yi (Georgia Inst. Of implications. Tech.). • This course utilizes only basic knowledge • Japan-Taiwan Conference on Dynamical in ODEs, PDEs and algebra. Students do not Systems, March 21-26, 2005 at NCTS. need extensive prerequisites in these Organizer: S.-S. Lin (NCTU), C.-W. Shih subjects. (NCTU), Hiroshi Kokubu (Kyoto Univ.). • NCTS Student Seminar on Dynamical • NCTS 2004 International Conference on Systems 2007 Dynamical Systems, June 23-28, 2004 at NCTS. Organizer: S.-S. Lin (NCTU), Y.-F. Yi (Georgia Inst. Of Tech.), C.-N. Chen (NCUE), Kenning Lu (MSU), Jiangong You Part II: The Accomplished and the (NJU) Anticipations [1] K.-C. Chen, Existence and Minimizing Student's Seminars and Schools Properties of Retrograde Orbits to the Three-Body Problem with Various Choices • NCTS 2007 Summer Course on Dynamical Systems of Masses. Annals of Math., to appear. • NCTS 2006 Summer Program ---Joint [2] S.-S. Lin, Patterns generation and spatial Program of Dynamical Systems and entropy in two-dimensional lattice models, Mathematics Biology to appear in Asian Journal of Mathematics

Highlights of the Programs -›› 20 (with J.-C. Ban and Y. H. Lin). [10] J. Juang, Eigen curve problems and application to the wavelet method of [3] C.-W. Shih, Multistability and convergence chaotic control, J. Math. Phys., 47 122702 in delayed neural networks, Physica D, to , 2006 (with C.-L. Li). appear (with C.-Y. Cheng and K.-H. Lin). [11] J. Juang, Eigen value problems and [4] M.-C. Li, Chaotic dynamics in an application to the wavelet method of overlapping generations model with chaotic control, J. Math. Phys., 47 myopic and adaptive expectations, Journal 072704, 2006 (with C.-L. Li). of Economic Behavior and Organization, to appear (with H.-J. Chen and Y.-J. Lin). [12] C.-W. Shih, Multistability in recurrent neural networks, SIAM J. Applied [5] J. Juang, Global synchronization in lattices Mathematics, Vol.66, No. 4, 1301-1320, of coupled chaotic systems, Chaos, to 2006 (with C.-Y. Cheng and K.-H. Lin). appear (with C.-L. Li and Y. H. Liang). [13] C.-W. Shih, Transition to intermittent [6] S.-S. Lin, Smooth solutions to a class of chaotic synchronization, Phys. Rev. E 72, quasilinear wave equations, J. Differential 036212, 2005 (with Liang Zhao and Y.-C. Equations, 224, 229-257, 2006 (with C.-H. Lai). Hsu and Tetu Makino). [7] K.-C. Chen, Removing Collision [14] S.-S. Lin, Patterns generation and Singularities from Action Minimizers for transition matrices in multi-dimensional the N-body problem with Free Boundaries. lattice models, Discrete and Continuous Arch. Rational Mech. Anal. 181, 311-331, Dynamical Systems, Vol. 13, 637-658, 2006. 2005 (with J.-C. Ban). [8] M.-C. Li, Topological horseshoes for [15] M.-C. Li, Qualitative property between perturbations of singular difference flows and numerical methods, Nonlinear equations, Nonlinearity, 19, 795-811, 2006 (with M. Malkin). Analysis, 59, 771-787, 2004. [9] M.-C. Li, Topological horseshoes for [16] S.-S. Lin, On spherically symmetric Arneodo-Coullet-Tresser maps, Regular solution of the relativistic Euler equation, and Chaotic Dynamics, 11, 181-190, 2006 J. Differential Equations, Vol. 201, 1-24, (with B.-S. Du and M. Malkin). 2004 (with C.-H. Hsu and Tetu Makino).

21 ‹‹- Highlights of the Programs D.4 Geometric Analysis at NCTS 2004-2007

Coordinator: Shu-Cheng Chang (National Tsing Hua University) and Dong-Ho Tsai (National Tsing Hua University)

Part I: Background and Activities in estimate of partial differential equation, the Program Hamiltonian mechanics, etc.) to study problems related to geometry. Furthermore, one may to construct fundamental solution for he field of Geometric Analysis (GA) Partial Differential Equation in terms of has seen spectacular growth and geometric invariants. development in the past twenty years. GA is one of the emphasizing research Analytic, geometric and topological program supported by NCTS. Activities at techniques are used in the setting of NCTS related to GA include seminars (with differential geometry to solve problems in talks given by local or foreign visitors of global geometry and topology, mathematical NCTS), mini-courses, international workshops physics, algebraic geometry, materials science, and conferences. These activities are run by image processing and optimization. A plethora local and/or foreign visitors. of important geometric heat flows are of current interest, including Ricci and Kaehler- Ricci flow, mean and inverse mean curvature Local Visitors flows, Yamabe flow, harmonic map flow, By local visitors we mean mathematicians Gauss curvature flow, flows of hypersurfaces residing in Taiwan. During the years of 2004- by symmetric functions of principal 2007, the following people have participated curvatures, Yang-Mills heat flow, flows of in GA program or activities at NCTS: curves and submanifolds, and heat flows in T.-P. Liu, J.-H.Cheng, S.-J. Kan, K.-M.Hui, contact geometry. These flows are C.-C. Hsieh, Derchi Wu (Academia Sinica), characterized by the deformation of geometric C.-C. Chen, Y.-I. Lee, T.-C. Lin, C.-S. Lin objects or structures such as metrics, (NTU), J.-S. Guo, C.-C. Lin, (NTNU), M.-R. connections, mappings, submanifolds, and Li, L.-Y. Tsai (NCU), F.-C. Liu, C.-T. Shieh forms by geometric quantities such as (Tamkang University), J.-L. Chern, C.-L. curvature and consist of partial differential Wang, H.-W. Lin, M.-L. Yau (NCU), H.-L. equations of parabolic type. Via geometric Chiu (Chung Yuan Christian University), S.-C. evolution equations, the powerful methods of Chang, D.-H. Tsai, R.-T. Chen (NTHU), M.-K. nonlinear analysis can be applied to Chuah, C.-K. Lin (NCTU), C.-N. Chen mathematical problems which can be (NCUE), C.-J. Sung, S.-C. Chu, S.-Y. Hsu approached geometrically. Another important (NCCU), Y.-J. Hung, Roger Chen, Eugene Xia subject in geometric analysis is sub-elliptic (NCKU), C.-T. Wu, Hsungrow Chan (NPUE), partial differential equations and sub- J.-C. Tsai (NTOU) Riemannian geometry which has very important applications in several complex There are also several Ph.D. students variables and even biomedical sciences. constantly involved in the GA activities at NCTS. They are from universities including GA at NCTS is considered as a broad field. NTU, NTHU and NCCU. One can view it as a combination of Differential Geometry and Partial Differential Foreign Short-term Visitors Equations. Roughly speaking, the main theme These foreign short-term visitors of NCTS is to use analytical methods (function and usually stay in Taiwan for several days or up operator theory, comparison method, a priori to at most two weeks. They were mostly

Highlights of the Programs -›› 22 invited by mathematicians of Taiwan, with the • Bing-Long Chen, Zhongshan University, hope of increasing future research China, 2004. Topic: Kaehler-Ricci Flow and collaboration and cultivating working Related Topics. relationships. The list of foreign short-term • P. T. Chrusciel, Universite de Tours, France, visitors for the years of 2004-2007 consists of 2004. Topic: Mathematical Aspects of the following. It does not include visitors of General Relativity. NCTS who just come to Taiwan for attending • J. Isenberg, University of Oregon, USA, an international conference. 2004. Topic: Mathematical Aspects of Richard Beals (Yale University), Alice General Relativity. Sun-Yung Chang (Princeton University), • Tai-Peng Tsai, University of British- Jianguo Cao (University of Notre Dame), Der- Columbia, Canada, 2004. Topic: Mini- Chen Chang (Georgetown University), Xinfu Course on Bose-Einstein Condensation. Chen (University of Pittsburgh), Bennett • Tai-Peng Tsai, University of British- Chow (UC-San Diego), Yenheng Ding Columbia, Canada, 2005. Topic: Nonlinear (Academia Sinica, Beijing), Wayne Eby PDE and Particle System. (Temple University), Kenro Furutani (Tokyo University of Sciences), Bernard Gaveau • Tai-Peng Tsai, University of British- (University of Paris 6), Peter Greiner Columbia, Canada, 2006. Topic: Regularity (University of Toronto), Eric Grinberg Problem for the Navier-Stokes Equations. (University of New Hampshire), Wen-Ling • Guofang Wang, Max Planck Institute, Huang (University of Hamburg), Qing Han Germany, 2004. Topic: Toda System and (University of Notre Dame), Chisato Iwasaki Liouville Type Equations. (University of Hyogo), Sergei Kuznetsov • Jiaping Wang, University of Minnesota, (University of Colorado), Bao Qin Li (Florida USA, 2005. Topic: Topics in Geometric International University), Conan Leung Analysis. (University of Minnesota), Peng Lu • Mu-Tao Wang, Columbia University, USA, (University of Oregon), Irina Markina (Bergen 2005. Topic: Introduction to Mean Curvature University) , Ngaiming Mok (University of Flow Equations. Hong Kong), Richard Palais (UC-Irvine), Jianguo Cao, University of Notre Dame, Peter Polacik (University of Minnesota), Yum- • USA, 2005-2006. Topic: Lecture on Gromov Tong Siu (Harvard University), Chuu-Lian Compactness Theorem. Terng (UC-Irvine), Jingzhi Tie (University of Georgia), Alexander Vasiliev (Bergen • Bang-Yen Chen, Michigan State University, University), Guofang Wang (Max Planck USA, 2006. Topic: Topics in Submanifolds. Institute), Paul Yang (Princeton University), • Der-Chen Chang, Georgetown University, Yisong Yang (Polytechnic University),Horng- USA, 2006, 2007. Topic: Sub-elliptic Partial Tzer Yau (Harvard University), Shing-Tung Differential Equations and sub-Riemannian Yau (Harvard University) Geometry. • Ovidiu Calin, Eastern Michigan University, Foreign Long-term Visitors USA, 2006. Topic: Analysis: Geometric These foreign long-term visitors of NCTS Mechanics on sub-Riemannian Manifolds. usually stay in Taiwan for more than two weeks and give a series of survey lectures or Post Doctors mini-courses. The list of foreign long-term • Marcello Lucia, 2004-2005. visitors for the years of 2004-2007 consists of • C.-T. Wu, 2004-2005. the following. Their topics of talks are also included. Mini-courses • Xi-Ping Zhu, Zhongshan University, China, For the years of 2004-2007, NCTS has 2004. Topic: Ricci Flow on Riemannian sponsored the following mini-courses run by Manifold. local and foreign scholars:

23 ‹‹- Highlights of the Programs • Symmetry Method and Their Applications, Taiwan. September, 2004 - January, 2005. • NCTS Workshop on Geometry and Analysis. • Advanced Course on Geometric Analysis, January 8-9, 2006. September 19 - December 26, 2005. • Workshop on Reaction-Diffusion Equations: • A priori Estimate for Partial Differential Theory and Applications. December 1-2, Equations of Elliptic Type and Related 2006. 6 speakers from foreign countries, 6 Topics, summer, 2005. speakers from Taiwan. • Summer Course on PDE in Mathematical • International Conference on Nonlinear Physics, Summer, 2006. Analysis. November 20-25, 2006. 30 • Topical Program in Analysis and speakers from foreign countries, 10 speakers Geometry, Spring, January-July, 2007. from Taiwan. • International Conference on Geometric Workshops and Conferences Analysis. January 16-18, 2007. The speakers For the years of 2004-2007, NCTS has were Alexander Vasiliev and Irina Markina organized the following GA related from Norway; Bernard Gaveau from France; international workshops and conferences: Peter Greiner from Canada; Chisato Iwasaki and Kenro Furutani from Japan; Der-Chen International Conference on Elliptic and • Chang and Jingzhi Tie from USA; Hung- Parabolic Problems: Recent Advances. Ling Chiu and Shu-Cheng Chang from February 16-20, 2004. 25 speakers from Taiwan. All speakers gave nice talks on foreign countries, 5 speakers from Taiwan. different topics in sub-elliptic partial • Workshop on Reaction-Diffusion Equations differential equations and sub-Riemannian and Related Topics. May 26-31, 2004. 16 geometry, analysis on CR manifolds, pseudo- speakers from foreign countries, 8 speakers differential operator and its applications to from Taiwan. complex analysis. • Workshop on Differential Geometry. October • Workshop in Analysis and Geometry. March 20-22, 2004. 16 speakers from foreign 5-6, 2007. This workshop was supported countries, 8 speakers from Taiwan. jointly by NCTS and the Academia Sinica. • Mini-course and Workshop on Conformal The speakers were Bernard Gaveau from Invariant-Analytic and Geometric Aspects. France; Peter Greiner from Canada; Richard June 6-14, 2005. 13 speakers from foreign Beals, Der-Chen Chang and Jingzhi Tie from countries. UAS; De-Chi Wu and Chun-Chung Hsieh • France-Taiwan Joint Conference on from Taiwan. Nonlinear Partial Differential Equations and • International Conference on Geometric Related Topics. July 18-22, 2005. 15 Analysis. June 18-22, 2007. This was a big speakers from foreign countries, 10 speakers international conference which was from Taiwan. supported by NCTS and Taida Institute of • Recent Development of Mathematics at Mathematical Sciences. Speakers included Tsing Hua University. June 6, 2006. 3 Peter Li, D.H. Phong, H.D. Cao, Jianguo speakers from Tsing Hua University, 1 Cao, Der-Chen Chang, Ahanyu Ji, John speakers from USA. Loftin, Lei Ni Jon Wolfson, Mu-Tao Wang, Jiaping Wang, Stephen S.T. Yau from USA; • Latest Development of Geometric Analysis. June 8-9, 2006. 8 speakers from Taiwan. Ben Andrews from Australia; G. Huisken from Deutschland; B. Wilking from • Taiwan-AMS Joint International Conference. Germany; Sumio Yamada from Japan; L.-F. December 14-18, 2005. 20 speakers from Tam, Nai Chung Leung from Hong Kong foreign countries, 8 speakers from Taiwan. and Shu-Cheng Chang, Yng-Ing Lee, Jih- • Workshop on Geometry and Nonlinear Hsin Cheng, J.L. Wang from Taiwan. All Analysis. December 20-21, 2005. 4 speakers speakers gave very nice lectures from foreign countries, 3 speakers from

Highlights of the Programs -›› 24 • NCTS 10 Years Anniversary Mini-workshop Part II: The Accomplishments on PDE. July 23, 2007. Geometric analysis has been one of the most powerful tools in attacking problems in The Role of NCTS in the Developments geometry. In recent years, we witness its great of GA in Taiwan successes of geometric analysis. The most NCTS have successfully organized about important event is of course the solution of the 15 workshops and conferences related to GA Poincare conjecture by the Ricci flow. In since 2004.Participants of these workshops particular, we are focusing on various aspects and conferences came from countries like of geometry and geometric analysis as USA, Japan, France,China, ..., etc. As a result, followings which are great successful in there are more than 100 foreign GA scholars establishing the close liaison between visiting NCTS, including those short-term and Mathematicians in Taiwan and foreign long-term visitors. countries. These visitors and activities of NCTS have 1. Geometric Evolution Equations. played an important role in the promotion and We are interested in geometric evolution development of GA in Taiwan. The problems concerning the deformation of both mathematicians of Taiwan have benefited a lot metrics and submanifolds by curvature tensors from it. These workshops and conferences and functions on manifolds. served as a mean to disseminate the most recent research developments and to cultivate In connection with Prof. S.-T. Yau (Harvard working relationships and mathematical University), Prof. Ben Chow (UCSD), Xi-Ping interaction between foreign scholars and Zhu( Zhongshan University) and M.-T. Wang mathematicians of Taiwan. (Columbia University), many fundamental and important works are done such as Students of Taiwan who would like to pursue graduate studies abroad also benefited a [1] D.-H. Tsai, Asymptotic closeness to lot from NCTS. Their contacts with foreign limiting shapes for expanding embedded visitors have broadened their knowledge and plane curves, Inventiones Mathematicae, help them choose the fields of future research. 162, 473-492, 2005. In recent years there has been increasing [2] C.-C. Poon, T.-C. Lin, D.-H. Tsai, interaction among researchers on GA. In Expanding convex immersed plane curves, particular, a large percentage of papers on GA to appear, 2007. now appearing are joint papers. Important [3] S.-C. Chu, Geometry of 3-dimensional advances are happening in many parts of the Gradient Ricci Solitons with positive world, and one of the goals of NCTS is to curvature, Comm. Anal. and Geom., vol. establish close liaison between mathematicians 13, no. 1, p. 129-150, 2005. in Taiwan and foreign countries. In the next couple of years the NCTS is planning to hold [4] S.-C. Chu, Type II Ancient Solutions to the extensive programs and workshops in Ricci Flow on Surfaces, Comm. Anal. and geometric analysis. This would include both Geom., vol. 15, no. 1, 2007. short and longer term visitors focusing on [5] S.Y. Hsu, A simple proof on the non- various aspects of geometric analysis, existence of shrinking breathers for the including geometric evolution equations, Ricci flow. Calc. Var. Partial Differential harmonic maps, and the calculus of variations. Equations 27, no. 1, 59-73, 2006. NCTS also tries hard to provide a [6] S.-C. Chang and C.-T. Wu, On the wonderful research environment for young Existence of Extremal metrics on Complete researchers through the support of funding or Noncompact 3-Manifolds, Indiana Univ. the reduction of teaching duties. Math. J. 53 (2004), 243-268. [7] S.-C.Chang, Recent Developments on the

25 ‹‹- Highlights of the Programs Calabi Flow, Contemporary Mathematics, Superiore di Pisa, Classe di Scienze (5), Vol 367, 17-42, AMS, 2005. 4(2005), 129-177. [8] S.-C. Chang, The 2-Dimensional Calabi [2] J.-T. Chen, C.-J. Sung, Dimension estimate Flow, Nagoya Math. J. Vol. 181 (2006), of polynomial growth harmonic forms, 63-73 Journal of Differential Geometry, Volume 73, Number 1, p. 167-183, 2006. [9] S.-C. Chang and C.-T. Wu, The Fourth- Order Q-Curvature Flow on Closed 3- [3] Roger Chen, Jiaping Wang, Polynomial Manifolds, Nagoya Math. J., Vol. 185 growth solutions to higher-order linear (2007), pp 1-15 (to appear). elliptic equations and systems. Pacific J. Math. 229, no. 1, 49-61, 2007. [10] J.-H. Cheng, S.-C. Chang, H.-L. Chiu, A fourth order curvature flow on a CR 3- 3. Geometric Strucures : manifold, Indiana University There are very important fields such that Mathematical Journal, to appear, 2007. Einstein manifolds and their moduli space, [11] C.-T. Wu, S.-C. Chang, The Fourth-Order Conformal and CR geometry, Complex Q-Curvature Flow on Closed 3- geometry, Special Lagrangian Submanifolds Manifolds, Nagoya Math. J., pp 1-15, and Mirror Symmetry, Manifolds of special 2007. holonomy and their submanifolds. 2. Harmonic Function and Harmonic Map In connection with Prof. S.-T. Yau (Harvard Theory. University), Prof. Alice Chang (Princeton University), Prof. Der-Chen Chang The classical de Rham-Hodge theory, (Georgetown University), Prof. Jianguo Cao which relates the cohomology group of a (University of Notre Dame), Conan Leung compact manifold to its space of harmonic (CUHK) and M.-T. Wang (Columbia forms, is one of the most fundamental theories University), many fundamental and important in modern mathematics. With the help of an works are done such as. analysis technique first introduced by Bochner (called Bochner technique), the theory has [1] S.-J. Kan, Complete hyperbolic Stein yielded many interesting and important results manifolds with prescribed automorphism relating topology to geometry. Even though groups, Commentarii Mathematici the theory is no longer valid on noncompact Helvetici, no. 82, 371-383, 2007. manifolds, the idea of using analysis to [2] S.-J. Kan, Some complete invariant metrics understand the interaction between topology in Grauert tubes, Mathematical Research and geometry is pivotal and fruitful in Letters, no. 14, 205-220, 2007. geometric analysis. Basic Principle ; To control a metric. find a function that we know [3] H.-L. Chiu, Compactness of well and give a gradient or higher-order pseudohermitian structures with integral estimate of this function. These functions bounds on curvature, Math. Ann, vol.334 , should be defined by geometric construction or p.111-142, 2006. differential equation arise in geometry. [4] H.-G. Chan, Simply-connected In connection with Prof. Peter Li (UCI) and nonpositively curved surfaces in R^3. Prof. Jiaping Wang (CUHK) , many Pacific Journal of Mathematics. 223, 1-4, fundamental and important works are done 2006. such as [5] Tsai, Y., Xia, E., Non-Abelian local [1] J.-H. Cheng, J.-F. Hwang, A. Malchiodi, invariant cycles. Proc. Amer. Math. Soc. and P. Yang, Minimal surfaces in 135 (2007), no. 8, 2365-267. pseudohermitian geometry and the [6] Joshi, K., Ramanan, S., Xia, E., Yu, J., On Bernstein problem in the Heisenberg vector bundles destabilized by Frobenius group, Annali della Scuola Normale pull-back. Compositio Math. 142 (2006),

Highlights of the Programs -›› 26 616-630. papers, D. Jerison and J. Lee initiated the study of this problem . They confirmed the CR [7] Ho, N., Jeffrey, L., The volume of the Yamabe problem in case of the CR Yamabe moduli space of flat connections on a constant is less than the one for a standard CR nonorientable 2-manifold, Comm. Math. sphere. Their methods can be compared to the Phy. 256 (2005), 539-564. partial completion of the proof of Riemannian [8] Ho, N., Liu, M., Connected Components of Yamabe problem by T. Aubin. By the the Space of Surface Group pseudohermitian analogue, the remaining Representations II, Inter. Math. Res. cases should be solved using a CR version of Notices 16 (2005), 959-979. the positive pseudohermitian-mass conjecture [9] Chiang, R., Complexity one Hamiltonian which is not available at this present stage of SU(2) and SO(3) actions. Amer. J. Math. research. 127 (2005) 129-168. In connection with Prof. S.-T. Yau (Harvard [10] Ho, N., The real locus of an involution University), Prof. J. Isenberg (University of map on the moduli space of flat Oregon) and Prof. X. Chang (Chinese connections on a Riemann surface, Inter. Academy Sciences), a few fundamental and Math. Res. Notices 61 (2004), 3263-3285. important works are done such as 4. Mathematical Aspects of General Relativity. [1] H.-G. Chan, Embedding negatively curved initial data of black-hole collisions in R3. The CR Yamabe problem is to find a Classical and Quantum Gravity., 23, 225- contact form on a close CR manifold with 234, 2006. constant Tanaka-Webster curvature. In serial

27 ‹‹- Highlights of the Programs D.5 Lie Theory and Related Algebra at NCTS 2004-2007

Coordinator: Meng-Kiat Chuah (National Tsing Hua University)

Part I : Background and Activities in Short Term Visitors the Program T. Arakawa (Nara Woman U.), S. Ariki (RIMS Kyoto), B. Griess (U. Michigan), A. Huckleberry (U. of Bochum), R. Inoue (U. ie Theory at NCTS is understood in a Tokyo), S. J. Kang (Seoul National U.), H. broad sense. This includes the Kiechle (Hamburg), S. Kumar (U. North structure theory and representation theory of Carolina-Chapel Hill), J. H. Kwon (Seoul), L. Lie groups, Lie algebras and vertex operator Ling (Iowa State), A. Matsuo (U. Tokyo), V. algebras, and related applications in number Mehta (Tata Institute), J. Meyer (Free State, theory and ring theory. Research programs in South Africa), D. Nakano (U. Georgia), R. Ng this area are very active in NCKU, NTHU and (Iowa State), B. Parshall (U. Virginia), L. Scott Academia Sinica. (U. Virginia), W. Wang (U. Virginia), H. The researchers jointly organize a weekly Yamada (Hitotsubashi), T. Yamasaki (Tohoku Lie Theory Seminar. Since 2004, about 30 U.), R. B. Zhang (U. Sydney). visitors have come from the USA, Japan, Korea, Germany, Hong Kong and Australia. Advanced Courses and Seminars Members of this focus group have won the • Introduction to Framed vertex operator Outstanding Research Award (NSC), Wu Ta- algebra, Aug, 2004: You Award (NSC), Academic Award (TMS), • This course is an 8-hour mini course given Young Mathematician Award (TMS), and the by H. Yamauchi. The main aim is to Academia Sinica Young Investigator Award. introduce the beautiful construction of Miyamoto of the Moonshine vertex operator Local Focus Group algebra using codes. S. J. Cheng (Sinica), M. K. Chuah • Groups of even order, Mar 2005: (NTHU), P. Y. Huang (NCKU), W. F. Ke • It is a 6-hour mini course given by Koichiro (NCKU), C. H. Lam (NCKU), N. Lam Harada. Its aim is to introduce the idea of (NCKU), C. F. Nien (NCKU), S. Y. Pan Brauer for classifying finite simple groups. (NTHU). Presently there are 3 PhD students in • Lie Theory Seminar, April 2007-June 2007: this group. • Weekly seminar given by S. J. Cheng, C. H. Post Doctor Lam, M. K. Chuah, S. Y. Pan and some graduates students. The Topics of the seminar C. C. Hu (NTHU 2006-07). include character formula of Lie algebras, vertex operator algebras, extended Vogan Frequent Visitors diagrams, and nilpotent orbits of semisimple M. Chebotar (Kent State), Koichiro Harada Lie algebras (Ohio State), J. S. Huang (Hong Kong U. Sci. Tech.), King Fai Lai (Sydney), Hiroki Conference and Workshops Shimakura (Chiba U.), Hiroshi Yamauchi International Conference of Algebra in (Aichi U. of Education). • Memory of Kostia Beidar, Mar 6-12, 2005 at NCKU. Organizers: W. F. Ke, Y. Fong and P. H. Lee.

Highlights of the Programs -›› 28 • Speakers: E. Zemanov, L. Small, Leonid invited speaker at the December 2007 ICCM Makar-Limanov, E. Puczyloski, R. R. in Hangzhou, China. Wisbauer, T. Arakawa In the winter 2005, C.H. Lam visited • Algebraic Aspects of Lie Theory and University of Tsukuba. During this visit, he Geometry, Third Pacific Rim Conference was one of the active members of the Komaba Special Session, Fudan U, Shanghai, July group theory seminar in Tokyo, whose 2005. Organizers: S. J. Cheng. members include M. Kitazume (Chiba), A. • Representation Theory, First AMS-TMS Matsuo (Tokyo), M. Miyamoto (Tsukuba), H. Joint Meeting Special Session, Tunghai U, Shimakura(Chiba), H. Yamada (Hitotsubashi), Taichung, December 2005. Organizers: S. J. H. Yamauhci (Tokyo) and also gave several Cheng, B. Parshall and W. Wang. seminar talks. In addition, he has made many • Algebraic Aspects of Lie Theory, Academia short term visits to Japan and was an invited Sinica, December 2007. Organizers: S.-J. speaker in several conferences in Kyoto, Cheng and W. Wang. Hamamachi, Nara and Tokyo. • Under planning: NCTS Winter School in In January 2007, S.-Y. Pan attended The Representation Theory, Hsinchu, January 25- Annual Meeting of American Mathematics 29, 2008. Organizers: M. K. Chuah and J. S. Soceity and gave an invited talk in the section Huang. of representation theory. Then he visited Louisiana State University for a few days. He International Cooperations is going to have a jointed project on nilpotent S.-J. Cheng visited the University of orbits of semisimple Lie algebras with H. He Virginia for one year in 2003-2004. During his of LSU. stay there he gave one seminar talk in the Infinite-dimensional algebra seminar at MIT, and the Lie groups and geometry seminar at Part II: The Accomplished and the the CUNY in New York. He gave an invited Anticipations talk at the International Conference on Selected publications of the local focus Representation Theory III in Chengdu in the group since 2004: July 2004, and was asked to organize a special session at the Third Pacific Rim Conference in [1] M. A. Chebotar, W.-F. Ke, P.-H. Lee. On Fudan University, Shanghai in July 2005. He Bresar-Semrl conjecture and derivations of visited the University of Sydney in the August Banach algebras. Quart. J. Math. 57 2005, and the University of Virginia in (2006), 469-478. November 2006. He is scheduled to give an [2] M. Chebotar, W.-F. Ke, P.-H. Lee, R. B. invited talk at the International Conference on Zhang. On maps preserving zero Jordan Representation Theory IV in Tibet in July products. Monatsh. Math. 149 (2006), 91- 2007. He is scheduled to visit the University of 101. Vienna in August 2007, and the University of Virginia in October 2007. [3] M. Chebotar, W.-F. Ke, P.-H. Lee. On maps preserving square-zero matrices. J. M. K. Chuah attends the Summer School Algebra 289 (2005), 421-445. on Representation Theory held at the Chern Institute of Mathematics (Nankai University, [4] S.-J. Cheng, N. Lam and R. B. Zhang, Tianjin) in 2006 as a guest, and in 2007 as an Character Formula for infinite-dimensional invited lecturer. This leads to a collaboration unitarizable Modules of the general linear with J. S. Huang on symmetric spaces. He is Superalgebra, J. Algebra 273 (2004), No. invited to give a seminar talk on Vogan 2, 780-805. diagrams at the conference Sapporo Lectures [5] S.-J. Cheng and R. B. Zhang, Howe on Representations in Lie Theory (Hokkaido Duality and Combinatorial Character University) in August 2007. He is also an Formula for Orthosymplectic Lie

29 ‹‹- Highlights of the Programs Superalgebras, Advances Math. 182 (2006), No. 1, 403-439. (2004), No. 1, 124-172. [17] S. Y. Pan, Local theta correspondences for [6] S.-J. Cheng, W. Wang and R. B. Zhang, A small unitary groups, Trans. Amer. Math. Fock Space Approach to Representation Soc. 358 (2006), 1511-1535. Theory of osp(2|2n), Transformation One focus of the research group, including Groups 12 (2007), No. 2, 209-225. S.-J. Cheng, W. Wang, and R. B. Zhang, is the [7] S.-J. Cheng, W. Wang and R. B. Zhang, study of the representations of Lie Super Duality and Kazhdan-Lusztig (super)algebras. In [5] Howe duality is applied Polynomials, Trans. Amer. Math. Soc., to to the study of Lie superalgebras where appear. characters of certain oscillator representations of the orthosymplectic Lie superalgebra are [8] M. K. Chuah, Symplectic induction and computed. One remarkable consequence is that semisimple orbits, Bull. London Math. a wide class of irreducible characters of these Soc. 37 (2005), 446-458. Lie superalgebras are determined by the [9] M. K. Chuah, The direct integral of some characters of certain infinite-dimensional Lie weighted Bergman spaces, Proc. Edinb. algebras. In [7] a precise connection between Math. Soc. 50 (2007), 115-122. the Kazhdan-Lusztig theories of the general [10] M. K. Chuah and C. C. Hu, A quick proof linear Lie superalgebra and the general linear on the equivalence classes of extended algebra is formulated and proved. It follows Vogan diagrams, J. Algebra 313 (2007), that their respective representation theories (in 824-827. certain categories) are equivalent. Such a connection between Lie algebras and Lie [11] M. K. Chuah, Geometric quantization and superalgebras has been observed for the very Zuckerman models of semisimple Lie first time. In [6] a certain q-deformed Fock groups, Forum Math., to appear. space is constructed whose combinatorics of [12] C. Dong, R. L. Griess and C.H. Lam, standard monomial, canonical and dual Uniqueness results of Frenkel-Lepowsky canonical bases, completely determined the -Meurman's moonshine vertex operator finite-dimensional representation theory of the algebra, Amer. J. Math. 129, No. 2 Lie superalgebra osp(2|2n). (2007), 583 609. Motivated by the works of Bloch and [13] C.H. Lam and H. Yamauchi, On the Okounkov who defined a certain refined structure of framed vertex operator version of the character for the infinite- algebras and their pointwise frame dimensional general linear algebra at level stabilizers, to appear in Comm. in Math. one, S.-J. Cheng and his co-workers also found Phys. a remarkable closed form for their correlation function in terms of certain theta functions. [14] C.H. Lam, S. Sakuma and H. Yamauchi, This result is extended to higher positive and Ising vectors and automorphism groups of negative levels, the correlation functions are commutant subalgebras related to root expressed in terms of certain q-hypergeometric systems, Math. Z. Vol. 255, No.3, Mar. series. 2007, 597-626. The papers [16] deals with the [15] C.H. Lam and M. Miyamoto, Niemeier representation theory of central extensions of Lattices, Coxeter elements and McKay's the infinite rank Lie superalgebras of type A E8 observation on the Monster simple and OSP. The main result in the paper is the group, Inter. Math. Res. Not., Vol 2006 classification of all irreducible highest weight (2006), 27 pages. quasi-finite modules. [16] N. Lam and R. B. Zhang, Quasi-finite In the last few years, our groupin vertex modules for Lie superalgebras of infinite operator algebra has obtained several rank, Trans. Amer. Math. Soc. 358 important results. In spring 2004, C.H. Lam,

Highlights of the Programs -›› 30 H. Yamada, H. Yamauchi began a project on algebras whose full automorphism groups are studying some mysterious connections almost simple 3-transposition groups. This between the Monster group and the affine E8 work has also been generalized by H. diagram, which was first observed by John Shimakura and C.H. Lam to the Leech lattice McKay 35 years ago. This collaboration leads vertex operator algebra. to works in which a vertex operator algebra Problems on finite planar nearrings are theoretical explanation for McKay's E8 observation were given. After that, M. studied in a series of papers by K. I. Beidar, Miyamoto and C. H. Lam obtained a natural W.-F. Ke, H. Kiechle. Using representation theory, W.-F. Ke, K.F. Lai and R.B. Zhang also explanation for McKay's E8 observation by using some twisted construction of the Leech derived a systematic construction method of lattice [15]. Recently, C.H. Lam, H. Yamauchi quantum error correcting codes which and G. Hohn also began to study some similar generalizes, in particular, the Shor's 9-qubit code. relations between affine E7 and E6 diagrams with the Babymonster group and the largest The theory of functional identity was Fisher group and a lot of progress has been invented about 10 years ago by Beidar and made. Chebotar. Many important problems, such as In winter 2005, C. H. Lam visited the Lie maps conjecture posted by Herstein, University of Tsukuba, with the support of was solved completely by this method. With JSPS. This visit ended up with several the same tool, many problems of linear successful collaborations. On the structure of preserver problem were attached and framed vertex operator algebras and their conquered with success during the past five orbifolds, C.H. Lam and H. Yamauchi showed years by the algebra group in National Taiwan that all framed vertex operator algebras are University and National Cheng Kung simple current extension of the corresponding University [1, 2, 3]. code vertex operator algebras, to appear in The main subject of Shu-Yen Pan s recent Comm. in Math. Phys. [13]. Based on this research is the L-functoriality of the local theta result, C.H. Lam, H. Yamauchi and H. correspondence. In particular, he proves that Shimakura started a program on classifying Adams/Harris-Kudla-Sweet s conjecture on holomorphic framed vertex operator algebras the Langlands parameters of the chain of of small central charges using binary codes. supercuspidal representation obtained by the This work is still under progress but a simple conservation principle of the local theta characterization of the moonshine vertex correspondence is true if these supercuspidal operator algebra has been obtained which representations have unipotent reduction. verifies a conjecture of Frenkel-Lepowsky- Meurman on the uniqueness of the moonshine One research interest of M.-K. Chuah is the vertex operator algebra. Around the same time, diagrammatic expression of involutions of another characterization of the moonshine simple Lie algebras, known as Vogan diagram. vertex operator algebra was also obtained by Several Vogan diagrams may represent the C. Dong, R. L. Griess and C.H. Lam under the same involutions, and in joint series of works assumptions that the algebra structure of the weight 2 space is isomorphic to the Monstrous with C. C. Hu, e.g. [10], such diagrams are Griess algebra [12]. In addition, S. Sakuma, H. sort out. The other direction in which progress Yamauchi and C.H. Lam have studied the are made by Chuah is the study of relations Ising vectors inside the lattice type vertex between group representations and symplectic operator and their commutant [14]. They geometry, known as geometric quantization, classified all Ising vectors in . Moreover, carried out in [8], [9], [11]. they constructed many new vertex operator

31 ‹‹- Highlights of the Programs D.6 Mathematical Biology at NCTS 2004-2007

Coordinator: Sze-Bi Hsu (National Tsing Hua University)

Part I: Background and Activities in Hwang (CCU), J.C. Tsai (CCU), Y.H. Hsieh the Program (NCHU), C.C. Li (San John Polytech.), C.P. Lo (Providence), I.F. Sun (THU, Biology), Y.H. Tzeng (Academia Sinica, Genomic athematical Biology is an Center). interdisciplinary area between mathematicians, statisticians, computer Post Doctor scientists and biologists. Currently the main Y.Y .Chen (NCTS 2007, Plant Biology) subject of the topical program of Mathematical Biology in NCTS is Population Dynamics. Frequent Visitors (Another important subject is Bioinformatics which is currently included in the Topical Yihing Du (U. New England, Australia), Program of Probability) In Population Lih-Ing Wu (Texas Tech.) Dynamics we limit our attentions to Mathematical Ecology, Mathematical Short Term Visitors Epidemiology and Mathematical Physiology. F.Brauer ( British Columbia), M. Chaplain In the traditional mathematical biology, (Dundee,UK),Y.S.Choi (Connecticut,USA), J. mathematicians study the oversimplified Glasser (US CDC, Atlanta), J.Lowengrub (UC mathematical models from biology with Irvine), R. Lui (WPI, USA), S. Ma (Public emphasis on their new mathematical properties Health, Singapore), A. Mogilner (UC Davis), but with little feedback to biology. The modern H. Othmer (Minnesota), S. Riley ( Hong Kong mathematical biology however emphasizes the University), H. Smith (Arizona State,USA), collaborations with biologists. Usually the H.O.Walther (U. Giessen, Germany), J.H. Wu mathematical models are more realistic and (York, Canada). P. Yan (Public Health Agency but too complicate to do mathematical analysis of Canada), X. Zhao (Memorial U of and hence large scale scientific computations Newfounder, Canada) are needed to explore more biological phenomenon. Advanced Courses in 2004-2007 There are over 15 short term visitors • Dynamics of Delays, Feb. 22-March 6, 2004, participating in the Mathematical Biology by Hans Otto Walther, New methods of program since 2004. They come for homoclinic transversality is introduced for conference-workshops, and/or for a visit up to the study of chaotic behavior of solutions of one month. Among them are the world leading the delay differential equations. mathematical biologists e.g. S.Hubbell(U. • Spatial Heterogeneous Mathematical Models Georgia), Hans Othmer (Minnesota), Hal in Population Biology, March 15-May 15, Smith (Arizona State),Mark Chaplan ( 2004, by S.B. Hsu and C.P. Lo. This course Dundee,UK), Jiahong Wu (York, Canada). covers maximal principle, comparison principle, monotone methods for elliptic and Local Group parabolic PDE, logistic equation in PDE S.B. Hsu (NTHU), C.W. Shih (NCTU), form, Predator-Prey system and competition M.C. Li (NCTU), M.C. Lai (NCTU), T.W. system in heterogeneous environment, blow- up behavior of elliptic PDE.

Highlights of the Programs -›› 32 • Monotone Dynamical Systems, by Sze-Bi • Mini-Workshop on Mathematical Biology, Hsu, Aug 1-Aug.31, 2006. This course May 9-10, 2007 at NCTS. Organizers: covers ODE of cooperative systems as an S.B.Hsu and H. Smith. Speakers: X. Zhao, example of monotone flow, monotone flow H. Smith, S.B. Hsu, Y.H.Hsieh, T.W.Hwang, in abstract space, Poincare-Bendixson like C.P.Lo,J.C. Tsai Theorem for 3-dimensional competitive system, applications to reaction-diffusion Exchange Programs and International equations, delay differential equations and Cooperations maps. During 2002-2004, with the support from • Reaction Diffusion System with NCTS fellowship, we sent Ph.D student Applications to Spatial Ecology, March 15- Y.H.Tzeng to the department of Evolution April 26,2007, by Yihong Du. This course biology and Ecology , University of Chicago covers classical and degenerate logistic to do research of molecular evolution under model, classical diffusive competition and the supervision of Professor Wen-Hsiung Li predator-prey model, the degenerate for two years. Now Dr. Tzeng is the first competition model and predator-prey model mathematics Ph.D in Taiwan with the training and their perturbations. in molecular evolution and bioinformatics. He • Spreading Speeds and Traveling waves for is currently working in the genomic Center in monotone semiflow with applications, April Academia Sinica. 27-May 28, 2007, by Xiaoqiang Zhao. This course covers the estimate of the spreading speed for a traveling wave solution for a Part II: The Accomplished and the reaction-diffusion systems with monotone Anticipations properties. Selected publications of the local group Undergraduate Course since 2004: Mathematical Theory of Molecular [1] Y.H.Hsieh and S.B.Hsu et. Impact of Evolution, Spring semester of 2006, by Y.H. quarantine on the 2003 SARS outbreak: A Tzeng. This course covers (i) Introduction to retrospective modeling study , J. population genetics, (ii) Dynamics of Theoretical Biology 244(2007) 729-736. nucleotide substitution, (iii) Estimating the [2] S.B.Hsu and Lih-Ing Wu, The final size of number of nucleotide substitutions between a SARS epidemic model without sequence, (iv) Computation molecular quarantine , JMAA 333(2007) 557-566. biology.. [3] Y.H. Hsieh and S.B.Hsu, On the role of Conferences and Workshops asymptomatic infection in transmission dynamics of infectious disease, to appear in Workshop of Mathematical Models and • Bulletin of Mathematical Biology 2007. Problems in Cell Motility and Tumor Growth, Jan.11-19, 2006 at NCTS. [4] Y.H.Hsieh and S.B.Hsu Modeling Organizers: S.B.Hsu and R. Lui. Speakers: intervention measure and severity H. Othmer, A. Mogilner,M. Chaplain, J. dependent public response during severe Lowengrub,Y.S. Choi, R. Lui, J.L. acute respiratory syndrome outbreak, Yang,,C.H. Lin, H. Ninomiya, S. McDougall. SIAM J. Appl. Math. 66,No.2 (2006) 627- • Workshop on Mathematical Modeling of 647. Infectious Disease Epidemiology, May 31- [5] S.B.Hsu and C.C.Li, A discrete delay June 2,2006 at NCTS. Organizers: S.B.Hsu model with plasmid-bearing plasmid free and Y.H.Hsieh. Speakers: S. Ma, S. Riley, competition in a chemostat, Discrete and J.H.Wu, P.Yan, J. Glasser, F.Brauer, S.B.Hsu, Continuous Dynamical Systems, vol Y.H.Hsieh. 5,No.3, (2005) 699-718.

33 ‹‹- Highlights of the Programs [6] Y.H.Du and S.B.Hsu, A diffusive predator- mathematical modeling in biology. prey model in heterogeneous environment The topical program of Mathematical Journal of Differential Equations 203 Biology usually joins with other topical (2004) 331-364. programs ,e.g., PDE , Dynamical Systems, [7] Y.H.Hsieh, S.B.Hsu and Cathy Chen. The Probability. We sometimes invite local severe Acute Respiratory Syndrome biologists or physicists to give talks on their outbreak in Taiwan: Lesson to be learn, work related to mathematical modeling. Emerging Infectious Disease (2004) vol. In Mathematical Ecology, we have a close 10, No.2 ,201-206. collaboration with ecologist Professor I-Fang [8] Tzeng Y.H. ,R.Pan,W.H.Li, Comparison of Sun of Tung-Hai University on the modeling three methods for estimating rates of on Ecology and Disease. Recently we hire a synonymous and nonsynonymous post doctor Y.Y.Chen ,a Ph.D of Plant Ecology nucleotide substitution, Mol. Biol. from University of Georgia. We expect to Evol.(2004) 21(12) 2290-2298. learn more biology and to cooperate with her on constructing mathematical modeling of [9] Shin S.H., W.Karlowski, R.Pan, Spatial Ecology and Neutral Theory in Y.H.Tzeng, K.F.Mayer and W.H.Li, Ecology. Comparative Analysis of the receptor-like kinase family in Arabidopsis thaliana and In Mathematical Epidemiology, S.B.Hsu rice, Plant Cell (2004) 16,1220-1234. and Y.H. Hsieh complete several modeling [10] J.C.Tsai and J.Sueyd,Existence and work and their mathematical analysis on the stability of traveling waves in buffered outbreak of SARS in Taiwan. Currently we systems, SIAM J.Appl. Math. Vol have finished the work on the mathematical 66,No.1,pp.237-265 (2005). models of Avian Flu .We plan to study the nosocomial infection in hospital with medical [11] J.S.Guo and J.C.Tsai, The asymptotic people. behavior of solutions of the buffered bistable system, Journal of Mathematical In Mathematical Physiology, J.C.Tsai Biology 53(2006) 179-213. studies the wave propagation of increased [12] J.C.Tsai, Asymptotic stability of traveling calcium concentration of cells in excitable wave front in the buffered bistable system. C.P.Lo and his collaborators in system, SIAM J.Math.Analysis Taichung Veteran Hospital study the 39(2007)pp.138-159. mathematical models of hearts and do some In additional to the training in ODE, PDE, computation work. Dynamical Systems, we encourage our We anticipate in the future we have more graduate students to take courses in life collaborations with biologists to construct science departments and learn how to mathematical models for the important communicate with biologists. Currently we ask problems arising from biology. the students to have solid training in mathematics and expect them to learn some

Highlights of the Programs -›› 34 D.7 Number Theory at NCTS 2004-2007

Coordinator: Jing Yu (National Tsing Hua University)

Part I: Background and Activities in G. Leu (NCU), A. Li (Fu Jen U.), H.-C. Li the Program (NTNU), C.-H. Lin (NCKU), C. Nien (NCKU), S.-Y. Pan (NTHU), J. T.-Y.Wang (Academia Sinica), W.-C. Yao (TMUE), Y. umber Theory at NCTS is understood Yang (NCTU), C.-F. Yu (Academia Sinica). in a broad sense, including traditional Presently there are also 10 Ph.D. students in algebraic number theory, arithmetic geometry this group, from NTHU, NCU, and NCTU. and automorphic representations. Diophantine geometry and arithmetic of algebraic function Long Term Visiting Scientists fields are also among the main interests. A C.-L. Chai (U. Penn.), 2004 Spring regular number theory seminar is run at NCTS semester. Winnie W.-C. Li (Penn. state U.), weekly, including lectures given by visitors to 2006/07 whole year as center scientist at NCTS and reports on research results given by NCTS. members of the local focus group. There are over 30 short term visitors Post Doctors participating in the number theory program C.-J. Wang (NCTS 2006-), Y.-C. Yi (NCTS since 2004. They come for conferences- 2005-07), C.-C. Li (Academia Sinica 2005- workshops, and/or for a visit up to one month. 07), C.-Y. Chang (NCTS 2007-). Among them are the world leading number theorists e.g. T. Saito (Japan), G. Wüstholz Frequent Visitors (Switzerland), H. Darmon (Canada), D. Jean-Yves Briend (Provence), W.-T. Kuo Brownawell (USA), J. Silverman (USA), and (U. Waterloo), M. Papanikolas (Texas A & M F. Beukers (the Netherlands). They, as well as U.), J. Tilouine (Paris Nord), J.-K. Yu (Purdue the long term visiting scientists, are naturally U.). our consultants on developing researches of number theory in Taiwan. Short Term Visitors The frequent visitors are 5 mathematicians A. Ashikhmin (Bell Lab.), F. Beukers (U. who visited NCTS more than once in the past, Leiden), G. Boeckle (U. Essen), N. Boston (U. and had or currently have joined research Wisconsin), P. Bundschuh (Köln), R. projects with members of the local focus Calderbank (Princeton U.), H.-H. Chan (NU. group. For a report in this respect, see Part II. Singapore), W. Cherry (North Texas U.), H. In 2006, 3 members of this focus group Darmon (McGill U.), A, Garcia (IMPA), A. received awards for their research works: one Hoshi (Waseda U.), M-D. Huang (USC), M. Wu Ta-You research award from NSC, and Kim (Purdue U.), K. Komatsu (Waseda U.), two young scholar's awards from the J.Korman (U. Toronto), K. F. Lai (U. Sydney), Academia Sinica Y.-R. Liu (U. Waterloo), L. Long (Iowa state U.), W. Luo (Ohio state U.), H. Maharaj Local Focus Group (Ciemson U.), J. V. Maillot (Paris 7), J. J. Yu (NCTS Center Scientist and NTHU), MaKay (Concordia), K. Miyake (Waseda U.), Y.-M. J. Chen (NCU), L.-C. Hsia (NCU), M.- Y. Mizusawa (Sophia U.), D. Ramakrishnan (Caltech), W, Raskind (USC), T. Saito (Tokyo

35 ‹‹- Highlights of the Programs U.), D. Savitt (U. Arizona), J.Silverman (NTU) and Winnie W.-C. Li. There are 6 (Brown U.), D. Thakur (U. Arizonz), G. speakers from abroad. Wüstholz (ETH), T. Yang (U.Wisconsin). • Workshop on arithmetic and algebraic geometry, number theory and representation Advanced Courses in 2004-2007 theory, December 30/31, 2004 and January • Modular forms and Galois representations, 6/7, 2005 at Academia Sinica and NTU. Fall 2006. This course is given by Winnie Organizer: C.-F. Yu. Speakers : Ching-Li W.-C. Li and C.-F. Yu. It s aim is the Chai, Chien-Jan Wang, W. Cherry, and connection between modular forms and Jungkai Chen. Galois representations. Starting point is the • Workshop on arithmetic geometry and Eichler-Shimura relations, then Deligne's representation theory, January 6-8, 12-13, generalization from weight two to higher 2004 at NCTS. Organizer: J. Yu. Speakers: weight modular forms. The reverse direction, C.-L. Chai, C.-J. Wang, T. Yang, and C.-F. by Wiles, Taylor, etc, giving criteria for l- Yu. adic representations to be modular is also discussed. Exchange Programs and International • Topics on Diophantine geometry, Fall 2004. Cooperations Lecturers includes : L.-C. Hsia, J. T.-Y. Besides individual visits by members of Wang and J. Yu. This course covers : heights, our focus group to centers and universities in Mordell-Weil theorem, abelian varieties, U.S.A., Canada, Germany, France, England, Roth's theorem, emphasizing geometric Italy, Spain, Japan, China, Hongkong, Korea, methods in number theory. Vietnam, we have strengthened cooperations • Topics on number theory and representation with three countries: theory, Spring semester and fall semester Japan. January 2005. Group consisted of J. 2004. Lecturers includes : J. Yu, L.-C. Hsia, Yu, L.-C. Hsia, C.-F. Yu, S.-Y. Pan, Y.-M. J. C.-J. Wang, C.-F. Yu, J. T.-Y.Wang, Y.-M. J. Chen and a Ph. D. student visited Japan for Chen. Themes are : Artin's L-functions, two weeks, being invited to Kyoto U., Nagoya modular forms, Weil representations, Hecke U., Tokyo U., speaking at their number theory characters, Maass forms and automorphic seminars and attending conference on representations of GL(2), Half-integral automorphic forms and automorphic L- weight modular forms. functions at RIMS. This visit was sponsored • Topics in one complex variable, Spring by grant from the Minister of Education. In 2004. Lecturers includes : J. Yu, J. T.-Y. December 2005, Y.-C. Yi and a Ph. D. student Wang, L.-P. Tee and Y. Yang. This course is were invited to RIMS conference on algebraic aimed at interactions with number theory, number theory, December 2006, Y. Yang was e.g. Nevanlinna theory, transcendence theory invited to RIMS conference on algebraic and analytic number theory. number theory. March 2006, J. Yu, W.-C. Yao and a Ph.D. student were invited to annual Conferences and Workshops algebraic number theory conference at Waseda • Conference on Galois representations and U., March 2007, L.-C. Hsia and a Ph.D. function field arithmetic, May 14-17, 2007 at student were invited to annual algebraic NCTS. Organizers : Winnie W.-C. Li and J. number theory conference at Waseda U. All Yu. There are 10 speakers from abroad. the graduate students participating in these • Workshop on Iwasawa theory and exchangeswere supported by Minister of automorphic representations, September 4- Education grant. 7, 2006 at NCTS. Speakers : K. komatsu, Y. France. July 17-29, 2006, Asian-French Mizusawa, C.-J. Wang and J. Yu. summer school in algebraic geometry and • Workshop on coding theory, June 28-July 23, number theory, at IHES. Organizers : J.-B. 2004, at NTU. Organizers : M.C. Kang Bost, J. P. Bourguignon, J. M. Fountaine, L.

Highlights of the Programs -›› 36 Lafforgue, N. B. Châu, M. Kim, M. Levine, T. geometry, modular forms and automorphic Saito (Japan), S. Ramdorai (India), L. Fu representation theory. (China), N. Mok (Hong Kong), C.-F. Yu We have also supported travels of Ph.D. (Taiwan). Taiwan participating group consisted students to join selected summer/winter of 9 graduate students, and H.-W. Lin, S.-Y. schools, or workshops abroad : 1 student to Pan, J.- H. Teh, C.-L. Wang, C.-F. Yu, and J. Clay institute summer school in arithmetic Yu. Also in summer 2004, J. T.-Y. Wang, J. geometry 2006, 2 students in 2004, 1 in 2005, Yu, Y.-M. J. Chen and L.-C. Hsia were invited and 3 in 2007 to the Arizona arithmetic to visit France, joining conferences and geometry winter school, 2 students to the workshops at Clermont-Ferrant, Toulouse and Fields institute summer school in 2006, 1 Marseille. Furthermore there are two Ph.D. student to MSRI Diophantine geometry students from France (Paris 7 and Paris nord) workshop in 2006, 2 students to the PAMQ joined 2005 summer research program in 2007 school on Langlands and geometric number theory at NCTS. Langlands program in Guanzhou, and 2 Korea. September 2004, J. Yu, A. Li, and W.- students to 2007 ICTP summer school on C. Yao were invited to visit KIAS and KAIST. automorphic forms and Shimura varieties at February 2007, J. Yu and two Ph.D. students Triesta. All of these students applied (mostly were invited to KAIST. S. Hahn, Bae (Korea), received) local support from the organizers of (China), Kaneko (Japan), J. Yu (Taiwan) are these international programs. organizing an East Asia number theory conference at Taejeon, Korea, January 21-24 2008. Part II: The Accomplished and the Anticipations Student's Seminars and Schools Selected publications of the local focus Since 2004 each year we have one week group since 2004 : winter school and one week summer school on various topics in number theory for graduate [1] Ta Yhi Haoi An and J. T.-Y. Wang, Unique students, sponsored by Minister of Education range sets and uniqueness polynomials for grant (national chair in science) and NCTS, algebraic curves, Trans. A.M.S. 359 usually this is taken place at a conference site (2007), 937-964. outside NCTS. In these schools, about half of [2] Ta Yhi Haoi An and J. T.-Y. Wang, An the talks are presented by Ph. D. students. effective Schmidt's subspace theorem There are also monthly special day programs for non-linear forms, J. of Number and weekly student's seminars during the Theorey, to appear 2007. semesters at NCTS. Every summer, besides the summer school, there is also a summer [3] M. Baker and L.C. Hsia, Canonical height, program for graduate students and advanced transfinite diameters, and polynomial undergraduates interested in number theory, dynamics, J. reine angew. Math. 585 and participating students (about a dozen each (2005), 61-92. summer) are guided by professors from the [4] C.-J. Chang and J. Yu, Determination of focus group. These students also receive algebraic relations among special zeta partial financial support from NCTS during the values in positive characteristic, to appear summere period. in Adv. Math. 2007. In 2005/06, a special efforts had been made [5] Y.-H. Chen, Y. Yang and N. Yui, on organizing a preschool for the IHES Asian- Monodromy of Picard-Fuchs differential French summer school in algebraic geometry equations for Calabi-Yau threefolds, to and number theory July 2006. This preschool appear in J. reine angew. Math. 2007 selected the 9 students who attended the IHES international program from Taiwan, and did [6] Y.-M. J. Chen and J. Yu, On primitive roots background preparations in algebraic of elliptic curves with complex

37‹‹- Highlights of the Programs multiplication, Journal of Number Theory logarithms. Extending this to Carlitz 114 (2005), 66-87. polylogarithms, C.-Y.Chang and J. Yu succeeds in 2005 to determining all the [7] Y.-M. J. Chen and J. Yu, On class number algebraic relations of Carlitz zeta values at relations in characteristic two, to positive integers (cf [4], to appear in Adv. appear in Math. Zeit. 2007 Math.), completely settles a 70 years old [8] Min Ru and J. T.-Y. Wang, A second main problem. Later on Papanikolas revisited NCTS theorem on parabolic manifolds, at end of 2005, and C.-Y. Chang visited Asian J. Math. 9 (2005), 349-371. Papanikolas during 2006 under NSF [9] L.-C. Hsia and J. T.-Y. Wang, Wronskians, scholarship, results of this collaboration (in and the ABC theorem for higher preparation and in preprint) establishes the dimensional function fields of arbitrary algebraic independence for rank two Drinfeld characteristic, Trans. A.M.S. 356 (2004), logarithms, and also determines all the No.7, 2871-2887. algebraic relations among families of Carlitz zeta values (as constant fields varies in the [10] Y. Yang, On differential equations same characteristic). This collaboration will satisfied by modular forms, Math. Zeit continue for years to come, targeting at the 246 (2004), 1-19. analogue of Schanuel conjecture for arbitrary [11] Y. Yang, Defining equations of modular Drinfeld modules, and determining algebraic curves, Adv. Math 204 (2006), 481-508. relations of all zeta values, Gamma values, etc, connected with global function fields. [12] C.-F. Yu, Irreducibility of the Siegel moduli spaceswith parahoric level After the Crelle paper [3] by Baker-Hsia on structures. Int. Math. Res. Not. 48 (2004), adelic polynomial dynamics which 2593-2597. successfully generalizes Bilu's equidistribution theorem, arithmetic dynamics is becoming one [13] C.-F. Yu, On the slope filtration of certain of the major lines in Diophantine geometry we Shimura varieties. Math. Zete. 251 are interested in. J. Silverman and L.-C. Hsia (2005), 859-873. is collaborating and organizing a workshop at [14] C.-F. Yu, The supersingular loci and mass AIM in January 2008 on this topic. Another formulas on Siegel modular varieties. direction is the interaction of Diophantine Doc. Math. 11 (2006), 449-468. geometry with Nevanlinna theory, in particular various versions of Schmidt's theorem, and the [15] C.-F. Yu and J. Yu, Mass formula of ABC theorem in the function field case (cf. supersingular Drinfeld modules, C. R. [1], [8] for example). J. T.-Y. Wang have been Acad. Sci. Paris, Ser. I 338 (2004), 905- collaborating with several international experts 908. on this subject for years, P. Wong, W. Cherry [16] J. Yu and Q. Yue, On the density of 4- and M. Ru made substantial contributions ranks of tame kernels for quadratic fields, (supported in the large part by Academia J. reine angew. Math. 567 (2004), 151- Sinica). They are organizing a program at 173. Fields Institute in 2008. In the direction of transcendence theory, In summer 2004, Y. Yang, as NCTS fellow, particularly motivic transcendence theory in visited N. Yui in Canada. This begins a positive characteristic which was first successful collaboration on the monodromy of developed twenty years ago by J. Yu, break hypergeometric differential equations, and lead throughs have been made in the last few years to the fascinating paper [5] to appear in Crelle, (cf. Bourbaki seminar March 2007 by F. about the monodromy of Picard-Fuch Pellarin). In 2004 summer, M. Papanikolas differential equations and Calabi-Yau visited NCTS writing up his NCTS preprint threefolds. Y. Yang is an expert on finding (05-1-19, to appear in Invent. Math.) on defining equations for modular curves (cf. [9]), algebraic independence of Carlitz (rank one) and connecting modular forms with

Highlights of the Programs -›› 38 differential equations. Those conjectures in [5] fills in a gap in the literature and complements will undoubtedly lead to many interesting and the well-known thesis of E. Artin where only important developments in the near furure. odd characteristic is treated. For function fields, approaches to even characteristic can be Supersingular abelian varieties and quite different from the odd characteristic supersingular Drinfeld modules are of special case. The other more traditional problems arithmetic interests. The classical mass studied by members of the group include the formula for these objects goes back to primitive roots problem for commutative Deuring-Eichler, for which [14] is a far- algebraic groups and Drinfeld modules (cf. reaching generalization. C.-F. Yu is now an e.g. [6]), and the density problem of 4-ranks of expert in writing down these beautiful tame kernels for quadratic fields (cf. 16]). formulas in various settings, e.g. in [15] the resulting formula is for arbitrary rank Drinfeld Finally representation theory relating to A-modules. In recent years, C.-L. Chai and C.- number theory is a relative recent research F. Yu have also been working on the Hecke direction to us. Representations of algebraic orbits problems on Hilbert modular varieties groups over local fields is one focus. Theta (in preprint and in preparation). This result has correspondence over local fields as well as interest in its own right, as it is a PEL-type over global fields is another focus, e.g. works analogue of the Hecke orbit problem for Siegel by S.-Y. Pan. We certainly want to put modular varieties investigated by Chai and Langlands program within our sight, and Oort, but it also plays an important reduction studies automorphic representations over step in the orignal Siegel situation. This joint number fields as well as function fields. work has been included in as part of Chai s Besides probing on representations theory of ICM 2006 report. classical groups, another goal is to make more The paper [7] by Y.-M. J. Chen and J. Yu use of automorphic representations as tool to concerns arithmetic in characteristic two. It our exploring of function field arithmetic.

39 ‹‹- Highlights of the Programs D.8 Optimizations and related Analysis at NCTS 2004-2007

Coordinator: Soon-Yi Wu (National Cheng Kung University)

Part I Background and Activities in 4. Hankel and Toeplitz operators and their the Program spectral theory. (A) Optimization 5. Degree theory, optimization, and variational problems in infinite dimension.

Local Focus Group ptimization at NCTS is understood in a broad sense, including traditional Soon-Yi Wu (National Cheng Kung optimization theory, mathematical University), Hong Kun Xu (National Sun Yat- programming and operational research. A sen University), Jen-Chih Yao (National Sun regular optimization seminar is run at NCTS, Yat-sen University), Yuen Fong (National including lectures given by visitors to NCTS Cheng Kung University), Mark C. Ho and reports on research results given by (National Sun Yat-sen University), Ying-Fen members of the local focus group. Lin (National Hualien University of Education), Jyh-Shyang Jeang (ROC Military There are short term visitors participating University), Ruey-Lin Sheu (National Cheng in the optimization program since 2004. They Kung University), Chun-Hao Teng (National come for conferences-workshops, and/or for a Cheng Kung University), Chern-Shuh Wang visit up to one month. Among them are the (National Cheng Kung University), Mue-Ming world leading optimization theorists, e.g. Wong (Meiho Institute of Technology), Ngai- M.Fukushima (Japan), T. H. Jongen Ching Wong (National Sun Yat-sen (Netherlands), E. Polak (USA), and Liqun Qi University), and Tsai-Lien Wong (National (Hong Kong). They, as well as the long term Sun Yat-sen University). There are also some visiting scientists, are naturally our consultants postdoctoral fellows actively participating into on developing researches of optimization in our program: Bui Trong Kien (NSC, since Taiwan. 2005), Kenji Kimura (NSC, since 2005), and (B) Analysis D. R. Sahu (NSYSU, since 2007). Among all, the joining of Hong Kun Xu in 2006 is a very The Analysis program covers mainly important event. Xu is famous in functional functional analysis, operator theory, nonlinear analysis and nonlinear analysis. He is an analysis and convex analysis, and their elected member of the Academy of Science of applications. Our major interests include: South Africa. 1. Banach manifolds and Jordan structure theory. Visiting Scientists 2. General theory of operator algebras and (A) Optimization operator spaces. Xiaoqi Yang (Hong Kong Polytechnic 3. General theory of linear preservers, Univ.), Duan Li (Chinese University of Hong composition operators, Jordan Kong), Alex Rubinov (University of Ballarat), homomorphisms and Lie homomorphisms Louis Caccetta (Curtin University), Shengjie on function modules and operator algebras, Li (College of Mathematics and Physics), Jane as well as, general algebras and rings. Ye (Univ. of Victoria), David Gao (Virginia Polytechnic Institute and State Univ.),

Highlights of the Programs -›› 40 Hubertus Th. Jongen (Maastricht University), Conferences and Workshops E. Polak (University of California at (A) Optimization Berkeley), James R. Wilson (North Carolina State Univ.), Xiaojiao Tong (Changsha • Conference on Sino-Japanese Optimization University of Science and Technology), Eric Meeting (SJOM), Aug 27-30, 2008. This K.-W Chu (Monash University), Chen Ling meeting will take place at NCTS, National (Zhejiang University of Finance and Cheng Kung University, Tainan, Taiwan. Economics), S. Gustafson (University of Organizers: M. Fukushima (Kyoto Stavanger), J. J. Rückmann (Universidad de University), S. Y. Wu (National Cheng Kung las Americas), O. Stein (University of University), Liqun Qi (Hong Kong Duisburg-Essen), G. Still (University of Polytechnic University) and J. C. Yao Twente). (National Sun Yat-Sen Univeristy). Plenary speakers: I. Ekeland (University of British (B) Analysis Columbia), T. Y. Li (Michigan State R. T. Rockafellar (Washington), W. University), A. Shapiro (Georgia Institute of Zelazko (Polish Academy), King-Fai Lai Technology), J. Sun (National University of (Syndey), Zhi-Kin Wu (Alabama), G. G. Ding Singapore), K. L. Teo (Curtin University of (Nankai), Chi-Kueng Ng (Nankai), Chi-Wai Technology), L. Qi (Hong Kong Polytechnic Leung (CU Hong Kong), Lu-Chuan Ceng University), M. Fukushima (Kyoto (Shanghai Normal U.), Chi-Kwong Li University), M. Kojima (Tokyo Institute of (William and Mary), Nguyen Dong Yen Technology), S. C. Fang (North Carolina (Vietnam Academy), Jim Jr. Douglas (Purdue), State University), S. Z. Zhang (The Chinese Nan-Jing Huang (Szechwan U.), Denny Lueng University of Hong Kong), Y. X. Yuan (Singapore), Xun-Hua Gong (Nanchang U.), (Chinese Academy of Sciences), Z. Q. Luo Yakov Alber (Israel), Xie-Ping Ding (University of Minnesota) (Szechwan Normal U.) and Genaro Lopez • International Workshop on Semi-Infinite Acedo (Seville). All of them offered either Programming, Aug 24-27, 2005 at NCTS, short courses or seminars on their National Cheng Kung University. specialization in functional analysis, operator Organizers: S. Y. Wu (National Cheng Kung algebras and theory, nonlinear analysis, and University), Marco Lopez (Alicante their applications. Especially, King-Fai Lai University), and Liqun Qi (Hong Kong provided us a month lone short course in Polytechnic University). Plenary speakers: S. Jordan structures and Banach manifolds from Gustafson (University of Stavanger), H. Th. the point of view of a number theorist. This Jongen (RWTH Aachen University), E. gave us, and especially the students, a very Polak (University of California at Berkeley), simulating experience. J. J. Rückmann (Universidad de las Americas), O. Stein (University of Duisburg- Frequent Visitors Essen), G. Still (University of Twente), K. L. (A) Optimization Teo (Curtin University of Technology) and J. S-C Fang (North Carolina State C. Yao (National Sun Yat-Sen University). University), K. L. Teo (Curtin University of • International Workshop on Optimization, Technology), Liqun Qi (Hong Kong May 17-20, 2004 at NCTS, National Cheng Polytechnic Univ.), M. Fukushima (Kyoto Kung University. Organizer: S. Y. Wu University), Macro Lopez (Alicante (National Cheng Kung University). Plenary University), Shunsuke Hayashi (Kyoto speakers: A. M. Bagirov (University of University). Ballarat), L. Caccette (Curtin University of (B) Analysis Technology), S-C Fang (North Carolina State University), D. Li (The Chinese Anthony To-Ming Lau (Alberta). University of Hong Kong), M. Mamedov (Suleyman Demirel University), L. Qi (Hong

41‹‹- Highlights of the Programs Kong Polytechnic University), A. Rubinov various branches of analysis and its (University of Ballarat), K. L. Teo (Curtin applications. University of Technology), Y. H. Wu and X. • In April 3-7, 2006, we held the international Yang (Hong Kong Polytechnic University). Workshop on Jordan Structures in Analysis (B) Analysis and Geometry. This was an important event in functional analysis and operator algebras. • In October and December 2005, we held two The list of invited speakers from aboard workshops in functional analysis and included C-H. Chu (London), C. M. Edwards operator theory. One of them was held at (Oxford), Y. Friedman (Jerusalem), R. National Dong Hwa University in Hualien. Iordanescu (Bucharest), J. M. Isidro The theme of them emphasized on (Santiago), W. Kaup (Tübingen), C. W. promoting new research problems and Leung (Hong Kong), M. Mackey (Dublin), encouraging fresh PhD's and graduate M. Neal (Denison), C. K. Ng (China), T. students to join the activities. Nomura (Kyushu), A. M. Peralta (Granada), • In December 25-28, 2004, we organized the L. Stacho (Szeged), H. Upmeier (Marburg), NCTS Workshop in Functional Analysis at and B. Zalar (Maribor). There were also a NSYSU and NCKU. The main speakers number of talks given by local analysts. were Liming Ge (New Hamspire, USA) and Ka-Sing Lau (Hong Kong). Other speakers Exchange Programs and International included Chi-Wai Leung (Hong Kong), Cooperations Bingren Li (China), Jin Liang (China), Jinchuan Hou (China), G. G. Ding (China), (A) Optimization Chi-Kueng Ng (China), Ti-Jun Xiao (China) Prof. R. L. Sheu was invited by Prof. S. C. and Ryotaro Sato (Okayama, Japan). The Fang to visit Department of Industrial papers presented in the Workshop were Engineering and Operations Research Program included in a special issue of Taiwanese J. at North Carolina State University from Math. The Chinese colleagues were very September 25 to November 30, 2004. Prof. S. interested in this activity. In 2005 and 2006, Y. Wu was invited by Prof. K. L. Teo to visit they continued the series in Chengdu by Department of Applied Mathematicas, Hong Chinese Academy of Science, and in Kong Polytechnic University from November Huangshan by the Chinese University of 18 to November 21, 2004. Prof. S. Y. Wu was Science and Technology. Each of them invited by Prof. Liqun Qi to visit Department attracted more than 300 participants, and of Applied Mathematics, Hong Kong some of us were invited as the main guests Polytechnic University from January 28 to and steering committee members. February 1, 2005 and April 13 to April 19, • A biweekly seminar series on functional 2006. Prof. S. Y. Wu was invited by Prof. Jane analysis was held in National Sun Yat-sen Ye to visit Victoria University, Canada for University in 2005 and 2006. Graduate research collaboration from May 13 to May students were invited to speak in the 22, 2005. Prof. C. S. Wang was an invited talk seminars. Postdoctoral fellows and young to attendant Sixth International Workshop on researchers were also welcome. Talks given Accurate Solution of Eigenvalue Problems in by Jyh-Shyang Jeang were on on local U.S.A from May 20-27, 2006. Prof. S. Y. Wu automorphisms and local derivations on was an invited talk in Euro XXI Operation operator algebras. Chin-Cheng Lin also Research Conference in Iceland from June 1-6, gave a talk on boundedness of the 2006. Prof. R. L. Sheu was invited by Prof. S. Marcinkiewicz integral. C. Fang to visit Tsing Hua University at • In October 21-23, 2005, we held the 6th Beijing, China from June 1-6, 2006. Taiwan-Philippine Symposium on Analysis Optimization Research group of National at NSYSU. About 20 Philippines analysts Center of Theoretical Sciences have an joined us to explore in new advances in contract with the optimization center of Hong Kong polytechnic University with

Highlights of the Programs -›› 42 collaboration research. Prof. S. Y. Wu was and the Hankel operators in $\mathcal invited by Prof. E. Polak to visit Department S_\pi$, Indiana University Math. Journal, of Electrical Engineering, Berkerly University 55, no. 5, 1646-1669. in USA from March 11 to March 15, 2006 for [7] Wen-Fong Ke, Bing-Ren Li and Ngai- research collaboration. Ching Wong (2004), Zero product preserving maps of continuous operator Student's Seminars and Schools valued functions, Proc. Amer. Math. Soc., (A) Optimization 132, 1979-1985. C. S. Wang: A biweekly seminar series on [8] G. Marino and H.K. Xu (2007), Weak and optimal control: theory and computation was strong convergence theorems for strict held in NCTS, National Cheng Kung pseudo-contractions in Hilbert Spaces, J. University in 2005 and 2006. Graduate Math. Anal. Appl., 329, 336-346. students and young researchers were invited to attend the seminar. [9] G. S. Wei, H.K. Xu, and Z.B. Xu, Left- definite spaces of singular Sturm-Liouville problems, Journal of Differential Equations. (Accepted for publication in Part II The Accomplished and the January 2006.) Anticipations [10] Ngai-Ching Wong, The triangle of [1] Z. L. Wu and S. Y. Wu (2004), Weak Sharp operators, topologies and bornologies, in Solutions of Variational Inequalities in the Proceedings of the 3rd International Hilbert Spaces, SIAM Journal on Congress of Chinese Mathematicans, Optimization, Vol. 14, 1011-1027. AMS-IP, to appear. (NSYSU) [2] S. J. Li, S. Y. Wu, X. Q. Yang and K. L. (A) Optimization Teo (2006), A Relaxed Cutting Plane Method for Semi-Infinite Semi-definite The special issue for International Programming, Journal of Computational Workshop on Semi-Infinite programming will and Applied Mathematics,Vol.196, 459- be published by Journal of Computational and 473. Applied Mathematics in 2007. This special issue contained 11 papers by international [3] Z. L. Wu and S. Y. Wu (2006), professors. In the direction of Infinite Characterizations of the Solution Sets of programming, the exchange explicit method Convex Programs and Variational was developed by S. Y. Wu, have been made a Inequality Problems, Journal of very important algorithm for semi-infinite and Optimization Theory and infinite programming problems. The Application,Vol.130, 341-360. implementation of the exchange explicit [4] S. C. Fang, S. Y. Wu and S. I. Birbil, method for Infinite programming is very (2006) Solving Variational Inequalities powerful by compare it with the routine in Defined on A Domain with Infinitely MATLAB. For the infinite programming in Lp Many Linear Constraints, Computational space and measure space, we have developed Optimization and Applications, Vol. 37, algorithms for it. The implementation of 67-81. algorithms is very well. Since many algorithms and theoretical work has been done [5] L. C. Ceng and J. C. Yao (2007), in semi-infinite and infinite programming by Approximate proximal methods in vector S. Y. Wu, a research book in infinite optimization, European Journal of programming is prepared coauthors by S. Y. Operational Research, to appear. Wu, M. Lopez, and L. P. Zhang. The research [6] M. C. Ho and M. M. Wong (2006), book will published by Springer. This will be Applications of the theory of s. n. functions an important achievement in the area of to the duality of analytic function spaces infinite programming.

43 ‹‹- Highlights of the Programs (B) Analysis theory of operator ideals on locally convex spaces starting from his 1988 paper published In operator algebras and function algebras, in Math. Ann. characterizing multiplicative maps among linear maps is a classical problem. In his Mark C. Ho has been working on Hankel seminal paper, Kadison [1951, Ann. Math.] operators for several years. The paper [6] is extended the classical Banach-Stone Theorem some new break through of him in this subject. to show that every surjective isometry between Hong Kun Xu joined us in 2006. He has C*-algebras is a Jordan isomorphism followed published many papers in functional analysis, by a multiplication of unitary. Moreover, its fixed point theory and nonlinear analysis. One by-dual map is the sum of an automorphism of his early papers was awarded by ISI as the and an antiautomorphism between W*- most highly cited paper in Mathematics. algebras. Ngai-Ching Wong extended this to Beside [8], the paper [9] is his attempt to apply the non-surjective case in 2004, and to other his technique to differential equations. Jen- cases including JB*-triples and various Chih Yao is very productive recently and function algebras subsequently. He is also an publishes many papers a year. The paper [5] is invited 45-minute speaker in the ICCM2004. one of them, which is sample of his elegance, The paper [10] in the Proceedings of and expected to be significant. ICCM2004 concludes his 20 year works in the

Highlights of the Programs -›› 44 D.9 Partial Differential Equations at NCTS 2004-2007

Coordinator: Jong-Shenq Guo (National Taiwan Normal University), Tai-Chia Lin (National Taiwan University) Chun-Kong Law (National Sun Yat-sen University), Chiun-Chuan Chen (National Taiwan University)

Part I: Background and Activities in Visitors in 2004-2007 the Program Qing Han (University of Notre Dame), Yenheng Ding ( Academia Sinica, Beijing), Sergei Kuznetsov (University of Colorado at onlinear PDE at NCTS is a very broad Boulder), Horng-Tzer Yau (Harvard field. It covers not only theory of University), Mimura Masayasu (Meiji different types of PDE, but is also close related University), Yisong Yang (Polytechnic to applied sciences and other fields of University), Peter Polacik (University of mathematics such as geometric analysis and Minnesota), Tai-Peng Tsai (University of dynamical systems. The activities in the British Columbia), Xinfu Chen (University of program include regular PDE seminars, Pittsburgh), Hongjun Yu (South China courses, workshops/conferences, and University of Technology), Jiahong international cooperation. Wu(Oklahoma State University), Boyan Sirakov (The University of Paris 10), Renjun There have been more than 70 foreign Duan (City University of Hong Kong), David visitors and a lot of local people participating Kinderlehrer (USA), Eiji Yanagida (Japan), in the PDE program since 2004. Many of the Ken-Ichi Nakamura (Josai University), visitors not only come for Vladimir Sharafutdin (Russia), Toshiko conferences/workshops, but also have joined Ogiwara (Japan), Vladimir Zykov (Germany), research projects with members of the local Marek Fila (Slovakia), Hirokazu Ninomiya focus group. For a report in this respect, see (Japan), Daishin Ueyama (Japan), Jame Sneyd Part II. (New Zealand), Noriko Mizoguchi (Japan), The PDE group in Taiwan has strong Peter Polacik (USA), Bei Hu(University of connection with the PDE people in Japan and Notre Dame), Dongho Chae (Korea), Yuan France. A few joint conferences with people Lou (USA), Dimitrios Tzanetis (Greece), mainly from these two countries have been Nikos Kavallaris (Greece), Bernard Brighi held in recent years. We believe many other (France), Hiroshi Matano (Japan), Francois similar conferences and research projects will Hamel (University of Aix-Marseille be follow up continuously in the near future. III,France), Sun-Yung Alice Chang (Princeton University), Paul Yang (Princeton University), Local Focus Group Gabriella Tarantello (Università di Roma Tor Jong-Shenq Guo (NTNU), I-Liang Chern Vergata), Joel Spruck (Johns Hopkins (NTU), Chang-Shou Lin (NTU), Chiun-Chuan University), Bogdan Bojarski (Polish Chen (NTU), Tai-Chia Lin (NTU), Jenn-Nan Academy of Sciences), M. Chipot (Zurich, Wang (NTU), Chun-Chi Lin (NTNU), Huey- Swiss), Y. Giga (Tokyo, Japan), N. Kenmochi Er Lin (NTNU), Jenn-Long Chern (NCU), Je- (Chiba, Japan), W.-M. Ni (Minneapolis, USA), Chiang Tsai (CCU), Sheng-Chen Fu (NCCU), M. Otani (Waseda, Japan), K. Sakamoto Mao-Sheng Chang (Fujen U), Chung-Tsun (Hiroshima U.), Z. Xin (Chinese U. of Hong Shieh (Tamkang U), Dong-Ho Tsai (NTHU), Kong), Shih-Hsien Yu (City U. Hong Kong), Chi-Kun Lin (NCTU), Chao-Nien Chen Yoshitsugu Kabeya (Prefecture U), Jyotshana (NCUE), Chun-Kong Law (NSYSU) V. Prajapat (Fundamental Research), Der-Chen Chang (Georgetown University), Ovidiu Calin

45 ‹‹- Highlights of the Programs (Eastern Michigan University), Augusto Ponce Vladmir Romanov (Institute of Mathematics (University of Tours, France), Chun Liu (Penn at Novosibirsk) discussed stability estimates State University), Guofang Wang (Germany), of one-dimensional and multi-dimensional Mu-Tao Wang (U of Columbia), Yung-Sze wave equations, as well as integral geometry Choi (University of Connecticut), Tao Lu (only two-dimensional case for simplicity). (Szechuen University), Min Mei (University of • A priori estimates in elliptic equations and Concordia), V. Pivovarchik (South-Ukrainian related topics, July-August 2005, organized State Pedgagogical Univerity), V.G. Romanov by Jong-Shenq Guo and Chiun-Chuan Chen: (Institute of Mathematics at Novosibirsk), This was a 6-week summer program for Juncheng Wei (Chinese University of Hong graduate students. The first part covered the Kong), V. Yurko (Saratov State University), maximum principle, Schauder estimates, Jun Zou (Chinese University of Hong Kong). regularity theory of elliptic equations. This part was given by Jong-Shenq Guo, Sheng- Courses in 2004-2007 Chen Fu and Je-Chiang Tsai. The second • Topics in PDEs and Calculus of part, given by Tai-Chia Lin and Chiun- Variations, March-June, 2007. Lecturer: Chuan Chen, aimed at applications of the Xiaofeng Ren (Utah State U). The course elliptic theory to several nonlinear equations aimed at the rigorous study of singularly perturbed problems and variational problems • Mini-course in Nonlinear stability of with non-locality. Models considered in this reaction diffusion equations, May, 2005, lecture included the Allen-Cahn problem in organized by Chi-Kun Lin. The 8-hour short phase transition, the Cahn-Hilliard problem course was delivered by Ming Mei for binary alloys, the Ginzburg-Landau (Concordia University). It contains a detailed problem for superconductors, charged analysis of the stability of traveling wave Langumir monolayers, chiral liquid crystals, solutions for a model of reaction diffusion and most famously block copolymers. equation with delay. This model came from biology, the blowfly problem in Australia. • Basic theory of ODEs and its applications, July-August, 2006, organized by Jong-Shenq • Mini-course in Dimension Analysis and Guo: This was a 6-week summer program Differential Equations, April-May 2005, for senior undergraduate students. Students organized by Chun-Kong Law. This is a 12- in any level are welcome to attend. There hour short course delivered by Chi-Kun Lin were about 15 students from sophomore to (Cheng-Kung University) In this course the Ph.D. program. Basic theory in ODE was concept of dimensional analysis was introduced first and then some applications introduced and applied to study the to special solutions (such as steady state, differential equations. In particular, we self-similar solution, traveling wave solution, focussed on the Riesz potential, Hardy- etc.) of some PDE problems were given. Littlewood-Sobolev inequality, and the related Sobolev type inequalities which are • Summer Courses on PDE in important in differential equations. The Mathematical Physics, July 10-31, 2006, method of dimensional analysis was also organized by Yng-Ing Lee and Chiun-Chuan used to give an intuitive idea about the Chen. This course covered two topics PDE fundamental solutions of the differential and submanifolds in general relativity, given equations. by Mu-Tao Wang, and regularity problem for • Short Course on Integral Geometry, the Navier-Stokes equations, given by Tai- January 17-26, 2005, organized by Jenn-Nan Peng Tsai. Wang. Nine lectures were given by Vladimir • Mini-course on Stability estimates related Sharafutdin. The course started from the to inverse problems for hyperbolic boundary rigidity problem: how far is a equations, April, 2006, organized by Chun- Riemannian metric on a compact manifold Kong Law. In the 6-hour minicourse, with boundary determined by distances

Highlights of the Programs -›› 46 between boundary points? After students in the Tainan-Kaohsiung area. linearization, this gives the integral geometry problem: to which extent is a symmetric Conferences and Workshops tensor field on a Riemannian manifold • NCTS 10 Years Anniversary Mini- determined by its integrals over geodesics Workshop on PDE July 23, 2007 at NTU. joining boundary points? The latter question Organizers: Chiun-Chuan Chen and Tai-Chia is equivalent to an inverse problem for the Lin. kinetic equation on the unit tangent bundle. • Speakers: Hung-Chi Kuo (Dept. of To treat the kinetic equation, some tensor Atmospheric Sciences, NTU), Chun-Hsiung analysis machinery based on the structure of Hsia (U. of Illinois at Chicago), Horng-Tzer the tangent bundle was developed. Yau (Harvard U.) Corresponding periodic integral geometry • Workshop on Reaction-Diffusion: Theory problems for closed Riemannian manifolds and Applications December 1-2, 2006 at was discussed also. These problems are NTNU. Organizers: Jong-Shenq Guo and closely related to the spectral rigidity Chiun-Chuan Chen. problem and need the technique of Anosov • Speakers: Masayasu Mimura (Meiji U.), flows. Jong-Shenq Guo (National Taiwan Normal • Mini-course Course in Hamiltonian U.) Sze-Bi Hsu (National Tsing Hua U.) Sytems and Its Quantization, January 31- Shin-Ichiro Ei (Kyushu U.) Yoshikazu February 3, 2005. Shao-Shiung Lin (NTU) Tateishi (Kyushu U.) Yoshitsugu Kabeya gave three lectures. The contents included: (Perfecture U.) She-Feng Hsieh (National (1) Newton's equations and the Hamilton Taiwan Normal U.) Huey-Er Lin (National formulation, symmetry and the complete Taiwan Normal U.) Satoshi Sasayama integrability; (2) The KAM theory, and the (National Taiwan Normal U.) Tatsuyuki transition to chaos; (3) Quantization, Nakaki (Hiroshima U.), Toshi Ogawa (Osaka Eninstein-Bohr-Summerfield quantization U.), Li-Chang Hung (National Taiwan U.), conditions, and the quantum chaos. The Chiun-Chuan Chen (National Taiwan U.), Je- lectures were given in the morning and the Chiang Tsai (National Chung Cheng U.), students participated discussion sessions in Yuzo Hosono (Kyoto Sangyo U.), Tai-Chia the afternoon. Lin (National Taiwan U.) • Symmetry Methods and Their • Workshop on Partial Differential Applications, September, 2004 - January, Equations November 27, 2006 at NTU. 2005, organized by C.-P. Lo (Providence Organizers: Chiun-Chuan Chen. University). The lecturers were L. Wen • Speakers: David Kinderlehrer (Carnegie (Peking U and Providence U), S.-S. Lin Mellon University), Yoshitsugu Kabeya ( (NTU) C.-C. Chen (NTU), C.-P. Lo Osaka Prefecture U), Jyotshana V. Prajapat (Providence U). This course covered the (Tata Institute), Mitsuharu Otani ( Waseda topics (1) Lie group (2) symmetry breaking U), Michel Chipot ( U of Zurich) in biological systems (3) moving planes • International Conference on Nonlinear method. Analysis November 20-25, 2006 at NCTS. • Mini-course in Harmonic Analysis and Its • Organizing Committee: C.-C. Chen (Taipei, Applications, April-June, 2004, organized Taiwan), M. Chipot (Zurich, Swiss), P.G. by Chi-Kun Lin. This 24-hour short course Ciarlet (Hong Kong, China), J.-S. Guo was composed of two topics: basic theory of (Taipei, Taiwan), N. Kenmochi (Chiba, harmomic analysis and its application to the Japan), C.-S. Lin (Chai-Yi, Taiwan), X. Pan Dirac-Klein-Gorden equations. The talks (Shanghai, China), D.-H. Tsai (Hsinchu, were delivered by Chin-Cheng Lin (National Taiwan), Z. Xin (Hong Kong, China), E. Central University) and Yung-Fu Fong Yanagida (Sendai, Japan) (National Cheng Kung University). The • Scientific Committee: Y. Giga (Tokyo, participants included related researchers and Japan), C.-S. Lin (Chai-Yi, Taiwan), W.-M.

47 ‹‹- Highlights of the Programs Ni (Minneapolis, USA) National U.), Noriko Mizoguchi (Tokyo • Speakers: Bogdan Bojarski (Polish Academy Gakugei U.), Tai-Chia Lin (National Taiwan of Sciences), Dong-Ho Chae (Korea), Jann- U.) Long Chern (Jhongli, Taiwan), M. Chipot • Prospects of Mathematical Biosciences (Zurich, Swiss), P.G. Ciarlet (Hong Kong, December 12-17, 2005 at NTNU. Organizer: China), Y. Giga (Tokyo, Japan), J.-S. Guo Jong-Shenq Guo. Speakers: Avner Friedman (Taipei, Taiwan), N. Kenmochi (Chiba, (MBI, Ohio State U.) Japan), D. Kinderlehrer (Pittsburgh, USA), • Workshop on Nonlinear PDE and Particle Tai-Chia Lin (Taipei, Taiwan), Tai-Ping Liu Systems July 5, 2005 at NTU. Organizers: (Academia Sinica, Taiwan ), Y. Morita Chiun-Chuan Chen. Speakers: Tai-Peng Tsai (Ryukoku, Japan), W.-M. Ni (Minneapolis, (U. of British Columbia), Horng-Tzer Yau USA), M. Otani (Tokyo, Japan), M. (Stanford University). Ramaswany (Bangalore, India), K. Sakamoto (Hiroshima, Japan), I. Shafrir • Workshop in Inverse Problems April, (Haifa, Israel), S. Ukai (Hong Kong, China), 2005 at NSYSU. Organizer: Chun-Kong J. Wei (Hong Kong, China), Z. Xin (Hong Law. Speakers: Ming Jiang (Peking U.), Kong, China), E. Yanagida (Sendai, Japan), Chin-Lung Lin (Chung-Cheng U.), Chun- Shih-Hsien Yu (Hong Kong, China), Tatsuki Kong Law (Sun Yat-sen U.). Kawakami (Tohoku U), Kota Ikeda (Tohoku • Workshop on Computer-Aided Analysis U) , Shota Sato (Tohoku U), Yoshitsugu and Reaction-Diffusion Systems Kabeya (Prefecture U), Jyotshana V. Prajapat September 13-14, 2005 at NTNU. Organizer: (Fundamental Research), Makoto Narita Jong-Shenq Guo. Speakers: Masayasu (National Taiwan U), Yong-Hoon Lee (Pusan Mimura (Meiji U.), Daishin Ueyama National U), Inbo Sim (Pusan National U), (Hiroshima U.), Yoshio Yamada (Waseda Tetsuya Ishiwata (Gifu U), Kimie U.), Mau-Hsiang Shih (National Taiwan Nakashima (Technology), Jongmin Han Normal U.), Shih-Feng Shieh (National (Hankuk U of Foreign Studies), Jihoon Lee Tsing Hua U.), Chiun-Chuan Chen (National (Sungkyunkwan U), Akira Yanagiya Taiwan U.) (Waseda U), Yoshidazu Kobayashi (Chuo • France-Taiwan Joint Conference on U), Noriaki Yamazaki (Muroran Institute of Nonlinear PDEs and Related Topics July Technology), Ken Shirakawa (Kobe U), 18-22, 2005 at NYU. Organizers: Chiun- Toyohiko Aiki (Gifu U), Takesi Fukao (Gifu Chuan Chen, Thierry Gallay, Jong-Shenq National College of Technology), Yusuke Guo (coordinator), Franc cois Hamel, Tai- Murase (Chiba U) Chia Lin and Lih-Chung Wang. • NCTS Workshop on Harmonic Analysis • Speakers: Fabrice Bethuel (Universite Paris and Schrodinger Equations, July 11-12, VI & IUF), Chiun-Chuan Chen (National 2006 at NTU. Organizers: Chiun-Chuan Taiwan U.), Kuo-Chang Chen (National Chen and Horng-Tzer Yau. Tsing Hua U.), Alain Chenciner (IMCCE & • Speakers: Horng-Tzer Yau (Harvard U.), Universite Paris VII), Olivier Druet (Ecole Der-Chen Chang (Georgetown U.), Chi-Kun Normale Superieure de Lyon), Maria J. Lin (National Cheng Kung U.), Yung-Fu Esteban (Universite Paris-Dauphine), Fang (National Cheng Kung U.), Tai-Peng Thierry Gallay (Universite Joseph Fourier Tsai (U. of British Columbia), Ovidiu Calin Grenoble I), Jong-Shenq Guo (National (Eastern Michigan U.) Taiwan Normal U.), Francois Hamel • Workshop on Asymptotic Analysis (Universite Paul Cezanne Aix-Marseille III), December 13, 2005 at NTNU. Organizer: Cheng-Hsiung Hsu (National Central U.), Jong-Shenq Guo. Sze-Bi Hsu (National Tsing Hua U.), Chang- • Speakers: Avner Friedman (MBI, Ohio State Shou Lin (National Chung Cheng U.), Chun- U.), Jong-Shenq Guo (National Taiwan Chi Lin (National Taiwan Normal U.), Tai- Normal U.), Minkyu Kwak (Chonnam Chia Lin (National Taiwan U.),Tai-Ping Liu (Academia Sinica, Taiwan), Yvan Martel

Highlights of the Programs -›› 48 (Universite de Versailles-Saint-Quentin-en- Bochum), Liliana Gratie (City U. of Hong Yvelines), Nikolai Nadirashvili (CNRS, Kong), Patrick Guidotti (U. of California at LATP), Michel Pierre (ENS Cachan, Irvine), Jong-Shenq Guo (National Taiwan Antenne de Bretagne), Jean-Michel Normal U.), Jongmin Han (Hankuk U. of Roquejoffre (Universite Paul Sabatier Foreign Studies), David Kinderlehrer Toulouse III & IUF), Jean-Claude Saut (Carnegie Mellon), Chun-Chi Lin (National (Universite Paris-Sud), Dong-Ho Tsai Taiwan Normal U.), Tai-Chia Lin (National (National Tsing Hua U.), Je-Chiang Tsai Chung Cheng U.), Stephan Luckhaus (National Taiwan Ocean U.), Laurent Veron (Universität Leipzig), Alessandra Lunardi (Universite de Tours), Jenn-Nan Wang (Università di Parma), Monica Musso (National Taiwan U.), Frederic Weissler (Politecnico di Torino) Frank Pacard (Paris (Universite Paris 13) 12), Mariarosaria Padula (Università di • Workshop on Reaction-Diffusion Ferrara), Jyotshana Prajapat (Indian Equations and Related Topics May 26-31, Statistical Institute), Pavol Quittner 2004 at NCTS. Organizers: Chang-Shou Lin, (Comenius U.), José Francisco Rodrigues Eiji Yanagida and Chiun-Chuan Chen. (U. of Lisbon), Pavel E. Sobolevskii • Speakers: Chao-Nien Chen (Changhua U. of (Hebrew U. of Jerusalem), Vsevolod Education), Chiun-Chuan Chen (National Solonnikov (Università di Ferrara), Gabriella Taiwan U.), Jann-Long Chern (National Tarantello (Roma Tor Vergata), Eiji Yanagida Central U.), Shin-Ichiro Ei (Kyushu U.), (Tohoku U.) Jong-Shenq Guo (National Taiwan Normal U.), Qing Han (U. of Notre Dame), Sze-Bi Hsu (National Tsing Hua U.), Kazuhiro Part II: The Accomplished and the Ishige (Tohoku U.) Yoshitsugu Kabeya Anticipations (Miyazaki U.), Chun-Kong Law (National Selected publications of the local focus Sun Yat-sen U.), Chang-Shou Lin (National group since 2004 : Chung Cheng U.), Tai-Chia Lin (National Chung Cheng U.), Yuki Naito (Kobe U.), [1] Xinfu Chen and Jong-Shenq Guo, Self- Hirokazu Ninomiya (Ryukoku U.), Toshi similar solutions of a 2-D multiple phase Ogawa (Osaka U.), Tetsutaro Shibata curvature flow, Physica D, 229 (2007) 22- (Hiroshima U.), Yoshie Sugiyama (Tsuda 34. College), Izumi Takagi (Tohoku U.), Shingo [2] Jong-Shenq Guo and Bei Hu, Blowup rate Takeuchi (Kogakuin U.), Masaharu estimates for the heat equation with a Taniguchi (Tokyo Institute of Technology), nonlinear gradient source term, to appear in Dong-Ho Tsai (National Tsing Hua U.), Eiji Discrete and Continuous Dynamical Yanagida (Tohoku U.), Paul Yang (Princeton Systems. U.), Yisong Yang (Polytechnic U.),Shoji Yotsutani (Ryukoku U.) [3] Xinfu Chen, Jong-Shenq Guo, Francois Hamel, Hirokazu Ninomiya, and Jean- International Conference on Elliptic and • Michel Roquejoffre, Traveling waves with Parabolic Problems - Recent Advances paraboloid like interfaces for balanced February 16-20, 2004 at NCTS. Organizers: bistable dynamics, Annales de l'Institut Chang-Shou Lin, Michel Chipot and Chiun- Henri Poincar\'e - Analyse Non Lin\'eaire} Chuan Chen. 24 (2007), 369-393. • Speakers: Herbert Amann (Universität Zürich), Henri Berestycki (EHESS Paris), [4] S.M. Chang, C.S. Lin, T.C. Lin, W.W. Lin, Fabrice Bethuel (Paris 6), Dongho Chae Segregated nodal domains of two- (Seoul National U.), Jann-Long Chern dimensional multispecies Bose-Einstein (National Central U.), Manuel Del Pino (U. condensates, Physica D 196(2004) no.3-4, of Chile), Pierpaolo Esposito (Roma Tor pp. 341-361. Vergata), Brice Franke (Ruhr Universitaet [5] Tai-Chia Lin, Juncheng Wei, Spikes in two

49 ‹‹- Highlights of the Programs coupled nonlinear Schrodinger equations, [15] Chang-Shou Lin, Augusto C. Ponce, Annales de L'institut Henri Poincare, Yisong Yang, A system of elliptic Analyse non lineaire-nonlinear analysis, 22 equations arising in Chern-Simons field (2005) 403-439 theory, Journal of Functional Analysis 247 (2007) 289-350. [6] Tai-Chia Lin, Juncheng Wei, Ground state of N. coupled nonlinear Schrödinger [16] Chang-Shou Lin, Pengfei Guan, Guofang equations in, Rn,n≤3, Comm. Math. Phys. Wang, Local Gradient Estimates for 255 (2005) 629-653. Quotient Equations in Conformal Geometry, to appear in International [7] Tai-Chia Lin, Juncheng Wei, Symbiotic Journal of Mathematics (2007) bright solitary wave solutions of coupled nonlinear Schrödinger equations, [17] Mikko Salo and Jenn-Nan Wang, Nonlinearity 19(2006)2755-2773. Complex spherical waves and inverse problems in unbounded domains, Inverse [8] Lin, Tai-Chia; Zhang, Ping Incompressible Problems, Vol 22 (2006), 2299-2309. and compressible limits of coupled systems of nonlinear Schrödinger equations. [18] Horst Heck, Gunther Uhlmann, and Jenn- Comm. Math. Phys. 266 (2006), no. 2, Nan Wang, Reconstruction of obstacles 547-569 immersed in an incompressible fluid, Inverse Problems and Imaging, Vol. 1 [9] T.-L. Horng, S.-C. Gou, and T.-C. Lin, (2007), 63-76. Bending-wave instability of a vortex ring in a trapped Bose-Einstein condensate, [19] Gunther Uhlmann and Jenn-Nan Wang, Phys. Rev. A 74, 041603(1-4) (2006) Complex spherical waves for the elasticity system and probing of [10] Chen, C.-C., Lin, C.-S. and Wang, G., inclusions, SIAM J. Math. Anal., Vol 38 Concentration phenomena of two-vortex (2007), 1967-1980. solutions in a Chern-Simons model., Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3, no. 2 [20] Ching-Lung Lin, Gen Nakamura, and (2004), 367-397 Jenn-Nan Wang, Three spheres inequalities for a two-dimensional elliptic [11] Bartolucci, Daniele, Chen, C.-C., Lin, system and its application, J. Differential Chang-Shou and Tarantello, Gabriella, Equations, Vol 232 (2007), 329-351. Profile of blow-up solutions to mean field equations with singular data., Comm. In [1], X. Chen and J.-S. Guo studied self- Partial Differential Equations 29, no. 7-8 similar shrinking, stationary, and expanding (2004), 1241-1265. solutions of a two-dimensional motion by curvature equation modeling evolution of [12] Chen, C.-C., Chen, I-K., Liu, T.-P. and grain boundaries in poly-crystals. Here the Sone, Y., Thermal Transpiration for interfacial energy densities were assumed to Linearized Boltzmann Equation, Comm. depend only on the grains and the Herring Pure Appl. Math 60, no 2 (2007), 147-163 condition was used for triple junctions (the [13] Han, Qing; Hong, Jia-Xing; Lin, Chang- intersections of three grain boundaries). In Shou On the Cauchy problem of particular, in the isotropic case, a total of six degenerate hyperbolic equations. Trans. configurations were classified as the only self- Amer. Math. Soc. 358 (2006), no. 9, similar shrinking solutions. 4021-4044 (electronic). In [2], J.-S. Guo and B. Hu studied an [14] Jost, J"urgen; Lin, Changshou; Wang, initial boundary value problem for the heat Guofang, Analytic aspects of the Toda equation with a nonlinear gradient source system. II. Bubbling behavior and term. It was shown that the blowup rate will existence of solutions, Comm. Pure Appl. never match that of the self-similar variables. Math. 59 (2006), no. 4, 526-558 In the one space dimensional case with assumptions on the initial data so that the

Highlights of the Programs -›› 50 solution is monotonically increasing in time, consider degenerate case in [10] and singular the exact blowup rate is found. source case in [11]. In [3], X. Chen, J.-S. Guo, F. Hamel, H. In [12], C. C. Chen, I. K. Chen, T. P. Liu Ninomiya, and Jean-Michel Roquejoffre and Y. Sone studied the flow of thermal constructed cylindrically symmetric traveling transpiration induced by the gradient of the waves with paraboloid like interfaces for wall temperature. This interesting flow cannot reaction-diffusion equations with balanced be explained at the level of the Navier-Stokes bistable nonlinearities. The main interest is equations. It has been known since the time of about solutions having interfaces that travel Maxwell, but its mathematical formulation on upwards in the vertical direction with a the basis of kinetic equations was done only in constant speed. In particular, an answer to the the 1960s. They have constructed a steady De Giorgi conjecture in parabolic version is state flow of this phenomenon for the given. linearized Boltzmann equation and been successful to explain it at a rigorous level of The above three works are international mathematics. cooperation under the support of NCTS, which In [15], C. S. Lin, A. C. Ponce, and Y. Yang are acknowledged in these papers. proved the existence of topological vortices in Separation on systems of nonlinear a relativistic self-dual Abelian Chern-Simons Schrödinger equations (SNLS) (cf. [4]) is a theory with two Higgs particles and two gauge joint work of the focus group of NTU and fields through a study of a coupled system of NTHU. C.S.Lin and T.C.Lin (NTU) analyzed two nonlinear elliptic equations over the entire the problem; S.M.Chang and W.W.Lin plane. (NTHU) simulated the problem numerically. In [16], C. S. Lin, P. Guan and G. Wang Spike solutions of coupled nonlinear extended the local gradient estimates to the Schrödinger equations (eg. [5]-[7]) is an conformal quotient equations. An existence of international cooperation of Taipei and solutions of the conformal quotient equations HongKong. Under the support of NCTS, follows from the local gradient estimates in T.C.Lin (NTU) and J.Wei (CUHK) have this paper and the paper of Gursky and published a series of papers recently. Viaclovsky. Compressible and incompressible limits The stability of the inverse problem is an of SNLS (cf. [8]) is an international important issue since most inverse problems cooperation of Taipei and Beijing. Due to are notoriously ill-posed. A log type estimate NCTS supports, T.C.Lin (NTU) and P.Zhang was already known for the inverse (CAS) have more chance to work together. conductivity problem with full data. In [18], J. N. Wang with H. Heck and G. Uhlmann Bending-wave instability of Vortex ring successfully derived a log-log type estimate dynamics in Bose-Einstein condensates (cf. for the inverse conductivity problem with [9]) is a cross-disciplinary work accomplished partial data. by a domestic physicist (S.C.Gou) and two The theoretical aspect of the inverse nodal mathematicians. Such a work can be regarded as a successful cooperation of physicists and problem is now well-studied. Uniqueness, mathematicians in recent three years. reconstruction and stability issues are solved. X. Chen, Y.H. Cheng and C.K. Law try to Recently, a lot of work has been devoted to approximate the potential function with just a Liouville type equation which arises from prescribing curvature problem, Euler flows, one measurement of the nodal data. They Chern-Simon-Higgs model and chemotaxis propose three methods for the reconstruction, model. In two papers (published in CPAM, one of which is the Tikhonov regularization 2003), C. C. Chen and C. S. Lin obtained a method. All the three reconstructions in formula of the Leray-Schauder degree for this preprint approximate the exact potential at an equation. They continued their work to order of 1/n.

51 ‹‹- Highlights of the Programs D.10 Probability Theory at NCTS 2004-2007

Coordinator: Yuan-Chung Sheu (National Chiao Tung University)

Part I: Background and Activities in Symposium on Network Biology the Program This symposium was token place on Friday, November 11, 2005. We aim to stimulate the interaction of probability theory with biology, he wealth of complex genetic data communication and related scientific from human and other genome applications. There were about one hundred projects has lead to the need for new twenty participants. Organizers: M.C.Huang probability models to understand both the (AC), C.C.Lu (NTHU), H.H.S.Lu (NCTU), structure of the data and the laws(if they exist) Y.C.Sheu (NCTU), W.H.Lee (AC). Speakers: that govern biological systems. Also in the C.-H Yuh (National Health Research Institute), financial markets, the application of B.-S Chen (EE, NTHU), C.-P Hsu (Institute of probability has revolutionized the industry. In Chemistry, Academia Sinica), W. V. Ng NCTS, we focus on probability theory with (Department of Biotechnology and Laboratory applications to finance and biology. We also Science in Medicine, National Yang Ming study convergence to equilibrium for ergodic University), K.-L Ng (Department of Markov processes. We report briefly our Biotechnology and Bioinformatics, Asia activities on probability theory during the past University), H.-C Huang (Institute of five years. Bioinformatics, National Yang-Ming University), W.C. Liu (Institute of Biomedical Local Focus Group Sciences, Academia Sinica), C. Y. Lin Bor-Sen,Chen (EE, NTHU), Guan-Yu Chen (National Health Research Institutes) (NCTS, NCTU), Chuan-Hsiang Han (QF, NTHU), Wen-Ping Hsieh (IS, NTHU),Chung- Special Topics in 2004-2007 Chin Lu (EE, NTHU), Henry Horng Shing Lu • Credit Risk and Interest Rate Models (IS, NCTU), Yuan-chung Sheu (AM, NCTU), (summer, 2005) WY Shu (IS, NTHU), Ching-Tang Wu (AM,NCTU) • New mathematical challenges arising from finance include how to measure and control risk, how to model and hedge against Short Term Visitors default, how to incorporate market frictions, Cho-Jieh Chen (University of Alberta, and more generally, how to deal with Canada), Ren-Raw Chen (Rutger Busi-ness imcomplete markets. We invited Jow-Ren School,Rutger University), Jin-Chuan Duan Chan to give a short introductory course in (Rotman School of Management, University of credit risk. Also we invited Ren-Raw Chen, Toronto, Canada), Chuan-Hsiang associate professor of Rutger Business Han(University of Minnesota and Ford Motor School, Rutger University, to visit NCTS for Co.), S.E.Kuznetsov (University of Colorado, one week. During his stay at NCTS, USA), Wen-Hsiung Li(University of Chicago, Professor Chen gave three lectures on his USA), Alexander Schied (Technical research related to credit risk. University Berlin, Germany) • Cutoff Phenomenon for Markov Chains (summer, 2005) • The cut-off phenomenon (or threshold

Highlights of the Programs -›› 52 phenomenon) for finite state Markov chains Student's Seminars and Summer Courses was first studied by Aldous and Diaconis. It • Student's Seminar on Probability Theory is wide-believed that this phenomenon (2004) should be hold for most families of Markov We ran this regular seminar once a week. chains. However it is rather difficult to verify • The main purpose of this seminar was to that a given family of chains satisfies the provide a solid foundation on probability for definition of cut-off phenomenon. We invited those who are interested in probability theory Guan-Yu Chen to give a series of lectures on and its applications. The main topics covered recent progress on this interesting and are: characteristic functions, moment- challenging subject. generating functions, weak convergence, • Perturbation Methods in Financial independence and convolution, weak law of Mathematics (spring, 2006) large numbers, strong limit theorems, series • Within the last decade, there have been of independent random variable, strong law progresses made to unveil the character-istic of large numbers, and central limit theorem. "smile" phenomenon in financial derivatives • Summer Course on Stochastic Processes market. Professor Chuan-Hsiang (2004) Han(Department of Quantitative Finance, Markov chains and martingales are among NTHU) was the speaker of this special topic. • the most basic mathematical models for Firstly, this short course introduces the random phenomena in both natural and celebrated Black-Scholes formula and the social sciences. We gave ten lectures on smile (or skew) effect in finance as an these two topics from early July to inverse problem. Then we utilize a September,2004. The topics covered were: perturbation method to tackle such problem conditional expectations, Markov chains, based on some multiscale stochastic models. stopping times, countable state Markov In addition, we discuss the Monte Carlo chains, ergodic theorem, martingales, pricing problem and its variance reduction martingale convergence theorem, optional by hedging portfolios in an incomplete stopping times, up-crossing inequality. market. • Student's Seminar on Stochastic Analysis • Model Uncertainty, Robustness, and Risk (2005) Measure (spring, 2006) • We run this regular seminar once a week • Professor Ching-Tang Wu gave a mini- from August, 2005 to December, 2005. The course to introduce the probability theo-ries main purpose of this seminar was to provide that are needed in the financial mathematics. a solid foundation on stochastic analysis. Topics include: Change of mea-sures, Utility The main topics covered are : stochastic maximization, Superhedging, Stochastic integration, infinitesimal generators, differential equations and their relation to diffusions and Itô processes, linear PDE, Risk measures, Robust representation continuous Markov processes. of convex risk mea-sures. Also Professor Alexander Schied (Department of • Summer Course in Graphical models with Mathematics, Technische Universitaet Biological Applications (2005) Berlin) gave a series of talks from March 23, • Graphical model is the combination of graph 2006 to April 23, 2006. Professor Schied and probability theory. It has many presented several recent approaches for applications in the complicated biological dealing with model risk. In particular, he also system. This course gives students the basic highlighted the use of convex risk measures. foundation in this field and also introduces Another key topic was construction of many important method and applications optimal investment strategies under robust toward analyzing the biological network. preferences. This course cover: graphs and hypergraphs, Conditional independence and Markov

53 ‹‹- Highlights of the Programs properties, Contingency tables, Multivariate prediction of the splice sites in the coding normal models, Models for mixed data. region of a gene is a crucial part in the gene Lecturers includes: T.Y Huang, M. Fuchs, structure prediction, it is believed that the S.Y. Haung, Y.C. Sheu, C.C. Lu, J.N. Tseng, results of this paper will contribute to the H.H.S. Lu, H.S. Huang, W.Y. Shu. development of an advanced program for the • Summer Course on Probabilistic and prediction of gene structure from the genomic Statistical Methods in Bioinformatics (2007) DNA sequence. • Themes are: the analysis of one DNA (Ergodic Markov Processes) The sequence, the analysis of multiple DNA or convergence question for ergodic Markov protein sequences, BLAST, gene expression, processes arises in many fields including microarrays, evolutionary models, statistical physics, computer science, biology phylogenetic tree estimation. Lecturers and more. In statistical physics, it is common include: C.C.Lee, W.P. Hsing, H.H.S. Lu, to have to estimate the average entropy of a W.Y. Hsu, Y.H. Zhang. Two special lectures dynamical mechanism. In biology, the were given by Wen-Hsiung Li and Bor-Sen question could concern the position of the last Chen. common ancestor of two related species in the history of evolution or the expected spatial structure of a protein. The common problem Part II: The Accomplished and the posed by these questions is to estimate the Anticipations average of a function with respect to a probability measure . From the perspective (Graphic Models) Graphical models bring of the Markov Chain Monte Carlo method, this together graph theory and probability theory in is achieved by simulating a Markov process a powerful formalism for large-scale with limiting distribution and choos-ing the multivariate modelling. While maintaining state at a certain time T as a random sample. control over the computational cost associated Mathematically, Markov processes are with these models, graphical models have analyzed in both qualitative and quantitative become a focus of research in many applied aspects. Classical results on operator theory fields, including bioinformatics, information are applicable to the qualitative study of the theory, signal and image processing. The ergodicity and the optimal convergence rate is mathematical structure of network/pathway closely related to many constants, e.g. spec- analysis (which is one of the most challenging tral gap, Sobolev constant and logarithmic problems in the era of functional genomics) is Sobolev constant. However, knowing the related to graphic models and their qualitative behavior is not sufficient to probabilistic properties. The theoretic understand the mixing time, e.g. the random properties for reconstruction of regulatory time T introduced above. In practice, various networks have been explored by the heuristics are used to choose T. perspectives of probability and statistics [9]. We also investigated the regulatory networks Logarithmic Sobolev constant. The of yeast as a model for eukaryotic cells [11, logarithmic Sobolev inequality and the related 12] . These researches are conducted with the constant are introduced in the groundbreaking collaborations with Dr. Wen-Hsiung Li at the paper of Gross. In his work, the entropy of a University of Chicago, Dr. Lei Li at the Markov process was proved to converge University of South California, Dr. Huai- exponentially with rate the logarithmic Kuang Tsai and others in Acdemia Sinica. The Sobolev constant. However, the computation main purpose of the paper [5] is to determine of the logarithmic Sobolev constant is still the precise exon-ntron boundaries, i.e. the limited to very simple cases. We obtained in splice sites, in the coding region od a gene. A [4] that the logarithmic Sobolev constant is dependency graph model is developed to fully exactly a half of its spectral gap for simple capture the intrinsic interdependency between random walk on n-cycle, when n is even. This base positions in a splice site. Since the is the first nontrivial result in this direction.

Highlights of the Programs -›› 54 Very different from the even case, Discanois securities and examples include option theory and Saloff-Coste computed out the case n=3 and credit risk modelling. While empirical and concluded that 2α3<λ3. In [1], the case n=5 studies have been indicating the failure of is settled and the consequence is 2α5=λ5. It is diffusion model, the seminal work of Merton believed that such a relation is retained on jump-diffusion model receives more throughout odd integers greater than 5. We attentions in recent years. However, unlike the will keep, on one hand, on the computation for diffusion case in which many functionals are simple random walks on odd cycles and available, this is no longer the case for jump propose, on the other hand, an algorithm for diffusion process. This is where the difficulty finite birth and death chains. To the latter , we in the pricing of securities under jump have in fact an algorithm for the spectral gaps diffusion process arises. of finite birth and death chains with In [6], we consider the jump diffusion exponential convergence rate. For the case of process. In the case that jump distribution is a continuous state space, we are interested in two-sided phase-type one, by a Fourier diffusions on flat tori. transform argument, we transform the integro- Cutoff phenomenon. Chains (or processes) differential equation of the expected presenting a cutoff shows a sharp phase discounted penalty into a homogeneous transition in their behavior. The first example ordinary differential equation. Next, by ODE presenting such a phenomenon is the random theory, we know that the solution for the transition model studied by Diaconis and expected discounted penalty is a linear ShahShahani using the group representation combination of some known exponential theory. In a recent work joint with Saloff- functions. Moreover, by using the limit Coste in [3], we successfully extend the behavior of expected discounted penalty and concept of cutoffs to the extent of ergodic the integro-differential equation, we can Markov processes. There, an equivalent determine these coefficients (under some relation is established for the max–Lp cutoff conditions). All these distinguish not only our with 1 < p < ∞ if the underlying processes are approach from that by Wiener-Hopf normal. Concerning the L 2 cutoff, if the factorization of the Lévy processes but also targeting process is reversible, we are able to itself from the classical method to solve give a criterion(both necessary and sufficient) differential equations in which the knowledge on the existence of an L2 cutoff and formulate of boundary values is required. The present the L 2 mixing time using the spectral method could possibly be extended to decomposition. For an illustration of our transform more integro-differential equations results, a family of randomized riffle shuffles into ordinary differential equations and hence are studied in [2]. Our next step is to compare give an alternative approach to compute prices the L2 mixing times of discrete-time and in jump diffusion model. In [10],A. Schied and continuous-time reversible Markov processes. C.-T. Wu mainly investigate the duality theory For the Lp cutoff with 1 < p ≤∞, we will pay for the robust utilityoptimization problem in a attention to Brownian motions on semisimple general incomplete market model. In spring Lie algebras using representation theory and 2006, A. Schied visited NCTS for one month our earlier results. For p=1, an equivalent and he began with C.-T. Wu a new project relation for the total variation cutoff is still about the robust utility optimization problem open and we will study this case by in a partial information model. considering some specific random walks on On the other hand, motivated from what finite trees. trading strategies are under financial model (Lévy Finance and Computation) uncertainties, C.H. Han has been developing Expected discounted penalty is a generalized some mathematical techniques and working on notion of ruin probability in the insurance real data in order to resolve these problems. A literature. This function has also been a major recent paper [8], C.H. Han and J.-P.Fouque concern in the pricing of perpetual financial propose the use of stochastic flow techniques

55 ‹‹- Highlights of the Programs to analyze errors of hedging strategies when [5] T.-M. Chen, C.-C. Lu, and W.-H. Li. trading a risky financial derivative. The central Prediction of splice sites with dependency problem considered is to study some averaging graphs and their expanded Bayesian effect by means of singular and regular networks, Bioinformatics, vol. 21, no. 4, perturbation theory. It turns out this study pp. 471-482, 2005. reveals an interesting implication in finance. [6] Yu-Ting Chen, Cheng-Few Lee and Yuan- Namely the key parameters of hedging errors Chung Sheu. An ODE Approach for the are dominated by very few factors though the Expected Discounted Penalty at Ruin in original pricing models can be complicated. Jump Diffusion Model, Finance and On the current stage, C.H. Han has Stochastics, vol. 11, no. 3, pp. 323-355, successfully tested his theory by means of 2007. Monte Carlo simulations. In the forthcoming research, C.H. Han plans to study the [7] J.-P. Fouque and C.-H. Han. Evaluation of following problems: 1. Provide a variance Compound Options using Perturbation analysis to explain that some well-known but Approximation, Journal of Computational separate developed variance reduction Finance, Vol.9/No. 1, 2005, pp. 41-61. methods are asymptotically the same under [8] J.-P. Fouque and C.-H. Han. A Martingale weak assumptions. 2. Develop efficient Monte Control Variate Method for Option Pricing Carlo methods to evaluate optimal stopping under Stochastic Volatility Models, problems such as American options or game ESAIM: Probability and Statistics 11, 40- options. These problems are typically related 54, 2007. to some nonlinear martingale representations. 3. Study the method of Quasi Monte Carlo by [9] L.M.,Li and H. H.-S., Lu. Explore means of error analysis. Biological Pathways from Noisy Array Data by Directed Acyclic Boolean Networks. Journal of Computational References: Biology, 12, 2, 170-185, 2005. [1] Guan-Yu Chen, Wai-Wai Liu, and Laurent [10] Alexander Schied and Ching-Tang Wu. Saloff-Coste. The logarithmic Sobolev Duality theory for optimal investments constant of some finite Markov chains. under model uncertainty, Statistics and Annales de la Faculté des Sciences de Decisions 23 (4), 199-217, 2005. Toulouse, accepted, 2007. [11] H.-K. Tsai, H. H.-S. Lu and W.-H. Li. [2] Guan-Yu Chen and Laurent Saloff-Coste. Statistical methods for identifying yeast The cutoff phenomenon for randomized cell cycle transcription factors. PNAS riffle shuffles.Random Structures and (Proceedings of the National Academy of Algorithms, accepted, 2007. Sciences of the United States of [3] Guan-Yu Chen and Laurent Saloff-Coste. America), 102, 38, 13532-13537, 2005. The cutoff phenomenon for ergodic Markov processes. Submitted, 2007. [12] H.-K. Tsai, G. T.-W. Huang, M.-Y. Chou, H. H.-S. Lu and W.-H. Li. Method for [4] Guan-Yu Chen and Yuan-Chung Sheu. On identifying transcription factor binding the log-Sobolev constant for the simple sites in yeast. Bioinformatics, 22, 14, random walk on the n-cycle: the even cases. J. Funct. Anal., 202(2):473-485, 1675-1681, 2006. 2003.

Highlights of the Programs -›› 56 D.11 Scientific Computation at NCTS 2004-2007

Coordinator: I-Liang Chern (National Taiwan University) and Wen-Wei Lin (National Tsing Hua University)

omputational Science and Tony W. H. Sheu, Yu-Chen Shu, K. M. Shyue, Engineering now has become a Din Ping Tsai, W. Wang, D. L. Yang, J. Y. rapidly growing multidisciplinary research Yang; Fu-Jen --- C. C. Yen; NTOC --- S. F. area in the scientific world. The rapid growth Tsai; NTNU --- Wei-Chih Liu, T. M. Hwang, of high performance computers have S. F. Shieh; NTOU --- Railing Chang, Hai- transformed the methodology of scientific Pang Chiang; FEG --- Shen-Chung Chen; investigation. Computing is nowaday joined NCUE --- Shih-Hung Chen; NCHC --- Li-Gan experiment and theory as one of the Tien; LIT --- Yuan Fong Chau; NCU --- Pi- fundamental tools of investigation. It is safe Gang Luan, S. Y. Yang; NCTU --- M. C. Lai, and cheap. Due to recent advances in software C. T. Wu, L. M. Yeh; NTHU --- W. W. Lin, W. and hardware of computing technology, C. Wang; Yuanpei University --- H. Y. Fan; scientific computation is already regarded as NCCU --- Tai Huei Wei; NCKU --- Kuan-Ren an equal and indispensable partner, together Chen, Yung-Chiang Lan, C. S. Wang and with the theoretical and experimental studies NKU --- Y. C. Kuo. There are also 4 Ph.D in the pursuit of scientific knowledge and students in this group from NTHU. engineering design. In additional to promoting interdisciplinary research activity with other Post Doctor sciences, the Scientific Computation program S. M. Chang (NTHU, 2003 - 2008), Y. C. at NCTS also cooperates with other programs Kuo (NCTS, 2004 - 2005), H. Y. Hu (NCTS, in Mathematics Division such as the PDE, 2004 - 2005) and Y. L. Huang (NTHU, 2004 - Mathematical Biology, and Dynamical 2008). Systems programs. To stimulate such research activity, we conduct collaborative research that Visitors involves international renowned scholars, local In 2004, Eric K.-W. Chu (Monash scientists, graduate students, and post-docs. University), So-Hsiang Chou (Bowling Green We also provide timely short courses and State University), Zhilin Li (North Carolina seminars to bring the newest ideas to our State University), Musheng Wei (East China students and local researchers. Accordingly, in Normal University, Shanghai), Biswa Nath the years 2004-2007, we have integrated Datta (Northern Illinois University), Shufang researchers from mathematics, physics and Xu (Peking University), Huaxiong Huang engineering. Regular joint seminars and short (Depart. of Math. and Statistics, York courses have been organized. We also held University) and Qianshun Chang (The Chinese international workshops on scientific Academy of Sciences) visited NCTS and gave computing to bring international researches one or more speeches. and local researchers together. In 2005, Ben-Yu Guo (Shanghai Normal Local Focus Group University) visited NCTS and taught one NTU --- Chien-Cheng Chang, Chien Liu NCTS & PU Joint Course - High-order Chang, Yu Ming Chang, I-Liang Chern, Ruey- Methods for PDEs and Related Topics which Lin Chern, Ren-Wu Fang, Guang Yu Guo, starts in Spring term every Thursday at Michitoshi Hayashi, M. J. Huang, J. H. Lee, Providence University. Professors Chi-Tien Lin (PU), Tsung-Min Hwang (NTNU) and

57 ‹‹- Highlights of the Programs Ming-Chih Lai (NCTU) were the organizers of Poisson system, the quantum dot (interface) this course. W. Hui (HK Science and problems, the BEC problems that are of Technology), Richard Y-H Tsai (Univ. of common interest to a lot of local researchers. Taxes-Austin), S. Altschuler (Harvard Univ.) Shuyu Sun (Clemson University), Zhowei and L. Wu (Harvard Univ.) visited NCTS- Shen (National Univ. of Singapore), Richard Taipei. Y-H Tsai (Univ. of Taxes - Austin) and Chiu- Yen Kao (Ohio State Univ.) visited NCTS- In 2006, Chern Shuh Wang (NCKU), So- Taipei. In addition, Gene Golub (Stanford Hsiang Chou (Bowling Green State University, University) will visit NCTS next Jan. 3 to Jan. USA), Eric Chu (Monash University, 10. Australia), Zhaojun Bai (University of California), Haw-ren Fang (University of Maryland) and Dan'l Pierce (Director of Seminars, Short Courses and Workshops Business Development and Product Marketing (1) Regular seminars (NCTS-Taipei): Cray Inc.) visited NCTS and gave one or more i. Biweekly seminar on scientific speeches. Further, So-Hsiang Chou taught a computing and Applied Mathematics short course A Posteriori Estimation and (2004-2007). Adaptive Methods. The subject of a posteriori error estimation and adaptive methods for ii. Computation and Simulation Monthly partial differential equations is an exciting area Seminars on Nano-photonics (2004- in scientific computation. The purpose of this 2007). short course is to introduce some basic ideas in (2) NCTS Student's Seminar on Computational the subject, assuming minimal knowledge in Dynamical Systems: Jun. 28 - Sep. 6, 2004. convex analysis and numerical PDEs. Essential topics of error estimation and The purpose of this seminar is to help adaptive methods were covered in this course. graduate students understand the basics of He wrote an eighty-five page lecture note for computational dynamical systems. the course. Chiu-Yen Kao (Univ. of Organizers are Wen-Wei Lin, Shih-Feng Minnesota), Edward Jack (NCSU), Weizhu Shieh and Shu-Ming Chang (Dept. of Bao (National Univ. of Singapore), SauroSucci Math., NTHU). (National Research Council, Rome, Italy), Li- (3) NCTS 2005 Winter School on Scientific Tien Cheng, (University of California, San Computation: Jan. 17 - 27, 2005. Diego), Selim Esedoglu, (University (4) NCTS & PU Joint Course: High-order Michigan, Ann Arbor) and Richard Tsai Methods for PDEs and Related Topics, (University of Texas, Austin) visited NCTS- Spring term, 2005 (Every Thursday), Feb. Taipei. 24-Apr. 14, 2005, Providence University. In 2007, Jian-Guo Liu (University of This was a joint course and the course Maryland), Roger Lee (University of consists of four different topics which were Maryland, College Park), LieJune Hsiao taught by different researchers. In (University of Houston, USA), Eric Chu particular, we invited Prof. Ben-Yu Guo (Monash University, Australia) and So-Hsiang from Shanghai Normal University to talk Chou (Bowling Green state University) visited about Spectral Methods for PDEs. Prof. NCTS and gave one or more speeches. Guo is a well-known expert on Spectral Furthermore, So-Hsiang Chou gave a short Methods. The four topics are course on Finite Element Methods and Eigenvalue Problems from Jun. 21 to Jul. 24. 1. Finite difference methods for The purpose of this course is to provide a conservation laws, (Prof. Chi-Tien Lin, forum for introducing some interesting PU). research topics on eigenvalue problems. These 2. Spectral methods for PDEs on bounded include the computation of the steady solutions or unbounded domains, (Prof. Guo Ben- arising from self-consistent Schrodinger-

Highlights of the Programs -›› 58 Yu, Shanghai Normal University). Source and Eigenvalue Problems. 3. Direct method for solving linear systems (11) International Workshop on Scientific for general sparse linear systems, (Prof. Computing (Tutorial Week): Jun. 15-23, Tsung-Min Hwang, NTNU). 2006. 4. Introduction to incompressible flow In the summer break of 2006, we organized computations, (Prof. Ming-Chih Lai, a short course on Scientific Computation NCTU). that lasted three days. There were five lectures which covered different topics of (5) An Introduction to Surface Plasmon I, II, numerical analysis and methods: Numerical III Apr. 2005, by Ruei-Lin Chern (Applied approximations of high frequency wave Mechanics, NTU). propagation, Inverse problems, Level set The aim is to give a brief introduction of methods, Tsitsiklis' algorithms for solving surface plasmon problems to eikonal equations, and Image processing. mathematicians. Day 1: Tutorial 1. Mathematical models (6) Lagrangian-Type Computational Fluid and numerical methods for high- Dynamics, May-June, 2005, by Prof. Hui frequency waves (Prof. Olof (HKST). Runborg, KTH, Sweden). This two-month course provides a thorough Day 1: Tutorial 2. Inverse Problems study on the Lagrange-type method and Involving Shapes (Prof. Chiu-Yen unified Euler and Lagrange method for Kao, University of Minnesota). compressible Euler equations. Day 2: Tutorial 3. Local Level Set Methods (7) International Symposium on Dynamical (Prof. Li-Tien Cheng, University of System and Numerical Analysis in honor California, San Diego). of Tien-Yien Li's 60th Birthday, May 10- Day 2: Tutorial 4. Fast Algorithms for 12, 2005. Solving Static Hamilton-Jacobi (8) NCTS Seminar on Scientific Computation Equations (Prof. Richard Tsai, 2006: Jan. 20-25, 2006. University of Texas, Austin). (9) Lattice Boltzmann Methods: Basic Theory Day 3: Tutorial 5. Level Set and Diffuse and Selected Applications I-IV, Feb. 2006, Interface Models in Image by SauroSucci (National Research Council, Processing (Prof. Selim Esedoglu, Rome, Italy). University Michigan, Ann Arbor). The course is based on the lecturer's new (12) International Workshop on Scientific book on Lattice Boltzmann Method. Computing: Jun. 26 - 30, 2006. (10) A Short Course 2006 on a Posteriori There has been significant progress in Estimation and Adaptive Methods: May 17 scientific computing, particularly in the - Jun. 15, 2006. diverse fields of multiscale computations The purpose of this short course is to and imaging. One of the focuses of introduce some basic ideas in the subject, multiscale computation concentrates on assuming minimal knowledge in convex problems where classical single physics analysis and numerical PDEs. The main models are either inadequate or not topics covered are as follows. accurate enough, and a coupling of multiple physics models needs to be considered. In 1. Finite Element, Finite Difference, and particular, there is an emergence of Finite Volume Methods. methods that replace heuristics and 2. Posteriori Error Estimation. empirical observations in coarse scale single physics models by direct numerical 3. Design of Adaptive Methods for Solving simulations of more accurate models

59 ‹‹- Highlights of the Programs defined on finer scales. PDE-based degrees of freedom of ultrashort pulse in techniques for imaging received a lot of linear and nonlinear processes. (3) Two- attention due to its success in removing pulse (interferometric) coherent control - noise and segmenting salient features in full suppression or enhancement of near images. Many of the approaches are closely field hot spots for two-photon effects. (4) related to inverse problems and interface Surface plasmon amplification by problems. This workshop brings some of stimulated emission of radiation (SPASER). the world's leading experts in these fields (16) Discontinuous Galerkin Methods for together and aims at (1) providing an Flow and Transport Problems I-IV, Jan. opportunity for direct communication and 2007, by Shuyu Sun (Clemson University). exchange of ideas; (2) promoting interaction and collaboration of local and This short course gives an introduction of international scholars. The workshop the discontinuous Galerkin method and its included 35 invited speakers and total applications. number of participant is 120 roughly. (17) A Short Course 2007 on Finite Element (13) School on Modern Numerical Methods in Methods and Eigenvalue Problems: Jun. Math and Physics: Jul. 3 - 5, 2006. 21-Jul. 24, 2007. In recognizing this trend, NCTS sponsored (18) Nanophoto Nanophotonic Bandgap a school on modern numerical methods and Structures and Optical Microsystems, algorithms in math and physics for Spring 2007. interested graduate students and novices in This short course is given by Ai Qun Liu. the field. The topics include large scale The aim of this course is to introduce the matrix computation, Monte Carlo method, fundamental theory, fabrication process and Bayesian approach in curve fitting, applications of plasmonic bandgap numerical gravity, and GRID computing. structures. The workshop included eight plenary speakers (Masayuki Asakawa, Ying Chen, In addition, a workshop Recent Advances Anthony Kennedy, Simon Lin, Chuan Liu, in Numerical Methods for Eigenvalue Jian-Guo Liu, Wai-Mo Suen and Chao Problems (RANMEP2008) will be taken place Yang). They are world-known in these between Jan. 4-8, 2008. areas of Applied Mathematics and the total number of participant is 85 roughly. Selected Publications of the Local Focus Group since 2004 (14) Nanoplasmonics: Optical Properties of Plasmonic Nanosystems, Winter 2006. Martix analysis and computation This short course is given by Nikolay (Inverse Quadratic Eigenvalue Problems) Zheludev. The content of this course Given k pairs of complex numbers and vectors include a broad introduction to the topic of (closed under conjugation), we consider the plasmonic nanophotonics. It's aim is to inverse quadratic eigenvalue problem of discuss how fundamental causality, i.e., the constructing nxn real symmetric matrices M, impossibility to change the past, defines C, and K (with M positive definite) so that the possible and impossible in optics and quadratic pencil has the given k pairs as nanoplasmonics. eigenpairs. Using various matrix decompositions, we first construct a general (15) Coherent, Nonlinear and Ultrafast solution to this problem with k is lower or Nanoplasmonics, Winter 2006. equal to n. Then, with appropriate choices of This short course is given by Mark degrees of freedom in the general solution, we Stockman. This course covers: (1) Problem construct several particular solutions with of nanoscale control of local optical fields. additional eigeninformation or special (2) Coherent control using phase (temporal) properties [1,13,15].

Highlights of the Programs -›› 60 In [2], we propose a minimax scaling singularity can be elevated easily [5]. procedure for second order polynomial In [6], we propose a simple finite difference matrices that aims to minimize the backward scheme for the elliptic interface problem with errors incurred in solving a particular a discontinuous diffusion coefficient using a linearized generalized eigenvalue problem. body-fitted curvilinear coordinate system. The We consider the regularization problem for resulting matrix is symmetric and positive the linear time-varying discrete-time periodic definite. Standard techniques of acceleration descriptor systems by derivative and such as PCG and multigrid can be used to proportional state feedback controls. Sufficient invert the matrix. The main advantage of the conditions are given under which derivative scheme is its simplicity: the entries of the and proportional state feedback controls can be matrix are simply the centered difference constructed so that the periodic closed-loop second order approximation of the metric systems are regular and of index at most one. tensor. In particular [10], a fast direct solver The construction procedures used to establish derived from the equation and the semi- the theory are based on orthogonal and coarsening multigrid are shown to be almost elementary matrix transformations and can, scalable with the problem size and outperform therefore, be developed to a numerically other preconditioners significantly. efficient algorithm. The problem of finite pole We propose two iterative methods, a assignment of periodic descriptor systems is Jacobi-type iteration and a Gauss-Seidel-type also studied [4]. iteration (GSI), for the computation of energy Numerical methods and simulation in PDE states of the time-independent vector Gross- Pitaevskii equation (VGPE) which describes a In [3], the work investigates the existence multi-component Bose-Einstein condensate of monotonic traveling wave and standing (BEC). A discretization of the VGPE leads to wave solutions of RTD-based cellular neural a nonlinear algebraic eigenvalue problem networks in the one-dimensional integer lattice (NAEP). We prove that the GSI method Z1. For nonzero wave speed c, applying the converges locally and linearly to a solution of monotone iteration method with the aid of real the NAEP if and only if the associated roots of the corresponding characteristic minimized energy functional problem has a function of the profile equation, we can strictly local minimum. The GSI method can partition the parameter space ( , )-plane thus be used to compute ground states and into four regions such that all the admissible positive bound states, as well as the monotonic traveling wave solutions corresponding energies of a multi-component connecting two neighboring equilibria can be BEC [7,8,9]. On the other hand, we present classified completely. two efficient and spectrally accurate numerical We extend our previous work (M.-C. Lai methods for computing the ground and first and W.-C. Wang, Numer Methods Partial excited states in Bose-Einstein condensates Differential Eq., 18:56-68, 2002) for [12]. developing some fast Poisson solvers on 2D In [11], we present an asymmetric polar and spherical geometries to an elliptical watermarking method for copyright protection domain. Instead of solving the equation in an that uses different matrix operations to embed irregular Cartesian geometry, we formulate the and extract a watermark. It allows for the equation in elliptical coordinates. The solver public release of all information, except the relies on representing the solution as a secret key. We investigate the conditions for a truncated Fourier series, then solving the high detection probability, a low false positive differential equations of Fourier coefficients probability, and the possibility of unauthorized by finite difference discretizations. Using a users successfully hacking into our system. grid by shifting half mesh away from the pole The robustness of our method is demonstrated and incorporating the derived numerical by the simulation of various attacks. boundary value, the difficulty of coordinate

61 ‹‹- Highlights of the Programs We describe an integral equation approach multigrid (AMG) are established on uniform for simulating diffusion problems with moving rectangular meshes for a model problem. Our interfaces. The solutions are represented as analysis shows that GMG with line Gauss- moving layer potentials where the unknowns Seidel smoothing and bilinear interpolation are only defined on the interfaces. The converges, and AMG with the same smoother resulting integro-differential equation system converges more rapidly than GMG. is solved using spectral deferred correction At the heterogeneity scale the flow is techniques developed for general differential described by a two-phase flow model with a algebraic equations, and the time dependent generalized Darcy law, classical phase potentials are evaluated efficiently using fast permeabilities and capillary pressure. The convolution algorithms [14]. macroscale flow model is obtained by the two- In [16], we give an error estimate for the scale asymptotic homogenization method. To energy and helicity preserving scheme (EHPS) solve the cell problems we have developed the in second order finite difference setting on two-phase version [19]. axisymmetric incompressible flows with In [20], we devoted to analyze a splitting swirling velocity. This is accomplished by a method for solving incompressible inviscid weighted energy estimate, along with careful rotational flows. The problem is first recast and nonstandard local truncation error analysis into theve locity-vorticity-pressure formulation near the geometric singularity and a far field by introducing the additional vorticity decay estimate for the stream function. A key variable, and then split into three consecutive ingredient in our a priori estimate is the subsystems. permutation identities associated with the Jacobians, which are also a unique feature that [1] M. T. Chu, Y. C. Kuo, and W. W. Lin, On distinguishes EHPS from standard finite Inverse Quadratic Eigenvalue Problems difference schemes. with Partially Prescribed Eigenstructure, SIAM Matrix Anal. Appl., Vol. 25, No. 4 We present a simple volume-of-fluid (2004), 995-1020. approach to interface tracking for inviscid compressible multicomponent flow problems [2] H. Y. Fan, W. W. Lin, and P. Van Dooren, in two space dimensions. The algorithm uses a Normwise Scaling of Second Order uniform Cartesian grid with some grid cells Polynomial Matrices, SIAM Matrix Anal. subdivided by tracked interfaces, Appl., Vol. 26, No. 1 (2004), 252-256. approximately aligned with the material [3] C. H. Hsu and Suh-Yuh Yang, Wave interfaces in the flow field. A standard propagation in RTD-based cellular neural volume-moving procedure consists of two networks, J. Differential Equations, 204 basic steps. We validate our algorithm by (2004), pp. 339-379. performing the simulation of a Mach 1.22 shock wave in air over a circular R22 gas [4] Y. C. Kuo, W. W. Lin, and S. F. Xu, bubble, where sensible agreement of some key Regularization of Singular Linear flow features of the computed solutions are Discrete-Time Periodic Systems by observed when direct comparison of our Derivative and Proportional State results are made with the existing experimental Feedback, SIAM Matrix Anal. Appl., Vol. and numerical ones that appear in the literature 25, No. 4 (2004), 1046-1073. [17]. [5] Ming-Chih Lai, Fast direct solver for In [18], the discrete convection-diffusion Poisson equation in a 2D elliptical domain, equations obtained from streamline diffusion Numer. Methods Partial Differential finite element discretization are solved on both Equations 20 (2004), no. 1, 72-81. uniform meshes and adaptive meshes. [6] Wei-Cheng Wang, A jump condition Estimates of error reduction rates for both capturing finite difference scheme for geometric multigrid (GMG) and algebraic elliptic interface problems, SIAM J. Sci.

Highlights of the Programs -›› 62 Comput. 25 (2004), no. 5, 1479-1496. [16] Jian-Guo Liu and Wei-Cheng Wang, Convergence analysis of the energy and [7] S. M. Chang, W. W. Lin, and S. F. Shieh, helicity preserving scheme for Gauss-Seidel-type Methods for Energy axisymmetric flows, SIAM J. Numer. States of a Multi-Component Bose-Einstein Anal. 44 (2006), no. 6, 2456-2480. Condensate, J. Comp. Physics, Vol. 202, Issue 1 (2005), 367-390. [17] Keh-Ming Shyue, A wave-propagation based volume tracking method for [8] Tsung-Min Hwang and Weichung Wang, compressible multicomponent flow in two Energy States of Vertically Aligned space dimensions, J. Comput. Phys. 215 Quantum Dot Array with Nonparabolic (2006), no. 1, 219-244. Effective Mass, Computers and Mathematics with Applications, 49:39-51, [18] Chin-Tien Wu and Howard C. Elman, (2005). Analysis and comparison of geometric and algebraic multigrid for convection- [9] Y. C. Kuo, W. W. Lin, and S. F. Shieh, diffusion equations, SIAM J. Sci. Bifurcation Analysis of a Two-Component Comput. 28 (2006), no. 6, 2208-2228. Bose-Einstein condensate, Physica D, Vol. 211, No. 3-4 (2005), 311-346. [19] Li-Ming Yeh, Homogenization of two- phase flow in fractured media, Math. [10] Ming-Chih Lai and Yu-Hou Tseng, A fast Models Methods Appl. Sci. 16 (2006), no. iterative solver for the variable coefficient 10, 1627-1651. diffusion equation on a disk, J. Comput. Phys. 208 (2005), no. 1, 196-205. [20] Chiung-Chiou Tsai and Suh-Yuh Yang, Analysis of a splitting method for [11] Jengnan Tzeng, Wen-Liang Hwang, and I- incompressible inviscid rotational flow Liang Chern, An asymmetric subspace problems, J. Comput. Appl. Math. 200 watermarking method for copyright (2007), no. 1, 364-376. protection, IEEE Trans. Signal Process. 53 (2005), no. 2, part 2, 784-792. The development of computational science needs integration of researchers from different [12] Weizhu Bao, I-Liang Chern, and Fong disciplines: mathematics, physics, chemistry, Yin Lim, Efficient and spectrally accurate biology, geoscience, engineering, computer numerical methods for computing ground science, etc. The funding of NCTS-Taipei and first excited states in Bose-Einstein provided opportunities to bring researchers condensates, J. Comput. Phys. 219 from different disciplines together. In this (2006), no. 2, 836-854. three-year period, we focus on three [13] J. Carvalho, B. N. Datta, W. W. Lin, and interdisciplinary topics: (1) core algorithms, C. S. Wang, Symmetric Preserving (2) computational fluid dynamics, and (3) Eigenvalue Embedding in Finite Element computational nano-optics. Model Updating of Vibrating Structures, J. Sound and Vibration, Vol. 290(3-5) Core algorithm (2006), 839-864. Core algorithm focuses on interface [14] Jingfang Huang, Ming-Chih Lai, and problems, multigrid methods, numerical Yang Xiang, An integral equation method methods for nanoscale transport based on for epitaxial step-flow growth quantum kinetic theory, fast iterative solvers simulations, J. Comput. Phys. 216 (2006), for unsymmetrical and indefinite large-size no. 2, 724-743. matrix equations [11, 25, 26, 27, 31]. [15] Y. C. Kuo, W. W. Lin and S. F. Xu, Solutions of the Partially Described Computational fluid dynamics Inverse Quadratic Eigenvalue Problem, Computational fluid dynamics focuese on SIAM Matrix Anal. Appl., Vol. 29, No. 1 CFD code implementation on PC-cluster, (2006), 33-53. multi-grid and multi-level, preconditioner

63 ‹‹- Highlights of the Programs designs for flow solver. Application of CFD [26] Tony W. H. Sheu, R. K. Lin, Development technique to computational medicine and of locally analytic prolongation operator industrial problems [23, 24, 25, 28, 29]. in two-grid three-level method for incompressible Navier-Stokes equations, Nano-optics focuses Numerical Heat Transfer. Part B: Nano-optics focuses on investigating the Fundamentals, Vol. 50(6) (2006), pp. 517- topics of optical responses in nanometer scale 533. and the resultant intriguing phenomena such as [27] R. K. Lin, Tony W. H. Sheu, Development surface plasmon resonances, plasmonic band of a class of multiple time-stepping gaps, and anomalous light propagation in scheme for convection-diffusion equations meta-materials [21, 22, 30, 32]. in two dimensions,International Journal [21] S. C. Chen, D. P. Tsai, Numerically for Numerical Methods in Fluids, Vol. Investigating Near-field Scattering for 52(12) (2006), pp. 1293-1313. Spatial Enhancement of Single Irregular [28] H. P. Rani, Tony W. H. Sheu, T. M. Nano Plasma particle, Scanning 26 (5), Chang, P. C. Liang, Numerical 109-112, (2004). investigation on non-Newtonian [22] R. T. Hong, M. J. Huang and Jaw-Yen microcirculatory blood flow in hepatic Yang, Molecular dynamics study of lobule, Journal of Biomechanics, Vol. 39 copper trench filling in damascene (2006), pp. 551-563. process, Materials Science in [29] Yang, J. Y., T. Y. Hsieh and Y. H. Shi, A Semiconductor Processing, 8, pp. 587- Kinetic Flux Vector Splitting Scheme for 601, (2005). Ideal Quantum Gas Dynamics, SIAM J. [23] Tony W. H. Sheu, C. W. Chou, Eric S. F. on Scientific Computing, Vol. 29, No. 1, Tsai, P. C. Liang, Three-dimensional pp. 221-244 (2007). analysis for radio-frequency ablation of [30] Y. H. Shi, J. C. Huang and Jaw-Yen Yang, liver tumor with blood perfusion effect, High Resolution Kinetic Beam Schemes in Computer Methods in Biomechanics and Generalized Coordinates for Ideal Biomedical Engineering, Vol. 8(4) (2005), Quantum Gas Dynamics, J. Comput. pp. 229-240 Phys., Vol. 222, pp. 573-591 (2007). [24] R. K. Lin, Tony W. H. Sheu, Application [31] Chern, I-Liang and Yu-Chen Shu, of dispersion-relation-preserving theory Coupling interface method for elliptic to develop a two-dimensional convection- interface problems, Journal of diffusion scheme, Journal of Computational Physics, no. 225 (2007), Computational Physics, Vol. 208 (2005), 2138-2174. pp. 493-526. [32] Tony. W. H. Sheu, Y. H. Chen, Numerical [25] P. H. Chiu, Tony W. H. Sheu, R. K. Lin, study of flow field induced by a Development of a dispersion-relation- locomotive fish in the moving meshes, preserving upwinding scheme for International Journal for Numerical incompressible Navier-Stokes equations Methods in Engineering, Vol. 69 (2007), pp. 2247-2263. on non-staggered grids, Numerical Heat Transfer. Part B: Fundamentals, Vol. 48(6) (2005), pp. 543-569.

Highlights of the Programs -›› 64 Activities of Onsite Scientists

TitleName Field Period Jiun-Cheng Chen Algebraic Geometry 2006/09/01-2007/08/31 Wen-Ching Winnie Li Number Theory 2006/09/01-2007/08/31 Song-Sun Lin Dynamical Systems 2004/08/01-2008/12/31 Center Scientists Wen-Wei Lin Scientific Computation 2006/09/01-2007/08/31 Dong-Ho Tsai Partial Differential Equations 2006/09/01-2007/08/31 Chin-Lung Wang Algebraic Geometry 2004/01/01-2008/12/31 Jing Yu Number Theory 2004/01/01-2008/12/31 2007/05/23-2007/08/23 Visiting Professor Der-Chen Chang Geometric Analysis 2006/12/23-2007/03/23 Visiting Assistant Probability Guan-Yu Chen 2006/08/01-2007/07/31 Professor Stochastic Processes Yan-Hsiou Cheng Dynamical Systems 2007/03/01-2008/02/29 Postdoctoral Fellow Chian-Jen Wang Number Theory 2006/08/01-2007/07/31 You-Chiang Yi Number Theory 2006/08/01-2007/07/31

.1 Center Scientists Geometry seminar, Chinese Hong Kong University, Hong Kong -Taiwan- I. Jiun-Cheng Chen TIMS Conference on Higher dimensional National Tsing-Hua University, Geometry, TIMS, Taipei, Taiwan Assistant Professor NCTS Activities Conferences and visiting Organizer, Workshop on the minimal model program, NCTS, Hsinchu, Taiwan -France- An algebraic geometry conference, IHP, Paris -Korea- Research Works Algebraic geometry seminar, KIAS, Seoul (joint with H. H. Tseng) A note on derived Korea McKay correspondence, mathAG0609737, -Japan- submitted to MRL Algebraic geometry seminar, RIMS, Kyoto, Japan -Hong Kong-

65 ‹‹- Activities of onsite Scientists II. Wen-Ching Winnie Li November 2006, invited participant Pennsylvania State University • Workshop on Expanders and Nano-scale National Center for Theoretical Sciences, Self-assembly, Hewlett Packard Lab, Palo Center Scientist Alto, CA, November 2006, organizer • Invited speaker, "Ramanujan graphs and hypergraphs" Teaching • International FNANO 2007 Conference, • Advanced graduate course on Modular Snowbird, Utah, April 2006 Forms and Galois Representations, fall 2006, • Invited paper, "Expanders and Nano-scale NCTS Self-assembly" (joint with A. Gamburd, M. Kang, P. Keukus, P. Vontobel), presented • Reading course on Arithmetic of Elliptic by A. Gamburd. Curves, with Ms. Pei-Yu Tsai, a junior at National Taiwan University, spring and summer 2007 Colloquium/Seminar/Workshop -Taiwan- Conferences • NCTS 2007 Winter School on Number Theory, February 2007 -Taiwan- 1 lecture • Taiwanese Mathematical Society Annual Meeting, Dec. 2006, Taipei • NCTS Number Theory Seminar, September • Plenary address "A century of modular 2006 forms" 1 lecture • International Conference on Galois • NCTS 10th Anniversary Lecture Series in Representations and Function Field Algebra and Number Theory, August 2007 Arithmetic, May 2007, organizer 2 lectures -Canada- • Algebra Seminar, National Taiwan • International Conference on Polynomials University, October 2006 over Finite Fields and Applications, Banff 4 lectures International Research Station, Banff, Colloquium, National Tsing-Hua University, November 2006 • October 2006 • Invited speaker, "Characterizations of 1 lecture pseudo-codewords of parity-check codes" • Colloquium, Tamkang University, March -China- 2007 • The 1st Workshop on Number Theory, 1 lecture Combinatorics and their Interactions, August 2007, Nanjing • Colloquium, National Chung-Cheng • Invited plenary speaker, "Zeta functions of University, March 2007 graphs and complexes" 2 lectures • International Conference on Algebra and • Colloquium, National Chiao-Tung Related Topics in honor of Professor University, April 2007 Zhexian Wan's 80th birthday, August 2007, 1 lecture Beijing • Meet Female Mathematicians Workshop (for • Invited speaker, "Pseudo-codewords of high school girls), Tung-Hai University, July low-density parity-check codes" 2007 1 lecture -United States- • Hot topics: Modularity for GL(n) and -China- Beyond, MSRI, Berkeley, CA, October- • Workshop on Coding Theory and

Activities of onsite Scientists -›› 66 Cryptography, August 2007, Yangzhou, • (with Ming-Hsuan Kang) Zeta functions for 1 lecture finite quotients of PGL(3), preprint, 2007 • Morningside Center of Mathematics, Academia Sinica, Beijing, August 2007 1 lecture III. Song-Sun Lin National Chiao Tung University, -Singapore- • Colloquium, National University of National Chair Professor and Chair Singapore, February 2007 Professor of National Chiao-Tung 1 lecture University. • Number theory Seminar, National University of Singapore, March 2007 1 lecture Conferences and Visitings -Taiwan- • Combinatorics Seminar, Nanyang International Conference on Chaos and Technological University, March 2007 • Dynamical Complexity, May 24-30, 2006, 1 lecture CTS, Hsinchu, Taiwan. -Switzerland- • 2007 CTS Workshop on Dynamical Systems, • Special Year on "Limits of Graphs in Group May 14-18, 2007, CTS, Hsinchu, Taiwan. Theory and Computer Science", Bernoulli center, EPFL, Lausanne, invited participants, -U.S.A.- April-May 2007 • Harvard University, Professor S. T. Yau, 2 lectures August, 2006.

Publications -United Kingdom- • (joint with Ralf Koetter, Pascal O. Vontobel, • Heriot-Watt University, Edinburgh, July, and Judy Walker) Characterizations of 2007. pseudo-codewords of LDPC codes, Advances in Math. 213, Issue 1 (2007), 205- Publications 229. • Smooth solutions to a class of quasilinear • Recent Trends in Coding Theory with wave equations, J. Differential Equations, Applications, AMS/IP Proceedings series, 224(2006), 229-257. (with C.-H. Hsu and T. editor, Providence (2007). Makino) • Upper and lower bounds for A(q). In: Recent • Patterns generation and spatial entropy in Trends in Coding Theory and Its two-dimensional lattice models, to appear in Applications, AMS/IP Proceedings series, Asian Journal of Mathematics (with J.-C. W. Li edited, Providence (2007), 15-23. Ban and Y.-H. Lin). • Elkies' modularity conjecture. In: Recent • Three-dmiensional cellular neural networks Trends in Coding Theory and Its and patterns generation problems, to appear Applications, AMS/IP Proceedings series, in International Journal of Bifurcation and W. Li edited, Providence (2007), 25-34. Chaos (with J.-C. Ban and Y.-H. Lin). • Improved algebraic geometry bounds. In: Recent Trends in Coding Theory and Its Applications, AMS/IP Proceedings series, IV. Wen-Wei Lin W. Li edited, Providence (2007), 73-81. National Tsing-Hua University • (with Yotsanan Meemark) Hecke operators Tsing-Hua Chair professor on Drinfeld cusp forms, submitted. Tsing-Hua Professor of Natural Sciences

67 ‹‹- Activities of onsite Scientists Editor in Chief of Taiwanese Journal of (2006), 393-412. (with X.-X. Guo and S. F. Mathematics (2004--2006) Xu) • A Numerical Method for a Generalized Algebraic Riccati Equation, SIAM Control Conferences and Visiting Optim, Vol. 45, No. 4 (2006), 1222-1250. -China- (with D. L. Chu and R. C. E. Tan) • Dalian University of Technology, July- • Solutions of the Partially Described Inverse August, 2006 (Visiting). Quadratic Eigenvalue Problem, SIAM • Fudan University, August, 2006 (Visiting). Matrix Anal. Appl., Vol. 29, No. 1 (2006), 33-53. (with Y. C. Kuo and S. F. Xu) • International Congress of Chinese Mathematicians (ICCM2007), Hangzhou, • Robust Partial Pole Assignment for China, December, 2007 (Invited Speaker). Vibrating Systems with Aerodynamic Effects, IEEE Trans. Auto. Control, Vol. 51, -Switzerland- Issue 12 (2006), 1979-1984. (with B. N. • 6th International Congress on Industrial and Datta and J. N. Wang) Applied Mathematics (ICIAM2007), Zurich, Switzerland, July, 2007 (Invited Speaker). • Updating Quadratic Models with No Spill- Over Effect on Unmeasured Spectral Data, Inverse Problem, Vol. 23, Issue 1 (2007), NCTS Activities 243--256. (with M. T. Chu and S. F. Xu) • Recent Advances in Numerical Methods for Eigenvalue Problems (RANMEP2008), • Projected Generalized Discrete-Time NCTS Hsinchu, Taiwan, January, 2008 Periodic Lyapunov Equations and Balanced (Organizer & Invited Speaker). Realization of Periodic Descriptor Systems, SIAM Matrix Anal. Appl., 2007, to appear. Publications (with E. K. W. Chu and H. Y. Fan) • Synchronization and Asynchronization in • A Numerical Method for Quadratic Coupled Lorenz-Type Maps, Int. J. Bifur. Eigenvalue Problems of Gyroscopic and Chaos, Vol. 16, No. 2 (2006), 269-280. Systems, J. Sound and Vibration, 2007, to (with S. F. Shieh and Y. Q. Wang) appear. (with J. Qian) • Symmetric Preserving Eigenvalue • Vibration of Fast Trains, Palindromic Embedding in Finite Element Model Eigenvalue Problems and Structure- Updating of Vibrating Structures, J. Sound Preserving Doubling Algorithms, J. Comp. and Vibration, Vol. 290(3-5) (2006), 839- Appl. Math., 2007, to appear. (with E. K. W. 864. (with J. Carvalho, B. N. Datta, and C. S. Chu, T. M. Hwang, and C. T. Wu) Wang) • Convergence Analysis of Structure- Preserving Doubling Algorithms for Riccati- V. Dong-Ho Tsai Type Matrix Equations, SIAM Matrix Anal. National Tsing-Hua University, Professor Appl., Vol. 28, No. 1 (2006), 26-39. (with S. Invited One-Month Research Professor at F. Xu) MSRI, Berkeley, USA, from August 14, • New Methods for Finite Element Model 2006 to May 18, 2007. Updating Problems, AIAA Jorunal, Vol. 44, No. 6 (2006), 1310-1316. (with Y. C. Kuo and S. F. Xu) Recent Invited Talk • A Structure-Preserving Doubling Algorithm Geometric Evolution Equations and for Nonsymmetric Algebraic Riccati Related Topics Seminar, Mathematical Equation, Numer. Math., Vol. 103, Issue 3 Sciences Research Institute, September 6,

Activities of onsite Scientists -›› 68 2006, Berkeley, USA. -China- • Hangzhou (December): ICCM2007 at NCTS Activity Zhejiang University, invited speaker. Organizer of the "International Conference on Nonlinear Analysis", November 20-25, NCTS Activities 2006. • NCTS Summer School in Algebraic Geometry, co-organizer (July 2007) Recent Publications • NCTS Student Seminar in Algebraic • Tsai, D. H. (2005) Expanding embedded Geometry, organizer (June-July, 2007) plane curves, Contemporary Mathematics, th American Mathematical Society, Vol. 367, • NCTS 10 Anniversary: Lecture Series on 189-227, 2005. Algebra and Number Theory (August, 2007) • Tsai, D. H. (2005) Behavior of the gradient Research Works for solutions of parabolic equations on the Flops, motives and invariance of quantum circle, Calculus of Variations & PDE, Vol. • rings, (with Y.-P. Lee and H.-W. Lin), to 23, 251-270, 2005. appear in Annals of Mathematics. • Tsai, D. H. (2005) Asymptotic closeness to Elliptic functions, Green functions and the limiting shapes for expanding embedded • mean field equations on tori, (with C.-S. plane curves, Inventiones Mathematicae, Lin), submitted 2006. 162, 473-492, 2005. • Invariance of quantum ring under stratified • Nien, C. H., Tsai, D. H. (2006) Convex Mukai flops, (with B. Fu), in preparation. Curves Moving Translationally in the Plane, Journal of Differential Equations, 225, 605- • Invariance of quantum rings under ordinary 623, 2006. flops, (with Y.-P. Lee and H.-W. Lin), in preparation.

VI. Chin-Lung Wang National Central University, Professor VII. Jing Yu National Center for Theoretic Sciences, National Tsing-Hua University Shiing-shen Chern Fellow National Chair professor National Central University Adjunct Professor of Mathematics Conferences and Visiting -Taiwan- • Taipei (January-June): TIMS Seminars in Conferences Ricci Flow. -Taiwan- • Taipei (March): TIMS "Workshop on Higher International Conference on Galois Dimensional Algebraic Geometry", co- representations and function field Arithmetic organizer and invited speaker. (May 2007 at NCTS) Organizer. • Taipei (June): "International Conference on -China- Geometric Analysis", co-organizer International Conference on Langlands and geometric Langlands program (June 2007 (Forthcoming events) Guanzhoa) -Japan- • Invited Speaker, On Drinfeld modularity • Tokyo (December): Algebraic Geometry and automorphir representations. Conference at Tokyo University (organizer: Y. Kawamata), invited speaker. -Vietnam-

69 ‹‹- Activities of onsite Scientists International Conference on Number Theory Tsing Hua University which was held at NCTS and related topics (December 2006, Hanoi) and CTS from January 16 to 18, 2007. The • Invited Speaker: Algebraic Independence speakers were Professor Alexander Vasiliev in Positive characteristic and Professor Irina Markina from University of Bergen, Norway; Professor Bernard Gaveau Number Theory Seminar/Workshop from Universite Paris 6; Professor Peter Greiner from University of Toronto; Professor -Taiwan- Chisato Iwasaki from University of Hyogo; • NCTS Number Theory Workshop (May Professor Kenro Furutani from Science 2007), 1 lecture University of Tokyo; Professor Hung-Ling • 2007 Summer School on Automorphir Chiu from Chung Yuan Christian University; Representations (September 2007), 1 lecture Professor Jingzhi Tie from University of Georgia; Professor Shu-Cheng Chang from • 2007 Winter School on Number Theory (February, 2007), 1 lecture Tsing Hua University and myself. All speakers gave very nice talks on different topics in sub- -Korea- elliptic partial differential equations and sub- • Lectures on transcendence theory (February, Riemannian geometry, analysis on CR 2007, KAIST) manifolds, pseudo-differential operator and its applications to complex analysis. Publications I was also invited to give talks at Workshop • Determination of algebraic relations among on Functional Analysis and Harmonic special zeta values in positive characteristic Analysis which was held at National Taitung (with Chieh-Yu Chang), Advances in University in January 2007 and International Mathematcis, 2007. Conference in Geometric Analysis which was • Algebraci independence of zeta values in held at Taida Institute of Mathematics positive characteristic as the constant field Sciences and NCTS Taipei Office in June varies. (with Chieh-Yu Chang and M. 18~22, 2007. Papanikolas), preprint 2007. Besides hat, I was invited to give • On class number relations in characteristic colloquium talks at many universities. These two (with Yen-Mei J. Chen), Math. Zeit. activities give me opportunities to exchange 2007. ideas in mathematics with colleagues in Taiwan. • On the independence of Heegner points in the function field (with Fu-Tsun Wei), Activities Promotion preprint 2007. During March 5 to 6, 2007, I co-organized a Workshop in Analysis and Geometry with Professor Hsuan-Pei Lee and Professor Chin- E.2 Visiting Professor Huey Chang at the Academia Sinica. The speakers were Professor Richard Beals from Yale University; Professor Bernard Gaveau Name: Der-Chen Chang from Universite Paris 6; Professor Peter Georgetown University and NCTS Greiner from University of Toronto; Professor De-Chi Wu from the Academia Sinica; Activities Participation Professor Chun-Chung Hsieh from the During my visit at NCTS, I gave a series of Academia Sinica; Professor Jingzhi from lectures on "Subelliptic PDEs and University of Georgisa and me. subRiemannian Geometry". I co-organized a I was invited to participate the evaluation Workshop on Geometric Analysis with process of the Mathematics Department at Professor Shu-Cheng Chang from National

Activities of onsite Scientists -›› 70 Tsing Hua University and Fu Jen Catholic complex variables. During my visit at NCTS, I University. These opportunities allowed me to have chances to discuss a joint project with give some input of my opinion on Professor Shu-Cheng Chang at Tsing Hua mathematical research and mathematical University and Professor Jin Shin Cheng at the education. Academia Sinica. We are going to finish a paper on "Laguerre calculus and Paneitz Courses and Lectures on advanced topics operator on the Heisenberg group". During my visit at NCTS, Professor Shu- I am working on a joint project with Cheng Chang and I organized a mini-course at Professor Ming-Yee Lee from National Central NCTS and CMS. Speakers and topics are: University on "Estimates of generalized 1. Professor Der-Chen Chang from Calder\'on-Zygmund operators in weighted Georgetown University, "Sub-elliptic Partial spaces". Differential Equations and Sub-Riemannian During my visit at NCTS, I had finished Geometry". two papers with Professor Ovidiu Calin from 2. Professor Wen-Ling Huang from University Eastern Michigan University (who visited of Hamburg, "The Positive Mass NCTS last summer) on two papers: 1. Conjecture". "Isometric embeddings of subRiemannian manifolds in R m" which will appear in 3. Professor Jiin-Chang Shaw from Chiao- Advanced Studies in Contemporary Tung University "Quantum Mechanics". Mathematics. 2. "SubRiemannian geometry: a 4. Professor Jih-Hsin Cheng from the Cademia variation approach" which will appear in Sinica, "The Positive P-Mass Conjecture appear in Journal of Differential Geometry, and CR Yamabe Problem". (2007). Professor Calin has visited NCTS in the summer of 2007 and will visit NCTS again 5. Professor Shu-Cheng Chang from Tsing during 2008. Hua University, "The CR Harnark Estimates" I am finishing up two papers with another two visitors: Professor Alexander Vasiliev and 6. Professor Jianguo Cao from University of Professor Irina Markina on "Generalized Notre Dame, "Morse Theory of Distance Hamilton-Jacobi equation and heat kernel on Functions on Curved Spaces". step two nilpotent Lie groups" and "Sub- We met every Friday from 10:30 am to Lorentzian Geometry on Anti-De Sitter Space". 12:00 pm and then 1:30 pm to 3:00 pm. There were many graduate students and faulty Invited Talks members from differential university attended During my visit at NCTS, I have invited to this mini-course. give lectures at many universities and I had many chances to discuss mathematics institutes in Taiwan, Hong Kong, China and and their career development with graduate Japan. Here is the list. students at Tsing Hua University. One of them 1. Colloquium, Tunghai University, Taichung, has decided to work on his Ph.D. thesis under Taiwan, January 3, 2007. my direction and in fact, has already arrived Maryland. I gave a project to a Ph.D. student 2. Workshop on Geometric Analysis, National at Tsing Hua University. He will come to visit Center for Theoretical Sciences, Hsinchu, me sometime in 2008 and try to finish this Taiwan, January 16-18, 2007. paper. 3. Symposium on Analysis and Its Algebraic Structures, National Taitung University, Current Projects Taitung, Taiwan, January 22-23, 2007. I am working on subRiemannian geometry 4. Special Colloquium, Fu Jen Catholic induced by subelliptic partial differential University, Taipei, Taiwan, January 31, equations which arise especially from several

71 ‹‹- Activities of onsite Scientists 2007. Taiwan, June 12, 2007. 5. Colloquium, Taida Institute of Mathematical 19. Colloquium, National Central University, Sciences, National Taiwan University, Chungli, Taiwan, June 14, 2007. Taipei, Taiwan, February 5, 2007. 20. Invited One Hour Address, International 6. Geometry Seminar, Institute of Conference on Geometric Analysis, Mathematical Sciences, The University of National Taiwan University, Taipei, Hong Kong, Hong Kong, February 8, 2007. Taiwan, June 18, 2007. 7. Special Program in Analysis and Geometry, 21. Colloquium, FuJen Catholic University, National Center for Theoretical Sciences, Taipei, Taiwan, June 25, 2007. Hsinchu, Taiwan, March 2,9,16, 2007. 22. Invited One Hour Address, Workshop in 8. Workshop in Analysis and Geometry, Complex Geometry, The University of Academia Sinica, Taipei, Taiwan, March 5- Hong Kong, Hong Kong, China, July 10, 6, 2007. 2007. 9. Colloquium, Chung Yuan Christian 23. Eight lectures at summer school, Wuhan University, Chung Li, Taiwan, March 9, University, Wuhan, China, July 24-27, 2007. 2007. 10. Colloquium, National Tsing Hua 24. Colloquium, Wuhan University of University, Hsinchu, Taiwan, March 12, Technology, Wuhan, China, July 24, 2007. 2007. 25. Colloquium, the Chinese Academy of 11. Colloquium, Tunghai University, Sciences, Wuhan Institute of Mathematics Taichung, Taiwan, March 14, 2007. & Physics, Wuhan, China, July 25, 2007. 12. Forum on Teaching Calculus, Fu Jen 26. Celebrating 10th anniversary of NCTS Catholic University, Taipei, Taiwan, March series of lectures, National Center for 19, 2007. Theoretical Sciences, Hsinchu, Taiwan, July 31, 2007. 13. Special Program in Analysis and Geometry, National Center for Theoretical 27. Special lecture on Game Theory, National Sciences, Hsinchu, Taiwan, April 13, 2007. Changhua Girl's High School, Changhua, Taiwan, August 6, 2007. 14. Invited One Hour Address, Workshop in Geometric Analysis, University of Bergen, Bergen, Norway, May 4, 2007. CTS Preprints 2007-8-002: DER-CHEN CHANG AND 15. Invited 45 minutes Address, International STEPHEN S.-T. YAU Conference on "New Trends on Complex "EOMETRIC ANALYSIS ON A and Harmonic Analysis", Voss, Norway, FAMILY OF PSEUDOCONVEX May 7-11, 2007. HYPERSURFACES" 16. Invited One Hour Address, 2007 2007-7-002: DER-CHEN CHANG " International Conference on Several – BERGEN LECTURE ON ∂- Complex Variables and Complex NEUMANN PROBLEM " Geometry, Xiamen University, Xiamen, China, May 28-31, 2007. 2007-7-001: OVIDIU CALIN, DER-CHEN CHANG, IRINA MARKINA 17. Invited One Hour Address, Workshop on "GENERALIZEDHAMILTON- Functional and Global Analysis, Tokyo JACOBI EQUATION AND University of Sciences, Tokyo, Japan, June HEAT KERNELON STEP TWO 4-6, 2007. NILPOTENT LIE GROUPS " 18. Colloquium, Tamkang University, Taipei, 2007-1-004: OVIDIU CALIN, DER-CHEN

Activities of onsite Scientists -›› 72 CHANG, IRINA MARKINA "GEOMETRIC ANALYSIS ON "The logarithmic Sobolev constant on finite H-TYPE GROUPS RELATED • cycles", Analysis seminar in Cornell TO DIVISION ALGEBRAS " University, April 2007 2007-1-003: Ovidiu Calin and Der-Chen "The L2 cutoff for finite Markov chains", Chang "Isometric Embeddings of • Probability seminar in Cornell University, SubRiemannian Manifolds in Rm " April 2007 2007-1-002: Ovidiu Calin, Der-Chen Chang and Irina Markina NCTS Preprints "SubRiemannian geometry on the "The cutoff phenomenon for randomized 3 • sphere S " riffle shuffles", Joint with Laurent Saloff- Coste, NCTS preprint 2006. Accepted by Lecture Notes Random Structures and Algorithms. 2007 NCTS&CMS Topical "The cutoff phenomenon for ergodic Markov Program in Analysis and Geometry:Subelliptic • processes", Joint with Laurent Saloff-Coste, PDEs and SubRiemannian Geometry NCTS preprint 2007. Submitted. (I)(II)(III)(IV)(V)(VI)(VII) • "The logarithmic Sobolev constant of some finite Markov chains", Joint with Wai-Wai E.3 Visiting Assistant Professor Liu and Laurent Saloff-Coste, NCTS preprint 2007. Accepted by Annales de la Faculte des Sciences de Toulouse. Name: Guan-Yu Chen Activities Participation • NCTS Student Seminar on Probability E.4 Report of Post Doctors (Organizer: 2006/7-2006/12) • NCTS 2007 Summer Course on Probabilistic Name: Yan-Hsiou Cheng and Statistic Methods in Bioinformatics My recent research focus on the nodal (2007/7/5-2007/7/26) problem and the spectral theory of the Sturm- Liouville problem. The second course, the Academic Visit spectral theory, is the topic I am studying in the seminar held by Processor C.L. Shen in Department of Mathematics, Cornell National Tsing Hua Univresity. The research University (3/1/2007-5/31/2007) of the nodal problem is a joint work with Professor C.K. Law in National Sun Yat-sen Current Projects University. We hope to apply the inverse nodal • The L2 cutoff for reversible Markov theory to some other eigenvalue problems. processes and the comparison of discrete time and continuous time thresholds. During the past half year, I have participated in the following academic • The logarithmic Sobolev constant for odd activities. cycles and flat tori. • Algorithms for spectral gaps and logarithmic Seminar/Visit/Conference Sobolev constants on finite birth and death 1. I joint the seminar held by Processor C.L. chains. Shen in NTHU. We discuss the spectral problem of the general Sturm-Liouville Invited Talks problems and also read some papers. • "The cutoff phenomenon for finite Markov 2. I attended some of seminars held by NCTS. chains", The topics include Harmonic Analysis,

73 ‹‹- Activities of onsite Scientists Math. Biology and Dynamical Systems, show the existence of certain distinguished Bioinformatics and so forth. representations on the metaplectic covers of GL(4), which generalize classical Theta 3. I will give a talk on October in Tamkang functions. This project is expected to complete University. by the end of the year. Future plans For future research, I would like to study 1. We hope to make the inverse nodal theory metaplectic forms from different perspectives; perfect and take more applications on other for example, using the technique of trace problems. The existence problem in inverse formulas to gain better understanding of the nodal problem is not solved yet and that is nature of these metaplectic forms. I would also what we want to study actively. like to explore further the Fourier coefficients of the distinguished representations, which are 2. On the other hand, I hope that some known to carry rich arithmetic information. interesting problems will be discussed in the seminar with Processor C.L. Shen. Talks/NCTS Activities Additionally, I wish to learn more technique During this year, I gave four lectures on the and knowledge about my research. converse theorems for GL(n) in the workshop at NCTS, and three more lectures on the Name: Chian-Jen Wang applications of the converse theorems in the winter school held at the Aspire Park, Research Taoyuan. I also gave talks regarding My research has been focusing on metaplectic representations in the Number questions related to the distinguished Theory Seminar at NCTS and contributed a representations of metaplectic groups recently. talk introducing metaplectic forms in the Some of these questions have been studied Workshop on Algebra and Geometry at earlier in my thesis in the case where the NCCU. These experiences have helped me to metaplectic groups involved are four-fold organize and convey my ideas in a more covers of GL(4). This year, I have extended effective way. part of the results obtained earlier in my thesis At NCTS, I attended the Number Theory to metaplectic covers of GL(n), and fixed Seminar and Lie Theory Seminar regularly. some gaps there towards establishing the There were several exciting activities held this desired distinguished representations on the year: the course on Modular Forms and Galois GL(4) coverings. Representations offered by Prof. Winnie Li in More specifically, this project involves a the Fall semester, the international conference local theory (Rankin-Selberg theory) and a on Galois Representations and Function Field global method (the converse theorem). Arithmetic in May, the summer school and Locally, we studied the Rankin-Selberg winter school discussing topics ranging from convolutions for metaplectic groups and class field theory, non-Archimedean geometry, assigned local Gamma factors to metaplectic Drinfeld modular forms to representation representations. The analytic behaviors of the theory, etc. Participating in these activities and local Gamma factors were examined. Globally, talking to number theorists local and from we generalized the work of Cogdell-Piatetski- abroad, I learned a lot and had fun. Shapiro on the converse theorems for GL(n) to metaplectic setting. Both of the local theory Papers and Preprints and the global method have now been settled 1. Chian-Jen Wang "Local Rankin-Selberg for the n-fold covers of GL(n). As an Convolutions for Metaplectic Groups" application, we applied the converse theorem preprint. of metaplectic version combined with the analytic information form the local theory to 2. Chian-Jen Wang "Converse Theorems for Metaplectic Groups" preprint.

Activities of onsite Scientists -›› 74 Preprints

Series I Title and Author

Efficient Numerical Schemes for Electronic States in Coupled 2007-1-01 Quantum Dots Tsung-Min Hwang, Wei-Hua Wang, and Weichung Wang

Motivic Integration and Algebraic Cycles 2007-1-02 Jyh-Haur Teh

Structured Doubling Algorithms for Weak Hermitian Solutions of 2007-1-03 Algebraic Riccati Equations Tsung-Min Hwang and Wen-Wei Lin

On A Doubling Algorithm for The Nonlinear Matrix Equation 2007-1-04 X+ATX-1A=Q when λ(X-1A)≤1 Eric King-wah Chu, Tsung-Min Hwang, Wen-Wei Lin and Shu-Fang Xu

A Continuation Method for Positive Bound States of m-coupled 2007-1-05 Nonlinear Schrödinger Equations Yuen-Cheng Kuo, Wen-Wei Lin, Shih-Feng Shieh and Weichung Wang

A Numerical Method for Quadratic Eigenvalue Problems of 2007-1-06 Gyroscopic Systems Jiang Qian and Wen-Wei Lin

SubRiemannian Geometry on the Sphere S3 2007-1-07 Ovidiu Calin, Der-Chen Chang and Irina Markina

Isometric Embeddings of SubRiemannian Manifolds in Rm 2007-1-08 Ovidiu Calin and Der-Chen Chang

Geometric Analysis on H-type Groups Related to Division Algebras 2007-1-09 Ovidiu Calin, Der-Chen Chang and Irina Markina

Vibration of Fast Trains, Palindromic Eigenvalue Problems and 2007-1-10 Structure-Preserving Doubling Algorithms Eric King-wah Chu,Tsung-Min Hwang,Wen-Wei Lin and Chin-Tien Wu

A John-Nirenberg Type Inequality for Qα(Rn) 2007-1-11 Hong Yue and Galia Dafni

Geometric Quantization and Zuckerman Models of Semisimple Lie 2007-1-12 Groups Meng-Kiat Chuah

Combinations of Collocation and Finite-Element Methods for 2007-1-13 Poisson's Equation Hsin-Yun Hu and Zi-Cai Li

75 ‹‹- Preprints Series I Title and Author The Spectrum of Chaotic Time Series(I): Fourier Analysis 2007-1-14 Goong Chen, Sze-Bi Hsu, Yu Huang, and Marco A. Roque-Sol.

The Spectrum of Chaotic Time Series(II): Fourier Analysis 2007-1-15 Goong Chen, Sze-Bi Hsu, Yu Huang, and Marco A. Roque-Sol.

2007-1-16 The Final Size of a SARS Epidemic Model without Quarantine Sze-Bi Hsu and Lih-ing W. Roeger

Nonlinear Dynamics Induced by Repetitive Optical Pulse Injection of 2007-1-17 a Semiconductor Laser Fan-Yi Lin, Shiou-Yuan Tu,Chien-Chih Huang, and Shu-Ming Chang

A Structured Doubling Algorithm for Discrete-time Algebraic 2007-1-18 Riccati Equations with Singular Control Weighting Matrices Chun-Yueh Chiang, Hung-Yuan Fan and Wen-Wei Lin

Generalized Hénon Maps and Half-orientable Smale Horseshoes 2007-1-19 Sergey Gonchenko, Ming-Chia Li, Mikhail Malkin

Numerically Stable, Structure-preserving Algorithms for 2007-1-20 Palindromic Quadratic Eigenvalue Problems Jiang Qian, Tsung-Min Hwang and Wen-Wei Lin

On a Simple Maximum Principle Technique Applied to 2007-1-21 Equations on the Circle Yu-Chu Lin and Dong-Ho Tsai

Expanding Immersed Convex Plane Curves 2007-1-22 Tai-Chia Lin, Chi-Cheung Poon, and Dong-Ho Tsai

The Cutoff Phenomenon for Ergodic Markov Processes 2007-1-23 Guan-Yu Chen and Laurent Saloff-Coste

Generalized Hamilton-Jacobi Equation and Heat Kernel on Step 2007-1-24 Two Nilpotent Lie Groups Ovidiu Calin, Der-Chen Chang and Irina Markina – Bergen Lecture on ∂-Neumann Problem 2007-1-25 Der-Chen Chang

A Homology and Cohomology Theory for Real Projective Varieties 2007-1-26 Jyh-Haur Teh

The Logarithmic Sobolev Constant of Some Finite Markov Chains 2007-1-27 Guan-Yu Chen, Wai-Wai Liu and Laurent Saloff-Coste

Heteroclinic Cycles in the Chemostat Models and the Winnerless 2007-1-28 Competition Principle Sze-Bi Hsu and Lih-Ing W. Roeger

Preprints -›› 76 Series I Title and Author

Structure-preserving Arnoldi-type Algorithms for Palindromic 2007-1-29 Quadratic Eigenvalue Problems Tsung-Min Hwang, Wen-Wei Lin and Jiang Qian

Geometric Analysis on a Family of Pseudoconvex Hypersurfaces 2007-1-30 Der-Chen Chang and Stephen S.-T. Yau

Average Values of L-functions in Characteristic Two 2007-1-31 Yen-Mei J. Chen

On the Independence of Heegner Points in the Function Field Case 2007-1-32 Fu-Tsun Wei and Jing Yu

Competition of Two Host Species for a Single-limited Resource 2007-1-33 Mediated by Parasites Sze-Bi Hsu and I-Fan Sun

Competitive Exclusion of Microbial Species for a Single-limited 2007-1-34 Resource with Internal Storage Sze-Bi Hsu and Ting-Hao Hsu

On the Role of Asymptomatic Infection in Transmission 2007-1-35 Dynamics of Infectious Diseases Sze-Bi Hsu and Ying-Hen Hsieh

Global Dynamics of a Predator-Prey Model with Hassell-Varley 2007-1-36 Type Functional Response Sze-Bi Hsu, Tzy-Wei Hwang and Yang Kuang

Concentration Phenomena in a Nonlocal Quasilinear Problem 2007-1-37 Modelling Phytoplanktion in Poorly Mixed Water Columns Yihong Du and Sze-Bi Hsu

The Direct Integral of Some Weighted Bergman Spaces 2007-1-38 Meng-Kiat Chuah

A Quick Proof on the Equivalence Classes of Extended Vogan 2007-1-39 Diagrams Meng-Kiat Chuah and Chu-Chin Hu

Pseudo-einstein and Q-flat Metrics with Eigenvalue Estimates 2007-1-40 on CR-hypersurfaces Jianguo Cao and Shu-Cheng Chang

The Bondi-mass Type Estimate on a Closed CR 3-manifold with 2007-1-41 Nonnegative Paneitz Operator Shu-Cheng Chang and Chin-Tung Wu

77 ‹‹- Preprints Series I Title and Author

On the CR Analogue of Obata's Theorem in a Pseudohermitian 2007-1-42 3-manifold Shu-Cheng Chang and Hung-Lin Chiu

The Li-Yau-Hamilton Inequality for Yamabe Flow on a Closed CR 2007-1-43 3-manifold Shu-Cheng Chang, Hung-Lin Chiu and Chin-Tung Wu

Algebraic Independence of Carlitz Zeta Values for Different 2007-1-44 Constant Fields Chieh-Yu Chang, Matthew A. Papanikolas and Jing Yu

Period Polynomials and Explicit Formulas for Hecke Operators

2007-1-45 on Γ0(2) Shinji Fukuhara and Yifan Yang

Determination of Hauptmoduls and Construction of Abelian 2007-1-46 Extensions of Quadratic Number Fields Hung-Jen Chiang-Hsieh and Yifan Yang

Differential Equations Satisfied by Modular Forms and K3 2007-1-47 Surfaces Yifan Yang and Noriko Yui

A Short Prooff of Milne's Formulae for Sums of Integer Squares 2007-1-48 Ling Long and Yifan Yang

On Atkin and Swinnerton-dyer Congruence Relations (2) 2007-1-49 A.O.L. Atkin, Wen-Ching Winnie Li, and Ling Long

Hecke Operators on Drinfeld Cusp Forms 2007-1-50 Wen-Ching Winnie Li and Yotsanan Meemark

Spreading Speeds and Traveling Waves for Non-monotone 2007-1-51 Integrodifference Equations Sze-Bi Hsu and Xiao-Qiang Zhao

Fully Consistent and Accurate Pressure Boundary Condition 2007-1-52 for MAC Scheme on Curvilinear Domains Yin-Liang Huang, Jian-Guo Liu and Wei-Cheng Wang

Exact Far Field Boundary Condition for Flows Past 2007-1-53 Axisymmetric Obstacles Yin-Liang Huang, Jian-Guo Liu and Wei-Cheng Wang

Fast Solver for Scalar and Vector Poisson Equation on 2007-1-54 Spherical Shells Yin-Liang Huang, Jian-Guo Liu and Wei-Cheng Wang

Preprints -›› 78 Series II Title and Author

Minimal Polynomials of Algebraic Derivations and Automorphisms 2007-2-01 Chen-Lian Chuang, Tsiu-Kwen Lee and Chi-Tsuen Yeh

An Example of Bergman's and the Extension Problem for Clean 2007-2-02 Rings Tsiu-Kwen Lee, Zhong Yi and Yiqiang Zhou

Blowup Rate Estimates for the Heat Equation with a Nonlinear 2007-2-03 Gradient Source Term Jong-Shenq Guo and Bei Hu

Half-Skyrmions and Spike-Vortex Solutions of Two-component 2007-2-04 Nonlinear Schrodinger Systems Tai-Chia Lin and Juncheng Wei

Construction of Galois Covers of Curves with Groups of SL2-type 2007-2-05 Chia-Fu Yu

Irreducibility and p-adic Monodromies on the Siegel Moduli Spaces 2007-2-06 Chia-Fu Yu

Kottwitz-Rapoport Strata in the Siegel Moduli Spaces 2007-2-07 Chia-Fu Yu

An Exact Geometric Mass Formula 2007-2-08 Chia-Fu Yu

Hydrodynamic Limits of Two-component Gross-Pitaevskii 2007-2-09 Equations with Rotating Fields and Trap Potentials Tai-Chia Lin, Chiun-Chang Lee

Algebraic Prime Subalgebras in Simple Artinian Algebras 2007-2-10 Tsiu-Kwen Lee and Yiqiang Zhou

2007-2-11 Quotient Rings and f-radical Extensions of Rings Chen-Lian Chuang, Tsiu-Kwen Lee and Cheng-Kai Liu

Operator Semi-Selfsimilar Processes Induced by Multi-dimensional 2007-2-12 Random Walk in Multi-dimensional Random Scenery Tatsuhiko Saigo and Narn-Rueih Shieh

Quotient Rings of Ore Extensions with More Than One 2007-2-13 Indeterminate Yuan-Tsung Tsai and Chen-Lian Chuang

79 ‹‹- Preprints Series III Title and Author

2007-3-01 Circular Choosability Via Combinatorial Nullstellensatz Serguei Norine, Tsai-Lien Wong, Xuding Zhu

Game Colouring the Cartesian Product of Graphs 2007-3-02 Xuding Zhu On the Adaptable Chromatic Number of Graphs 2007-3-03 Pavol Hell and Xuding Zhu Bounds on Circular Consecutive Choosability 2007-3-04 Serguei Norine, Zhishi Pan, Xuding Zhu Adapted List Coloring of Graphs and Hypergraphs 2007-3-05 A.V. Kostochka and Xuding Zhu Refined Activation Strategy for the Marking Game 2007-3-06 Xuding Zhu An Algorithm for Semi-infinite Transportation Problems 2007-3-07 Shen-Yu Chen and Soon-Yi Wu

Algorithms for Infinite Quadratic Programming in Lp Spaces 2007-3-08 Shen-Yu Chen and Soon-Yi Wu An Explicit Exchange Algorithm for Linear Semi-infinite 2007-3-09 Programming Problems with Second-order Cone Constraints Shunsuke Hayashi and Soon-Yi Wu Gap Functions for a System of Generalized Vector Quasi- 2007-3-10 equilibrium Problems with Set-valued Mappings Nan-Jing Huang, Jun Li and Soon-Yi Wu A Finitely Terminating Explicit Exchange Method for Convex 2007-3-11 Semi-infinite Programming Liping Zhang, Soon-Yi Wu and Marco A. L´Opez Robust Envelope-constrained Filter with Orthonormal Bases 2007-3-12 and Semi-definite and Semi-infinite Programming S. J. Li, K. L. Teo, X. Q. Yang and S. Y. Wu First Order Optimality Conditions for Generalized Semi-infinite 2007-3-13 Programming Problems J. Ye and S. Y. Wu Gateaux Differentiability of the Dual Gap Function of a 2007-3-14 Variational Inequality Z. L. Wu and S. Y. Wu An Infinite-dimensional Mathematical Programming Approach 2007-3-15 to Separation in Lp (X, A, M) M. Lopez, S. Y. Wu, C. Ling and L. Qi

An Explicit Algorithm for Convex Semi-infinite Programming 2007-3-16 Problem with Second-Order Cone Constraint S. Hayashi and S. Y. Wu

Preprints -›› 80 Series III Title and Author

Ising Vectors in the Vertex Operator Algebra VΛ+Associated 2007-3-17 with the Leech Lattice Λ Ching Hung Lam and Hiroki Shimakura Quantum Codes from Hadamard Matrices 2007-3-18 W.F. Ke, K.F. Lai, and R.B. Zhang A Characterization of The Moonshine Vertex Operator Algebra 2007-3-19 by Means of Virasoro Frames Ching Hung Lam and Hiroshi Yamauchi The Structure of Compact Disjointness Preserving Operators 2007-3-20 on Continuous Functions Ying-Fen Lin and Ngai-Ching Wong Geometric Pre-ordering on C*-Algebras 2007-3-21 Chi-Wai Leung, Chi-Keung Ng and Ngai-Ching Wong Jordan Isomorphisms and Maps Preserving Spectra of Certain 2007-3-22 Operator Products Jinchuan Hou, Chi-Kwong Li, and Ngai-Ching Wong Separating Linear Maps and Zero Product Preservers of 2007-3-23 Continuous Fields of Banach Spaces and C*-Algebras Chi-Wai Leung, Chi-Keung Ng, and Ngai-Ching Wong The Triangle of Operators, Topologies, Bornologies 2007-3-24 Ngai-Ching Wong Geometric Unitaries in Jb-Algebras 2007-3-25 Chi-Wai Leung, Chi-Keung Ng and Ngai-Ching Wong Property T for Non-Unital C*-Algebras 2007-3-26 Chi-Wai Leung, Chi-Keung Ng, Ngai-Ching Wong A Banach-Stone Theorem for Riesz Isomorphisms of Banach 2007-3-27 Lattices Jin Xi Chen, Zi Li Chen and Ngai-Ching Wong On C*-Algebras with Property T 2007-3-28 Chi-Wai Leung, Chi-Keung Ng and Ngai-Ching Wong Unitaries in Jb-Algebras 2007-3-29 Chi-Wai Leung, Chi-Keung Ng and Ngai-Ching Wong Compact Disjointness Preserving Maps of Continuous 2007-3-30 Functions Yin-Fen Lin and Ngai-Ching Wong Ambarzumyan-type Theorems for the Sturm-Liouville 2007-3-31 Operator on Star-shaped Graphs C.K. Law and C.T. Shieh Integrability of Rotationally Symmetric N-harmonic Maps 2007-3-32 Chao-Nien Chen, L.F. Cheung, Y.S. Choi, C.K. Law

Reconstructing Potentials from Zeros of One Eigenfunction 2007-3-33 Xinfu Chen, Y.H. Cheng, and C.K. Law

81 ‹‹- Preprints Series III Title and Author

Inverse Nodal Problems for Nonlinear Sturm-Liouville 2007-3-34 Equations Chao-Nien Chen and C.K. Law

Distinguishing Labeling of Group Actions 2007-3-35 Tsai-Lien Wong and Xuding Zhu

Multi-Colouring the Mycielskian of Graphs 2007-3-36 Wensong Lin, Daphne Der-Fen Liu aAnd Xuding Zhu

Lower Bounds for the Game Colouring Number of Partial K- 2007-3-37 Trees and Planar Graphs Jiaojiaowu and Xuding Zhu

Cartesian Powers of Graphs Can Be Distinguished by Two 2007-3-38 Labels Sandi Klavzar and Xuding Zhu

Distinguishing Labellings of Group Actionb on Vector Spaces 2007-3-39 and Graphs Sandi Klavˇzar, Tsai-Lien Wong and Xuding Zhu

Multiple Colouring of Cone Graphs 2007-3-40 Zhishi Pan and Xuding Zhu

The D-Relaxed Game Chromatic Index of K-degenerated 2007-3-41 Graphs Hungyung Chang and Xuding Zhu

Distinguishing Labeling of the Actions of Symmetric and 2007-3-42 Alternating Groups Tsai-Lien Wong and Xuding Zhu

Preprints -›› 82 Visiting Mathematicians 2007

2007

Name Field of Interest Period of Visit Appendix

Jiahong Wu Nonlinear Partial Differential 2006/09/01 ~ 2006/09/30 (Oklahoma State University) Equations M.H. Kang (Penn. State University) Number Theory 2006/09/03 ~ 2006/12/31 Keiichi Komatsu (Waseda University) Number Theory 2006/09/03 ~ 2006/09/16 Yasushi Mizusawa (Sophia University) Number Theory 2006/09/03 ~ 2006/09/16 Wu-Yi Hsiang (Hong Kong University of Differential geometry 2006/09/04 ~ 2006/09/11 Science and Technology) Yu Huang (Zhongshan SUN YAT SEN Dynamical System 2006/09/12 ~ 2006/10/11 University) Alain Perronnet Finite elements scientific 2006/09/12 ~ 2006/10/01 (Universite de Paris VI & VII) computation

Edmund R. Puczylowski Algebra(Ring Theory) 2006/09/12 ~ 2006/10/01 ( University of Warsaw, Poland)

Ser Peow Tan (National University of Geometry 2006/09/22 ~ 2006/10/01 Singapore)

Charles Li Algebra 2006/09/25 ~ 2006/09/30 (Academia Sinica)

Yakov Alber (Technion-Israel Institute of Functional Analysis 2006/10/05 ~ 2006/11/06 Technology) Frank Hwang (ATT and National Chiao Tung Dicsrete Mathematics 2006/10/10 ~ 2006/10/18 University) Joseph Silverman (Brown University) Number Theory 2006/10/15 ~ 2006/10/28 Xiaojiao Tong (Changsha University of Science Optimization 2006/10/15 ~ 2006/11/15 & Technology) Xie-Ping Ding (Sichuan Normal University) Functional Analysis 2006/10/24 ~ 2006/11/23

83 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Gurjar Rajendra Vasant

Appendix (Tata Institute of Fundamental Algebraic Geometry 2006/10/25 ~ 2006/11/14 Research)

Chia-Fu Yu (Academia Sinica) Geometry 2006/10/25 ~ 2006/10/27

Yongzeng (George) Lai 2006/11/06 ~ 2006/11/26 (Wilfrid Laurier University) Financial Mathematics Toshihiro Uemura (University of Hyogo) Probability 2006/11/08 ~ 2006/11/16 Peter Sasieni (Cancer Research UK) Biostatistics 2006/11/14 ~ 2006/11/16 Dongho Chae (Sungkyunkwan University) PDE 2006/11/15 ~ 2006/11/20 Kazuhiro Ishige (Tohoku University) PDE 2006/11/16 ~ 2006/11/20 Dong-Ho Chae (Seoul National University) Nonlinear PDE 2006/11/20 ~ 2006/11/25 Applied Mathematics, Michel Chipot Dynamical System, 2006/11/20 ~ 2006/11/25 (Institute für Mathematik Nonlinear PDE, Universitüt Zürich) Scientific Computation,

P. G. Ciarlet Applied Mathematics, 2006/11/20 ~ 2006/11/21 (City University of Hong Kong) Differential Geometry N. Kenmochi (Chiba University) Nonlinear PDE 2006/11/20 ~ 2006/11/25 David Kinderlehrer (Carnegie Mellon University) Nonlinear PDE 2006/11/20 ~ 2006/11/25

Y. Morita Applied Mathematics 2006/11/20 ~ 2006/11/25 (Ryukoku University) W.-M. Ni (University of Minnesota) Nonlinear PDE 2006/11/20 ~ 2006/11/25 Mythily Rawasmany (T. I. F. R. Center) Nonlinear PDE 2006/11/20 ~ 2006/11/25

Kunimochi Sakamoto Dynamical System, 2006/11/20 ~ 2006/11/25 (Hiroshima University) Nonlinear PDE Itai Shafrir (Technion-Israel Institute of Nonlinear PDE 2006/11/20 ~ 2006/11/25 Technology)

Appendix -›› 84 2007 Name Field of Interest Period of Visit S. Ukai Algebraic Geometry 2006/10/25 ~ 2006/11/14

(City University of Hong Kong) Appendix Juncheng Wei Applied Mathematics, (Chinese University of Hong 2006/11/20 ~ 2006/11/25 Kong) Nonlinear PDE Eiji Yanagida (Tohoku University) Nonlinear PDE 2006/11/20 ~ 2006/11/25 Bogdan Bojarski (Polish Academy of Sciences) Nonlinear PDE 2006/11/21 ~ 2006/11/22 Z. Xin (Chinese University of Hong Nonlinear PDE 2006/11/21 ~ 2006/11/25 Kong) Bogdan Bojarski (Polish Academy of Sciences) PDE 2006/11/22 ~ 2006/12/11 Mitsuharu OTANI Applied Mathematics, 2006/11/22 ~ 2006/11/25 (Waseda University) Dynamical System Yoshikazu Giga (University of Tokyo) Nonlinear PDE 2006/11/23 ~ 2006/11/25 Shih-Hsien Yu Nonlinear PDE 2006/11/23 ~ 2006/11/25 (City University of Hong Kong) Yoshitsugu Kabeya PDE 2006/11/25 ~ 2006/12/03 (Osaka Prefecture University) Alex Novikov (University of Technology, Probability 2006/11/26 ~ 2006/12/08 Sydney) Eric Chu (Monash University, AU) Scientific computation 2006/12/01 ~ 2007/01/09 Chuu-Lian Terng (University of California, Irvine) Geometry 2006/12/02 ~ 2006/12/10 S. Schaible Optimization and Control (University of California, 2006/12/08 ~ 2007/01/02 Riverside) theory Shengjie Li Optimization 2006/12/10 ~ 2007/01/09 (Chongqing University) Nikolai N. Leonenko (Cardiff University) Probability 2006/12/13 ~ 2006/12/27 Meng-Kiat Chua (National Chiao Tung Algebra 2006/12/14 ~ 2006/12/25 University)

Reyer Sjamaar Optimization 2006/12/14 ~ 2006/12/27 (Cornell University)

85 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Yuan Lou PDE 2006/12/16 ~ 2006/12/20 Appendix (Ohio State University)

Dinakar Ramakrishnan Algebraic Geometry, (California Institute of Number Theory, 2006/12/17 ~ 2006/12/19 Technology) Automorphic Forms

Chiu-Yen Kao (The Ohio State University) Scientific Computing 2006/12/18 ~ 2006/12/29

Jun Zou (National University of Discrete Mathematics 2006/12/18 ~ 2006/12/24 Singapore)

Bei Hu (University of Notre Dame) PDE 2006/12/19 ~ 2007/01/03

Yen-His Tsai (The University of Texas at Scientific Computing 2006/12/19 ~ 2007/01/14 Austin)

Shuyu Sun Finite element methods 2006/12/20 ~ 2007/01/08 (Clemson University)

Zhidong Bai (National University of Discrete Mathematics 2006/12/21 ~ 2006/12/30 Singapore)

King Fai Lai (Sydney University) Algebra 2006/12/22 ~ 2006/12/25

Galia Dafni (Concordia University) Analysis 2006/12/25 ~ 2007/01/07

Henri Darmon (Mc Gill University) Number Theory 2006/12/25 ~ 2007/01/01

Wentang Kuo Number Theory, 2006/12/25 ~ 2007/01/07 (University of Waterloo Canada) Representation Theory Differential Geometry & Irina Markina 2007/01/04 ~ 2007/01/28 (University of Bergen) Geometric Analysis, Real Analysis

Differential Geometry & Alexander Vasiliev Geometric Analysis, 2007/01/04 ~ 2007/01/28 (University of Bergen) Math. Physics

Alexandr Vasilievich Kostochka (University of Illinois at Urbana- Discrete Mathematics 2007/01/05 ~ 2007/01/15 Champaign)

Appendix -›› 86 2007 Name Field of Interest Period of Visit

Jie Sun

(Nat'l Univ. of Singapore) Optimization 2007/01/05 ~ 2007/01/11 Appendix

Eric K.-W. Chu (Monash University, AU) Optimization 2007/01/10 ~ 2007/01/23

Kenro Furutani Differential Geometry & 2007/01/10 ~ 2007/01/24 (Science University of Tokyo) Geometric Analysis

Chisato Iwasaki Differential Geometry & 2007/01/10 ~ 2007/01/24 (University of Hyogo ) Geometric Analysis

Marco Lopez (Alicante University, Spain) Optimization 2007/01/10 ~ 2007/01/21

Hidekazu Niibori (Tsukuba University) Algebra 2007/01/14 ~ 2007/01/19

H. Shimakura (Hokkaido University) Algebra 2007/01/14 ~ 2007/01/19

Hiroshi Yamauchi Algebra 2007/01/14 ~ 2007/01/19 (University of Tokyo)

Zhi Lu (FuDan University) Geometry 2007/01/15 ~ 2007/01/28

Jie Xiao Quantum Group, 2007/01/15 ~ 2007/01/23 (Tsinghua University) Ringel-Hall Algebras

Jae-Hoon Kwon ( University of Seoul) Algebra 2007/01/18 ~ 2007/01/18

Magnus Aspenberg Geometry 2007/01/21 ~ 2007/02/04 (University Paris-Sud)

Nikolaos Kavallaris (Osaka University) PDE 2007/01/22 ~ 2007/01/29

Dimitrios Tzanetis (National Technical University PDE 2007/01/22 ~ 2007/01/29 of Athens)

Wen-ling Huang (University of Hamburg) Geometry and Math. Physics 2007/02/24 ~ 2007/03/17

Richard W. Beals Analysis, (Yale University) Partial Differential Equations 2007/02/27 ~ 2007/03/18

87 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Koichiro Harada Algebra 2007/03/01 ~ 2007/03/25

Appendix (Ohio State University) Shunsuke Hayashi Optimization 2007/03/01 ~ 2007/03/15 (Kyoto University) Bernard Brighi (University of Haute Alsace) PDE 2007/03/10 ~ 2007/03/20 Sergey Norin (Georgia Institute of Discrete Mathematics 2007/03/11 ~ 2007/03/23 Technology) Dynamical System, Yihong Du Mathematical Biology, 2007/03/15 ~ 2007/04/26 (University of New England) Nonlinear PDE

Peter Horak (University of Washington, Discrete Mathematics 2007/03/16 ~ 2007/03/29 Tacoma)

Chuu-Lian Terng Geometry 2007/03/16 ~ 2007/03/22 (University of California, Irvine) Chen Ling (Zhejiang University of Finance Optimization 2007/03/17 ~ 2007/05/17 & Economics) Hiroshi Matano (University of Tokyo) PDE 2007/03/18 ~ 2007/03/23

Boris Kouniavski Galois cohomology,algebra, (Bar-Ilan University) algebraic geometry, number 2007/03/22 ~ 2007/04/05 theory

Meng Chen Algebraic geometry 2007/03/23 ~ 2007/04/15 (Fudan University) Tommaso De Fernex (University of Utah) Algebraic geometry 2007/03/26 ~ 2007/04/01 James Mckernan (University of California at Higher dimensional geometry 2007/03/26 ~ 2007/04/01 Santa Barbara)

Jason Michael Starr Birational geomerty 2007/03/26 ~ 2007/04/01 (Stony Brook University)

Bao-Hua Fu Algebraic geometry 2007/03/27 ~ 2007/04/02

Wu-Yi Hsiang Transformation group, 2007/03/27 ~ 2007/04/02 (University of California, Differential geometry Berkeley)

Appendix -›› 88 2007 Name Field of Interest Period of Visit Der-Chen Chang Classical Analysis 2007/04/12 ~ 2007/04/15 (Georgetown University) Appendix

Der-Chen Chang Classical Analysis 2007/04/18 ~ 2007/04/19 (Georgetown University) Francois Jean Raymond Hamel (University of Aix-Marseille III) PDE 2007/04/21 ~ 2007/04/29 King Fai Lai Number Theory 2007/04/23 ~ 2007/05/23 (University of Sydney)

Dynamical System, Xiaoqiang Zhao Mathematical Biology, (memorial University of 2007/04/27 ~ 2007/05/28 Nonlinear Differential, Newfoundland) Equations Boyan Slavchev Sirakov Elliptic and parabolic PDE and (The University of Paris 10) applications 2007/04/29 ~ 2007/05/08 Shigeharu Takayama Geometry 2007/04/30 ~ 2007/05/07 (University of Tokyo) Song Ping Zhu Mathematical and (University of Wollongong) Computational Finance 2007/05/02 ~ 2007/05/04

Numerical Analysis of PDEs, Fluid Dynamics related So-Hsiang Chou 2007/05/03 ~ 2007/08/03 (Bowling Green state University) applications, Mathematics of Finance Vjacheslav Yurko (Saratov University) Differential Equations 2007/05/03 ~ 2007/05/06

H. L. Smith Dynamical System, 2007/05/06 ~ 2007/05/20 (Arizona State University) Mathematical Biology

Dinesh S. Thakur Algebraic Geometry, (University of Arizona U.S.A.) Number Theory 2007/05/06 ~ 2007/05/18 Pawel Pilarczyk (Rutgers University) Dynamical System 2007/05/09 ~ 2007/05/19 Piotr Zgliczynski (Jagiellonian University) Dynamical System 2007/05/09 ~ 2007/05/22 Eusebius Doedel (Concordia University) Dynamical System 2007/05/11 ~ 2007/05/27 Arnaldo Garcia (IMPA, Brasil) Number Theory & Coding 2007/05/11 ~ 2007/05/25

David Savitt (University of Arizona) Number Theory 2007/05/11 ~ 2007/05/24

89 ‹‹- Appendix 2007 Name Field of Interest Period of Visit

W. Dale Brownawell Number Theory 2007/05/12 ~ 2007/05/25

Appendix (Penn. State University)

Matthew A. Papanikolas (Texas A&M University) Number Theory 2007/05/12 ~ 2007/05/22

Frits Beukres Number Theory 2007/05/13 ~ 2007/05/27 (Utrecht University)

Gebhard Boeckle Number Theory 2007/05/13 ~ 2007/05/19 (University Essen)

Jinqiao Duan Dynamical System 2007/05/13 ~ 2007/05/18 (Illinois Institute of Technology)

M.H. Kang (Penn. State University) Number Theory 2007/05/13 ~ 2007/08/13

Ling Long (Iowa State University) Number Theory 2007/05/13 ~ 2007/05/31

Richard Moeckel Dynamical System 2007/05/13 ~ 2007/05/18 (University of Minnesota)

Gareth E. Roberts (College of the Holy Cross) Dynamical System 2007/05/13 ~ 2007/05/18

Chia-Fu Yu (Academia Sinica, and Max- Number Theory 2007/05/13 ~ 2007/05/18 Planck Institute, Bonn) Number Theory & Jiu-Kang Yu 2007/05/13 ~ 2007/05/19 (Purdue University) Representation Theory

Anthony To-Ming Lau (University of Alberta, Functional Analysis 2007/05/17 ~ 2007/06/04 Edmonton, Alberta, Canada)

David Gao Optimization 2007/05/20 ~ 2007/06/04 (Virgina Institute of Technology)

Heng Huat Chan Analytic Number Theory, Basic (National University of Hypergeometric Series, Elliptic 2007/05/21 ~ 2007/05/30 Singapore) Functions Jiu-Kang Yu Number Theory & 2007/05/21 ~ 2007/06/02 (Purdue University) Representation Theory

Siu-Hung NG Algebra 2007/05/22 ~ 2007/05/29 (lowa State University)

Chieh-Yu Chang (National Tsing-Hua University) Number Theory 2007/06/01 ~ 2007/07/31

Appendix -›› 90 2007 Name Field of Interest Period of Visit Lih-Ing Wu Roeger Mathematical Biology 2007/06/01 ~ 2007/07/04

(Texas Tech University) Appendix Yi-Giang Zhou (Memorial University of Ring theory, Module theory 2007/06/01 ~ 2007/06/30 Newfoundland) Marc Eric Raimondo (University of Sydney) Statistics 2007/06/02 ~ 2007/06/15 Yongsheng Han (Auburn University) Harmonic Analysis 2007/06/03 ~ 2007/06/23 Genaro Lopez Acedo (University of Seville, Spain) Functional Analysis 2007/06/05 ~ 2007/06/12 Applied Mathematics, Jian-Guo Liu Nonlinear PDE, 2007/06/05 ~ 2007/06/30 (University of Maryland) Scientific Computation Kee Hoon Kang (University of Georgia) Statistics 2007/06/06 ~ 2007/06/15 P. Greiner (University of Toronto) Analysis 2007/06/08 ~ 2007/06/29 Laurent Cavalier (University Aix-Marseille 1) Statistics 2007/06/09 ~ 2007/06/17 Liu Yu (University of Science and Harmonic Analysis 007/06/10 ~ 2007/08/31 Technology Beijing) Ren-Jun Duan (City University of Singapore) Boltzmann equation 2007/06/15 ~ 2007/07/15 Luen-Fai Tam (\The Chinese University of Differential Equations 2007/06/15 ~ 2007/06/18 Hong Kong)

Khee Meng Koh (National University of Graph theory, Lattice theory 2007/06/16 ~ 2007/06/29 Singapore) Duong H. Phong (Columbia University, USA) Geometric analysis 2007/06/16 ~ 2007/06/23 Grahame Bennett (Indiana University) Harmonic Analysis 2007/06/17 ~ 2007/07/07 Eric Chu (Monash University, AU) Scientific Computation 2007/06/17~ 2007/07/15 Eric Grinberg Geometric Analysis, 2007/06/17 ~ 2007/06/23 (Temple University) Integral Geometry Tsung-Ming Hwang (National Taiwan Normal Scientific Computation 2007/06/17 ~ 2007/09/16 University)

91 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Lei Ni

Appendix (University of California, San Geometric analysis 2007/06/17 ~ 2007/06/23 Diego) Stephen Shing-Toung Yau Algebraic geometry 2007/06/17 ~ 2007/06/23 (University of Illinois) Huai-Dong Cao Geometric analysis 2007/06/18 ~ 2007/06/23 (Lehigh University) Chen-Yu Chi Algebraic Geometry 2007/06/18 ~ 2007/08/18 (Harvard University)

Peter Wai Kwong Li Geometry analysis 2007/06/18 ~ 2007/06/22 (University of California)

Jia-Ping Wang Geometry analysis 2007/06/18 ~ 2007/06/22 (University of Minnesota) Sanming Zhou (University of Melbourne) Discrete Mathematics 2007/06/19 ~ 2007/06/22 Shun-Jen Cheng Optimization 2007/06/22 ~ 2007/06/23 (Academia Sinica) Stephen S. T. Yau (University of Illinois at Geometry 2007/06/23 ~ 2007/06/26 Chicago)

Der-Fen Liu Graph Theory and (California State University) Combinatorics 2007/06/20 ~ 2007/06/30 Silvia Petra Heubach Graph Theory and 2007/06/21 ~ 2007/07/01 (California State University) Combinatorics Kwang-Ming Hwang Combinatorial Optimization, (National Chiao Tung Discrete Mathematics, 2007/06/21 ~ 2007/06/30 University) Communication Networks San-Ming Zhou Graph Theory and 2007/06/22 ~ 2007/06/30 (University of Melbourne) Combinatorics Sheng Bau Graph Theory and 2007/06/23 ~ 2007/06/29 (Fuzhou University) Combinatorics Wai-Hong Chan Graph Theory and 2007/06/23 ~ 2007/06/28 (Hong Kong Baptist University) Combinatorics Bei-Fang Chen Graph Theory and 2007/06/23 ~ 2007/06/28 (Hong Kong University of Combinatorics Science and Technology) Rong-Quan Feng Graph Theory and (Peking University) Combinatorics 2007/06/23 ~ 2007/07/04 Wen-Jie He (Hebei University of Graph Theory and 2007/06/23 ~ 2007/07/01 Technology) Combinatorics

Appendix -›› 92 2007 Name Field of Interest Period of Visit Weng-Song Lin Graph Theory and 2007/06/23 ~ 2007/06/30

(Southeast University) Combinatorics Appendix Mei Lu Graph Theory and (Tsinghua University) Combinatorics 2007/06/23 ~ 2007/06/30 Chee Wai Shiu Graph Theory and 2007/06/23 ~ 2007/06/28 (Hong Kong Baptist University) Combinatorics Zhi-Wei Sun Graph Theory and 2007/06/23 ~ 2007/06/30 (Nanjing University) Combinatorics Jian-Fang Wang Graph Theory and 2007/06/23 ~ 2007/06/29 (Chinese Academy of Science) Combinatorics Kai-Shun Wang Graph Theory and 2007/06/23 ~ 2007/07/04 (Beijing Normal University) Combinatorics

Tao Wang Graph Theory and 2007/06/23 ~ 2007/06/30 (Nankai University) Combinatorics

Da-Qing Yang Graph Theory and 2007/06/23 ~ 2007/06/30 (Fuzhou University) Combinatorics Xing-Xing Yu Graph Theory and (Georgia Institute of Combinatorics 007/06/23 ~ 2007/06/27 Technology) He-Ping Zhang Graph Theory and 2007/06/23 ~ 2007/06/30 (Lanzhou University) Combinatorics Xiao-Dong Zhang Graph Theory and 2007/06/23 ~ 2007/06/30 (Shanghai JiaoTong University) Combinatorics Zhong-Fu Zhang Graph Theory and 2007/06/23 ~ 2007/06/30 (Lanzhou Jiaotong University) Combinatorics

Yi Zhao Graph Theory and 2007/06/23 ~ 2007/06/30 (Georgia State University) Combinatorics Akinari Hoshi (Waseda University) Number Theory 2007/06/24 ~ 2007/06/28 Chang-Hong Lu Graph Theory and 2007/06/24 ~ 2007/06/29 (East China Normal University) Combinatorics Katsuya Miyake 2007/06/24 ~ 2007/07/03 (Waseda University) Number Theory Complex analysis and Duong H. Phong geometry, Mathematical 2007/06/24 ~ 2007/06/27 (Columbia University) Physics Yong-Qiang Zhao Graph Theory and 2007/06/24 ~ 2007/06/29 (Shijiazhuang College) Combinatorics Graph Theory and Geng-Hua Fan 2007/06/25 ~ 2007/06/30 (Fuzhou University) Combinatorics

93 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Cai Leizhen Graph Theory and

Appendix (Chinese University of Hong Combinatorics 2007/06/25 ~ 2007/06/30 Kong) Hua Mao Graph Theory and 2007/06/25 ~ 2007/07/02 (Hebei University) Combinatorics Thomas Simon Mountford (Ecole Polttechnique Fédérale de Prorobability and statistics 2007/06/25 ~ 2007/07/05 Lausanne) Yuan-Pin Lee (University of Utah) Algebraic Geometry 2007/06/26 ~ 2007/07/31 Wensong Lin (Southeast University) Discrete Mathematics 2007/06/30 ~ 2007/07/23 Daqing Yang (Fuzhou University) Discrete Mathematics 2007/06/30 ~ 2007/07/23 Changyuan Cheng (National Pingtung University of Dynamical System 2007/07/01 ~ 2007/08/30 Education) Wei-Chen Yao (TMUE) Number Theory 2007/07/01 ~ 2007/07/31 Paolo Cascini (University of California at Algebraic Geometry 2007/07/02 ~ 2007/07/09 Santa Barbara) Masayuki Kawakita (RIMS) Algebraic Geometry 2007/07/02 ~ 2007/07/13 Motoko Kawakita (Kyoto University) Algebraic Geometry 2007/07/02 ~ 2007/07/08 Caucher Birkar (Cambridge University) Algebraic Geometry 2007/07/04 ~ 2007/07/13 Yum-Tong Siu (Harvard University) Complex Geometry 2007/07/04 ~ 2007/07/04 Wayne M. Eby (Temple University) Harmonic Analysis 2007/07/06 ~ 2007/07/12 Bao Qin Li (Florida International Complex Analysis 2007/07/09 ~ 2007/07/29 University) Chin-Tung Wu Differential Geometry and (National Pingtung University of 2007/07/10 ~ 2007/09/09 Geometric Analysis Education) Generic polynomial, Generic Hoshi Akinari dimension, Noether's problem, (Waseda University) Rationality problem, Invariant 2007/07/17 ~ 2007/07/27 theory, Tschirnhausen transformation, Cremona group

Appendix -›› 94 2007 Name Field of Interest Period of Visit Ngaiming Mok Algebraic Geometry, 2007/07/20 ~ 2007/07/21

(University of Hong Kong) Differential Geometry Appendix Wen-Hsiung Li (University of Chicago) Bioinformatics 2007/07/27 ~ 2007/07/28

Yen-His Tsai (The University of Texas at Scientific Computing 2007/07/31 ~ 2007/08/25 Austin) Jann-Long Chern (National Central University) Nonlinear PDE 2007/08/01 ~ 2008/07/31 Algebraic Geometry, Applied Mathematics, Differential Geometry and Shing-Tung Yau Geometric Analysis, (Harvard University) Number Theory, Algebra, 2007/08/01 ~ 2007/08/06 Representation Theory and Related Topics, Scientific Computation

Xue-Xiang Huang (School of Management, Fudan Functional Analysis 2007/08/06 ~ 2007/09/02 University) Kainam Thomas Wong (Hong Kong Polytechnic Discrete Mathematics 2007/08/06 ~ 2007/08/09 University) Shunsuke Hayashi (Kyoto University) Optimization 2007/08/09 ~ 2007/08/24 Wenxun Xing (Tsinghua University, Beijing) Optimization 2007/08/10 ~ 2007/08/20

Chiu-Yen Kao Scientific Computing 2007/08/13 ~ 2007/09/10 (The Ohio State University) Douglas W. Vestal (University of Califormia, Santa Financial Mathematics 2007/08/15 ~ 2007/09/15 Barbara) Ching-Li Chai (University of Pennsylvania) Number Theory 2007/08/18 ~ 2007/08/29 Dan'l Pierce (Access Analytics Int'l) Scientific Computation 2007/08/20 ~ 2007/08/24 Edmund R. Puczylowski (University of Warsaw) Algebra(Ring Theory) 007/08/22 ~ 2007/09/21 Krzysztof Stempak (Politechnika Wroclawska) Harmonic Analysis 2007/08/24 ~ 2007/09/10

95 ‹‹- Appendix 2007 Name Field of Interest Period of Visit Jing-Song Huang Representation Groups 2007/08/29 ~ 2007/08/31

Appendix (HKUST)

Eiji Yanagida (Tohoku University) Differential Equations 2007/08/30 ~ 2007/09/08

Xun-Hua Gong (Nanchang University) Functional Analysis 2007/09/01 ~ 2007/09/30

Geometric Measure Theory, Wei Zhu Calculus of Variations, Partial 2007/09/01 ~ 2007/09/30 (Rice University, Zurich) Differential Equations

Richard Schoen Differential Geometry, Partial 2007/09/13 ~ 2007/09/26 (Stanford University) differential equations Emilio Acerbi (University of Parma) Calculus of variations, PDE 2007/09/20 ~ 2007/10/03

S.M Bhatwaddekar (Indian National Science Commutative algebra 2007/10/01 ~ 2007/10/28 Academy)

Yoshihito Oshita (Okayama University) PDE 2007/10/15 ~ 2007/10/21

Mikhail Chebotar Ring Theory,Linear (Kent state University) Algebra,Operator Algebra 2007/12/10 ~ 2008/01/09

Appendix -›› 96 NCTS 2007 Conference, Workshop & School

Time Conference & Workshop Place Appendix

NCTS Short Course on Introduction to Lecture Room of NCTS, Sept. 4-14, 2006 Iwasawa Theory National Tsing Hua Speaker: Keiichi Komatsu (Waseda Univ. University, Japan)

Topical Program in Modular Forms and Lecture Room of NCTS, Sept. 13, 2006- Galois Representations National Tsing Hua Jan. 12, 2007 Speaker: W. –C. Li (NCTS and Penn. State U.) Univ.

Topical Program in Symmetries in Chaos and Molecular Quantum Mechanics Lecture Room of NCTS, Sept. 14-Dec. 30, 2006 Speaker: Goong Chen (Texas A&M National Tsing Hua University) Univ.

NCTS Forum Mathematics Research in Taiwan Chandler Davis (U. Toronto & Math. Intelligencer) Hung-Lin Fu (NCTU) Lecture Room of NCTS, Sze-Bi Hsu (NTHU) Wen-Ching Winnie Nov. 8, 2006 National Tsing Hua Li (NCTS&NTHU) Chang-Shou Lin Univ. (TIMS&NTU) Song-Sun Lin (NCTS&NCTU) Wen-Wei Lin (NCTS&NTHU) Pei Yuan Wu (NCTU) Jing Yu (NCTS&NTHU)

Math. in 21th Century Lecture Room of NCTS, Nov. 9, 2006 S. T. Yau (Harvard University) National Tsing Hua Univ.

NCTS Workshop on the Converse Lecture Room of NCTS, Nov. 15-22, 2006 Theorems for GLn National Tsing Hua Organizer: Jing Yu (NCTU & NTHU) Univ.

International Conference on Nonlinear Analysis ORGANIZING COMMITTEE: C.-C. Chen (Taipei ) M. Chipot (Zurich) P.G. Ciarlet (Hong Nov. 20-25, 2006 Lecture Room of NCTS, Kong) J.-S. Guo (Taipei ) National Tsing Hua N. Kenmochi (Chiba) C.-S. Lin Univ. (Chai-Yi ) X. Pan (Shanghai ) D.-H. Tsai (Hsinchu) Z. Xin (Hong Kong) E. Yanagida (Sendai )

97 ‹‹- Appendix National Taiwan Normal National Taiwan Univ. Lecture Room of NCTS, Hua National Tsing Univ. National Cheng Kung Univ. Aspire Park, Taoyuan Lecture Room of NCTS, Hua National Tsing Univ. National Taiwan Normal National Taiwan Univ. ai- T Jih- Jong- zo Hosono Yu oshi Ogawa Shin-Ichiro Dong-Ho Tsai T en-Ling Huang Masayasu Mimura W Jiin-Chang Shaw Univ. & NCTS) Univ. Shu-Cheng Chang (NTHU) Univ.) Shu-Cheng Chang (NTHU) of Notre Jianguo Cao (Univ. Dame) (NCTU) Hsin Cheng (Academia Sinica) (University of Hamburg) aiwan University) (Kyoto Sangyo University) (Meiji University) (Osaka University) Ei (Kyushu University) Je-Chiang Tsai (National Chung Je-Chiang Tsai Cheng University) Chiun-Chuan Chen (National Chiun-Chuan Chen T Shenq Guo (National Taiwan Shenq Guo (National Normal University) Taiwan Chia Lin (National University) (National Tsing Hua University) (National Tsing orkshop on Reaction-Diffusion: orkshop epresentation theory epresentation Jein-Shan Chen in Analysis and Program NCTS Topical Geometry Chang (Georgetown Der-Chen Speaker: Mini Workshop on Lie algebra and on Lie algebra Mini Workshop r Lam (NCKU) Ching-Hung Organizer: on Number Theory School 2007 Winter (NCTU & NTHU) Jing Yu Organizer: 2007 A Series of Seminars on Optimization with Engineering Applications 2007 NCTS & CMS Workshop Geometric Analysis Chang (Georgetown Der-Chen Organizer: Invited Speakers: W Applications Theory and 65th of Masayasu Mimura's in honor Birthday ime & Workshop Conference Place T January 16-18, 2007 March 2- June 29, 2007 January 18, 2007 Feb. 2-6, 2007 March~Dec.,2007 Dec. 1-2, 2006 98 -›› Appendix

Appendix Time Conference & Workshop Place NCTS An Intensive Course in Reaction - Diffusion Systems with Application to Lecture Room of NCTS, March 22- April 19, Spatial Ecology National Tsing Hua 2007 Speaker: Yihong Du (University of New Univ. Appendix England, Australia)

Workshop on Higher Dimensioanl Algebraic Geometry Organizers: Jungkai Alfred Chen (Taiwan March 27-31, 2007 U. & TIMS) Juin-Cheng National Taiwan Univ. Chen (NTHU& NCTS) Chin- Lung Wang (Central Univ. & NCTS) NCTS Mini--Workshop on Mathematical Biology Organizers:Sze-Bi Hsu (Tsing-Hua Lecture Room of NCTS, May 9-10, 2007 University) National Tsing Hua Hal Smith (Arizona State Univ. University) 2007 NCTS Conference on Galois Representations and Function Field Lecture Room of NCTS, Arithmetic National Tsing Hua May 14-17, 2007 Organizers: Wen-Ching Winnie Li (Penn Univ. State U & NCTS) Jing Yu (NCTS & NTHU) 2007 NCTS Workshop on Dynamical Systems Lecture Room of NCTS, Organizers: Kuo-Chang Chen (NTHU) May 14-18 , 2007 National Tsing Hua Jong Juang (NCTU) Univ. Ming-Chia Li (NCTU) Chih-Wen Shih (NCTU) NCTS & NCU Colloquium on Number Theory Lecture Room of NCTS, Speaker: Prof. W. Dale Brownawell (Penn May 24, 2007 National Tsing Hua State University) Univ. Prof. Frits Beukers (University of Utrecht) NCTS Series Lectures in Harmonic Analysis: Multi-parameter Fourier Lecture Room of NCTS, June 6-20, 2007 Analysis I-V National Tsing Hua Univ. Prof. Y. Han (Auburn University)

NCTS Topical Program in Harmonic Lecture Room of NCTS, Analysis National Tsing Hua June 13-Aug. 29, 2007 Speaker: Yu Liu (University of Science and Univ& Math. epartment, Technology Beijing) National Central Univ.

99 ‹‹- Appendix National Sun Yat-Sen Univ. Lecture Room of NCTS, Hua National Tsing Univ. Lecture Room of NCTS, Hua National Tsing Univ. Lecture Room of NCTS, Hua National Tsing Univ. Lecture Room of NCTS, Hua National Tsing Univ. National Taiwan Univ. National Taiwan National Taiwan Univ. National Taiwan Shu- Jih- Ko- Mao- Mu-Tao Yng-Ing Jiaping Wang Xuding Zhu Jung-Kai Chen Chin-Lung Wang Paolo Cascini (UC M. Kawakita (RIMS) Genghua Fan (Fuzhou Hung-Lin Fu (NCTU) ang (Columbia U.) illiam Y. C. Chen (Nankai illiam Y. ei Lih (AS) ayuan Huang (NCTU) (Chinese U.) Hsin Cheng(AS) Lee (NTU) W Pei Tsui (U. of Toledo) Pei Tsui (U. of Minnesota) (NCU) Cheng Chang (NTHU) U.) W W U.) T (National Sun Yat-sen U.) (National Sun Yat-sen University) Cambridge) State University) University) (NTU) Santa Barbara) orkshop on Graph Theory and orkshop on Graph NCTS Short Course on Number Theory Katsuya Miyake (Waseda Speaker: 2007 NCTS Mini-Course in Algebraic Geometry of Caucher Birkar (Univ. Speaker: 2007 International & Fourth Cross-strait on Graph Theory and Conference Combinatorics J. Chang (NTU) Gerard Organizer: Organizer: Xuding Zhu (NSYSU) Organizer: A Short Course on Finite Element Methods and Eigenvalue Problems So-Hsiang Chou (Bowling Green Speaker: in Harmonic NCTS Series Lectures Analysis Grahame Bennett (Indiana Speaker: Organizers: Nai-Chung Conan Leung Nai-Chung Conan Organizers: W Network International Conference on Geometric Conference International Analysis ime & Workshop Conference Place T June 18-22, 2007 June 21-July 24, 2007 June 22-July 6, 2007 June 24-29, 2007 July 3-12, 2007 June 27, 28, July 2, 2007 June 20, 2007 100 -›› Appendix

Appendix Time Conference & Workshop Place

NCTS Algebraic Computation Workshop Lecture Room of NCTS, July 3, 10, 11, 13, 2007 Speaker: Jing Yu (NCTS) National Tsing Hua Appendix Wei-Chen Yao (Taipei Municipal Univ. University of Education)

NCTS 10th Year Anniversary Special Lectures:Multiplier Ideal Sheaves and Their Applications to Analysis and Lecture Room of NCTS, July 4, 2007 Algebraic Geometry National Tsing Hua Speaker: Yum-Tong Siu (Harvard Univ. University)

NCTS Summer Course on Probabilistic Lecture Room of NCTS, July 5-26, 2007 and Statistic Methods in Bioinformatics National Tsing Hua Organizers: Yuan-Chung Sheu (NCTU) Univ.

NCTS Mini Course on Lie Algebra Lecture Room of NCTS, July 17-18, 2007 From Linear Algebra to Lie Algebra National Tsing Hua Speaker: Meng-Kiat Chuah (NTHU) Univ.

NCTS 10th Anniversary Special Lectures: From boundary values of bounded holomorphic functions to the Lecture Room of NCTS, July 20, 2007 geometric theory of minimal rational National Tsing Hua curves Univ. Speakers: Ngaiming Mok (The University of Hong Kong)

NCTS 10 Years Anniversary Mini- Workshop on PDE Hung-Chi Kuo (Department of July 23, 2007 Atmospheric Sciences, NTU) National Taiwan Univ. Chun-Hsiung Hsia (University of Illinois at Chicago) Horng-Tzer Yau (Harvard University)

NCTS 10th Anniversary Special Lectures: Computational identification Lecture Room of NCTS, July 27, 2007 of regulatory elements in yeast National Tsing Hua Speaker: Wen-Hsiung Li (University of Univ. Chicago)

NCTS 10th Anniversary Special Lectures: Hardy Spaces and Elliptic Lecture Room of NCTS, July 31, 2007 Boundary Value Problem National Tsing Hua Speaker: Der-Chen Chang (NCTS & Univ. Georgetown Univ.)

101 ‹‹- Appendix Time Conference & Workshop Place NCTS 10 Year Anniversary: Lecture Series on Algebra and Number Theory Speaker: Chin-Li Chai (University of Appendix Lecture Room of NCTS, Aug. 1, 15, 22, 30, Penn) Jing-Song Huang National Tsing Hua 2007 (HKUST) Winnie Wen-Ching Li (NCTS & Penn State U.) Chin- Univ. Lung Wang (NCTS & National Central U.)

NCTS 10th Anniversary Special Plenary Lectures: Constructions of Geometric Lecture Room of NCTS, Aug 2, 2007 Structures on Manifolds National Tsing Hua Speaker: Shing-Tung Yau (Harvard Univ. University)

NCTS 10th Anniversary Special Public Lecture: Geometry, Nonlinear Analysis Lecture Room of NCTS, Aug. 3, 2007 and Theoretical Physics National Tsing Hua Speaker: Shing-Tung Yau (Harvard Univ. University)

NCTS 2007 Summer Course on Dynamical Systems Lecture Room of NCTS, Aug. 7-28, 2007 Speaker: Kuo-Chang Chen (NTHU) Chang-Yuan Cheng (NPUE) National Tsing Hua Shyan-Shiou Chen (NTNU) Univ. Wen-Chiao Cheng (NCCU)

NCTS 10th Anniversary--Growth Series Lectures Speaker: Kuo-Chang Chen (NTHU) Lecture Room of NCTS, Sept. 3, 2007 Cheng-Hsiung Hsu (NCU) National Tsing Hua Ching-Hung Lam (NCKU) Univ. Hui-Wen Lin (NCU)

Appendix -›› 102 Physics Division Report of the Division Head

General Remarks summer of 2007 (the Mathematics Division is located at the fourth floor). More coherent cooperation between the Mathematics and Physics Divisions is expected in the future. n the past year the operation of the Approximately two-ninth and one-ninth of NCTS Physics Division basically the NCTS annual budget are channeled follows the mode set up by the ex-director, through Subproject I at National Taiwan Professor Tu-Nan Chang, aiming at her short- University (NTU), and Subproject II at term objects: to nurture the next generation NCKU, respectively, to support the activities of theoretical scientists in Taiwan and to of a few selected focus groups (four at encourage interaction and collaboration Subproject I and three at Subproject II in among participants. The user-initiated 2007.) The rest of the NCTS budget is academic programs by the focus groups have allocated to the main project to support the been run smoothly, and made easier for group activities of other focus groups, the NCTS members to access NCTS resources with scientific personnel, and the additional NCTS higher flexibility. The scientific activities and sponsored functions, such as the joint outcomes of each focus group will be programs between Physics and Mathematics summarized in this report (see also at the Division. NCTS web-site http://phys.cts.nthu.edu.tw/). The highlights of the NCTS Physics Division in the past year include the evaluation Executive Committee and Young and the restructure of the focus groups, the Theorist Award establishment of the Young Theorist Award, The Executive Committee composed of the recruitment of outstanding scientific staff, Ching-Ray Chang of NTU, Hai-Yang Cheng and the promotion of international of Academia Sinica (AS), Der-San Chuu of collaborations with prestigious physics NCTU, Hsiang-nan Li (chairman), Sy-Sang centers. More details will be given later. It is Liaw of National Chung-Hsing University an encouraging expansion of our center (NCHU), and Wei-Ming Zhang of NCKU, scientist program that two brilliant young who represent the host institutes of the main physicists, Professors Yueh-Nan Chen and project and the subprojects of NCTS, the Chung-Hsien Chou, have been recruited by institute that sponsors NCTS programs, and Subproject II at National Cheng-Kung the institute from the middle of Taiwan. University (NCKU) Moreover, they also represent various fields in I want to take this opportunity to welcome theoretical physics, providing opinions and Professors Chung-Yu Mou from National suggestions based on their expertise, and Tsing-Hua University (NTHU) and Chon- serving as the second reviewers of applications Saar Chu from National Chiao-Tung and recruitments submitted to NCTS. University (NCTU), who have kindly accepted In order to encourage young colleagues to the duty of serving as the head and the deputy pursue theoretical research, to maintain active head of the Physics Division, respectively, and to produce excellent works, we established starting on Aug. 1st, 2007. Another key the Young Theorist Award in the Fall of 2006. development is that the Physics Division will The Mathematics Division also joins this move into the more spacious fifth floor of the effort, wishing that this award will soon third General Building at NTHU after the become as prestigious as the Ta-You Wu

Report of the Division Head -›› 104 Fellowship of National Science Council (NSC) systematic performance evaluation of all focus and the Young Scholar Award of Academia groups at the end of 2006. A Performance Sinica (AS). The Executive Committee has Evaluation Panel (PEP) was called for to selected Professors Chi-Tin Shih of Tung-Hai perform the detailed academic evaluation with University and Daw-Wei Wang of National the inputs from external reviewers based on Tsing Hua University as the recipients in 2007 the criteria recommended and endorsed by both the Executive Committee and the Program Committee. One of the key criteria Focus Groups and Scientific Activities emphasizes the progress made by the focus groups through the expenditure of the NCTS The majority of the NCTS scientific resource. The evaluation was then submitted to activities are planned and carried out by the the Executive Committee at mid-December, NCTS affiliated focus groups. More resources 2006 as the basis of restructuring the focus are allocated to sponsor workshops and groups and of adjusting their budget for the schools targeting at students and junior next fiscal year. scientists with emphasis on new ideas and concepts of emerging research subjects. Our The restructure of the focus groups is international visitors are encouraged and summarized as follows. "System Biology"and arranged to spend more time for informal "Nonlinear Phenomena in Physical and discussion with the focus group members Biological Systems" were separated. The during their visit. Interactions among focus former was then combined with "Soft-Bio groups have also increased with more joint Matters Physics", forming the new group activities. All NCTS sponsored activities have "Softmatter, Biophysics and System Biology". been posted on the NCTS web-site at "Strongly Correlated Electron Systems" and http://phys.cts.nthu.edu.tw/ as soon as it is "Spin-related Physics in Condensed Matter" planned, and also stayed on the web-site were combined into "Novel Quantum afterwards as a future reference. Through the Phenomena in Condensed Matter". "Plasma internet network, we should be able to Physics" is now classified as a working group, communicate openly and continuously with whose purpose and evaluation standards differ the larger theoretical science community. from those for a focus group. The mission of a working group is to attract and coordinate The policies for supporting long-term manpower, and to educate young generation in visitors (including multi-year international a smaller research field, while a focus group senior visitors) and for recruiting postdoctoral aims at production of works with significant fellows have been slightly modified. Not only impact. The coordinators of some focus groups the candidates for the above two categories have been changed too. need to be recommended and nominated, but their stations are determined by the focus groups themselves. With this additional flexibility, we hope that the interaction among Scientific Staff and International visitors, postdoctoral fellows, and the focus Collaboration groups can be further enhanced. Following the We have expanded our center scientist same design, the responsibility of executing program this year. Hsiu-Hau Lin (NTHU), the domestic visitor program, which Kingman Cheung (NTHU), Anatoly. G. encourages active participation by faculty Mal'shukov (NCTU), Chi-Jen David Lin members and research staff from universities, (NCTU) have been appointed by the Executive colleges, and other institutes with limited Committee and by their home departments as research resources and opportunities, has been the center scientists. The appointment of also assigned to the focus groups. Cheng-Hung Chang (NCTU), which was first After two years in operation under the made in early 2005, has been renewed. A current NCTS structure, we have conducted a senior center scientist is demanded by the

105 ‹‹- Report of the Division Head leadership in his research field, while a junior Hirayama (Strings), Dr. Hung-Cheuk Ho ( center scientist is entitled to be protected from , Atomic Physics), Dr. Wen-Hsuen Kuan the administrative and teaching loads. Two ( , Atomic Physics), Dr. Kao-Chin Lin brilliant young theoretical physicists, ( , Condensed Matter Physics), Dr. Yu- Professors Yueh-Nan Chen and Chung-Hsien Pin Luo ( , Biophysics). Chou, were recruited by Subproject II at NCKU. Their appointment marks a substantial contribution to our center scientist program. Administrative Staff To attract experienced foreign researchers There is no change both in personnel and to work in Taiwan for a longer period, a new job assignment involving our supporting staff position under the title "Staff Scientist" has at NCTS. Sherry Sieu-Huey Pang ( ) been created at NCTS this year. It is a non- is responsible for the administrative affairs in tenure track faculty position with research Physics at NCTS. Jia-yi Hsu ( ) is fund, travel grant, and a postdoctoral quota responsible for the financial management. from NCTS. Professor Kazuyuki Furuuchi, Hetty Chang ( ) and Meirue Shi ( being highly recommended by external ) are assigned to provide logistics support reviewers and by the Executive Committee, and to coordinate the scientific activities for has been recruited as our first staff scientist. the focus groups. Chia-chi Liu ( ) and Searching for the second candidate is now in Annie Lin ( ) are responsible for the process. logistics and administrative support at The international collaborations with subprojects I and II, respectively. The foreign prestigious physics centers have been response to the service provided by our staff promoted greatly this year. We shall organize from our target community is uniformly our first KITP-type topic program on positive under the current "one-window" "Superconductivity and Magnetism at structure. We are grateful to their dedication. Nanoscale" in December of 2007 as a joint activity with the Argonne National Laboratory. The coordinator from our side is Professor Concluding Remarks Baruch Rosenstein of NCTU. The number of outstanding visitors stationing at NCTU will Similar to what was stated last year, the remain several every week. A host is assigned NCTS is again blessed with a firm to each visitor to guarantee his interaction with commitment from NSC and the NCTS Board local community. The success of this program of Directors and a tremendous support from a will set up an example for other fields to robust physics community in Taiwan this year. follow in the future. APCTP has invited us to We have enjoyed a strong partnership with our submit a joint proposal for a Focus Program on host institutes NTHU, NCTU, NTU, NCKU, "Astroparticle and Nuclear Physics" in 2008. and AS. It is a good sign that NCTS has NCTS will co-sponsor the KITP Program on provided an important assistance in both "Advanced Topics on Flavor Physics" in the research and administration to our theoretical summer of 2008 held at the Kavli Institute for physics community. We have seen a Theoretical Physics, China. substantial increase in scientific activities and the development of more focused research In addition to the center and staff scientists, directions, which target at our immediate assistant research scholars at NCTS include objectives. I am confident that with a new Dr. Je-An Gu ( , Cosmology), Dr. leadership under Professors Chung-Yu Mou Shih-Yuin Lin ( , Gravitation), Dr. and Chon-Saar Chu, the NCTS Physics Kazutomu Shiokawa (Quantum Information Division will enjoy another successful year in Sciences), Dr. Yi Yang ( , Strings), Dr. 2008 and many years beyond. Tzu Chiang Yuan ( , Particle Physics). Postdoctoral fellows include Dr. Takayuki Hsiang-nan Li ( ) October 2007

Report of the Division Head -›› 106 Speacial Report on the Symposium on the 10th Anniversary of NCTS

Written by: Chung-Yu Mou

he NCTS has entered the 10th year Jen Chen of NSC came and gave opening since its establishment in 1997. address. Following his address, President Chen During the past 10 years, NCTS has helped in of NTHU, Vice President Lee of NCTU and shaping the research of theoretical physics in distinguished guests/directors from centers in Taiwan. It is therefore an excellent occasion to Asia gave addresses for this particular celebrate and overview the contribution of occasion. There was also nice retrospect of NCTS. A symposium on the 10th Anniversary NCTS by former divisional heads, Prof. Ting- of NCTS, organized by the Physics Division, Kuo Lee and Prof. Tu-Nan Chang.Current was held on September 3 and 4, followed by divisional head, Prof. Chung-Yu Mou, also the inauguration of Physics New Offices on gave an overview what has been achieved by the 5th floor in the 3rd General Building. All NCTS during the past nine years. The OCPA researchers who worked at the physics division AAA / Robert T. Poe Prize was presented to and former directors and divisional heads were the former divisional head, Prof. Hsiang-Nan invited and a reunion dinner was held. Li, for his contribution on perturbed QCD. The Distinguished guests and directors from inauguration of Physics New Offices on the 5th Yukawa Institute for Theoretical Physics, Asia floor in the 3rd General Building was held Pacific Center for Theoretical Physics, Korean following these speeches. Technical sessions Institute for Advanced Study, Kavli Institute (see detailed program in below) with for Theoretical Physics China were also presentation of scientific results associated invited to participate the symposium. with the physics division were held later in the In the morning of Sept. 3, minister Chien- afternoon and on Sept. 4.

Inaguration of new office (from left to right): Director Jing A scene of new office located at the 5th floor of 3rd Yu (NCTS), President Wen-Tsuen Chen (NTHU), Vice General Building, National Tsing Hua University President Chia-Hoang Lee (NCTU), Deputy Minister Hung- Duen Yang(NSC)

107 ‹‹- Report of the Division Head

Distinguished guests from Asia famous institutes on Presentation of the OCPA AAA / Robert T. Poe Prize the celebration of NCTS 10th anniversary (from left to (from left to right): Professor Tu-Nan Chang (former right): Director Yue-Liang Wu (KITPC), Director Tohru Director of NCTS, USC), Prof. Hsiang-Nan Li (former Eguchi (YITP), Director Ki-Myeong Lee (Phys. School, Phys. div. head of NCTS) KIAS) Highlights of Programs Complex System

Focus Group on Critical Phenomena and Complex Systems

Coordinator: Chin-Kun Hu (Academia Sinica; email: [email protected]) Committee members: Shu-Chiuan Chang (National Cheng Kung University), Chi-Ming Chen (National Taiwan Normal University), Chi-Ning Chen (National Dong Hwa University), Shu-Heng Chen (National Chengchi University), Chung-I Chou (Chinese Culture University), Ming-Chung Ho (National Kaoshiung Normal University), Ming-Chang Huang (Chung-Yuan Christian University), I-Ming Jiang (National Sun-Yat Sen University), hai-Yu Lin (National Chung Cheng University), Ning-Ning Pan (National Taiwan University), Wen-Jer Tzeng (Tamkang University), Ming-Chya Wu (National Central University)

I. Brief Description workshop, some invitors from other countries were invited to give a series of talks on topics related to the interest of this FG. Some members of our FG and researchers in Taiwan he purpose of this focused group is to were also invited to give talks so that related work on various model systems to research problems can be discussed. Some gain a better understanding of critical foreign visitors also work with researchers of phenomena and then apply the methods and this FG on join research problems. concepts from such studies to interdisciplinary In 2007, the key active members of this FG problems, especially the complex systems. The include Professor Shu-Chiuan Chang (National problems to be studied include: (1) lattice Cheng-Kung University), Professor Wen-Che models of critical systems (such as Ising, Tzeng (Tamkang University), Dr. Ming-Chya Potts, dimer models, spin glass, etc), (2) chaos, Wu (National Central University), Hsin-Chang synchronization, and non-equilibrium process, Chi (Department of Applied Science, National (3) networks and self-organized critical Hualien University of Education), Dr. Jung- systems (such as sandpile model), (4) structure Hsin Lin (Research Center for Applied and properties of biological macromolecules Sciences, Academia Sinica), Prof. Jui-Ling Yu (such as DNA, RNA, and protein), (5) (Dept. of Applied Math., Providence molecular biological evolution models, and (6) University) models for economic and social systems. Since members of this FG scatter in different universities and research institutes, the main academic activities of this FG include II. Activities six 2 3 days workshops and one International 1. From March to August 2007, we have Workshop on Biological Physics and Complex organized four 2007 NCTS Workshop on Systems on 6-11 August 2007. In each Critical Phenomena and Complex Systems.

Highlights of Programs -›› 110 The program of the workshops can be found 1. Prof. Chang and Lung-Chi Chen also at http://www.sinica.edu.tw/?statphys/ worked on enumerating the number of activities/workshop.html. dimers on the Sierpinski gasket with possible vacancies on the outmost vertices. 2. We had organized 2007 Taiwan They derived rigorously such numbers and International Workshop on Biological the corresponding entropies on the two- Physics and Complex Systems 6-11 August dimensional Sierpinski gasket and its 2007, at Institute of Physics, Academia generalization with three, four and five Sinica, Taipei. The program of the layers. The upper and lower bounds of the workshop can be found at entropies for the three, four and five http://www.phys.sinica.edu.tw/~statphys/act dimensional Sierpinski gaskets are also ivities/ conference/2007/ obtained. This work will be submitted for 3. We are organizing 2007 NCTS Workshop publication soon. October Workshop on 12, 13, and 15 2. Prof. Tzeng Wen-Jer (Tamkang Univ, Dept October. At this workshop, Professor Kensei Phys) visited NCTS (North) during summer Kobayashi (Graduate School of and winter break. He worked on genetic Engineering, Yokohama National switch in periodic-changing environments. University, JAPAN) will give two 80 minutes talks on "Chemical Evolution from 3. Prof. Hsin-Chang Chi (Deaprtment of Complex Organics in Space to Life", which Applied Science, National Hualien is a very interesting and stimulating topic. University of Education) visited NCTS Some other speakers from USA, France, (North) during summer break. He and Prof. Poland and Taiwan have been invited to K. N. Huang of Academia Sinica used give talks on protein research and complex relativistic many-body perturbation theory systems. to calculate energy levels and transition probabilities of molecules. A research paper 4. In December 2007, we will organize another is under preparation. workshop. 4. Olga S. Rozanova (Mathematics and 5. We have organized a series of seminars and Mechanics faculty, Moscow State group meetings on critical phenomena and University, RUSSIA) visited NCTS (North) complex systems at Physics Department during summer break. She and Prof. Jui- of Chung-Yuan Cristian University and Ling Yu (Dept. of Applied Math., Institute of Physics of Academia Sinica. Providence University, a visitor at Institute of Physics of Academia Sinica during sum- mer break) worked on a model typhoon III. Visitors and International trajectories and a manuscript is under Collaborations preparation. 1. Prof. Shu-Chiuan Chang (Physics 5. Dr. Philippe Arnaud1 (Laboratoire de Department, National Cheng Kung Chimie de Coordination du CNRS, France) University) visited NCTS (North) during visited NCTS (North) in October 2006. He winter and summer breaks. He already and Dr. Jung-Hsin Lin (Research Center for published two papers in J. Stat. Phys., and Applied Sciences, Academia Sinica) are Int. J. Mod. Phys. B on Spanning trees on using docking and molecular dynamics the Sierpinski gasket (with Prof. Lung-Chi simulations to study the targeting of Chen in Department of Mathematics, Fu Jen telomeres by small molecules, which is Catholic University) and zeros of the Potts nowadays one the most promising strategies model partition function in the large-q limit for the discovery of new antitumoral drugs. (with Professor Robert Shrock at SUNY They continue the cooperation and will Stony Brook). finish a paper in the near future. 6. Dr. N. Sh. Izmailian (Yerevan Institute of

111 ‹‹- Highlights of Programs Physics) visited NCTS (North) in early on Noise and Fluctuations on 9-14 2007. He and Dr. Chin-Kun Hu finished a September 2007 in Tokyo on "Quantum and paper for co-evolution of virus and immune lattice models of biological evolution". The system, which was published in [Phys. Rev. brief text of the talk was published at AIP E 75, 041104 (2007)]. They also worked on Conference Proceedings 922 (AIP, New a paper about finite-size effects for the Ising York, 2007) edited by M. Tacano, Y. model on the helical tori, which will appear Yamamoto, and M. Nakao, pp. 589-594. in [Phys. Rev. E 76 (2007)]. 3. Prof. Chi-Tin Shih (Physics Department, 7. Zbigniew Struzik (Graduate School of Tanghai University), Stephan Roche (CEA, Education, The University of Tokyo) visited France), and Rudolf A. Romer (University NCTS (North) in March 2007. He, Dr. of Warwick, UK) studied point mutations Ming-Chya Wu (National Central effects on charge transfer properties in the University), and Dr. Chin- Kun Hu finished DNA sequence of the tumor-suppressor p53 a paper on temporal evolution for the phase gene. On the basis of effective single-strand histogram of ECG during human ventricular or double-strand tight-binding models which fibrillation, which was published in AIP simulate hole propagation along the DNA, a Conference Proceedings 922 (AIP, New statistical analysis of charge transmission York, 2007) edited by M. Tacano, Y. modulations associated with all possible Yamamoto, and M. Nakao, pp. 573-576. A point mutations is performed. They that in new version of the paper which takes into contrast to non-cancerous mutations, account the survival probability is under mutation hotspots tend to result in preparation and will be sent to a journal for significantly weaker changes of publication in the near future. transmission properties. This suggests that charge transport could play a significant role for DNA-repairing deficiency yielding carcinogenesis. Their paper was submitted IV. Highlights of Research Results to Phys. Rev. Lett. for publication. 1. RNA folding is a very difficulty theoretical 4. M.-C. Wu, Z. R. Struzik, E. Watanabe, Y. problem. Most earlier studies neglect Yamamoto, and C.-K. Hu studied the pseudo knots in the theoretical calculations. temporal evolution for the phase histogram E. Sh. Mamasakhlisov (a visitor of this FG), of ECG during human ventricular Shura Hayryan, and Chin-Kun Hu included fibrillation. They found that some type of pseudo knots in the calculation and studied phase distribution is fatal. Their result was RNA folding in the presence of counterions. first published at AIP Conference They found that the freezing and melting Proceedings 922, (AIP, New York, 2007) temperature of RNA decrease linearly with edited by M. Tacano, Y. Yamamoto, and M. the logarithm of the ion strength [Phys. Rev. Nakao, pp. 573-576. A paper to be E75, 061907 (2007)], which is consistent submitted to a journal is under preparation. with experimental observation. 2. Under partial support by NCTS (North), Prof. David B. Saakian (Yerevan Physics Institute) had visited NCTS (North) and V. Publication Institute of Physics of Academia Sinica From January to August 2007, our FG has several times since 2004. He and Dr. Chin- 14 papers published or accepted by SCI Kun Hu published several papers at Proc. journals and 3 papers published at a AIP Natl. Acad. Sci. USA, Phys. Rev. E, and J. Conference Proceedings The SCI journal Stat. Phys.. In these papers, very general papers include 5 in Physical Review E, 2 in J. fitness functions for biological evolution Statistical Physics, 1 in J. Chemical Physics, 1 models have been studied. Hu was invited to in Biophysical J., 1 in J. Computational give a talk at 19th International Conference Cemistry, 1 in Physica A, 1 in Chaos, Solitons

Highlights of Programs -›› 112 and Fractals, 1 in Int. J. Mod. Phys. B, and 1 Evolution: Derivation of Exact Steady- in J. of the Korean Physical Society. The list of State Distributions, J. Statistical Phys. 128, these papers is showed below and the pdf files 781-798 (2007). of these papers can be found at [10] Shu-Chiuan Chang and R. Shrock, Zeros http://phys.cts.nthu.edu.tw/research/focus_gro of the Potts Model Partition Function in up.php?Sn=38. Our FG has sent 15 papers to the Large-q Limit, Int. J. Mod. Phys. B journals for publication. 21, 979-994 (2007). Papers published or accepted for publication [11] Ruben G. Ghulghazaryan, Shura Hayryan [1] Cheng-Hsiao Lin, Yan-Chr Tsai and Chin- and Chin-Kun Hu, Efficient Combination Kun Hu, Wrapping conformations of a of Wang-Landau and Transition Matrix polymer on a curved surface, Phys. Rev. E Monte Carlo Methods for Protein 75, 031903 (2007). Simulations, J Comput Chem 28, 715- 726, (2007). [2] N. Sh. Izmailian, Vl. V. Papoyan, V. B. Priezzhev and Chin-Kun Hu, Self- [12] Chuan-Ji Fu, Bing-Hong Wang, Chuan- organizing behavior in a lattice model for Yang Yin, Tao Zhou, Bo Hu, Kun Gao, co-evolution of virus and immune system, P.M. Hui, Chin-Kun Hu, Analytical Phys. Rev. E 75, 041104 (2007). studies on a modified Nagel Schreckenberg model with the Fukui- [3] Bidhan Chandra Bag and Chin-Kun Hu, Ishibashi acceleration rule, Chaos, Escape through an unstable limit cycle Solitons and Fractals 31, 772-776 (2007). driven by multiplicative colored non- Gaussian, Phys. Rev. E 75, 042101 (2007). [13] Ming-Chya Wu, Phase correlation of foreign exchange time series, Physica A [4] Yevgeni Sh. Mamasakhlisov, Shura 375, 633-642 (2007). Hayryan, V. F. Morozov and Chin-Kun Hu, RNA folding in the presence of [14] Ming-Chya Wu, Phase Statistics counterions, Phys. Rev. E 75, 061907 Approach to Time Series Analysis, (2007). Journal of the Korean Physical Society, [5] N. Sh. Izmailian and C.-K. Hu, Finite-size 50, 304-312 (2007). effects for the Ising model on the helical [15] M.-C. Wu, Z. R. Struzik, E. Watanabe, Y. tori, Phys. Rev. E 76, in press (2007). Yamamoto, and C.-K. Hu, Temporal [6] Yevgeni Sh. Mamasakhlisov, Shura evolution for the phase histogram of ECG Hayryan and Chin-Kun Hu, Random during human ventricular fibrillation, AIP sequences with power-law correlations Conference Proceedings 922 (AIP, New exhibit, J. Chem. Phys. 126, 145103 York, 2007) edited by M. Tacano, Y. (2007). Yamamoto, and M. Nakao, pp. 573-576. [7] Mai Suan Li, Maksim Kouza and Chin- [16] C.-K. Hu, Quantum and lattice models of Kun Hu, Refolding upon Force Quench biological evolution, AIP Conference and Pathways of Mechanical and Thermal Proceedings 922 (AIP, New York, 2007) Unfolding of Ubiquitin, Biophysical J. 92, edited by M. Tacano, Y. Yamamoto, and 547-561 (2007). M. Nakao, pp. 589-594. [8] Shu-Chiuan Chang, Lung-Chi Chen and [17] Y.-C. Hung and C.-K. Hu, Detecting Wei-Shih Yang, Spanning Trees on the essential nodes in complex networks from Sierpinski Gasket, J. Statistical Phys. 126, measured noisy time series, AIP 649-667 (2007). Conference Proceedings 922 (AIP, New [9] David B. Saakian, A New Method for the York, 2007) edited by M. Tacano, Y. Solution of Models of Biological Yamamoto, and M. Nakao, pp. 603-606.

113 ‹‹- Highlights of Programs Focus Group on Nonlinear Phenomena in Physical and Biological Systems

Coordinator: Sy-Sang Liaw (National Chung Hsing University; email: [email protected]) Committee members: Chao-Nien Chen (National Changhua University of Education), Kai-Jung Chi (National Chung Hsing University), Tzyy-Leng Horng (Feng Chia University), Jiunn-Ren Roan (National Chung Hsing University), Ming-Chih Shih (National Chung Hsing University)

I. Introduction About 10 to 15 people attend the seminar at each gathering. Regular meeting (II)

he focus group consists of the faculty Biophysical Journal Club (BJC)Thursday: members and Ph. D students from 12:00-13:00 various institutes in Taiwan, and two foreign This BJC has been well organized and collaborators. The main theme of the group successful in terms of broadness of attendance. focuses on the non-linear phenomena that The mailing list of BJC continues growing. appear in nature, including the biological About 15 to 25 people attend the Club at each world. Our activities include regular meetings, gathering. Details of the BJC can be found at workshops, and short visits from or to http://140.120.11.15/vedio/biophysics/Chinese institutes abroad. /ournal%20club/activity.htm Current projects under intensified Workshops discussion include: Biophysics workshop: Life among the 1. The mechanism of the Brazil nut effect and formulae of physics, Huisun Forest Station, its reverse (Granular Physics); NaTou, Nov. 2-4, 2007 2. Biological patterns and stability of the We focus on the biomechaics in this Turing equation (Pattern Formation); workshop. Four prestigious speakers: S. Vogel 3. Statistical behavior of agents in economics (Duke Univ.); A. Summers (UC, Irvine); D. (Econophysics). Hu (NYU); and S. Gorb (Max-Planck Int.) will give 2 lectures each in the workshop. The Main tools for the investigation are audience is expected to about 120 people. mathematics and physics. Because of the interdisciplinary nature of our topics, we Conferences constantly consult with experts from Under the support of the focus group, we economics and biology departments. have sent seven Ph. D students to attend international conferences: • C. Liu and C.H. Hung, Turin, Italy, 6/28- II. Activities 7/1, 2006 Regular meeting (I) The The 5th International Conference on Nonlinear phenomena seminar Friday: Applications of Physics in Financial 12:00-13:00 Analysis. They contributed to the conference by one oral and one poster

Highlights of Programs -›› 114 presentations. has puzzled physicists for more than 50 years. After two years of intense study, Prof. Liaw • R.T. Liu and F.F. Chung, Pohang, Korea, and his students have come up with a 7/12-7/15, 2006 mechanism that successfully describes a type The 4th International Conference on of horizontal segregation phenomenon very Nonlinear Science. They presented two similar to the Brazil nut effect. They are posters. optimistic in solving the long-standing puzzle • R.T. Liu, J.Y. Wang, F.F. Chung, Hangzhou in the coming year. They have completed three and Jinhua, China, 11/12-15, 2007 papers for reporting their findings. Prof. Liaw has been invited to present these results in The 3rd Cross-strait conference on Academia Sinica and NCTS. Prof. Liaw was statistical physics. They will do either oral also invited to give a plenary talk in 12th or poster presentation. Symposium on recent advances in Biophysics(5/23-25, 2007, NIH) on his previous work on the leopard's spots, which III. International collaborations was reported in Research Highlight of Nature magazine (Aug. 2006).We have found very 1. Biological pattern formation: Liaw, Liu, interesting phenomena in the emerging Maini econophysics using agent based simulation on Professor S.S. Liaw of NCHU, Professor the model of the Minority game.Our results on P.K. Maini of Oxford, and Dr. R.T. Liu of the minority game have some implications to NCHU have together worked on the biological systems having self-organization criticality. pattern formation for a few years. One of their joint publications has been highlighted by Nature magazine in 2006. They are currently finishing up a paper on the oscillatory Turing patern. V. Selected Publications [1] Fei-Fang Chung, Ruey-Tarng Liu, and Sy- 2. Sand flow through a vertical pipe: Liaw, Sang Liaw, "Horizontal size segregation in Liu, Shih, Matsushita granular matter", J. Korean Phys. Soc. 50, The experiment was proposed by Prof. 224 (2007). Matsushita of Chuo University during his visit [2] Fei Fang Chung, Sy-Sang Liaw, and Chia- to our group in September, 2005. We set up the Yi Ju, "Brazil nut effect in a rectangular experiment immediately and have observed plate under horizontal vibration", to be many interesting phenomena since then. We published in New Journal of Physics are constructing a model to simulate the (2007). density flow of the sand in the pipe, and to analyze its power law. [3] Chia-Hsiang Hung and Sy-Sang Liaw, "Effective history length of the minority game", Physica A382, 129 (2007). [4] S.S. Liaw, C. Liu, and C.H. Hung, "Three IV. Highlights of Research Results phases of the minority game", Physica The Brazil nut effect in granular physics A374, 359(2007).

115 ‹‹- Highlights of Programs Focus Group on Soft-matters, Biophysics and Systems Biology

Coordinator: Pik-Yin Lai (National Central University; email: [email protected]), Hoong Chien Lee (National Central University; email: [email protected]) Committee members: Cheng-Hung Chang (National Chiao-Tung University & National Center for Theoretical Sciences), Chi-Ming Chen (National Taiwan Normal University), Hsien-Da Huang (National Chiao-Tung University), Hsueh-Fen Juan (National Taiwan University), Chun-Yi David Lu (National Taiwan University), Ann- Pin Tsou (National Yang- Ming University)

I. Brief Description various institutions which is listed at the beginning. SBSB focus group also organizes regular and irregularly scheduled seminars, n the past year, the focus groups of workshops, conferences on soft-matter Soft-Bio Matters and Systems physics, biophysics and systems biology held Biology have been reformed and combined as at various associated institutions. We have one under the new name Soft-matter, been organizing the weekly "Soft-Bio Matters Biophysics & Systems Biology (SBSB) focus Seminar/Journal Club" for more than 4 years, group. The new SBSB focus group is now at NCU. This active seminar series has been bigger and contains participants from even inviting local and foreign visiting researchers more diversified fields, especially with many on various areas of soft-matter and biophysics more biology background researchers. and it turns out that various research ideas and Academic activities have increased actual collaborations are indeed come out as appreciably, especially for workshops and direct/indirect consequences of this seminar seminars. In the past year, we have organized a series. In the past year, some topics are more number of activities to promote collaborations emphasized in the areas of DNA both within Taiwan and internationally. Our conformations, genomic/protenomic analysis, purpose is to encourage the use of theoretical evolution theory, nonequilibrium physics in means to investigate the fundamental pulling biomolecular bonds, polyelectrolytes; principles in soft-matter and bio-related rheology & pattern formation in complex sciences and aiming at obtaining some fluids; excitable bio-systems such as cardiac quantitative understanding in soft materials and neural biophysics; collective motions in and biological processes with emphasis on the active organisms; membrane biophysics; more recent hot topics using systems dynamics on complex and bio networks; Brain approaches to investigate biological systems. physics; physics of DNA & proteins, etc. Emphasis is also put on the communications and collaborations with experimentalists, as reflected by the fact that some of the active members of the focus group are II. Activities experimentalists also. In recent years, we have We organized a number of encouraged strongly on creating actual workshop/schools as well as one international collaboration environment between our local scale meetings. We have attracted a number of members and researchers in the Asian-Pacific young and established local researchers, as regions and we are starting to see some well as participants from nearby countries. It is concrete outcomes. The (SB) focus group is worth to mention that these run by a committee of 6 researchers from workshop/conferences always attract a good

Highlights of Programs -›› 116 collection of active researchers from various 7. Mini-workshop on Complex Systems 2007 local institutions to participate/organize these (NCU) July 16~19 activities in an active way. 1. Biophysics Camp 2006 (NCU) Oct. 21~22, 2006

Discussions during the Mini-workshop on Complex Systems 2007

Participants of Biophysics Camp 2006 In May, we organized the "2007 Taipei 2. Miniworkshop on Quantitative Biology International Workshop for Soft Matter and (NCU) Dec. 27, 2006 Biophysics" at Taipei. World renowned physicists and biophysicists delivered series of 3. BioPhysics & Soft-Matter Days 2007 lectures in the conferences. Speakers include: (Kenting) January 26~28 Prof. Robert H. Austin (Physics Dept., Princeton Univ.) Prof. Jacob Kiein (Dept. of Chemistry, Oxford Univ.) Prof. Gerard C. L. Wong (Dept. of Materials Science and Engineering, Univ. of Illinois.) Prof. Sean Ling (Dept. of Physics, Brown Univ.) Prof. Chengde Mao (Dept. of Chemistry, Purdue Univ.) Prof. Meredith Betterton (Physics Dept., Univ.of Colorado). A large number of researchers of different backgrounds Soft-Matter & Biophysics Days 2007 at Kenting's YOHO participate in these workshops. Many of them resort are already involved with SBSB research and 4. Second Workshop on Systems Biology and found this workshop very stimulating. In Bioinformatics (NCU) April 14~15 addition, there are many potential future 5. 2007 Taipei International Workshop for Soft researchers and students that were fascinated Matter and Biophysics (Taipei) May 20~24 by the rapid advances and promising future potential in this area. These activities clearly 6. The 18th Complex Systems Symposium reflected a strong rise in researchers/students' (NCU) June 2~3 interest in bio-related theoretical sciences. Biological related theoretical sciences are expanding in a rapid pace, and it seems that it will keep on growing in the foreseeable future. Soft-matter physics is the foundation to the understanding of the material nature of these biological systems. We anticipate that with the support of NCTS, SBSB research in Taiwan would have a very good chance to contribute promising results in these very competitive areas. Student speaker at the 18th Complex Systems Symposium

117 ‹‹- Highlights of Programs III. Visitors and International Growth of Cortical Neuronal Networks in Collaborations vitro: modeling and analysis, Phys. Rev. E.73, 051906-1~9 (2006). Also selected in SBSB focus group also supported a number Virtual Journal of Biological Physics of foreign visiting scientists aiming at Research 11, issue 10 (2006). academic inteflow of ideas and set up collaborations. We have both short and long- [4] J.R. Roan, Soft Nanopolyhedra as a Route term visitors, delivering lectures and carrying to Multivalent Nanoparticles, Phys. Rev. out collaborations. Foreign visitors in the past Lett. 96, 248301 (2006). Also reported in year include: Dr. Jih-Chiang Tsai Phys. Rev. Focus 17, story 22, June, 2006. (Northwestern U.), Dr. Wan-Chen Lin [5] C. T. Shih, Characteristic length scale of (University of California, Davis), Prof. Qi electric transport properties of genomes, Ouyang (Peking U.), Dr. Armen E. Phys. Rev. E 74, 010903 (2006). Allahverdyan(Yerevan Physics Institute), Prof. Kuan Wang(National Institutes of Health), [6] D.-w. Huang, Ramp-induced transitions in Prof. David B Saakian(Yerevan Physics traffic dynamics, Phys. Rev. E73, 016123 Institute), Prof. Jenifer Thewalt (Simon Fraser (2006). U.), Prof. Hai Jun Zhou (Chinese Academy of [7] C.-H. Cheng, Boundary condition of Sciences, Beijing), Prof. Hyoung Jin Choi polyelectrolyte adsorption, Phys. Rev. E73, (Inha U.), Dr. Wei-Yuan Yang(Harvard U.), 012801 (2006). Prof. Dongchuan Yu (Qingdao U.). [8] J. Henriksen, A. C. Rowat, E. Brief, Y. W. In the past year, we have been specially Hsueh, J. L. Thewalt, M. J. Zuckermann, focused on attracting/promoting students to and J. H. Ipsen, Universal Behavior of enter into our field by organizing the Membranes with Sterols, Biophys. J. 90, Biophysics Camp, the response was very 1639 (2006). positive. The format of the 18th Complex Systems Symposium was also modified to [9] Zi-Hao Wang, Ming-Hua Chang, Jenq-Wei become a symposium with speakers consisted Yang, Jyh-Jang Sun, H.C. Lee and Bai- of solely graduate students. In this two-day Chuang Shyu, Layer IV of the primary symposium, graduate students from various somatosensory cortex has the highest institutions reported their concrete research complexity under anesthesia and cortical results. The best two speakers were awarded complexity is modulated by specific with best presentation awards. Students found thalamic inputs, Brain Research 1082 this to be very stimulating and the positive (2006) 102-114. competition among the students transformed [10] Dominique Chu, Jonathan Rowe, and into an enthusiastic atmosphere. We shall Hoong-Chien Lee, Evaluation of the continue such kind of activity in the future. Current Models for the Evolution of Bacterial DNA Uptake Signal Sequences, J. of Theoretical Biology 238 (2006) 157- IV. Selected Publications 166. [1] Hsuan-Yi Chen and Kwan-tai Leung, [11] S. Bastrukov and Pik-Yin Lai, On the Rotating states of self-propelling particles Surface Gyromagnetic Plasmons in a in two dimensions, Phys. Rev. E73, 056107 metal sphere, Surf. Rev. & Lett. 13 (2006). (2006). [2] Jia-Yuan Wu, and Hsuan-Yi Chen, [12] S. Bastrukov, Pik-Yin Lai, D. Podgainy Membrane-adhesion-induced phase and I. Molodtsova, Optical Response of separation of two species of junctions, magnetically aligned nematic soft matter Phys. Rev. E73, 011914 (2006). by transverse nemato-magnetic waves, J. of Mag. & Mag. Materials (2006). [3] Pik-Yin Lai, L.-C. Jia, and C. K. Chan,

Highlights of Programs -›› 118 [13] C.H. Chen and Hsuan-Yi Chen, Finite- Condensation of DNA, Phys. Rev. E75, size domains in membranes with active 041922 (2007). two-state inclusions, Phys. Rev. E74, [19] O.I. Kanakov, G.V. Osipov, C. K. Chan, 051917 (2006). and J. Kurths, Cluster synchronization [14] L. C. Jia, C. R. Han, C. H. Chang, M. T. and spatio-temporal dynamics in Tsai, Y. S. Chou, Pik-Yin Lai, and C. K. networks of oscillatory and excitable Luo- Chan, Synchronized Bursting induced by Rudy cells, Chaos 17, 015111 (2007). network connectivity in cortical neuronal [20] D. W. Huang, Bi-directional ant traffic on cultures, J. Korean Phys. (invited article), trails, International Journal of Modern 50, p.207~218 (2007) Physics C 18 , p.407 (2007). [15] H.J. Lin, H. Y. Chen, Y.J. Shen, and H. K. [21] D. W. Huang, Phase diagram of a traffic Tsao, Bell's Expression and the roundabout, Physica A 383, p.603 (2007). Generalized Garg Form for Forced Dissociation of a Biomolecular Complex, [22] Y.-S. Tsai and C.-M. Chen, Driven Phys. Rev. Lett. 98, 088304 (2007). polymer transport through a nanopore controlled by a rotating electric field: Off- [16] Y. W. Hsueh et. al., Ergosterol in POPC lattice computer simulations, J. Chem. Membranes: Physical Properties and Phys., 126, 14491 (2007). Comparison with Structurally Similar Sterols, Biophys. Journal 92, 1606 (2007). [23] D.-M. Ou, C.-C. Chen, and C.-M. Chen, Contact-induced structure transformation [17] W. C. Hung, M.T.Lee, and F.Y. Chen, The in transmembrane prion propagation, Condensing Effect of Cholesterol in Lipid Biophys. J., 92, 2704 (2007). Bilayers, Biophys. J. 92, 3960 (2007)

[18] F. T. Chien, S. G. Lin, Pik-Yin Lai and C. * The above publications are direct or indirect outcomes of K. Chan, Observations of Two forms of the activities organized by our focus group. However, not Conformations in the Re-entrant allof these publications have shown affiliation with NCTS.

119 ‹‹- Highlights of Programs Highlights of Programs Condensed Matter Physics

Focus Group on Computational Materials Research

Coordinator: Tsan-Chuen Leung (National Chung Cheng University; email: [email protected]) Committee members: Chun-Ming Chang (National Dong Hwa University), Ching Cheng (National Cheng Kung University), Guang-Yu Guo (National Taiwan University), Ming-Hsien Lee (Tamkang University), Shiow-Fon Tsay (National Sun Yat-sen University)

I. Introduction (postdoc. at NCKU), C. H. Cho (Ph. D. student at CCU), and C. H. Yao (Ph. D. student at NDHU) to attend international school. We also supported C. Y. Ren (NKNU) and B. R. Wu he chief purpose of this group is to (CGU) to visit NCTS this summer in order to enhance the domestic research promote the collaboration among local capacity in computational material science members. The gatherings of this kind have especially quantum mechanics-based ab initio provided an essential channel for fruitful electronic structure calculations and molecular discussions among members of the dynamics simulations, through promoting community, and in particular, benefit our exchange and collaboration among local postgraduate students and young postdoctoral members as well as between Taiwan and fellows tremendously. foreign members, and also through attracting The CMR focus group consists of 42 more young researchers into this field. To this members (29 faculties and 13 Ph. D. students end, like previous years, we have organized ab and postdocs). It is run by a committee from initio methods study group meeting, mini- various institutions. The missions of the schools with leading international scientists as committee are to allocate the budget, to initiate main lecturers, and also program-wide annual research activities, to invite the long-term and conference. Furthermore, to attract younger short-term visitors and to recommend researchers as well as experienced ones to the candidates (Ph. D. student or junior scientist) field of CMR and also promote awareness of to attend international school, conference, or the important role in the modern scientific workshop with the financial support of research played by the computation using CMRFG. present-day computers, we have also organized spring school (introductory level) and summer school (advanced level) on first- principles computational materials research. II. Activities We have encouraged members especially 1. Mini-School on Time-Dependent Density young ones to attend relevant international Functional Theory: Foundations and conferences, workshops and schools. Applications Specifically, we supported Ru-Fen Liu

Highlights of Programs -›› 120 The ground-state based nature of the and young postdocs, were encouraged to give conventional Density Functional Theory a talk in this workshop. The workshop will (DFT) method has difficulties in tackling cover the subjects related to our program such electronic excitations. An alternative method as description of physics and computational which is comparatively simpler in formalism is methods or report of results. The scientific the time-dependent (TD) DFT. TDDFT has program consisted of four 40-50-minutes great success in describing excitations in finite lectures, eight 30-minutes research reports and systems such as nanoclusters. The Mini- ten 20-minutes talks by student. School on Time-Dependent Density 4. Spring school on First-Principles Functional Theory: Foundations and Computational Materials Research - Applications, organized by G. Y. Guo (NTU), Introductory Level is held in National Taiwan University in March 16-17, 2007. Two of the leading The spring school on first-principles figures in the field, namely, Prof. Eberhard K. computational materials research-introductory U. Gross (Berlin Free Univ.) and Prof. Shih-I level, lectured by T. C. Leung (CCU), is held Chu (Univ. of Kansas and National Taiwan in National Center for High-Performance Univ.), gave five lectures on the foundations, Computing. The purpose of this school is to recent new developments, and applications of offer an introduction to the fundamentals of ab TDDFT. initio density functional theory, of pseudopotentials, and large scale calculations, 2. Mini-School on Tight Binding Simulation as well as a practical hands-on training for on Nanomaterials young students and non-specialists. The The ability to perform reliable simulations response from both young students and non- of molecules and solids systems with specialist researchers were very positive, there thousands of atoms has enormous payoffs in were more than hundred participants in this many fields. The Mini-School on Tight spring school. Binding Simulation on Nanomaterials, 5. Summer School on First-Principles organized by T. C. Leung (CCU), is held in Computational Materials Research – NCTS in June 22-23, 2007. Prof. C. W. Wang Advanced Level from Ames Lab. (USDOE) gave four lectures to review the tight binding theory, formulism The summer school on first-principles and the development of tight binding computational materials research – advanced potentials for molecular simulation of level, organized by C. Cheng (NCKU) and T. materials. Application of tight binding C. Leung (CCU), is held in NCTS. The molecular dynamics to the studies of purpose of this school is to offer the audiences nanoclusters, carbon nanotubes, and surface- a deeper understanding on the fundamentals of based nanostructures were discussed. ab initio density functional theory, of pseudopotentials, and large scale calculations. 3. The 7th Workshop on First-Principles Particular emphasis will be laid on a thorough Computational Materials Physics discussion of the problems that can be solved The 7th Workshop on First-Principles directly with the basic code. There were more Computational Materials Physics, organized than fifty participants in this summer school. by S. F. Tsay (NSYSU), was held on Jan. 29- 6. Asian Workshop on First-Principles 31, 2007 in National Sun Yat-sen University. Electronic Structure Calculations The aim of this conference is to promote interaction and collaboration among local The 9th Asian Workshop on First-Principles physicists. The Program Committee would Electronic Structure Calculations was held in also like to take this opportunity to hear about Korea, Nov. 1 – 3, 2006. This is a big event in interests of the community in order to plan the Asian community of ab initio research. future activities at the Center. Like previous This series of workshop is initiated at 1998 by years, all participants including PhD students Prof. K. Terakura of Japan and K. J. Chang of

121 ‹‹- Highlights of Programs Korea, more than 100 scientists from the Asian electronic properties of a variety of different countries such as China, Hong Kong, Japan, systems, ranging from bulk materials to Korea, India, Singapore, and Taiwan, and also surfaces, nanotubes, and molecules, whereas four to five leading experts from Europe and the linear optical response is routinely studied USA participate in this workshop. The 4th by solving the Bethe-Salpeter Equation (BSE) Asian Workshop was held in National Taiwan with comparable success. ABINIT is a University in 2001, the 7th Asian Workshop package whose main program allows one to was held in Tamkang University in 2004, and study the excited states using the GW the 11th Asian Workshop will be held in approximation. On the other hand, the EXC is National Sun Yat-sen University. Eighteen an exciton code which uses the output of members of CMRFG participate the 9th Asian ABINIT to calculate the dielectric and optical Workshop last year. The next meeting will be properties for a large variety of systems by held in Japan and we will continue being solving the Bethe-Salpeter equation. In order active in this Asian community of ab initio to familiar with the principles used in the research. program and how they are implemented so that the program can be properly applied to the 7. OpenMx Study Group Meeting systems we want to study, Exited State Study It is well known that the computing time of Group Meeting was organized by G. Y. Guo currently popular electronic structure methods (NTU) and held in NTU. The key members based on Density Functional Theory scale like involved in this project are G. Y. Guo (NTU), N2-3, with N being the number of atoms in the T. C. Leung (CCU), Y. J. Tsai (CCU), H. C. simulation cell. In the last few years, much Hsueh (TKU) , M. Hayashi (CCMS), C. K. effort has been devoted to overcome this Yang (CGU), H. T. Jeng (AS), and B. R. Wu problem, and a number of methods have been (CGU). developed with "order – N "[O(N)] scaling, i.e., whose computational cost scales only linearly with the number of atoms. One of the successful order N ab initio computing code is III. Collaborative Activities OpenMx (Open source package for Material The examples of these collaborations between explorer) developed by Dr. Taisuke Ozaki CMRFG members are listed as follows: from National Institute of Advanced Industrial 1. C. M. Chang (NDHU), C. Cheng (NCKU) Science and Technology in Japan. In order to and C. M. Wei (AS) on the Quantum Monte familiar with the principles used in the Carlo simulation on nanomaterials. program and how they are implemented so that the program can be properly applied to the 2. H. T. Jeng (AS) and C. S. Hsue (NTHU) on systems we want to study, several study group the Orbital Ordering in transition-metal meeting on OpenMx was organized by T. C. oxides. Leung (CCU) and held in NCTS. The key 3. C. Y. Ren (NKNU), S. F. Tsay (NSYSU) members involved in this project are C. S. and F. C. Chuang (NSYSU) on the Hsue (NTHU), Y. T. Lu (NCKU), W. C. Kuo electronic structure of Au/Si(111) (5x2). (NSYSU), T. L. Li (NCYU), T. C. Leung (CCU), Y. C. Hsu (NCKU), S. F. Tsay 4. B. R. Wu (CGU) and T. C. Leung (CCU) on (NSYSU), G. Y. Guo (NTU), S. H. Chiou the electronic and optical properties of (ITRI), C. Y. Ren (NKNU), and B. R. Wu ribbon under external electric field. (CGU). 5. G. Y. Guo (NTU), T. C. Leung (CCU) and H. C. Hsueh (TKU) on the ab initio study 8. Excited State Study Group Meeting on excited state of nanomaterials. The conventional DFT method fails to give accurate excitation properties, e.g., band gaps, International collaborations are listed as excitonic binding energies, of solids. The GW follows: method has been successfully used to predict 1. K. Terakura (Japan) and G. Y. Guo (NTU)

Highlights of Programs -›› 122 on the static dielectric response of BN and crystallographic lattices in perovskite

nanotubes from ab initio finite electric field manganites such as La1-xCaxMnO3 in the low calculations, temperature insulating charge ordered phase. We have investigated the electronic structures 2. C. T. Chan (Hong Kong) and T. C. Leung of SrRuO in the distorted orthorhombic (CCU) on the field emission properties of 3 structure using LDA+U. The obtained band nanomaterials. energies agree well with those from 3. M. Y. Chou (USA) and C. M. Wei (AS) on photoemission and X-ray absorption the quantum well states in metal thin films. spectroscopy. Our finding unravels the nature 4. Steven G. Louie (USA) and H. C. Hsueh of the orbital ordering, the close connection to (TKU) on the quasiparticle excitations in the JT distortions, and the importance of the nanomaterials. on-site correlation U in the relatively extended Ru 4d orbitals. H. T. Jeng, S. H. Lin, C. S. Hsue, Phys. Rev. IV. Highlights of Research Results Lett. 97, 67002, (2006) 1. Current and strain-induced spin 3. Highly Spin-polarized field emission polarization in InGaN/GaN superlattices induced by quantum size effects in ultathin films of Fe on W(001) Main team members: Main members: G. Y. Guo (NTU) and Y. F. Chen (NTU, experimentalist) T. C. Leung (CCU) and C. T. Chan (Hong Kong) It has been proposed theoretically that a transverse spin current, the so called spin Hall Nanostructured systems have enhanced current, can be generated in strongly spin-orbit effects due to the confinement of quantized coupling systems by external electric field. states, and, for the particular case of ultrathin We have investigated the current-induced spin supported films, many amazing structural and polarization in InGaN/GaN superlattices. It is electronic properties have been discovered. found that the degree of polarization changes Although tungsten is the metal of choice for sign as the direction of the current flow is emitter tips, it does not produce spin-polarized reversed. The strain-induced spin Hall effect field emission currents. We use density discovered here paves an alternative way for the creation of spin polarized current, which functional calculations to study the spin- should be useful for the realization of the polarized field emission from pseudomorphic future applications in spintronics. Fe ultathin films on W(001). We found that nearly completely spin-polarized field H. J. Chang, T. W. Chen, J. W. Chen, W. C. emission currents can be realized in two and Hong, W. C. Tsai, Y. F. Chen, and G. Y. Guo, Phys. Rev. Lett. 98, 239902 (2007). four Fe layers on W(001) and that these systems have the additional advantages of 2. Orbital Ordering and Jahn-Teller thermal stability and low work functions. The Distortion in Perovskite Ruthenate thickness dependent field emission properties SrRuO 3 are traced to spin-polarized quantum well and Main team members: surface resonance states localized in the Fe H. T. Jeng (AS) and C. S. Hsue (NTHU) layers. Orbital, charge, spin, and lattice degrees of Bin Li, T. C. Leung, C. T. Chan, Phys. Rev. freedom play important roles in the electronic, Lett. 97, 87201 (2006). magnetic, and transport properties of Remark: For detail publications, please see the webpage transition-metal oxides. It was proposed that http://phys.cts.nthu.edu.tw/research/focus_group orbital ordering is closely related to magnetic .php

123 ‹‹- Highlights of Programs Focus Group on Low-Dimensional Systems and Nanostructures

Coordinator: Jang-Yu Hsu (National Cheng Kung University; email: [email protected]) Committee members: De-Hone Lin (National Sun Yat-sen University), Min-Fa Lin (National Cheng Kung University), Chi-Tin Shih (Tung Hai University), Yan-Chr Tsai (National Chung Cheng University), Chih-Kai Yang (Chang Gung University)

I. Brief Description II. Activities The focus group has, for serving our members and young scholars alike, organized he nanostructure and low workshops and tutorial schools by inviting dimensionality presents peculiar domestic and foreign scholars to review the physics uncommon to the classical or the experimental and theoretical progress and infinite-sized quantum system. The beautiful prospect in nanoscience. As part of the effort fullerene is a zero dimensional system, the to achieve the center of excellence for NCTS, carbon nanotube, a one dimensional system, summer residency of theoreticians is strongly and the graphene, a two dimensional system. encouraged. Moreover, NCKU has earmarked The opportunities for scientific discovery and 100% matching fund to promote the NCTS for technology breakthrough therefore abound. activities and to, in additional funding, The nanoparticles or nanostructures are promote the neighboring institutions for intermediate between atomic and macroscopic academic excellence. scales representing an emerging field of intense research, known as the mesoscopic In the four seasons, we organize the major physics. The nonlinear many body effect workshops at various universities with the however, manifests itself in rich phenomena participants numbered around fifty people and present many challenges, both theoretical each time. The availability of high speed bullet and experimental to the researchers in the train will further enhance the collaboration and field. partnership of scientists between the south and the north Taiwan, and will increase the foreign This focus group formed in year 2004 is the scholar visits. The summer residence at youngest among the NCTS siblings, and NCTS-south has 4 scientists and called our represents a new, evolving and novel direction attention to propose adding shower room and of research. Its main purpose is to promote dormitory accommodation. We have collaborations among faculty members, implemented the video conferencing, eJournal postdoctors, graduate students as to integrate club web pages, and the database for video the available research methods, resources and presentations and power point files. Each the manpower. In particular, this group has workshop has compiled proceedings of helped neighboring universities to organize abstracts to document members' recent workshops and summer schools, to finance the research results and to encourage foreign trips and invited speakers, and to collaborations and innovations. frequent the summer resident scholars of the Miniworkshops are organized in the hot young, the diligent and the innovative. The summer days. Foreign trips for postdocs and research interest while diverse may be graduate students have been financed through categorized into the following: carbon related, NCTS and NCKU funding. Weekly luncheon nanoparticle, molecular device, and bio and meetings were held during the school advanced concepts. semesters with participants mainly within

Highlights of Programs -›› 124 Tainan area as understandably limited by time gradient approximation are, respectively, used and effort for long distance travel, but the to calculate electronic states and energy loss invited speakers of the followed seminar do spectra. Prof. Shih-Jye Sun will study the come without. Short term foreign visitors are adsorption of gas molecules by CNT and the invited in conjunction with the Autumn electrical conductivity. Workshop as it is the largest planned. International Conference Participation: By the support of NCTS, Prof. R. B. Chen attended the 16th International Conference on III. Visitors and International Electronic Properties of Two-Dimensional Collaborations Systems in Albuquerque, New Mexico in 2005 Foreign Visitors: and Prof Jung F. C. of NSYSU visited China Professor Zhao Jijun from Dalin University in 2007. With the matching fund from NCKU, of Technology in China, is an expert of first C. W. Lo and J. Y. Hsu will attend the principle calculations on nanostructures. CCP2007. During his visit, he provided very instructive lectures on genetic algorithms, gold nanoparticles and structural, electronic, IV. Highlights of Research Results vibrational and magnetic properties of Carbon related: fullerene and variants. Under our invitation to come in September is Dr. Stephan Roche of (M. F. Lin) A carbon nanotube (CNT) can France, an author of the recent review article exhibit interesting excitation properties, since in Review of Modern Physics, 79, 677 (2007) the linear and angular momenta of electrons (56 pages) on 'Electronic and transport are conserved on a cylindrical surface. The properties of nanotubes'. We have also Slater-Koster tight-binding model and the extended our invitation to Professor Weitao random phase approximation were, Yang, the Philip Handler Professor of respectively, used to study the magneto band Chemistry at Duke University, with expertise structures and electronic excitations. The in quantum chemistry, DFT and biomolecules. excitation spectra strongly depend on the magnitude and the direction of magnetic field, Domestic Visitors and Summer Residency: the transferred momentum, the temperature, By the joining effort with Professor Y. C. the nanotube geometry, and the Zeeman Hsue, many domestic speakers were invited to splitting. The scattering rate of electrons in the the Ph. D. student seminars. The summer nanotube and graphene was studied. The residency we had three scholars in year 2006: lowest two conduction bands in moderate-gap Prof. C. P. Chang, Prof. C. H. Lin and Prof. R. CNTs have the vanishing decay rates owing to B. Chen and five scholars in year 2007: Prof. the absence of low-frequency deexcitation C. P. Chang, Prof. C. H. Lin and Prof. R. B. channels. The decay rate of the metallic CNTs, Chen, Prof. Shih-Jye Sun. Prof. Chang worked sensitive to the wavevector, has a linear on electronic properties of the AA- and ABC- temperature dependency. The decay rate of the stacked few-layer graphites in the presence of band-edge state is faster as the nanotube radius an electric field, perpendicular to the layers increases. The increased carrier density through the tight-binding method. Prof. C. H. significantly enhances the intraband loss Lin investigated the wrapping conformations spectrum and thus the decay rate. As to other of a polymer on the nanoparticle surface. states, the decay rate under the negative energy Under the assumption of invariant length for transfer is comparable to those under the each polymer segment, he obtained a set of positive energy transfer. (C. Y. Yang) The analytic equations describing the conformation boron-nitrate nanotube as a "nano-cable", at the minimum free energy. Prof. R. B. Chen shielding and protecting materials from studied energy loss spectra of finite carbon outside interference was examined. nanotubes. The sp2 tight-binding model and the

125 ‹‹- Highlights of Programs Nanoparticle: issue of polarity in III-V nitride semiconductors. (F.C. Chuang) Motivated by (C. Y. Yang) Ab initio calculations were the STM experiments of Ma et al., Science employed to study the physical properties of a 2003, 299, 1874, a combined GA-DFT variety of nano-scale materials. Of particular procedure to search for the structure of [110] interest was using the fullerene C molecules 60 silicon nanowires (SiNWs) up to 60 atoms per to store hydrogen molecules. (F. C. Chuang) A unit cell were investigated and reported in genetic algorithm was developed to search for Nano Letters. (C. Y. Yang) Transport the lowest energy surface structure. These properties were studied for systems with structures were further optimized using first- nanotubes or molecules connected between principle calculations. Several high-index two electrodes, and with magnetic impurities surfaces [e.g. Si(105), Si(114), Si(337), and encapsulated or doped for spin transport as in Si(103)] were successfully identified. (J. Y. the spintronics. Hsu) The global minimum energy state of nanoparticle structure is an NP hard problem. Bio and advanced concepts: As the number of particles goes up, the (C. T. Shih) Transport property of p53 gene problem becomes intractable and is studied by a tight-binding model. The unreasonable, since the neighboring solutions change of the transmission coefficient is scale as a super-polynomial function. evaluated for all possible point mutations of Adopting a coarse grain (CG) scheme, both p53. On the average, the mutations found in GA and SA were speeded up by the divide- the tumor tissues reduce the transmission and-conquer strategy, and the calculation is coefficients. The result provides an further expedited by the local evaluation and explanation on how the cancerous mutations deterministic search (ES) that improves the fend off the DNA-repairing mechanism and algorithm from the diffusive to a deterministic cause cancers. (D. H. Lin) The Friedel theorem process. The proof of principle was for the relativistic spin-1/2 system and the demonstrated by the fullerene structure with connections among the Friedel sum, Levinson use of the Tersoff potential. theorem, and the Atiyah-Singer (AS) index Molecular device: were derived. Since the AS index is important in studying the relations among the invariants (M. H. Tsai) Conduction through a in modern quantum field theory and string molecular junction and the growth rate of a theory, the present result provides an avenue to GaN nanorod faster than that of the film were discover new invariant. It is important in studied theoretically from the first principles. studying the 2D graphene system the structure Comparing with the experimental data shows of neutron star, and the application in good quantitative agreement. Our first- controlling a spin bus - a controllable coupler principles calculation for the electronic of many qubits. structures of nm-scale [0001] GaN films shows that the internal electric fields and the band tilt of these films are in opposite direction to those predicted by the generic V. Publication polarization of Bernardini, Fiorentini and Since the NCTS funding to support Vanderbilt (PBFV). Additionally, it is determined individual researcher makes an epsilon impact that an intrinsic self-regulated charge transfer on his/er pocket book in general, it is across the film limits the electrostatic potential understandable that few of the published difference across the film, which renders the papers acknowledged NCTS financial support. local conduction band energy minimum (at the The funding for workshop, trip, and summer Ga-terminated surface) approximately equal to residency however will in the long run the local valence band energy maximum (at enhance greatly the collaboration, and will the N-terminated surface). This finding cast advance the innovative research as anticipated. doubt on the popular use of PBFV to address the The short term gain while is less pronounced,

Highlights of Programs -›› 126 NCTS funding will result in the long term benefit as hereby acknowledged to be money well spent. In the past 3 years, more than 50 SCI papers were published by the members of this group. For detail publications, please see the webpage http://phys.cts.nthu.edu.tw/ research/focus_group.php

VI. One Picture Is Worth Ten Thousand Words

Fig. 3. (a) The Coulomb decay rates of narrow-gap CNs for the first conduction bands. (b) Those associated with positive decay energies and (c) correspond to the interband c➝v decay.

Fig. 1. The inelastic scattering rates of the (5,5) nanotube. They are calculated for the low energy states at T=300 K. Also shown in the inset are those of the conduction-band states from the intraband excitations.

Fig. 4. The Energy Surface and Dirac Cone at K point of Graphene

Fig. 2. The Coulomb decay rates of moderate-gap CNs for the first conduction bands. Also shown in the inset are those associated with positive decay energies.

127 ‹‹- Highlights of Programs Focus Group on Mesoscopic and Spin Physics

Coordinators: Chon-Saar Chu (National Chiao Tung University; email: [email protected] ) Chung-Hou Chung (National Chiao Tung University; email:[email protected]) Committee members:Cheng-Hung Chang (National Chiao Tung University and National Center for Theoretical, Science), Yu-Chang Chen (National Chiao Tung University), Shun-Jen Cheng (National Chiao Tung University), Hsiu-Hau Lin (National Tsing Hua University), Juhn-Jong Lin (National Chiao Tung University)

I. Brief Description C.S. Chu and C.H. Chang have benefited from the discussions with Prof. Roland Winkler in detail about the effects of gate-bias on the local chemical potential. This can be oals: implemented in their future consideration of gate-controlled spin dynamics. Two graduate To understand and discover interesting students: one Ph.D. student, L.Y. Wang, and new phenomena on electronic and spin the other master student, K.Y. Chen presented transport in nanostructures. their work to Prof. E.I. Rashba (Harvard), and Research topics: separately, to Prof. S.Q. Shen (U. of Hong- Kong). These two students had benefited from Electronic transport in semiconductor • their comments and suggestions. C.H. Chung nanostructures. Topics include: quantum and the invited speaker Walter Hofstetter (U. phase transition and non-equilibrium of Frankfurt) discussed their research transport in quantum dots associated with collaboration in quantum dots and Kondo Kondo effect (C.H. Chung), dissipation and effect. noise in nano-juction devices (Y.C. Chen and C.H. Chung), dephasing and decoherence in International Workshop on Disorder and disordered nano-wires/nano-junctions (J.J. Interactions in Low Dimensions, June, 2007 Lin). Many of our FG members and PhD • Spintronics in nanostructures. Topics students had benefited a lot from discussions include: novel magnetic properties in diluted with invited speakers S. V. Kravchenko magnetic semiconductor (H.H. Lin), spin (Northeast U.), E. Abrahams (Rutgers U.) and transport and spin Hall effect in Rashba-type Dobrosavljevic (NHMFL, Florida State U.) on 2-D electron gas (2DEG) (C.S. Chu and C.H. their common research interests on 2D metal- Chang), spin-characteristic charged excitons insulator transitions, disordered systems in in self-assembled quantum dots (S.J. Cheng). low-dimensional materials and transport in Kondo dots. The discussions inspired new Strongly correlated effects in • ideas along these lines. PhD and Mater nanostructures. Topics include: edge states students also got trainings from some of the and magnetic properties of carbon nanotubes broader overview talks in the workshop. (H.H. Lin), quantum criticality in coupled quantum dots and in cold atoms (C.H. Seminars and regular discussions: Chung). We have invited many local experts and foreign visitors to give seminar talks in NCTS to discuss our research interest. The goals are II. Activities to develop new ideas, to encourage new collaborations, to educate students/postdocs International Workshop on Mesoscopic and and to invite people from institutions with Spin Physics, NCTU, Jan., 2007: relatively limited resources to participate. Such

Highlights of Programs -›› 128 examples include: (ii). Invited visits to internationally prestigious institutions by our young scholars: • New projects/ ideas were developed: (i) among J.J. Lin (experimentalist) C.H. Chung APCTP, Pohang, Korea: H.H. Lin (Aug. and Chi-Tong Chen (Academia Sinica) on 2007) and C.H. Chung (Feb. 2007) the transport through quantum dots coupled KITP, Santa Barbara, USA: C.H. Chung to nanowires. (ii) between J.J. Lin's (Aug. 2007) experimental group and C.H. Chung on Kondo effect in transport through nanowires. KITPC, Beijing, China: C.H. Chung and The recent experimental results done by H.H. Lin (Jul. 2007) Lin's group can be explained very well by (iii). A one-day PhD students workshop the 2-impurity Kondo model. (iii) among organized by the NCTS post-doc, Kao- C.S. Chu, Malshukov, H.H. Lin and C.H. Chin Lin, and Ph.D. students in the Focus Chang in the spin Hall effect in Rashba-type group is to be held on Sept. 8, 2007. This 2DEG. (iv) between S.J. Cheng and Wei- is intended to be a meeting for these Tong Sheng on excitons in semiconductors.. young physicists to discuss, to share, and (iv) between H.H. Lin and Horng-Tay to collaborate. Cheng (Academia Sinica) on magnetism in carbon- nanotubes. They have very fruitful (iv). C.H. Chung and H.H. Lin's students results. attended the joint summer school jointly by APCTP and Max-Planck Dresden on • Education for students/postdocs/young strongly correlated systems in nano- faculty: Prof. Y.C. Lee (SUNY, Buffalo) has stuctures, Jul. 2007, Pohang, Korea. visited NCTS from March till July. During this period, he has given a series of lectures on topics including Bose-Einstein condensation, High Tc superconductivity, III. Visitors and International and a basic investigation of the spin Collaborations nonconservation in spin-orbit interaction. • G. Mal'shukov (NCTS visiting professor Prof. B.L. Young (NCTU) and T.F. Jiang from Moscow), R. Winkler (Argonne Lab.), (NCTU) had discussions with Prof. Lee for a Prof. E.I. Rashba (Harvard): visitors and couple number of times. Prof. Lee also was collaborators of Chon Saar Chu and Cheng- invited to present his results in NTU, NCKU, Hung Chang. and NSYSU. • W. Hofstetter (Frankfurt U.): visitor and • Participants from institutions with less collaborator of Chung-Hou Chung resources: We have invited and interacted Wei-Tong Sheng (Fudan U., China): visitor with quite a few such speakers: Prof. Jyh- • and collaborator of Shun-Ren Cheng. Shyang Wang and Prof. Ji-Lin Shen (Chung- Yuan Christian U.), Shih-Jye Sun • Toshiya Hikihara (Hokkaido U.), Dung-Hai (Kauhsiung U.) Lee (UC Bekerley), Gil Rafael (Cal Tech): international collaborators of Hsiu-Hau Lin. Training for young generation physicists: Peter Woelfle (Karlsruhe, Germany), (i) Ph.D. student, Lu Yao Wang, was invited to • Matthias Vojta (Koeln, Germany), Gergely attend a workshop on spintronics, by the Zarand (Budapest, Hungary), Pascal Simon organizer Prof. Brataas, in the Center for (Grenoble, France), Kevin Ingresent (U. Advanced Studies in Oslo for two months: Florida), Subir Sachdev and Lars Fritz Sept. and Oct. of 2006. C. S. Chu also (Harvard), Karyn Le Hur (Yale), Leon visited the same place in Sept. 2006. The Balents (KITP, UCSB), Guang-Ming Zhang workshop lasted one year, with invited (Tsing Hua, Beijing), Lu Yu (Academia scientists working on spintronics discussing Sinica, Beijing), Yong Baek Kim (Toronto): their findings and sharing their insights in international collaborators with Chung-Hou an informal way. Chung

129 ‹‹- Highlights of Programs • E. Abrahams (Rutgers, USA), V. • Chung-Hou Chung Dobrosavljevic (Tallahassee, USA), V. (i). We proposed (for the first time) the Kagalovsky (Beer-Sheva, Israel), S.V. experimental realization of the quantum Kravchenko (Boston, USA), V. Mitin critical non-Fermi liquid state, originally (Buffalo, USA), Y. Ochiai (Chiba, Japan), D. discovered in the 2-impurity Kondo model, Popovic (Tallahassee, USA) , A. Punnoose in the coupled double quantum dot (New York, USA) , G. Senatore (Trieste, systems. We clarify a common misleading Italy), A. A. Shashkin (Chernogolovka, belief that particle-hole asymmetry would Russia): visitors for disorder and localization smear out the transition. It has been workshop. presented in invited conference talks in • Y.C. Lee (SUNY, Buffalo): long-term visitor, Dresden, Germany by Zarand (2007) , in March-July, 2007. APCTP, Korea and in KITPC, Beijing by C.H. Chung (2007). (ii). We found a new type of quantum phase IV. Highlights of Research Results transition between localized and • Chon Saar Chu delocalized phases in a dissipative quantum dot. Our analytical (i). We consider the spin accumulation in the Renormalization Group (RG) and neighborhood of a normal scatterer in a Numerical RG calculations reach an Rashba-type 2DEG. We find there is spin excellent agreement. This work was accumulation–spin dipole–in the presence presented by K. Ingresent in a conference of a driving electric field, even though it is in Dresden, Aug. 07'. well known that the electric field could not generate a transverse spin current (iii). We found a new scaling behavior for a dissipative quantum dot coupled to (ii). We consider the spin accumulation effect Luttinger-liquid leads at non-equilibrium due to spin-orbit interaction (SOI) arising quantum criticality. from in-plane potential gradient. In a 2DEG in which a driving electric field C.H. C acknowledges the general support does not give rise to a spin current, we from the NCTS. Its activities play an find, again, spin dipole in the important role in carrying out the above- neighborhood of a ring-shaped potential mentioned work. Part of his work was pattern. More importantly, the dipole done in collaboration with the NCTS strength is greatly amplified near a visitor W. Hofstetter. quantum resonance, and the resonant • Hsiu-Hau Lin characteristics allow for an electrical mean of switching the sign of the spin direction: (i) Develop self-consistent Green's function by a gate-control of the chemical potential method to describe the diluted magnetic of the system. semiconductor. (iii). We found the polarization of electrons in (ii) Discover the role of Fermi surface a symmetric quantum well by a topology in carrier-mediated perpendicular electric current due to the ferromagnetism for spintronics devices. revival of a Dresselhaus SOI term. (iii) Demonstrate dynamical symmetry Averaging with the confined state in the enlargement in carbon nanotubes by the quantum well, this term is zero. But in the combination of renormalization group and presence of a perpendicular electric bosonization techniques. current this Dresselhaus SOI becomes • Cheng-Hung Chang finite. The semiclassical path integral (SPI)

Highlights of Programs -›› 130 method has been successfully applied to V. Selected Publications explain spin dynamics in several mesoscopic (for more details, please see http://phys.cts. systems under Rashba spin orbit interaction, nthu.edu.tw) including spin current transports and spin relaxations. Recently we extend the [1] A.G. Mal'shukov, and C.S. Chu, Phys. application of this technique to spin relaxation Rev. Lett. 97, 76601 (2006). problems in quasi-1D channel under Rashba [2] A.G. Mal'shukov, L.Y. Wang, and C.S. spin-orbit interaction. By applying SPI Chu, Phys. Rev. B 75, 85315 (2007). method, our recent preprint confirms several previous discoveries and predictions. It [3] K.Y. Chen, C.S. Chu, and A.G. clarifies the underlying mechanism responsible Mal'shukov, Phys. Rev. B (2007) for those phenomena, extends the validity of (accepted). some prediction, and derives and numerically [4]. G. Zarand, Chung-Hou Chung, P. Simon confirms the Bessel-function spin relaxation in and M. Vojta, Phys. Rev. Lett. 97 166802 such quasi-1D channel. (2006). • Shun-Jen Cheng [5]. Chung-Hou Chung and Walter Hofstetter We study spin characteristics of excitonic Phys. Rev. B 76 045329 (2007). absorption in self-assembled quantum dots. [6] Chung-Hou Chung, Matthew Glossop, We carry out a theoretical investigation of Lars Fritz, Marijana Kircan, Kiven spin-characteristic excitonic absorption in Ingersent, and Matthias Vojta., cond- bias-controlled charged quantum dots. Spin mat/0706.2085 (2007) (Physical Review B Pauli blockade, Coulomb (exchange and accepted). correlation) interactions, and symmetry of dot [7] J. E. Bunder and Hsiu-Hau Lin*, Phys. shape are identified as the three main Rev. B 75, 075418 (2007). underlying mechanisms, sensitively depending on Ne, in the spin characteristic spectra. We for [8] Wen-Min Huang, Cheng-Hung Chang and the first time reveal that polarized absorption Hsiu-Hau Lin*, Phys. Rev. B 73, in triply charged dots exhibits anomalous spin- 241307(R) (2006). dependent features, resulting from the intrinsic [9] J. E. Bunder, Shih-Jye Sun and Hsiu-Hau correlations in charged exciton X-3. Lin*, Appl. Phys. Lett. 89, 072101 (2006). • Yu-Chang Chen [10]. Wen-Hsuan Kuan, Chi-Shung Tang, We discuss how the shot noise in quantum Cheng-Hung Chang, Phys. Rev. B 75, channels is affected by the quantum nature of 155326 (2007). the transverse momenta K in ballistic regime. [11]. Wen-Min Huang, Cheng-Hung Chang, We demonstrate, from first principle Hsiu-Hau Lin, Phys. Rev. B 73, calculations that the Fano factor may increase 241307(R) (2006). linearly with the number of well-separated parallel wires by the interference effects [12] S.-J. Cheng, Phys. Rev. B 76, 075329 through the reservoirs. This is in sharp contrast (2007). to the case of mesoscopic system, where the [13]. J.Yao, Y-.C. Chen, M.Di Ventra and Z. Fano factor is independent of the number of Yang, Phys. Rev. B 73, 233407 (2006). well-separated parallel wires because of the restoration of quantized parallel channels. [14]. Z. Huang, B. Xu, Y.-C. Chen, M. Di These research activities are collaborated with Ventra and N.J. Tao, Nano Lett. 6, 1240 Prof. Di Ventra at UCSD and Prof. Z. Yang at (2006). Fudan University, who visited Taiwan sponsor by NCTS in 2006 and 2007.

131 ‹‹- Highlights of Programs Focus Group of Novel Quantum Phenomena in Condensed Matter

Coordinator: Chung-Yu Mou (National Tsing Hua University; email: [email protected]) Wen-Chin Wu (National Taiwan Normal University; email: [email protected]) Committee members: Yung-Chung Chen (Tung Hai University), Chung-Hou Chung (National Chiao Tung University), Di-Jing Huang (National Synchrotron Radiation Research Center), Chang-Ming Ho (Tamkang University),Ying-Jer Kao (National Taiwan University), Hsiu-Hau Lin (National Center for Theoretical Sciences and National Tsing Hua University), Jiunn-Yuan Lin (National Chiao Tung University), Shin-Tza Wu (National Chung Cheng University)

I. Brief Description II. Activities During past one year period, the activities organized or sponsored by our group are: (1) The Fifth Joint Workshop on Physics of he "Novel Quantum Phenomena in Metal Oxides: Experiment and Theory, Condensed Matter (NQPCM)" focus 2006/12/01-03, Yi-Lan. group is the newly combined one of previous "Spin-Related Physics in Condensed Matter (2) The 6th Asia-Pacific Workshop on (SRPCM)" (led by Chong-Der Hu) and Frontiers of Condensed-Matter Science and "Strongly Correlated Electron Systems Symposium on 20-years Anniversary of (SCES)" (led by Chung-Yu Mou) focus Discovery of YBCO: 2007/04/13-16, groups. Its goal is to provide a platform for the Taipei. condensed matter theorists in greater Taiwan (3) 2007 Summer Workshop on Novel to interact strongly with each other, and Quantum Phenomena in Condensed ultimately work together to focus on some Matter: 2007/07/13 -15, NDHU. frontier areas. To achieve this goal, a program committee is formed and devoted to promote (4) Miniworkshop on Numerical Method in mutual interactions in all formats that lead to Strongly Correlated Electronic Systems: fruitful collaborations. 2007/12/14, NTHU. In addition to committee members, (5) The topic program on Superconductivity currently there are twenty active members and Magnetism at Nanoscale: Effects of (professors) and twenty young members quantum fluctuations and disorder: (postdocs & senior graduate students) or so. 2007/12/01 - 2008/01/31, NCTS. Focused topics selected and studied by group Activity details can be accessed via: members are: (1) Superconductors & Oxides, http://phys.cts.nthu.edu.tw/research/focus_ (2) Spintronics and spin Hall effect, (3) group.php?Sn=36. Multiferroics, (4) Low-dimensional system (graphene, quantum dot, nanotube, etc.), (5) Activities (2) & (5) are aiming at inducing Strongly correlated system of cold atoms, (6) possible cooperation among participants and Numerical methods in strongly correlated foreign visitors on frontier areas in condensed electronic systems, and (7) Quantum matter physics. They are also useful to make computing. our scientific results more visible. Activities (1), (3), & (4) are aimed at providing a platform for domestic condensed matter experimentalists and theorists to work together

Highlights of Programs -›› 132 on selected hot topics. They are also important • Ying-Jer Kao+ Anders Sandvik on the in introducing new fields and/or new effects of doped impurities in spin models; theoretical technique to young researchers. In development of numerical methods in addition to the above activities, weakly strongly correlated systems. condensed matter seminars are organized in • Ying-Jer Kao + Roger Melko (Waterloo), NTU & NTHU/NCTU (occasionally also in Stefan Wessel (Stuttgart) on supersolid other universities). There are also visiting phases in lattice boson models. programs hosted in NCTS during the summer and winter time. To train young generation, • Ying-Jer Kao + Yong-Baek Kim, Hae-Young travel funding is awarded on the priority of Kee, Michel Gingras (Waterloo) on aspects young researchers. of frustrated systems. • Hsi-Sheng Goan (NTU) + Gerard J. Milburn (Queensland), Choo Hiap Oh, Xiao-Zhong III. Visitors and International Yuan (Shanghai Jiao Tong U), Xin-Qi Li Collaborations (Beijing) on topics of quantum computing. (1) International Visitors (Dec. 06 ~ Dec. 07) Konstantin Bliokh (Ukraine), Koung-An IV. Highlights of Research Results Chao (Lund), Steven Girvin (Yale), Eberhard (1) Superconductors and oxides: Gross (Berlin Free), Toshiya Hikihara (Hokkaido), Fabian Heidrich-Meisner Ting-Kuo Lee, Chang-Ming Ho, Chi-Tin (ORNL), Hae-Young Kee (Toronto), Yong- Shih and their collaborators have studied the Baek Kim (Toronto), Dung-Hai Lee (UC spectral weights for adding and removing an Berkeley), Yung-Chang Lee (SUNY Buffalo), electron of the Gutzwiller projected d-wave Sadamichi Maekawa (Tohoku), Choo Hiap Oh superconducting state of the t-J-type models. (Singapore), Gil Rafael (Caltech), Emmanuel They show that the product of weights is the Iosifovich Rashba (Harvard), Anders Sandvik same as in the weakly coupled case. A (Boston), Krishnadu Sengupta (India), Ivan rigorous relation of spectral weights with Sergienko (ORNL), Shun-Qing Shen (Hong doping in the electron doped system was Kong), Chin-Sen Ting (Houston), David derived with consistent results with the Thouless (Washington, Seattle), Xincheng Xie experiments [1]. They also studied more (Oklahoma State), Nei-Chang Yeh (Caltech). systematically the low-energy physical properties of the plain vanilla d-wave RVB (2) International Collaborations state. Overall qualitative agreement with the • Ting-Kuo Lee (AS), Chang-Ming Ho, Chi- experiments is obtained [2]. Tin Shih (THU) + Tao Xiang (Chin Acad Wen-Chin Wu and Cheng-Shi Liu have Sci, Beijing), Fu-Chun Zhang (Chinese U, studied extensively the coexistence of an AF HK) on the problems of high-Tc. order and the d-wave superconducting order • Ming-Che Chang (NTNU) + Qian Niu parameter in electron-doped cuprate (Austin) on the problems of spin Hall effect. superconductors. Through the investigation of Raman scattering, neutron scattering, and the • Chung-Hou Chung+ Walter Hofstetter doping-dependent [110] Andreev bound states, (Johann Wolfgang Goethe-U), Gergely positive and consistent results are obtained Zarand (Karlsruhe), Matthias Vojta when the experiments are compared [3]. (Karlsruhe), K. Ingerson (Florida) and etc. on the problems of quantum dots. (2) Spintronics and spin Hall effect: • Yong-Chung Chen + Fabian Heidrich- Hsiu-Hau Lin and his collaborators have Meisner (ORNL) on applying DMRG developed a self-consistent Green's function method in quantum spin systems. method to describe the diluted magnetic semiconductors [4]. The role of Fermi surface

133 ‹‹- Highlights of Programs topology is discovered in carrier-mediated have investigated an electrically controllable ferromagnetism for spintronics devices [5]. spin filter based on multiferroic tunneling The dynamical symmetry enlargement has junction. This spin filter combines the been demonstrated in carbon nanotubes by the exchange splitting of ferromagnets and combination of renormalization group and asymmetry in energy potential due to the bosonization techniques [6]. screening of ferroelectric polarization charges at electrodes. Calculations show an enhanced Using a semiclassical approach, Ming-Che spin filtering efficiency and a positive-to- Chang and Qian Niu have demonstrated that it negative tunneling magnetoresistance [11]. is necessary and sufficient to include the Berry curvature and orbital moment in order to (4) Low-dimensional system account for all physical effects to first order in Chung-Hou Chung and his collaborators external fields. They show that these gauge have focused on quantum phase transitions and invariant quantities are also sufficient for a charge transports in semiconductor quantum correct quantum theory. They apply the ideas dots. They successfully showed the Kondo-to- to semiconductor bands, and show how the spin singlet phase transition/crossover based effective theories in a hierarchy should on a simple setup and have applied the renormalize [submitted]. numerical renormalization group (NRG) Ching-Ray Chang (NTU) and his method to extract the transmission coefficient collaborators have investigated electron spin through the double dots [12]. In addition, they precession in nonuniform Rashba-Dresselhaus have proposed the realization of the quantum two-dimensional electron systems along critical non-Fermi liquid state in the double arbitrary continuous paths [7]. A persistent dot systems [13]. For this excellent work, spin helix in spin-orbit coupled two- Chung gave an invited talk at the workshop in dimensional electron systems, predicted Asia-Pacific Center for Theoretical Physics recently to exist in two particular cases, is also (APCTP) on quantum criticality (Pohang, investigated [8]. Korea, 2007/02). Paper [13] was selected as the Highlights of the Poster Session in the (3) Multiferroics international conference in strongly correlated As a joint effort between theorists and electron systems (Houston, 2007/05). experimentalists, Di-Jing Huang, Chung-Yu Chung and his collaborators have also Mou and their collaborators recently proposed managed to obtain NRG results for the the idea of an internal electric field to explain pseudogap Bose-Fermi Anderson model for the behavior of multiferroics in TbMn O . The 2 5 spinless electrons. The NRG results are in electric field is composed by quadratic good agreement with the analytical RG combination of Fourier transformation of the predictions [14]. magnetic order parameter. The soft x-ray data shows excellent agreement with the theory. (5) Strongly correlated system of cold atoms The paper was accepted by PRL [9]. Chien-Hua Pao (CCU), Shin-Tza Wu, and Chong-Der Hu (NTU) studied the magnetic Sungkit Yip (AS) have worked on BEC-BCS oxides, in which ferroelectricity coincides with crossovers in cold atoms. One of their earlier the onset of a second incommensurate papers [15] has recently been selected as a

magnetic order. The wave function of Eg New Hot Paper by the Thomson Corporation's electrons is solved. The coupling between the Essential Science Indicators. (See magnetic and electric orders is provided by the http://www.esi-topics.com/nhp/2007/july-07- spin-orbit interaction. It was found that the net Pao-Wu-Yip.html.) More recently they work electric dipole moment of the system came on the general case of pairing between from the bond between the transition metal fermions of unequal masses. For the unitarily and oxygen atoms[10]. limit, a regime which has most experimental interests currently, they have just published a Guan-Yu Guo (NTU) and his collaborators paper based on a mean-field study [16]. A

Highlights of Programs -›› 134 paper that extends to general coupling V. Selected Publication strengths is just submitted. We apologize that group members associated with publications [1,2,7,8,12-14] forgot to acknowledge the (6) Numerical methods in strongly correlated support of NCTS in the papers. These are definitely research results under the support of NCTS. electronic systems [1] C.-P. Chou, T.K. Lee, and C.M. Ho, Phys. Ying-Jer Kao and his collaborators have Rev. B?74, 092503 (2006). identified a realization of the random-field [2] K.Y. Yang, C.T. Shih, C.-P. Chou, S.M.

Ising model. They show in LiHOXY1–XF4 that Huang, T.K. Lee, T. Xiang, F.C. Zhang, the field-induced magnetization along x Phys. Rev. B 73, 224513 (2006). direction, combined with the local random [3] C.S. Liu and W.C. Wu, Phys. Rev. B 76, dilution-induced destruction of crystalline 014513 (2007); submitted (2007). mirror symmetries generates random fields [4] J.E. Bunder, S.-J. Sun, and H.-H. Lin, along the Ising z direction. This identifies Appl. Phys. Lett. 89, 072101 (2006).

LiHOXY1–XF4 in Bx as a new random field Ising [5] W.-M. Huang, C.-H Chang, and H.-H. Lin, system [17]. Kao and his collaborators have Phys. Rev. B 73, 241307(R) (2006). also studied the effects of Fermi-surface [6] J.E. Bunder and H.-H. Lin, Phys. Rev. B fluctuations on the single-particle lifetime near 75, 075418 (2007). the diagonal electronic nematic phase on a 2D [7] M.H. Liu, C.-R. Chang and etc., Phys. Rev. B 74, 235322 (2006). square lattice. They showed that there exists a quantum critical point between the diagonal [8] M.-H. Liu and C.-R. Chang, Phys. Rev. B 74, 195374, (2006). nematic and isotropic phases [18]. [9] J. Okamoto, D.J. Huang, C.-Y. Mou, and In addition, Kao and his collaborators have etc., Phys. Rev. Lett., 98, 157202 (2007). recently studied in details the ground state [10] C.D. Hu, Phys. Rev. B 75, 172106 (2007). phases of the hardcore boson-Hubbard model [11] S. Ju, T.Y. Cai, G.Y. Guo, Z.Y. Li, Phys. on the square lattice [submitted]. Rev. B 75, 064419 (2007). Independently Yong-Chung Chen, Chung-Hou [12] C.-H. Chung and W.Hofstetter, Phys. Rev. Chung, and their collaborators investigated the B, in press (2007). triangular and Kagome lattices [submitted]. [13] G.Zarand, C.-H. Chung, P. Simon, and M. The numerical methods employed by both Vojta, Phys. Rev. Lett. 97, 166802 (2006). teams including Gutzwiller mean field, [14] C.-H. Chung, M. Glossop, L. Fritz, M. variational Monte Carlo, and quantum Monte Kircan, K. Ingersent, and M. Vojta, Phys. Carlo. Rev. B, in press (2007). (7) Quantum computing [15] C.-H. Pao, S.-T. Wu, and S.K. Yip, Phys. Rev. B 73, 132506 (2006). Hsi-Sheng Goan and his collaborators have [16] S.-T. Wu, C.-H. Pao, and S.K. Yip, Phys. investigated the non-Markovian decoherence Rev. B 74, 224504 (2006). and entanglement dynamics of one or two [17] S. M. A. Tabei, M. J. P. Gingras, Y.-J. central spins under respectively the quantum Kao, P. Stasiak, and J.-Y. Fortin, Phys. Heisenberg XY spin [19] and Rev. Lett. 97, 237203 (2006). antiferromagnetic [20] environments. The non- [18] Y.-J. Kao, H.-Y. Kee, Phys. Rev. B 76, Markovian entanglement dynamics of two 045106 (2007). interacting nano-mechanical oscillators in [19] X.Z. Yuan, H.-S. Goan, and K.D. Zhu, thermal environments is also studied [21]. A Phys. Rev. B 75, 045331 (2007). scheme for implementing unconventional [20] X. Z. Yuan, H.-S. Goan and K. D. Zhu, geometric quantum computation by using the New Journal of Physics 9, 219 (2007). interaction of two atoms with a two-mode [21] K.-L. Liu and H.-S. Goan, Phys. Rev. A cavity field has also been proposed [22]. 76, 022312 (2007). Owing to these excellent works, Goan was [22] C. Wu, H.-S. Goan, C.H. Oh and etc., invited to speak at the International Workshop Phys. Rev. A76, 024302 (2007). on Quantum Dynamics and Biomolecular [23] Z. T. Kao, J. Y. Lin, and C. -Y. Mou, Function (Yeppoon, Australia). Phys. Rev. B 75, 012503 (2007).

135 ‹‹- Highlights of Programs Highlights of Programs Particles and Fields

Focus Group on Collider, Astroparticle and BSM

Coordinator: Kingman Cheung (National Tsing Hua University and National Center for Theoretical Sciences; email: [email protected]) Committee members: Wei-Shu Hou (National Taiwan University), Cheng-Wei Chiang (National Central University), Chung-Wen Kao (Chung Yuan Christian University), Chuan-Hung Chen (National Cheng Kung University), Tzu-Chiang Yuan (National Center for Theoretical Sciences)

I. Introduction quite a number of visitors during the Winter break, and we organized a number of seminars. Most of them were about the dark matter. We have established a e focus on collider phenomenology collaboration with Shigeki Matsumoto, and astroparticle physics, in relation Nobuchika Okada of KEK, and Eibun to new physics beyond the standard model Seneha of NCU to work on the light-stop (SM). baryogenesis scenario. It is still in progress. Most of us believe that the new physics should come in in the TeV scale. Many new (ii) The 7th Particle Physics Phenomenology models predict new particles or new dynamics Workshop, June 2007 -- jointly organized at TeV scale so as to halt the gauge hierarchy. by the focus groups on particle physics in There is a hope that the upcoming LHC is the Hsinchu and Taipei. This is a biannual place for the next big discovery. Together with meeting of particle phenomenology in other planned cosmology experiments, testing Taiwan. new ideas will be the major activities in the (iii) A Joint Summer Institute -- during June next ten years. Our activities concentrate on and July 2007 was organized by the focus the particle physics phenomenology, which groups on particle physics in Taipei and links up the theory and experiments. We have Hsinchu. We made use a group of visitors accomplished a number of interesting of PPP7 and invited them to stay longer so published works, which are the consequenece that we could have more interactions. We of our group activities. have established a collaboration with Jae- This year we have important results on Sik Lee of SNU to work on the Higgs Higgs boson searches and on "unparticle", boson decay in CP violating MSSM which will be described later. scenario. It is under investigation. (iv) Workshop on Unparticle Physics in June 2007 jointly organized by the focus groups II. Major Activities held in 2007 on particle physics in Hsinchu, Taipei, and Tainan.This is an urgent response (i) The Winter Program in January 2007 -- workshop to a new emergent topic --

Highlights of Programs -›› 136 Unparticle. Taiwan has three groups at the Large Hadron Collider", authored by working on this topic since the first paper Kingman Cheung, Jeonghyeon Song, and Qi- by Georgi. We have studied the most Shu Yan, published in Phys. Rev. Lett. important features of the unparticle and The emergence of the Higgs boson decay related them to experiments. We will give mode into two pseudoscalar bosons, which can more details below. The aim of the relieve the so-called little hierarchy problem workshop was to further strengthen the and reduce the LEP2 Higgs boson mass bound, activities in this area and promote further may affect the golden search modes (h →γγ, collaborations. Students are benefitted – bb) of the Higgs boson significantly. The LHC from this workshop. may not be able to find the Higgs boson if the two-pseudoscalar decay mode dominates. Our work explicitly shows that the associated III. Visitors and International production of the Higgs boson with a W or Z Collaborations boson can recover the loss of sensitivity in the Tom Weiler (Vanderbilt U.), Nobuchika golden modes. With the Higgs boson Okada (KEK), Shigeki Matsumoto (KEK), decaying into two pseudoscalar bosons, which Jeonghyeon Song (Konkuk U.), Hiroaki further decay into 4 b jets, together with at Sugiyama (KEK), Masaki Asano (KEK), least a charged lepton from the W or Z boson Yasuhiro Okada (KEK), Wai-Yee Keung decay, a significant Higgs boson signal is (UIC), Chung Kao (Oklahoma U.), Ian Low observable at the LHC. The ultimate goal of (UC-Irvine), Lock-Seng Goh (Arizona U.), Jae the LHC is hunt for the Higgs boson, which is Sik Lee (SNU), C.S. Kim (Yonsei U.), K. Tobe responsible for electroweak symmetry (Tohoku U.). breaking and mass generation. We have invited Wai-Yee Keung to join the multi-year visitor program of the NCTS. This year with his visit, Kingman Cheung, Wai-Yee Keung, and Tzu-Chiang Yuan have written an important paper on "unparticle physics", accepted by Phys. Rev. Lett. We have also established a collaboration with Jeonghyeon Song of Konkuk U. Kingman Cheung, Qi-Shu Yan (a postdoc in NTHU), and Song have written a paper on "Role of h →ηηin intermediate-mass Higgs boson searches at the LHC", which is now published We show in Fig. 1 the invariant mass in Phys. Rev. Lett. Details will be given spectrum of the 4 b-tagged jets. The peak below. clearly shows the presence of the Higgs boson, We have also established a collaboration which stand out of the continuum with Nobuchika Okada and Shigeki backgrounds. With the crucial cut of M4b one Matsumoto of KEK, together with Eibun can also reconstruct the mass bump of the η's. Seneha of NCU. (ii) Novel signals in unparticle physics The paper was authored by Kingman Cheung, Wai-Yee Keung, and Tzu-Chiang IV. Highlights of Research Results Yuan, and has been accepted by Phys. Rev. (i) A twist in the search for the Higgs boson Lett. The title of the paper is "Role of h →ηη in Recently perceived by Georgi a scale the search of intermediate-mass Higgs boson invariant sector with a non-trivial infrared fixed point at a higher energy scale may

137 ‹‹- Highlights of Programs actually describe the real world at high energy. [3] K. Cheung, J. Song and Q.S. Yan, "Role of

The unparticle with a scale dimension dU can h →ηηin the search of intermediate-mass

be interpreted as a collection of dU invisible Higgs boson at the LHC", Phys. Rev. Lett. massless particles, which can be unveiled by 99, 031801 (2007). measurements of various energy distributions – [4] K. Cheung, S.K. Kang, C.S. Kim and J. in the processes Z ƒƒ U and e-e+ U at → →γ Lee, "Correlation between lepton flavor e-e+ colliders, as well as mono-jet production – violation and B – B mixing in SUSY at hadron colliders. (d,s) (d,s) GUT," Phys. Lett. B652, 319 (2007). The new result of our Letter is the [5] K. Cheung and T.C. Yuan, "Hidden propagator effect of the unparticle. The novel fermion as milli-charged dark matter in features, induced by scale invariance, include a Stueckelberg Z' model,'' JHEP 0703, 120 spectacular phase factor exp(-i d ) associated U π (2007). with the propagator in s-channel. Such a factor can give rise to non-trivial behavior in a [6] K. Cheung and J. Song, "Light number of processes. We studied the effects in pseudoscalar η and H →ηηdecay in the the Drell-Yan process and in the one-loop simplest little Higgs model," Phys. Rev. muon anomaly. In Fig.2, we show the D76, 035007 (2007). fractional difference from the standard model [7] K. Cheung, C.S. Kim, K.Y. Lee and J. prediction around the Z pole. Interesting Song, "Associated production of a single interference pattern can be seen clearly. heavy T-quark in the littlest and simplest little Higgs models", Phys. Rev. D74, 115013 (2006). [8] A. Arhrib, K.-Cheung, T.-J.-Hou and K.- W.-Song, "Associated production of a light pseudoscalar Higgs boson with a chargino pair in the NMSSM," JHEP 0703, 073 (2007). [9] C.S. Chen, K. Cheung and T.C. Yuan, "Novel collider signature for little Higgs dark matter models," Phys. Lett. B644, 158 (2007). [10] C.W. Chiang and E. Senaha, "Update V. Publications analysis of two-body charmed B meson [1] K. Cheung, W.Y. Keung and T.C. Yuan, decays", Phys. Rev. D75, 074021 (2007). "Collider Phenomenology of Unparticle [11] W.S. Hou, H.-N. Li, S. Mishima, and M. Physics," Phys. Rev. D76, 055003 (2007). Nagashima, "Fourth generation CP [2] K. Cheung, W.Y. Keung and T.C. Yuan, violation effect on B → Kπ, φK and ρK in "Novel signals in unparticle physics," NLO PQCD", Phys. Rev. Lett. 98, 131801 Phys. Rev. Lett. 99, 051803 (2007). (2007).

Highlights of Programs -›› 138 Focus Group on Gravitation, Cosmology and Quantum Gravity

Coordinator: Hoi-Lai Yu (Academia Sinica; email: [email protected]) Committee members: Chiang-Mei Chen (National Central University), Hing-Tong Cho (Tamkang University), Da-Shin Lee (National Dong Hwa University), Wo-Lung, Lee (National Taiwan Normal University), James Michael Nester (National Central University), Kin-Wang Ng (Academia Sinica), Chopin Soo (National Cheng Kung University), Hwei-Jang Yo (National Cheng Kung University)

l. Brief Description Hing-Tong Cho (TKU) on gravitation and black holes Da-Shin Lee (NDHU) on non-equilibrium physics and cosmology he subject materials that we have Wo-Lung Lee (NTNU) on large scale identified so far are not only the structures of Universe hottest current research topics, more James Michael Nester (NCU) on gravitation important, these are the areas that our and Quasi-local masses community have enough technical know how, expertise, and insights to make major Kin-Wang Ng (Academia Sinica) on contributions. cosmology and data analysis Chopin Soo (NCKU) on quantizing gravity In Cosmology: and cosmology To investigate the detailed mechanisms of Hwei-Jang Yo (NCKU) on numerical general inflation from non-equilibrium point of relativity view(in particular, stochastic inflation) and Hoi-Lai Yu (Academia Sinica) on quantizing compare with CMB data and large scale gravity and cosmology structures of the universe; the origin of dark matter within or beyond the Standard Model; Frequent visitors are: the physics, properties, and origin of dark Bei-Lok Hu (University of Maryland); energy. Roh-Suan Tung (Shanghai Normal In General Relativity: University); Gravitational energy, gravitational radiation Yun-Kau Lau (Applied Mathematics Institute, reactions and quasi-normal modes of black Academia Sinica, Bejing); holes which affect lots of topics in cosmology Larry H. Ford (Tufts University); will be our main activities. Misao Sasaki (Kyoto University); In Quantum Gravity: Ray Rivers (University of London). Canonical quantization of gravity using The purposes of this focus group are: Ashtekar variables, stochastic gravity using (1) To generate long-term collective force in closed-time-path techniques, and quantum to Cosmology and Gravity be searched classical transitions will be studied. activities among the local communities and Major members of our focus group are: Asia Pacific areas; Chiang-Mei Chen (NCU) on gravitation and (2) Using non-equilibrium field theories and string theories general relativity as keys to generate interdisciplinary and cutting-edge research

139 ‹‹- Highlights of Programs activities on cosmology, classical and venturing into an uncharted territory, large quantum gravity and quantum information piles of precise observational data and efficient science; numerical techniques have helped the study on the Universe continue to thrive in the 21st (3) To train and create chances for talented century.The purpose of this School/Workshop graduate students and postdocs to make was to introduce students and faculties in major contributions by helping them to Taiwan the progress and the state of the art in identify hot and important interdisciplinary this fascinating frontier of physics and problems in the area of cosmology, astronomy. The lectures were delivered by: gravitation and quantum gravity. Li-Zhi Fang( Dept. of Physics, University of Arizona), Prof. Houjun Mo( Dept. of Astronomy, Univ. of Massachusetts), Prof. ll. Activities Yipeng Jing(Shanghai Astronomical The following major activities are carried Observatory), Prof. Long-Long Feng(Purple out last year on top of our regular/irregular Mountain Observatory) journal club meetings in Institute of Physics, (3) Collaborate with the Quantum Academia Sinica and Department of Physics, Information Sciences focus group in National Central University. running the Summer School on Non- (1) 2007 Tainan School and Workshop on equilibrium Dynamics and Quantum Cosmology and Gravitation at NCKU Coherence (4th – 6th July, 2007, NCKU) th th (13 – 16 January, 2007): This Summer School on Non-equilibrium This was the first school/workshop in this Dynamics and Quantum Coherence field in Taiwan so far. The main purpose of Phenomena was aimed to provide the basic this meeting is to introduce to students and ideas and concepts of the method of non- researchers the latest developments in equilibrium theory including the Feynman- stochastic quantum gravity, cosmology and Vernon and coherent state path integral semi-classical quantum gravity. formulation, and Schwinger- Keldysh's non- equilibrium Green's function method. The We have about 70 graduate students, lecturers from our focus group members and postdocs and local faculities and faculties from visitors are: B. L. Hu and D. S. Lee. Asia Pacific area in the meeting. Major lectures were delivered by researcher from We want to emphasize that our postdocs, overseas:L. Ford (Tufts U.), Bei-Lok Hu C.S Chou's and S.Y. Lin's works on topics on (Maryland U.), Misao Sasaki (Kyoto U.), Quantum Entanglement and Moving Atoms in Albert Roura(Los Alamos), E. Verdaguer Quantum Fields provide excellent examples (Universitat de Barcelona), Y. K. Lau (Inst. of on how interdisciplinary works between non- Applied Math., Academica Sinica, Beijing), R. equilibrium field theories, general relativity S. Tung (Shanghai Normal U.) and quantum information science can be combined coherently to achieve major Research topics in applying stochastic breakthrough towards the understanding of gravity to cosmology and black holes were these hot topics which have found important carried out by D.S. Lee, K.W. Ng, W.L. Lee applications in quantum information science and H.T. Cho among group members and the gravitational wave detecting LIGO immediately after the workshop and papers physics. were also published (see publication list in the below) in these related areas. (4) Visiting prestigious academic institutes (2) 2007 Taipei School/Workshop on Large (1) With the help of Prof. L. Ford and B.L. Scale Structures of the Universe(28th May Hu our postdocs (S.Y. Lin, C.S. Chou – 2nd June, 2007, NTNU): and C.H. Wu)were arranged to visit and conduct research at Princeton Though the discovery of dark energy led us

Highlights of Programs -›› 140 University, Univsersity of Maryland , presented in the general setting of the Tuft University and International Center Barbero-Immirzi extension of Ashtekar's for Gravitation Research at University contraints, and when a cosmological of Pennsylvania. constant is also present, Class. Quantum Grav. 24 (2007) 1547-1555. (2) With the help of Prof. Y.K. Lau, 10 graduate students (from NCU, NDHU and NCKU) were arrange to attend the gravitation workshop at Institute of V. Publication Applied Mathematics, Academia Sincia, [1] G. C. Liu, S. Lee and K. W. Ng, Phys. Rev. Bejing during the summer. Lett. 97, 161303 (2006). [2] C. Soo, Class. Quantum Grav. 24, 1547- 1555 (2007) . III. Visitors and International Collaborations [3] J. Nester, J. Phys. A: Math. Theor. 40, 2751-54 (2007). Please refer to the above descriptions. [4] H.T. Cho, A.S. Cornell, J. Doukas, and W. Naylor, Phys. Rev. D75, 104005 (2007). IV. Highlights of Research Results [5] H.-T. Cho and C.-L. Ho, J. Phys. A40, 1325 (2007). (1) We have proved that black holes are elementary particles in superspace and [6] C.-M. Chen, D. V. Gal'tsov and D. G. quantum geometry with spherical Orlov, Phys. Rev. D75, 084030 (2007). symmetry is unitary and singularity free. [7] Shih-Yuin Lin and B. L. Hu, Phys. Rev. D This work will be published in PRD and 73, 124018 (2006). H.L.Yu will be invited to deliver a talk at The Eighth Asia-Pacific International [8] Shih-Yuin Lin and B. L. Hu, Phys. Rev. D, Conference on Gravitation and in press (2007). th Astrophysics held in Nara in 28 , August, [9] C.H. Wu, K.W. Ng, W. Lee, D.S. Lee and 2007. Y. Y. Charng, JCAP 0702006 (2007). (2) Obtained the most stringent limit on the [10] D.S. Lee, C. Y. Lin and R. J. Rivers, parity violating coupling of Dark energy to Phys. Rev. Lett. 98, 020603 (2007). light by using observed cosmic microwave background power spectra. Phys. Rev. Lett. [11] J.T. Hsiang, T.H. Wu, and D.S. Lee, 97, 161303 (2006). arXiv:hep-th/0706.3075 (submitted to Phys. Rev. D ). (3) Riemann normal coordinates: a complete accounting; J. Phys. A: Math. Theor. 40, [12] C.H. Chou, B. L. Hu and T. Yu, 2751-54. arXiv:quant-ph/0703088 (submitted to Phys. Rev. D ). (4) Prof. D.S. Lee is invited by Prof. R. Rivers to visit London University and conduct [13] C.H. Chou, C. Soo and H.L. Yu, arXiv:gr- research on applying non-equilibrium qc/0703072 (to appear in Phys. Rev. D76, techniques to experimental studies of 084004 (2007). analog gravity using Bose-Einstein condensation. Note: Some publications listed in this report may not (5) A reformulation of the Wheeler-DeWitt acknowledge the support of NCTS. We apologize for some members of the group who forgot to put it on equation which highlights the role of the papers. Those works are definitely research gauge-invariant three-geometry elements is results under the support of NCTS.

141 ‹‹- Highlights of Programs Focus Group on Particle, Nuclear and Cosmology

Coordinator: Ting-Wai Chiu (National Taiwan University; email: [email protected]) Committee members: Chia-Hung Chang (National Taiwan Normal University), Hai-Yang Cheng (Academia Sinica), Cheng-Wei Chiang (National Central University), Xiao-Gang He (National Taiwan University), Choon-Lin Ho (Tamkang University), Kin-Wang Ng (Academia Sinica), Kwei-Chou Yang (Chung-Yuan Christian University)

I. Brief Description physics phenomenologists. In fact, many new ideas and insights were initiated at (1), through intensive discussions among several participants, and also between experimentalists he main theme of PNC focus group is and theorists. to tackle the important physics within Besides the regular weekly seminars and the Standard Model (SM), as well as to journal clubs, we have The 20th Spring School identify any signals which may suggest new in Particles and Fields http://www.phys. physics beyond the SM. To achieve this goal, sinica.edu.tw/~ss2007/index.files/Page873.htm we call for the collective efforts of theorists in April, and The 7th Particle Physics and experimentalists. The topics under active Phenomenology Workshop http://phys.cts. investigations are: (1) Phenomenologies of ntu.edu.tw/ppp7 (PPP7) in June. The purpose Strong and Electroweak Interactions, (2) of the Spring School is to introduce recent hot Flavor physics and CP violation, (3) Grand topics to graduate students at a pedagogical unification, (4) Supersymmetry, (5) Models level. Also, it is one of the main activities in beyond the SM, (6) Hadron physics, (7) Taiwan HEP community. Most graduate Effective Field Theory of QCD, (8) Lattice students and faculty attend The Spring School QCD, (9) Baryon asymmetry in the universe, every year. At PPP7, we had many (10) Accelerating universe and CMB effects. distinguished speakers from US and Japan, Even though our projects appear to cover a including the KEK Director Atsuto Suzuki, wide range of topics, they are unified under and former Belle spokesman Steve Olsen. the main theme. There were many scientific discussions in PPP7, which may have impacts to the development of HEP. For example, during II. Activities PPP7, Steve Olsen and Ting-Wai Chiu had many discussions on the heavy charmonium- Our weekly seminar and journal clubs are: like vector mesons, which indeed motivated (1) Particle physics journal club, (2) Belle Collaboration to search for charged Theoretical physics seminar, (3) Cosmology heavy meson. In August, Belle announced the and astrophysics journal club, and (4) Lattice discovery of a new charged resonance Z(4430) QCD journal club http://twcp3.phys. [arXiv:0708.3496]. This would be the first ntu.edu.tw/lqcdjc/. Among them, (4) is a new observation of a genuine tetraquark activity which has started since March 2007. charmonium state. These weekly activities are crucial for the successes of High Energy Physics in Taiwan. In particular, (1) has played a crucial role to bring HEP experimentalists and theorists III. Visitors and International together, which is crucial for the advancements Collaborations of the NTU Belle group as well as our B- During 2006-2007, we have set up an

Highlights of Programs -›› 142 international collaboration between JLQCD decays in the next-to-leading order and TWQCD Collaborations. It is well known perturbative QCD formalism. With an that JLQCD Collaboration constitutes an elite enhancement of the color-suppressed tree group of lattice field theorists, who have been amplitude and possibility of a new CP playing a vital role in the lattice QCD phase in the electroweak penguin, we can community. Since 2006, JLQCD has started account better for the data of the direct and the project of simulating dynamical overlap mixing-induced CP asymmetries in the B - fermion using the newly installed IBM > K pi, phi K and rho K decays. Our BlueGene supercomputer with peak speed ~50 proposal provides a possible resolution to Teraflops. In the summer of 2005, Shoji the well-known puzzles observed by the B Hashimoto (the group leader of JLQCD) asked factories. [Wei-Shu Hou , Hsiang-nan Li , Ting-Wai Chiu and TWQCD members to Satoshi Mishima, Makiko Nagashima, collaborate with JLQCD on the dynamical Phys.Rev.Lett.98:131801,2007]. overlap project. Since then, we have had many mutual visits between JLQCD and TWQCD, and now we have worked out several important results (see Sections IV and V). Furthermore, we also encourage local people (faculty and graduate students) to work on lattice QCD, and to join this international collaboration. This is one of the goals of the lattice QCD of journal club. In the summer 2007, PNC focus group has supported 3 NTU graduate students to attend the INT summer school on lattice QCD (http://www.int.washington.edu/PROGRAMS/ 07-2b.html) at University of Washington. Our Fig. 4th generation effect on CP asymmetries 3 graduate students also received supports from INT to cover their local expenses at the B. Observation of Direct CP Violation school. This is the first time our graduate The obersevation of direct CP violation in students to attend international summer school B-> K+- pi-+ and finding the difference of and also to receive financial supports from the CP violating asymmetry between B-> K+- organizing institution. In the future, we will pi-+ and B+- -> K+- pi0. The figures below encourage more Ph.D. students to participate illustrates the difference between decay the renowned summer/winter schools in high rates of B meson and its anti-particle. [S.W. energy physics, e.g., TASI, Les Houches, Lin et al (Belle Collab.)"Observation of ERICE, etc. Obviously, these schools will direct CP violation in B -> K pi decays", provide excellent trainings to our students. submitted to Nature, 2007.] Also, their interactions with other participants at the schools will be an invaluable experience to them.

IV. Highlights of Research Results A. 4-th Generation Effects on CP asymmetries

We study the effect from a sequential C. Cosmic microwave background fourth generation quark on penguin- dominated two-body nonleptonic B meson We present the full set of power spectra

143 ‹‹- Highlights of Programs of cosmic microwave background (CMB) [2] Kuang-Ta Chao, Xiao-Gang He, Jian-Ping temperature and polarization anisotropies Ma, Comment on 'Chiral suppression of due to the coupling between quintessence scalar glueball decay', Phys. Rev. Lett. and pseudo-scalar of electromagnetism. 98:149103 (2007). This coupling induces a rotation of the [3] Kuang-Ta Chao Xiao-Gang He, Jian-Ping polarization plane of the CMB, thus Ma, Comment on 'Chiral suppression of resulting in a non-vanishing B mode and scalar glueball decay', Phys. Rev. Lett. parity-violating TB and EB modes. Using 98:149103 (2007). the BOOMERANG data from the flight of 2003, we derive the most stringent [4] Xiao-Gang He, Jusak Tandean, G. constraint on the coupling strength. We find Valencia, Does the HyperCP Evidence for that in some cases the rotation-induced B the Decay Sigma --> p mu+ mu- Indicate a mode can confuse the hunting for the Light Pseudoscalar Higgs Boson, Phys. gravitational lensing-induced B mode. Rev. Lett. 98:081802 (2007). [Guo-Chin Liu , Seokcheon Lee , Kin- [5] JLQCD and TWQCD Collaborations (H. Wang Ng , Phys.Rev.Lett.97:161303, Fukaya et al.), Two-flavor lattice QCD 2006.] simulation in the epsilon-regime with exact D. Topological Susceptibility in QCD chiral symmetry, Phys. Rev. Lett. 98:172001 (2007). We determine the topological

susceptibility (χt ) in two-flavor QCD with [6] JLQCD and TWQCD Collaborations (H. exact chiral symmetry. The topological Fukaya et al.), Two-flavor lattice QCD in charge density is unambiguously defined the epsilon-regime and chiral Random on the lattice using the overlap-Dirac Matrix Theory, Phys. Rev. D76:054503 operator which possesses exact chiral (2007). symmetry. Simulations are performed on a [7] TWQCD Collaboration (Ting-Wai Chiu et 3 16 32 lattice at lattice spacing ~0.12 fm at al.), Beauty mesons in lattice QCD with six sea quark masses ranging ms ~ ms /6 exact chiral symmetry. Phys. Lett. with ms the physical strange quark mass. In B651:171-176 (2007) the small mq regime, our result of χt is [8] Jiunn-Wei Chen, Eiji Nakano, Shear proportional to mq as expected from chiral viscosity to entropy density ratio of QCD effective theory. Using the formula χt = below the deconfinement temperature. m∑/Nf, we obtain the chiral condensate in QCD. [T.W. Chiu et al., talk at Lattice Phys. Lett. B647:371-375 (2007) 2007; S.Aoki et al.(JLQCD and TWQCD [9] Cheng-Wei Chiang, Yu-Feng Zhou, Flavor Collaboration), submitted to PRL]. SU(3) analysis of charmless B meson decays to two pseudoscalar mesons, JHEP 0612:027 (2006). V. Selected Publications [10] Yu-Chun Chen, Chung-Wen Kao, Shin- [1] Wei-Shu Hou, Hsiang-nan Li, Satoshi Nan Yang, Is there model-independent Mishima, Makiko Nagashima, Fourth evidence of the two-photon-exchange generation CP violation effect on B ---> K effect in the electron-proton elastic pi, phi K and rho K in NLO PQCD. Phys. scattering cross-section? Phys. Lett. Rev. Lett. 98:131801 (2007). B652:269-274, (2007).

Highlights of Programs -›› 144 Focus Group on Strings

Coordinator: Jen-Chi Lee (National Chiao tung University; email: [email protected]) Committee members: Chuan-Tsung Chan (TungHai University), Chiang-Mei Chen (National Central University), Choon-Lin Ho (TamKang University), Pei-Ming Ho (National Taiwan University), Hsien-Chung Kao (National Taiwan Normal University), Feng-Li Lin (National Taiwan Normal University)

I. Brief Description so that people can have time enough to ask questions and learned how to work on a particular subject. After the seminar, there were many discussions of the audiences with he active member of string focus the speaker as well as with each others. Many group include: Makoto Narita (Nat'l ideas and collaborations came out of these Taiwan Univ.), Shunsuke Teraguchi discussions. (Academic Sinica), Dan Tomino (Nat'l Taiwan 2. Biweekly high energy seminar at NTNU: Normal Univ.), Toshihiro Matsuo (Nat'l Taiwan Normal Univ.), Wen-Yu Wen (Nat'l http://home.phy.ntnu. edu.tw/~highenergy/ Taiwan Univ.), Syoji Zeze (Nat'l Taiwan In addition to string theory, this seminar Univ.), Furuuchi Kazuyuki (Nat'l Taiwan includes topics such as cosmology and particle Univ.), Dmitry Orlov (Nat'l Central Univ.), Yi physics so that people working at different Yang (NCTS), Peter Matlock (Nat'l Chiao fields can communicate with each others. Tung Univ.) and around 10 graduate students. There are five string faculties and postdocs at The purpose of forming the string Focus NTNU which constitute one of the main string Group is to bring together string theorists in research group at Taiwan. Many foreign Taiwan and to encourage mutual visitors visiting NTU stayed some days on collaborations to enhance their researches. NTNU campus and gave talks there. Currently, the regular group activities include Some string seminars at NCU and Hsinchu weekly seminars, mini-workshops and were arranged occasionally in joint name with lectures. Some of them are given by invited local regular high energy physics seminars. visitors overseas. For the last few years, some String theorists from these areas were research topics in our group are: AdS/CFT encouraged to attend seminars held at Taipei. string duality and its applications, non- commutative geometry, string black hole, 3. Mini-workshop on AdS/QCD: string cosmology and high energy string Recently there is much research interest on scatterings. the applications of String/Gauge duality. One of them is the AdS/QCD, the so called Sakai- Sugimoto model. Prof. Sugimoto was invited II. Research Activities to visit Taiwan early this year in March. In 1. Weekly string seminars at NTU: preparation of his visit, the string group held a 2-day mini-workshop on this current research http://www.phys.ntu. edu.tw/string/index.htm topic in February. All speakers were local This is the main regular activity which was researchers and the aim was to educate started in 1996. Participants (15 to 20) from ourselves and learned the subject from each many institutes including AS, NTNU, NCU, others. It turns out that these activities end up NCTS and NCTU come to attend the seminar with many collaborated papers on this subject every Friday. The seminar lasted for two hours published in many honorable journals by members of the group (see section IV).

145 ‹‹- Highlights of Programs III. Visitors and International the exchange program of Taiwan and Japan. Collaborations He has also been helping us to invite many foreign visitors and organize activities in For the last few years, string focus group Taiwan. He has been making strong effort to continued to attract many foreign scientists to help scientists in Taiwan and to collaborate visit Taiwan. Many of them were impressed by with us. We have benefited a lot from him. our active research activities and the In fact, one of our member, Hsien-Chung enthusiasm of our group members. Some of Kao, was visiting Chu at Durham for the them even brought their own grants to visit us last academic year. and gave seminars here. The majority of them are Japanese visitors from prestigious Last year, Prof. Chu had joint papers with institutes such as Tokyo University, Kyoto Pei-Ming and with Feng-Li. Another project University and YITP. is being set up recently with Jen-Chi and Yi. 1. For the last year, Chiang-Mei, Feng-Li and 3. A joint paper on BPS bubbling solution in Chuan-Tsung were supported by a NSC IIB supergravity of Prof. James Liu from Taiwan-Japan exchange program to visit University of Michigan and Feng-Li and many institutes in Japan. Before this Wen-Yu was published recently. program was approved by NSC on Taiwanese side, there was a 3-year mutual exchange program supported by the IV. Highlights of Research Results Japanese organization "Koryu Kyokai" under the direction of Prof. Takeo Inami 1. High Energy String Scatterings: (Chuo U.). The financial support of the This is a long term project which was string focus group also helped facilitate the started in 2003 based on many earlier works of visits of scientists from Japanese side, and Jen-Chi in 90's. Following a breakthrough of much collaboration has been initiated since Chuan-Tsung and Jen-Chi in 2003, Taiwan then. Early this year, Jen-Chi Lee and Yi group has published more than 15 papers on Yang were supported by NSC and NCTU to this single subject (about 10 of them are in visit Tokyo University. Many connections Nucl. Phys.B), and about half of the group and possible future collaborations were members participated in the project. Although further initiated. Besides, after four year these works have not well recognized yet, they postdoc research here at Taiwan, one of our are truly initiated in Taiwan, and it is hoped members, Dr. Shunsuke Teraguchi, is going that they will eventually attract more to take an assistant professorship at Nagoya international attention in the near future. In the University in Japan. last year, Chuan-Tsung, Jen-Chi and Yi, and Some collaborations between Taiwan and Jen-Chi and Yi generalized the linear relations Japan have been set up due to these mutual (stringy symmetry) to D-brane. More visits. To name some, recently Pei-Ming had importantly, Jen-Chi and Yi have shown the a joint paper with Prof. Yutaka Matsuo of coexistence of the linear relations and the Tokyo University, Choon-Lin (Tam-Kang softer exponential fall-off behavior of high University) had many joint papers with energy string scattering amplitudes. Currently, Prof. Ryu Sasaki of YITP and Jen-Chi and together with Prof. Yoneya of Tokyo Yi have set up a collaborated project with University, Jen-Chi and Yi are trying to fit Prof. Tamiaki Yoneya of Tokyo University. their results to Yoneya's "space time There are also many on-going collaborated uncertainty relation'. Pei-Ming and his student projects among postdocs on both sides. also published a paper on this subject last year. 2. In addition to the Japanese visitors, another Publications important connection we have is Prof. [1] Jen-Chi Lee and Yi Yang, Linear Relations Chong-Sun Chu of Durham University in and their Breakdown in High Energy UK. He is actually the person who initiated Massive String Scatterings in Compact

Highlights of Programs -›› 146 Spaces, 0705.1872, To be published in Tomino, Hagedorn Strings and Nucl. Phys. B (2007). Correspondence Principle in AdS(3), arXiv:0705.4514 (2007) [2] Jen-Chi Lee and Yi Yang, Linear relations of high energy absorption/emission [2] Bin Chen, Sera Cremonini, Aristomenis amplitudes of D-brane, hep-th/0612059, Donos, Feng-Li Lin, Hai Lin, James T. Phys. Lett. B646, 120 (2007). Liu, Diana Vaman and Wen-Yu Wen, Bubbling AdS and droplet descriptions of [3] Jen-Chi Lee, Zero-norm states and BPS geometries in IIB supergravity, superstringy symmetries,hep-th/0610272 arXiv:0704.2233 (2007) (to be published by World Scientific). [3] Feng-Li Lin, Dan Tomino, One-loop effect [4] Chuan-Tsung Chan, Jen-Chi Lee and Yi of null-like cosmology's holographic dual Yang, Power-law behavior of strings super-Yang-Mills, JHEP 0703:118 (2007). scattered from domain-wall at high energies and breakdown of their linear [4] Feng-Li Lin, Toshihiro Matsuo, Jet relations, hep-th/0610219 (2007) Quenching Parameter in Medium with Chemical Potential from AdS/CFT, Phys. [5] Chuan-Tsung Chan, Jen-Chi Lee and Yi Lett. B641:45-49 (2006). Yang, Scatterings of massive string states from D-brane and their linear relations at [5] Feng-Li Lin, Wen-Yu Wen,Supersymmetric high energies, hep-th/0610062, Nucl. Phys. null-like holographic cosmologies, JHEP B764, 1-14 (2007) 0605:013 (2006). [6] Chuan-Tsung Chan, Jen-Chi Lee and Yi [6] W. Y. Wen, Note on deconfinement Yang, Notes on High energy limit of temperature with chemical potential from Bosonic closed string scattering AdS/CFT, arXiv:0707.4116 (2007). amplitudes, hep-th/0604122, Nucl. Phys. [7] E. Nakano, S. Teraguchi, W. Y. Wen, Drag B749, 280 (2006). force, jet quenching, and AdS/QCD, JHEP [7] Pei-Ming Ho and Xue-Yan Lin, Linear 0610, 055 (2006). relations among 4-point functions in the 3. International Collaborated Papers high energy limit of string theory, Phys. Rev. D73, 126007 (2006). [1] Pei-Ming Ho, Yutaka Matsuo, A Toy model of open membrane field theory in 2. AdS/CFT Duality and its Applications constant 3-form flux, hep-th/0701130 Recently there is much interest on the (2007). applications of String/Gauge duality. The [2] Chong-Sun Chu, Pei-Ming Ho, Time- NTNU group, led by Feng-Li, has published dependent AdS/CFT duality and null several papers in this topic. Two papers are on singularity, JHEP 0604:013(2006). null-like cosmology's dual SYM, one is on the jet-quenching in AdS/QCD with chemical [3] Bin Chen, Sera Cremonini, Aristomenis potential, and one is to systematically Donos, Feng-Li Lin, Hai Lin, James T. Liu, construct the BPS bubbling solution in IIB Diana Vaman and Wen-Yu Wen, Bubbling supergravity. Another one is on the Hagedorn AdS and droplet descriptions of BPS strings in AdS space. Wen-Yu and Eiji geometries in IIB supergravity, Nakano, Shunsukei and Wen-Yu also arXiv:0704.2233 (2007) published two papers on studying several [4] Yeuk-Kwan E. Cheung, Konstantin observable quantities in RHIC (Relativistic Savvidy, and Hsien-Chung Kao, Galaxy Heavy Ion Collider) based on the AdS/QCD, Rotation Curves from String Theory, astro- the so called Sakai-Sugimoto model. ph/0702290 (2007). Publications [5] Non-local matching condition and scale- [1] Feng-Li Lin, Toshihiro Matsuo, Dan invariant spectrum in bouncing cosmology,

147 ‹‹- Highlights of Programs Chong-Sun Chu, Ko Furuta, Feng-Li Lin [2] Jen-Chi Lee, Zero-norm States and Phys.Rev.D73:103505, (2006). Superstringy symmetries, talk presented at XXXIII International Conference on High [6] Choon-Lin Ho and Ryu Sasaki, Deformed Energy Physics (ICHEP06), Moscow, Fokker-Planck Equations, cond- Russia, July 26-Aug 2, 2006. hep- mat/0612318 (2006). th/0610272. (to be published by world [7] Choon-Lin Ho and Ryu Sasaki, Deformed scientific) multi-variable Fokker-Planck Equations, [3] Jen-Chi Lee, Linear Relations and their cond-mat/0703291 (2007). Breakdown in High Energy String [8] Choon-Lin Ho and R. Sasaki, Quasi- Scatterings, talk presented at International exactly Solvable Fokker-Planck Equations, Europhysics Conference on High Energy arXiv:0705.0863 (2007) Physics (EPS2007), Manchester, England, [9] V.R. Khalilov, Choon-Lin Ho, Scattering of July19-25, 2007. arXiv:0705.1872. (to be Spin-polarized Electron in an Aharonov- published by Journal of Physics: Bohm potential, arXiv:07083131 (2007) Conference Series) [10] C.-M. Chen, D. V. Gal'tsov and D. G. [4] Hsien-Chung Kao, Second order Orlov, Extremal black holes in D=4 Perturbative Calculation of Quasinormal Gauss-Bonnet gravity, Phys. Rev. D75, Modes, talk presented at 13th International 084030 (2007). Symposium on Particles, Strings and Cosmology, London, UK, July 2-7, 2007. 4. Talks presented at International

Conferences Note: Some publications listed in this report may not [1] Pei-Ming Ho, Infinite Symmetries in the acknowledge the support of NCTS. We apologize for the ignorance of some members of the group who high energy limit, talk presented at String forgot to put it on the papers. Those works are 2006, Beijing, China, June 19-24, 2006. research results under the support of NCTS.

Highlights of Programs -›› 148 Highlights of Programs Interdisciplinary Fields

Focus Group on Atomic Physics

Coordinator: Daw-Wei Wang (National Tsing Hua University; email: [email protected]) Committee members: Ying-Cheng Chen (Academia Sinica), Chung-Hou Chung (National Chiao Tung University), Shin-Chuan Gou (National Changhua University of Education), Dian-Jiun Han (National Chung Cheng University), Tsin-Fu Jiang (National Chiao Tung University), Jiang-Nan Liu (Fu-Jen Catholic University), Yi-Wei Liu (National Tsing Hua University), Wen-Chin Wu (National Taiwan Normal University)

I. Brief Description Quantum Monte Carlo, Density Matrix Renormalization Group, and Dynamical Meanfield Theory etc. We will also explore the exotic many-body phases of cold atom systems roup size: as well as the dynamical and finite temperature properties. Active faculty members are about 20, including experimentalists. (2) Weakly interacting Bose gases: A certain portion of our group members have Goal: developed their own numerical technique to 1) encourage more cooperation between study the static as well as the dynamic faculty in this community, including properties of Bose-Einstein condensation of cooperation between theorists and cold atoms in the mean-field level. Several experimentalist. 2) attract more analytic work on the transition temperature researchers/students to join to form a stable properties of interacting bosonic atoms as well research environment. 3) enhance the research as magnetic dipoles are also developed. quality by actively cooperating with (3) Atomic structure theory: We have had a international frontier researchers and good start in atomic structure theory in the past concentrating on some promising projects. few years when Prof. Tu-Nan Chang (USC, Research direction: USA) was in Taiwan as NCTS director. We will keep such cooperation on-going and Our FG encourage the following four encourage more national-wide activities in this directions of research: subfield. (1) Strongly correlated effects in cold (4) Intensive laser and plasma: Although so atoms: This is a new team formed by some far there are not many theoretists in this new junior faculty from condensed matter field in Taiwan, there has been some great background. Besides of the analytic methods progress in the experiments in Academia developed in many-body theory, some of us Sinica and NCU recently. We hope this group also developed several advanced numerical can grow larger and stronger by cooperating tools for strongly correlated systems, like with local experimentalist as well as some

149 ‹‹- Highlights of Programs oversea researchers, like Chii-Dong Lin (UKS, III. Visitors and International USA), regularly. Cooperation Visitor: We invite Prof. Jianping Yin at the physics II. Activities department and key laboratory of spectroscopy Summer School: of East China Normal University in Shanghai From 8/20-8/24 in 2007, we held the 4th from Aug. 8 to 15, 2007. During his visit in AMO summer school in National Tsing Hua Taiwan Prof. Jianping Yin had intense University. Different from the style in previous discussions with local researchers (especially years, this time we select a specific topic: Ying-Cheng Chen and Dian-Jiun Han) in the Condensed matter theory in ultracold atoms to fields of cold atoms and molecules, atom and highlight the important and main string molecule optics, etc. both in theory and research direction. The course was organized experiment. This visit stimulates his from atom cooling to BEC-BCS crossover and collaboration with the local scientists in the cold molecules. There are more than 100 future and, as we expected, will have a students to join and the feedback was very positive impact on the local related research good. This is also a good training for those fields. who have been in this field. Visitors in the near future: Local Workshop: 1) We also have invited Prof. T.-L. Ho On 9/7-9/8 in 2007, we held AMO (Ohio State University, USA) to visit Taiwan workshop in Tung Hai University. The goal of in the end of Nov. of 2007. Prof. Ho is a this workshop is to provide a flexible forum world-wide famous theorist in systems of for domestic physicists working in AMO ultracold atoms and he is very willing to know physics and other related fields as well as to more about the local research in the related help initiate possible collaborations between field in Taiwan. We expect his visit will form a participators. We had a very flexible time close connection with people in strongly schedule to encourage speakers and other correlated systems. 2) We have invited Prof. C. researchers to discuss the potential research Greene (Director of JILA, USA) to visit direction and related problems in details. Taiwan for at least one week in May 2008. We Several ideas are exchanged and discussed for expect that Prof. Greene's coming will broaden future cooperation. the horizon of local research in atomic structure, atomic scattering and systems of International Workshop: ultracold atoms. We are planning to hold one international International cooperation: workshop in the end of 2008 or early of 2009 on some specific topics of cold atoms (for Our group members have active example, dipolar atoms/molecules), which are international cooperation with frontier closely related to the interest of local researchers. For example, Daw-Wei Wang researchers and main string development. (National Tsing Hua University) recently has a paper with Prof. P. Zoller in Innsbruck, to Seminar/Journal Club: develop a new scenario for dipolar lattice We are going to host two bi-weekly (or structure. Prof. Ying-Jer Kao (National Taiwan monthly) seminars, one in National Tsing Hua University) cooperated with Prof. A. Sandvik University and one in National Changhua (BU) in the development of quantum Monte University of Education, to serve different Carlo calculation. Prof. Tsin-Fu Jiang local researchers in different locations. The (National Chiao Tung University) developed a goal is to update the most important research new numerical method for high intensity laser, and enhance cooperation between students as cooperating with Prof. Chii-Dong Lin (Kansas well as faculty. State University). Prof. Te-Kuei Fang works

Highlights of Programs -›› 150 with Prof. Tu-Nan Chang (USC) in atomic Gases. [3, 4] structure theory, etc. Results of these B. Vortex ring in BEC: Shin-Chuan Gou and cooperation have been or will soon be his cooperators study the quantized vortex published. ring is a 3-dimensional structure of solitary waves having the shape of "smoke ring" that is formed by closing the core of a IV. Highlight of Research Results vortex line upon itself. They develop Strongly interacting cold atoms/molecules: analytic solutions of the vortex ring motion and other related properties in a semi- A. Exotic quantum phases of polar molecules: classical manner. [5] Daw-Wei Wang and his cooperators investigate the quantum phase transitions of C. Collective mode of BEC: Wen-Chin Wu and bosonic polar molecules in double layer [1] his student have used a modified Gaussian and multi-layer systems [2]. This work has distribution to study the physical properties been presented in academic institutes like of one and two-component ultracold atoms Yale, NIST, KITP, Maryland, Stuttgart and [6]. Jiang-Nan Liu and his cooperator apply Innsbruck etc. Recently Prof. Wang the hyperspherical (HS) method to study a cooperated with Prof. P. Zoller to develop a BEC in quasi-2D free space stabilized and dipolar lattice system, which has been confined under the influence of an submitted to Phys. Rev. Lett. oscillating magnetic field. Analysis of the stationary state solutions shows that the B. Supersolid phase in square optical lattice: hyperspherical single-particle density Ying-Jer Kao and his cooperators study the exhibits certain characteristic scaling ground state phases of the boson-Hubbard dependence on energy akin to the Townes model using quantum Monte Carlo soliton [7] methods. They observe supersolids with checkerboard, striped, and quarter-filled Atomic structure and spectroscopy: crystal symmetry, when the system is doped Te-Kuei Fang and Tu-Nan Chang have away from commensurate fillings. This recently employed a B-spline-based complex work has been submitted to Phys. Rev. Lett. rotation (BSCR) method with spin-dependent C. Incommensurate supersolid phase in interaction to study atomic photo-ionization triangular lattice: Chung-Hou Chung and for two-electron and divalent atoms. Their his cooperators study the ground state preliminary results are in good agreement with phases of the the Bose-Hubbard model in the observed spectra. [8] an anisotropic triangular optical lattice with High intensity laser theory: special emphasis on the supersolid phase. They find a possible "quasi- An essential modification to the kernel in incommensurate" supersolid phase in the the calculation of hydro-genic momentum thermodynamic limit. This work has been wave functions in finite space is developed by submitted to Phys. Rev. Lett. Tsin-Fu Jiang and his cooperators, using only a few hundreds grid points the modification Weakly interacting bosonic atoms: allows eigenvalues accurate to about 10-7. This A. Statistical mechanics of weakly interacting method can be applied to general diatomic bosons: Tsin-Fu Jiang and Yee-Mou Kao molecule with single-active-electron (SAE) developed a two-fluid theory to study the under laser pulse, too. fractional change of Bose-Einstein condensation transition temperature due to the trap potential, the finite number of V. Support AMO experimentalists particles, and the mutual atomic We invite Prof. Jianping Yin to help the interactions. They also explored the experimental setup of Prof. Ying-Cheng Chen peculiar structure for the systems of dipolar

151 ‹‹- Highlights of Programs (IAMS, Academia Sinica) and Prof. Dian-Jiun in a trapped Bose-Einstein condensate, Han (National Chung Cheng University). Physical Review A 74, R041603 (2006) Besides, we also support a student of Prof. [6] C.-C. Huang and W.C. Wu, Using modified Chin-Chun Tsai (National Cheng Kung Gaussian distributions to study the physical University) to present their current nice work properties of one- and two-component in Cs spectroscopy measurement in an ultracold atoms, Phys. Rev. A 75, 023609 international conference [9]. We believe a (2007). close connection between theoretical development and the local experimental [7] C.N. Liu, T. Morishita and S. Watanabe, observation is necessary. Time-dependent hyperspherical studies for a two-dimensional attractive Bose-Einstein condensate, Phys. Rev. A 75, 023604 (2007). VI. Selected Publications [8] T.K. Fang and T.N. Chang, B-spline-based [1] D.-W. Wang, Quantum phase transitions of complex-rotation method with spin- polar molecules in bilayer systems, Phys. dependent interaction, Phys. Rev. A, 76, Rev. Lett. 98, 060403 (2007). 012721 (2007). [2] D.-W. Wang, M.D. Lukin, and E. Demler, [9] Wei-Xiang Chen, Ray-Yuan Chang, Thou- Quantum fluids of self-assembled chains of Jen Whang, Chanchal Chaudhuri, and C. polar molecules, Phys. Rev. Lett. 97, C. Tsai, The third and fourth 1 g states of 180413 (2006). Na2: A pair of twins, Chem. Phys. Lett. [3] Y. M. Kao and T. F. Jiang, Transition 439, 29 (2007). temperature of a weakly interacting Bose gas, Phys. Rev. A 73, 043604 (2006) Remarks: [1,2] are stimulated in a mini-workshop of AMO focus group workshop, [3-6,8] are by the financial and [4] Y. M. Kao and T. F. Jiang, Transition administrative support of NCTS, [7] is also initiated in temperature of the interacting dipolar Bose the discussion during AMO workshop, and [9] are gas, Phys. Rev. A 75, 033607 (2007). supported for the international conference [5] T.-L. Horng, S.-C. Gou and T.-C. Lin, presentation. Bending-wave instability of a vortex ring

Highlights of Programs -›› 152 Focus Group on Quantum Information Sciences

Coordinator:Yueh-Nan Chen (National Cheng Kung University; email: [email protected]) Hsi-Sheng Goan (National Taiwan University; email: [email protected]) Committee members: Yia-Chung Chang (Academia Sinica), Pochung Chen (National Tsing Hua University), Chi-Yee Cheung (Academia Sinica), Chung-Hsien Chou (National Cheng Kung University), Li-Yi Hsu (Chung Yuan Christian University), Chopin Soo (National Cheng Kung University), Zheng-Yao Su (National Center for High-Performance Computing), Wei-Min Zhang (National Cheng Kung University)

I. Introduction visitor of our focus group, one of the major QIS focus group research topics was focused on the field of quantum decoherence. The 2007 summer school on he main mission of the QIS focus "Non-equilibrium dynamics and quantum group is to build a platform of coherence" suggested by Prof. Hu was the communication and discussion for researchers second summer school (the previous one in this area in Taiwan. In the last few years, we held in 2006) focusing on this particular have brought QIS researchers in Taiwan to topic. It attracted many participants (~70), work and discuss research together and to hold including faculties, postdocs and students. activities, such as scientific seminars, The participants and QIS focus group workshops and short-term schools. We have members benefited much from the two also been seeking to establish links and summer schools. As a result of the summer exchanges as well as to initiate collaborations schools, several focus group members have with other QIS researchers worldwide. engaged in the research on "Non-Markovian dynamics of qubits and continuous variable Focused research topics: Quantum systems in external environments". Some decoherence, quantum computation, quantum preliminary results have come out and some measurement, quantum entanglement and have been published (or to be published). communication. 2. We also successfully attracted young researchers and new graduate students into this field, such as the postdoctoral fellows II. Activities and Beneficiaries (Dr. M. T. Lee and Dr. J. H. An) and • Activities graduate students (Mr. W. Y. Tu, Mr. H. B. 1. Summer school on, "Non-equilibrium Chen, Mr. D.B. Tsai, Mr. C.H Li and Mr. dynamics and quantum coherence" at Y.Y. Lai). NCKU, July 4 ~ 6 (2007). • Training of young-generation physicists 2. Winter school and workshop on, "Quantum 1. Financial supports for international Information Science", January 4 ~ 6 (2008). conferences 3. Seminars at NCKU and NTU. (1) Dr. Ming-Tsung Lee (NCKU) -- HCIS15 at Tokyo • Beneficiaries 1. Ever since Prof. B. L Hu (Univ. of (2) Dr. Che-Ming Lee (NCTU) Maryland) became the senior multi-year -- Young European Physicists meeting 2007

153 ‹‹- Highlights of Programs (3) Mr. Wei-Yuan Tu (NCKU) focus on non-Markovian dynamics of -- 4th APWQIS at Singapore quantum dot qubits. 2. Inviting potential young-generation 2. Prof. G. J. Milburn at the University of physicists as speakers at summer school Queensland and Prof. Xin-Qi Li at the Chinese Academy of Science (1) Dr. Ming-Tsung Lee (NCKU) -- With Prof. H.-S. Goan on quantum (2) Mr. Son-Hsien Chen (NTU) measurement and quantum feedback (3) Mr. Ming-Hao Liu (NTU) control of qubits and continuous variable (4) Mr. Tu-Wei Yuan (NCKU) systems.

III. Visitors and International IV. Highlights of Research Results Collaborations • Research results • Visitors 1. Quantum computation 1. Prof. B. L. Hu, Univ. of Maryland, USA A. Charge-to-spin conversion of electron (Jan. 2007 and July 2007) entangled states and spin interaction free -- Collaboration with Prof. C. H. Chou on solid-state quantum computing: Non-Markovian dynamics of qubits We have proposed an implementation 2. Prof. S. A. Gurvitz, Weizmann Institute, of scalable spin quantum computation in Israel (Nov. 2007 ~ Jan. 2008) semiconductor nanostructure without resorting to spin-spin interaction. [1]. -- Collaborations with Prof. W. M. Zhang, The techniques of single electron Prof. H. S. Goan, and Prof. Y. N. Chen on transitions and the nanostructure of Quantum measurement and quantum quantum-dot cellular automata (QCA) transport are used to generate charge entangled 3. Prof. Zhanjun Zhang, Anhui University, states of two electrons, which are then China (Oct 2006 ~ Oct. 2007) converted into spin entanglement states using single spin rotations only. -- Collaboration with Prof. W. M. Zhang on Deterministic two-qubit quantum gates Quantum cryptography are also manipulated using only single 4. Dr. Neil Lambert, Univ. of Tokyo, Japan spin rotations with the help of QCA. (Nov. 2007) B. Geometric phase quantum computing: -- Collaboration with Prof. Y. N. Chen on By collaborating with Prof. Oh's group Quantum transport and shot noise in Singapore, a scheme for implementing 5. Mr. Lukas Gilz, Univ. of Kaiserslautern, unconventional geometric quantum Germany (Aug. 2007 ~ Sep. 2007) computation by using the interaction of two atoms with a two-mode cavity field -- Collaboration with Prof. Y. N. Chen on has been proposed. [2] Retardation effect between qubits 2. Dynamical decoupling 6. Mr. Yeong-Cherng Liang, University of Queensland, Australia (Sep. 2007) We develop a numerical framework to investigate the renormalization of the • International Collaborations non-Markovian dynamics of an open 1. Prof. T. Brandes at Technische Universität quantum system to which dynamical Berlin, Germany decoupling is applied. Our results indicate that the renormalization of the -- A three-year international collaboration non-Markovian dynamics critically project with Prof. Y. N. Chen. Mainly

Highlights of Programs -›› 154 depends on the spectral density of the verified by the maximal violation of environment and the envelope of the stabilizer-based Bell-type inequalities. decoupling pulses. It also opens a new • Invited presentations avenue to further optimize the decoupling via pulse shaping. [3] 1. Science seminar at Max. Planck. Institute, Dresden, Germany 3. Shot-noise spectrums of non-Markovian quantum dot excitons Prof. Y. N. Chen, Title: Entanglement and teleportation via superradiance We propose to detect non-Markovian decay of an exciton qubit coupled to 2. 4th Asia Pacific conference on quantum multi-mode bosonic reservoir via shot- Information Science noise measurements. Non-equilibrium Profs. W. M. Zhang, C.-Y. Chueng, H.-S. current noise is calculated for a quantum Goan, and Mr. W.-Y. Tu. dot embedded inside a p-i-n junction. An additional term from non-Markovian 3. International Workshop on Quantum effect is obtained in the derivation of Dynamics and Biomolecular Function, noise spectrum. [4] Yeppoon, QLD, Australia 4. Quantum electromechanical systems Prof. H.-S. Goan We have investigated to use a circuit 4. Seminar at the University of Queensland, QED cavity [5] as a motion transducer to Brisbane, Australia probe the properties of a quantum Prof. H.-S. Goan electromechanical system (QEMS). 5. Quantum entanglement and communication V. Publications A. Decomposing the Lie Algebra su(N) [1] Free spin quantum computation with An algebraic structure, the quotient semiconductor nanostructures, Wei-Min algebra, universally embedded in the Lie Zhang, Y. C. Wu, M. Feng and C. P. Soo, algebra su(N) is discovered. [6] In this quant-ph/0502002 (submitted to Phys. Rev. structure, the Lie algebra su(N) is Lett. with a revised version, 2007). partitioned into a certain number of [2] Unconventional geometric quantum abelian subalgebras or vector subspaces, computation in a two-mode cavity, C. Wu, each of which is considered an Z. Wang, X.-L. Feng, H.-S. Goan, L.C. individual element. This structure Kwek, C.H. Lai and C.H. Oh, Phys. Rev. A enables systematic and exhaustive 76, 024302 (2007). decompositions for the Lie algebra, such [3] Dynamical decoupling-induced as a fast scheme for the Cartan renormalization of non-Markovian decomposition. The applications of this dynamics, Pochung Chen, Phys. Rev. A 75, work include design of optimal quantum 062301, (2007). gates, classification of quantum entanglement, analysis of quantum [4] Super-Poissonian noise of quantum dot p-i- control and others. n junction, Y. N. Chen, Appl. Phys. Letts. 90, 162114 (2007). B. Mixed States with an Incomplete Set of Stabilizer Generators [5] A microwave transducer for a nano mechanical resonator, G. J. Milburn, C. A. We investigate a family of mixed Holmes, L. M. Kettle and H.-S. Goan, entangled states with common stabilizers cond-mat/0702512. among the mixtures of the corresponding density matrix. [7] The non-locality of [6] A Scheme of Cartan Decomposition for these mixed entangled states can be su(N), Z. Y. Su, quant-ph/0603190.

155 ‹‹- Highlights of Programs [7] Mixed entangled states with two or more states of colloidal CdSe/ZnS quantum common stabilizers, L. Y. Hsu, Phys. Rev. dots under high pressures, C. T. Yuan, Y. A 76, 022322 (2007). C. Lin, Y. N. Chen, Q. L. Chiu, W. C. Chou, D. S. Chuu, W. H. Chang, H. S. [8] Electron transport of a driven three-level Lin, R. C. Ruaan and C. M. Lin, system in an asymmetric double quantum Nanotechnology 18, 185402 (2007). dot irradiated by an external field, Y. Y. Liao, D. S. Chuu, and Y. N. Chen, Phys. [13] Entanglement detection via the condition Rev. B 75, 125325 (2007). of quantum correlation, C. M. Li, L. Y. Hsu, Y. N. Chen, D. S. Chuu, and T. [9] Non-Markovian reduced dynamics and Brandes, accepted by Phys. Rev. A entanglement evolution of two coupled (2007). spins in a quantum spin environment, X. Z. Yuan, H.-S. Goan and K. D. Zhu, Phys. [14] Secure Quantum Bit Commitment Using Rev. B 75, 045331(2007). Unstable Particles, C. Y. Cheung, International Journal of Modern Physics [10] Non-Markovian entanglement dynamics B (in press, 2007). of quantum continuous variable systems in thermal environments, K.-L. Liu and [15] Detection inefficiencies in Cabello's proof H.-S. Goan, Phys. Rev. A 76, 022312 of the three-qubit Bell theorem without (2007). inequalities, Li-Yi Hsu and Jau-Han Chen, Phys. Letts. A 364, 101 (2007). [11] Influence of an external magnetic field on the decoherence of a central spin coupled [16] Generation of entangled photon pairs by semiconductor quantum dots in a to an antiferromagnetic environment, X. structure of quantum cellular automata, Z. Yuan, H.-S. Goan and K. D. Zhu, New M. Feng, J. H. An, and W. M. Zhang, J. J. Phys. 9, 219 (2007). Phys.: Condens. Matter 19, 326215 [12] Studies on the electronic and vibrational (2007).

Highlights of Programs -›› 156 Highlights of Programs

Plasma Science Program

Coordinator: Kuan-Ren Chen (National Cheng Kung University; email: [email protected]) Committee members: Lin-Ni Hau (National Central University), Jang-Yu Hsu (National Cheng Kung University), Chwung-Shan Kou (National Tsing Hua University), Wei-Chih Liu (National Taiwan Normal University), Jyhpyng Wang (Academia Sinica)

I. Description 1. Objectives: A. Promoting theoretical plasma research in Taiwan.

he NCTS Plasma Focus Group was B. Stimulating research collaborations with recommended to become a working experimentalists, of inter-disciplinary, and group because NCTS believed that local beyond national boundaries. plasma research is not so focused. By mutual C. Incubating young generations of plasma agreement with Div. Head H. N. Lee, the scientists. NCTS Plasma Science Program was formed in 2. Guidelines: this February. The Program identifies the following plasma research frontiers: space and 1. Following the NCTS written guidelines. astrophysical plasma, fusion plasma, laser 2. Providing the needed administrative plasma, surface plasma, coherent radiation, assistances and a flexible and reliable service plasma applications, low temperature plasma, for easy budget access. 3. The NCTS budget and gluon plasma. The local community has should be used efficiently. 4. Suggestions for research activities in all but the last one. In activities and positions are encouraged. 5. fact, it has world-leading research result in Proposal and report in written should be brief; almost every area, although the size of local in most cases, an email may be enough as long plasma physics community is still small. as key information and justifications included. Education is essential for this community to 6. The program committee makes the decision increase its enabled manpower and future only based on the objectives, the guidelines, prosperity. Plasma researches are often across the academic merit, and available budget. 7. disciplinary boundaries and important in both Activities aiming to stimulating collaboration scientific frontiers and critical applications. and interaction are encouraged and have a The NCTS Plasma Science Program is higher priority for budget supporting. 8. expected to provide a forum for the local Activities aiming to incubating young plasma science community, to achieve the generations are encouraged and have a higher following objectives, and to operate under the priority for budget supporting. 9. Sponsored guidelines listed below. foreign visitors should be superior in particular

157 ‹‹- Highlights of Programs methodology and knowledge. 10. Local metallic/dielectric structures, and to experts and groups are encouraged to offer investigate novel optical phenomena. About tutorial courses, schools, and workshops. 11. two speakers per month are invited for Self-organized working groups across presentation. It is organized by Professors D. institutions are encouraged. 12. Each working P. Tsai of NTU and W. C. Liu of NTNU. The group should have focused interest and organizers and some of its participants have activities, and is encouraged to be bounded successfully landed a National Nano Project. with specific experimental concerns. 13. The 3. Laser-Plasma Interaction Summer School plasma sub-areas and working groups are coupled through common interest in A. Purpose simulation and theory, such as nonlinear In Taiwan and possibly many other places dynamics.? 14. Anyone in the community is in Asia, it is not uncommon to meet a welcome to participate in any of the groups of prospective graduate student who is interested his/her interest. in experimental sciences but poorly prepared for laboratory work. Many students can do textbook exercises well, but do not know how II. Activities to describe the thread of a screw, or how to read the color code of a resister. They cannot 1. Surface Plasma Working Group Meetings operate a milling machine or a soldering iron, Surface plasma on metallic surface is a or tell the difference between epoxy and newest frontier in plasma research. It is a silicon rubber. The reason is simple: these are research area of multi-disciplines, involving not part of their education or experience. In physics, mathematic, electro-optics, bio- this summer school held at National Taiwan medical, electronics, materials, nano- University by Jyhpyng Wang of Academic technology, mechanical, and electrical Sinica from July 16 to 20, we wish to extend engineering. This biweekly meeting was their education in this direction, even though it organized by Professor Y. C. Lan in 2006 and is not possible to provide them a real Professor S. J. Chen in 2007. Active laboratory experience. participants include five NCKU professors and one professor with Kaohsiung Univ. of B. Courses Applied Science and their students. In addition Forty hours of lectures that form fourteen to working group discussion, external and courses were delivered. The objective is to internal speakers are invited. The purpose is to introduce to the participating students a near educate students and to stimulate complete set of basic knowledge that is collaboration. In this July, NCKU realized the required in a laser-plasma laboratory. In importance of a simulation result by the group. addition, recognizing computer simulation as a A NCKU experimental team supported by the form of numerical experiments, the courses Top University fund is formed and a joined also cover basic knowledge of computer biweekly meeting is being held. The number simulation. The courses are: characteristics of involved professors is increased to about and applications of optical components, fifteen. ultrafast optics and high-power lasers, basic laser-plasma interaction, experimental 2. Computational Plasmonic Nano-Photonics techniques in laser-plasma interaction, basic Meetings numerical simulation, Particle-in-cell At nano scale, charge is the most effective simulation, handy computation: Introduction media to interact with photons. Thus, for many to Matlab, Mathematica, and Mathcad, experts, plasmonic is the most important area working with electronics, computer control of of nano-photonic research. While covering instruments, introduction to electro-optics both fundamental physics and applications, instruments, working with vacuum, data this monthly working group meeting aims to analysis and curve fitting, mechanical design understand the interactions of photons and

Highlights of Programs -›› 158 and drafting, data plotting and presentation, simulation; the quantitative comparison is and using LaTeX for preparing scientific being done. The three are expected to get documents. together for in-depth discussion in November during the annual meeting of Plasma Physics C. Participation Division of American Physical Society, held at There are 160 participants enrolled. In Orlando, FL, USA. additional to a few faculties and some full- time research assistants, most of them are 2. Professor C. M. Ryu, Postech, Korea master students, undergraduate students, and Professor C. M. Ryu visited NCTS from Ph.D. students. At the end, we have conducted 6/26 to 7/8, 2007. He is a well rounded plasma a poll to see how students evaluate the courses. physicist and has done research in various In the poll we asked students to rate each areas of plasma physics.? He made course in two scales, one on the level of presentations on "Magnetic Field Generated by difficulty and the other on the pace of Transport Flow" at both NCKU and NCU. lecturing. The cost per participant is about During the visit, he started collaborative work 1,500NT for this five days intensive school. with Professor J. Y. Hsu on the spheromak plasma equilibrium. He pointed out the 4. Particle-in-cell Mini-school correlation dimension to quantify the fractal Particle-in-cell is a first-principle and the dimension and one student has implemented a most powerful method to simulate plasmas. numerical code successfully to examine for Aiming to educate students and young plasma example the Henon map, and will apply the scientists in a joined effort, this mini-school same to arc root dynamics, and other brings local experts together. It is organized by stochastic systems. The spheromak plasma Professor Y. C. Lan and will be held at NCKU equilibrium paper while submitted to APS on September 29 and 30. meeting still needs further effort to finish, however.

III. Visitors and International Collaborations IV. Highlights of Research Results 1. Professor Liu Chen, UC Irvine, USA Taiwan's plasma physics community is Professor Liu Chen visited NCTS from relatively small in size as compared with other 11/8-26, 2006. He spent the first week in research fields of physics. However, the NCU, the second week in NCKU, and then in academic performance is impressive and the NDHU and NCU. In addition to giving series international reputation is high. For example, lectures on gyrokinetic theory and toroidal in the areas of electron cyclotron maser, dusty physics, he started the collaboration on the plasmas, space plasma, laser plasma, red- work of relativistic ion cyclotron instability Sprite observation, fast ion cyclotron under non-uniform magnetic field with instabilities, and recently surface plasma, Professor K. R. Chen and student, Mr. T. H. Taiwan's groups are making outstanding Tsai. After his visit, Mr. Tsai went to UC original contributions and, in fact, are among Irvine at the end of March 2007 to carry out leaders of the international research the theoretical derivation, under the support of community. National Science Council. It is expected for There are many outstanding research Mr. Tsai to stay there till January 2007. results in the local plasma community. Due to During the meantime, Professor Liu Chen has page limitation, only one of the most recent visited Taiwan twice (one in July and the other advances in surface plasma is introduced here. in September) and discussed with Professor K. Diffraction, a general characteristic of wave R. Chen, under the support of NCU with a phenomena, occurs whenever a wave front Chair Professorship. Preliminary result yielded encounters and propagates past an obstruction, is consistent qualitatively with Particle-in-cell has being studied since L. da Vinci in 1400s.

159 ‹‹- Highlights of Programs It sets a lower limit on the spot size of light diffraction limit. The simulation results are and thus the ultimate resolution of numerous being verified by experiments in both visible diagnostic and fabrication instruments. In fact, light and microwave frequency ranges. The the diffraction limit inspired Heisenberg for light focusing process, besides its academic his uncertainty principle of quantum interest, is expected to open up a wide range of mechanics; they can be deduced from each application possibilities; e.g., photolithography other. A novel scheme with surface plasma that is the critical issue stopping the Moore's effects is being studied to address the law of semiconductor industry.

Highlights of Programs -›› 160 Research Activities of Individuals

Research Activities on Spintronics and N-leg Ladders

Judith E. Bunder (email: [email protected]) Postdoctoral researcher, 2003/11/12~2007/7/31

n the past few years I have been temperature such large TMR in DMS-based interested in spintonic materials, and MTJ are only expected at extremely low specifically dilute magnetic semiconductors temperatures, deceasing rapidly as the (DMS). In part a) I present a brief description temperature increases. However, this is not of my recent work on DMS-based magnetic true for all DMS and some, such as GaN tunnel junctions. Another research interest is doped with Mn and Cr, are known to have ground-state properties and gapless excitations critical temperatures above room temperature in N-leg ladders. In part b) I discuss spin- [4]. charge separation in N-leg ladders. To describe the variation in conductance with temperature T and relative magnetization a) Spin-polarized transport in dilute orientation θ I define the function magnetic semiconductor tunnel junctions (1) One of my recent research interests is transport in magnetic tunnel junctions (MTJ) where G(θ,T) is the conductance. This is [1] which contain dilute magnetic related to the TMR by semiconductors (DMS). A conventional TMR=R(π,T)G(0,T)/G(π,T). The conductance magnetic tunnel junction usually consists of an was evaluated using the Landauer formula [5] insulator between two ferromagnets, though while the magnetization in the DMS was any magnetic material can in principle be used. determined from self-consistent Green's I was particularly interested in transport effects functions [6]. Fig 1. and 2. show R(θ,T) for Fig in MTJ in which the magnetic materials are identical except for their relative magnetization orientations. A DMS is created by doping group III-V or II-VI semiconductors with a transition metal and these impurity ions couple to the itinerant carriers, giving the DMS some unique magnetic properties [2]. Experimental studies have shown that using DMS as the magnetic material in a MTJ can provide quite a large tunneling magnetoresistance (TMR) such as almost 300% in Ga(Mn)As/GaAs/Ga(Mn)As at 0.39K [3]. Unfortunately, as most DMS Fig 1: The R(q,T) ratio for carrier concentration have critical temperatures well below room 0.3 nm-3.

161 ‹‹- Research Activities of Individuals two different carrier concentrations in a MTJ separation in N-leg ladders is limited to N=1. containing DMS Ga(Mn)As and insulator It is already known that odd and even legged AlAs. The shape of these curves with respect ladders have quite different properties [9]. For to the temperature resemble the shape of example, the ground state of odd legged itinerant carrier magnetization while the ladders at half filling belongs to the same angular dependence is ~sin2(θ/2). This angular universality class as the single Heisenberg spin dependence agrees with what is observed chain. They have long-ranged ferromagnetic experimentally. order and gapless spin-wave excitations. In contrast, the even legged ladders are all spin liquids with a spin gap. So, the possibility that the odd legged ladders would also resemble one-dimensional chains in their ability to support spin-charge separation was intriguing. We used a Hubbard Hamiltonian with on- site interactions. On solving the renormalization group flow equations we find that the coupling constants obey several general rules which remain true for all parameter variations. In addition, these coupling constants always retain the same sign Fig 2: The R(q,T) ratio for carrier concentration which is a fair indication of an absence of a 0.1 nm-3. phase transition. Whether or not an N-leg ladder undergoes a phase transition has been in The Julliere formula [1] may be used to dispute for some time. give a semiclassical approximation of R(q,T), To proceed further we bosonize the Hamiltonian, i.e., we map the fermion fields in (2) the Hamiltonian to boson fields [8]. We use a where P is the polarization. Although this non-standard mapping of the boson fields semiclassical formula does give the correct which gives a far simpler, albeit still complex, angular dependence, the temperature Hamiltonian than the standard mapping. We dependence is quite different to what I use the Hamiltonian to determine zero energy obtained from the Landauer formula, gap excitations, i.e., when a set of boson fields especially for large carrier concentrations can be changed by a specific amount without indicating that the Julliere formula is not a affecting the Hamiltonian. particularly good approximation. Quantum numbers, such as the total charge

Qi and the total spin Si in the ith leg may be b) Spin-charge separation in weakly written in terms of the boson fields [8] and coupled N-leg ladders then used to determine whether or not spin In a one dimensional chain it is known that charge separation can exist in an N-leg ladder. electrons can separate into two components, a If we can retain a constant Hamiltonian when holon which carries the charge of the electron Qi=1 while Sj=0 for all j then we have shown but no spin, and a spinon which carries the that a particle with the same charge as an spin of the electron but no charge. This is a electron but with no spin is permitted in the phenomenon known as spin-charge separation ladder, i.e, there is a zero energy gap for the [7]. A two-leg ladder, i.e., two identical one creation of holons in the absence of spinons in dimensional chains bound weakly together, the ladder and therefore we have spin-charge does not have spin-charge separation [8]. separation. Alternatively, we could show that S =1/ while Q =0 for all i. This latter case Together with Hsiu-Hau Lin I have j 2 i describes the existence of a spinon without a investigated whether or not spin-charge

Research Activities of Individuals -›› 162 holon so again would indicate spin-charge Fitzgerald, Nature Mat. 4, 173 (2005). separation is possible. [5] Z. Zheng, Y. Qi, D. Y. Xing and J. Dong, Our bosonized N-leg Hamiltonian remains Phys. Rev. B 59, 14505 (1999). invariant when N is odd and the central leg ic [6] J. E. Bunder, S.-J. Sun and H.-H. Lin, has charge Qic=1 but Sj=0 for all j. Therefore Appl. Phys. Lett. 89, 72101 (2006). we have shown that a holon can exist in the [7] C. Kim, A. Y. Matsuura, Z.-X. Shen, N. central leg of an odd legged ladder. The other Motoyama, H. Eisaki, S. Uchida, T. N-1 legs cannot support spin-charge Tohyama and S. Maekawa, Phys. Rev. Lett. separation. Even legged ladders have no spin- 77, 4054 (1996). charge separation. Thus we have shown that [8] H.-H. Lin, L. Balents and M. P. A. Fisher, spin-charge separation is not unique to one- Phys. Rev. B 58, 1794 (1998). dimensional chains. [9] S. White, R. Noack and D. J. Scalapino, Phys. Rev. Lett. 73, 886 (1994) References [1] E. Y. Tsymbal, O. N. Mryasov and P. R. LeClair, J. Phys.: Condens. Matt. 15 R109 (2003). [2] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova and D. M. Treger, Science 294, 1488 (2001). [3] D. Chiba, F. Matsukura and H. Ohno, Physica E 21, 966 (2004). [4] J. M. D. Coey. M. Venkatesan and C. B.

163 ‹‹- Research Activities of Individuals Research Activities on Interdisciplinary Research

Cheng-Hung Chang (Institute of Physics, National Chiao Tung University; e-mail: [email protected]) Center scientist, 2007/2/1~2009/1/31

n the past year, I continue my study in (I) spintronics and (II) biophysics. Two topics in these two fields are highlighted below and the other are listed in the references. (I) Spintronics The semiclassical path integral (SPI) method has been successfully applied to explain spin dynamics in several mesoscopic systems under Rashba spin orbit interaction in our previous works. Examples include spin current transports through open quantum dots like rings, Sinai billiards, and square billiards, Fig. 1 The spin relaxation time τS of [1,0,0] sample (blue spin relaxations in triangular billiard, circular circle) and [1,1,0] sample (green star) versus billiards, generalized Sinai billiards, and channel width w are obtained from Awschalom's

billiards with rough boundary. This year we experiments (n-doped InGaAs). The τS calculated extend the application of this technique to spin from the SPI method are the red diamond and the black triangle curves, taken from different fitting relaxation problems in quasi-1D channel of functions. The inset demonstrates three examples narrow width w. Experimentally this system of spin polarization relaxation for channel width (a) has been studied in Awschalom's group w=1µm, (b) w=1.8µm, and (c) w=12µm. recently, where several interesting and unexplained questions have been addressed (II) Biophysics [PRL 97, 036805 (2006)]. By applying SPI Being able to introduce bioactive molecules method, our recent work Ref. [1] (i) confirms such as DNA, proteins or chemical reagents the experimental relaxation time in large width into living cells and then examine the regime and explains the reason for the consequent responses is critical to the saturation in small width regime, (ii) gives a advancements of modern biology. Certain slowdown onset of spin relaxation compounds are readily "membrane approximately the same as the experiment permeable", they can enter the cells by simple value, (iii) theoretically derives and diffusion. On the other hand, delivery of numerically confirms the Bessel-function spin membrane impermeable molecules to living relaxation in a quasi-1D impurity-free channel, cells or tissues can be achieved by a variety of and (iv) confirms the linear dependence of the chemical, physical, or biological methods. relaxation rate versus width square predicted Each technique has its own advantages and recently [PRB 61, R2413 (2000)]. The SPI drawbacks. In general, molecular delivery can method again proved itself to be a powerful be better done in relatively undifferentiated approach to understand the spin dynamics of rather than differentiated cells. Cell lines are systems with spin-orbit interaction. more effective targets for transfection than

Research Activities of Individuals -›› 164 primary cultured cells or tissue explants and proteins are more difficult to be delivered into cells than DNA. In Ref. [5] we contrive a new References molecular bombardment method to tackle [1] Cheng-Hung Chang, Hui-Fen Lo, A.G. some of these challenges. Mal'shukov, Semiclassical path integral approach on spin relaxations in quasi-1D wires, (preprint). [2] W.-M. Huang, C.-H. Chang, and H.-H. Lin, Non-collinear magnetic junction mediated by Rashba interaction, J. Magn. Magn. Mater. 310, e759 (2007). [3] T.Y. Tsong and C.-H. Chang, A Markovian engine for a biological energy transducer: The Catalytic Wheel, Biosystems 88, 323 (2007). [4] W. H. Kuan, C. S. Tang, and C. H. Chang, Spectral properties and magneto-optical excitations in semiconductor double rings under Rashba spin-orbit interaction, Phys. Rev. B, 75, 155326 (2007). [5] W.-N. Lian, C.-H. Chang, Y.-J. Chen, R.-L. Dao, Y.-C. Luo, J.-Y. Chien, S.-L. Hsieh and C.-H. Lin, Intracellular delivery can be mediated by bombarding cells or tissues with accelerated molecules or bacteria without the need for carrier particles, Exp. Cell Res. 313, 53 (2007). [6] C.-H. Chang and T.Y. Tsong, Energy transduction in molecular machines, to appear in Nano (2007).

Fig. 2 (A and B) The ratio of cells containing molecules delivered by bombardment (orange bars), by diffusion for 1 min (pink bars), or 10 min (blue bars) was calculated. (Bottom plot) The hypothetic model for the molecular bombardment assay. Molecules in small water droplets (blue dots) are accelerated by the high-pressure gas and used to bombard the cells. The combination of wave front and plasma membrane penetration by high speed molecules causes some of the affected cells (cells #2 and #3, but not cell #1) to become transiently permeable to non-accelerated molecules (red dots) added to the medium, allowing their entry by diffusion. The membranes reseal within 10 min after the bombardment.

165 ‹‹- Research Activities of Individuals Research Activities on Quantum Transport and Measurement

Yueh-Nan Chen (Department of Physics, National Cheng-Kung University; email: [email protected]) Center scientist, 2006/10/13~2008/10/12

y research is mainly on the theory of Effect from the nonrelativistic cutoff quantum transport and measurement. frequency of the exciton decay may be There are three major results in the past year: revealed with the feature of super-poissonian noise without making the Markovian Super-poissonian noise in a quantum approximation (Fig. 2). To become practically p-i-n junction observable in experiments, high quality I investigated theoretically the shot-noise quantum well or quantum dot arrays, which spectrum of a quantum dot p-i-n (p- exhibits superradiance, in a p-i-n junction is type/intrinsic/n-type) junction (Fig. 1) suggested to enhance the zero-frequency noise (Fano factor).

Electron transport of a driven three- level system in an asymmetric double quantum dot We investigated Electron tunneling through a three-level system in an asymmetric double quantum dot irradiated by an external field (Fig. 3).

Fig.1 Energy-band diagram of a QD inside a p-i-n junction.

Fig.3 Schematic view of a three-level system which consists of the ground state in the left dot, the ground state and first excited state in the right dot in a double quantum dot device. An external field irradiates on the device and leads to the transition between two states in the right dot. Fig. 2 Shot-noise spectrum of QD excitons in a p-i-n junction. Sub-poissonian noise represented by the For a resonant external field, two black line is the result of Markovian approximation. symmetric peaks occur in the current Super-poissonian noise (red and blue lines) is the spectrum. If the field frequency is detuned, consequence of non-Markovian effect. To plot the unequal contributions from two channels lead figure, the exciton spontaneous lifetime (=1/γ) used here is 1.3ns, and the cutoff frequency for blue to two asymmetric peaks with population (red) line is 9x 1016 (1.2x 1017)Hz. Inset: Noise inversion, which can be observed with the increased by the enhancement of the effective increasing of Rabi frequency. On the other dipole moment (400 times) via superradiance. hand, as the ground states in two dots are

Research Activities of Individuals -›› 166 equal, a suppression of current occurs around the resonant frequency. In contrast, an enhanced behavior is found for the case of unequal ground states.ground states.

Fig.5 PL peak positions as a function of applied pressures

Fig.4 Current as a function of energy difference ∆ε between two ground states for different Rabi frequencies. The inset shows the currents IR (dashed curve) and Iε (dotted curve) for γ=5Γ. References [1] Yueh-Nan Chen, Appl. Phys. Lett. 90 Studies on the electronic and 162114 (2007). vibrational states of colloidal [2] Y. Y. Liao, D. S. Chuu, and Y. N. Chen, CdSe/ZnS quantum dots under high Phys. Rev. B. 75, 125325 (2007). [3] C. T. Yuan, Y. C. Lin, Y. N. Chen, Q. L. pressure Chiu, W. C. Chou, D. S. Chuu, W. H. In addition to the theoretical works, I also Chang, H. S. Lin, R. C. Ruaan, and C. M. collaborated with the experimental group in Lin, Nanotechnology 18, 185402 (2007). National Chiao-Tung University. We studied the electronic and vibrational states of colloidal core/shell CdSe/ZnS quantum dots at room temperatures by using high pressure optical measurements. Pressure dependent quadratic lattice behavior can be observed clearly from photoluminescence (PL) and Raman spectras up to ~7 GPa. This quadratic relationship is consistent with theoretical prediction. The average pressure coefficients for PL and Raman measurements, as well as deformation potential are 32 meV/GPa , 4.2 cm-1 and -1.69 eV, respectively.

167 ‹‹- Research Activities of Individuals Research Activities on Particle Physics Phenomenology

Kingman Cheung (Department of Physics, National Tsing Hua University; email: [email protected]) Center scientist, 2007/11/1~2009/10/31

I joined the Center as a Center The Higgs boson decay mode into two Scientist on November 2006. I am pseudoscalar bosons (h ➝ ηη) plays the role also the convener for the focus group on of relieving the so-called little hierarchy "Collider, Astroparticle and BSM". You may problem and easing the tension between the find some materials here the same as those LEP2 Higgs boson mass bound and the listed under the focus group. My research area precision data. However, the emergence of h is in particle physics phenomenology. ➝ ηη decay mode has undesirable effects on the golden search modes (h ➝ γγ,ηη) of the Introduction Higgs boson at the LHC. This is because when ➝ The upcoming LHC is the place for the the branching ratio B(h ηη) increases to 0.7 next big discovery. More than half of the (in order to solve the little hierarchy problem), ➝ resources in high energy community will be the branching ratio B(h ηη) goes down to ➝ put into it. Together with other planned about 0.25 and B(h γγ) will go down by a cosmology experiments, testing new ideas factor of 4 or more. This will significantly beyond the standard model (SM) will be the worsen the chance of detecting an major activities in the next 10-20 years. My intermediate-mass Higgs boson at the LHC. role is to link up theory and experiments. In The LHC may not be able to find the Higgs past years, I have accomplished a number of boson if the two-pseudoscalar decay mode works on supersymmetry, Higgs physics, extra dominates. Our Letter explicitly shows that the dimensions, and other new physics. I made associated production of the Higgs boson with predictions for the most interesting features of a W or Z boson can recover the loss of some well-motivated models, such as split sensitivity in the golden modes. With the supersymmetry, large extra dimensions, Higgs boson decaying into two pseudoscalar unparticle, etc. In addition, I also made bosons, which further decay into 4 b jets, interpretations for some anomalous results in together with at least a charged lepton from the experiments, including the muon anomalous W or Z boson decay, a significant Higgs boson magnetic moment, pentaquarks, quark-lepton signal is observable at the LHC. We found that complimentarity, etc. They will be some of the the invariant mass spectrum of the 4 b-tagged most important physics topics at the LHC. In jets (shown in the figure) can beautifully the following, I highlight two topics that I feel distinguish the Higgs signal peak from the very exciting. continuum background. One can also reconstruct the mass of the Higgs boson as A twist in the search for the Higgs well as the mass of the pseudoscalar boson. boson Since the ultimate goal of the LHC is hunt ➝ The title of the paper is "Role of h ηη in for the Higgs boson, which is responsible for the search of intermediate-mass Higgs boson electroweak symmetry breaking and mass at the Large Hadron Collider", authored by generation, our work fully establishes the Kingman Cheung, Jeonghyeon Song, and Qi- feasibility in searching for the intermediate- Shu Yan, published in Physical Review Letters mass Higgs boson if h ➝ ηη dominates and [1]. The paper consists of a well-motivated solves the little hierarchy problem. study and the result is very important to future search for the Higgs boson at the LHC.

Research Activities of Individuals -›› 168 collection of dU invisible massless particles, which can be unveiled by measurements of various energy distributions in the processes Z

➝ U and e-e+ ➝ – > γU at e-e+ colliders, as well as mono-jet production at hadron colliders. The new results of our Letter are that not only we work out the most important channels to observe unparticle effects at high energy colliders, but also we discover the novel propagator effect of the unparticle. Figure 1: Invariant mass spectrum M4b of the signal and various backgrounds for the bench-mark point B The novel features, induced by scale of the NMSSM. invariance, include effective 4-fermion Novel signals in unparticle physics interactions and a nontrivial phase factor, which interferes with the SM amplitudes in an This is a current hot topic in particle interesting manner The spectacular phase physics. We have finished two papers on the factor exp(–id π) associated with the subject. There are at least two more works are U propagator in s-channel can give rise to non- in progress. The first paper is a Letter, trivial behavior in a number of processes. We authored by Kingman Cheung, Wai-Yee studied the effects in the Drell-Yan process Keung, and Tzu-Chiang Yuan, and has been and in the one-loop muon anomaly. In the published in Physical Review Letters [2]. This figure, we show the fractional difference from Letter communicates very interesting results the standard model prediction around the Z that are useful to other researchers taking up pole. Interesting interference pattern can be the challenge in unparticle physics. seen clearly. We have also written a comphrensive paper on the subject, which is also published in Physical Review D [3]. The paper listed the formalism, derivations, and the results for important phenomenology of unparticle. We believe that the paper will be well cited and useful to others. The subject is about the scale invariance or, in broader terminology, conformal invariance. Our existing particle theory is not conformal invariant, as the invariance is obviously Figure 2: Fractional difference from the SM prediction of the Drell-Yan invariant mass spectrum for broken by all the discrete masses of particles. 2 various at the Tevatron in units of 1 . Banks and Zaks in the 80s showed that a λ number of supersymmetric field theories References contain a conformal window such that the [1] K. Cheung, J. Song, and Q.-S. Yan, Phys. theories can develop IR fixed points, where the Rev. Lett. 99, 031801 (2007). scale is invariant. [2] K. Cheung, W.-Y. Recently, perceived by Georgi a scale Keung, and T.-C. invariant sector (coined unparticle) with a non- Yuan, Phys. Rev. Lett. trivial infrared fixed point at a higher energy 99, 051803 (2007). scale may actually describe the real world at [3] K. Cheung, W.-Y. high energy. So he visualized what kind of Keung, and T.-C. physics that such a sector can induce in high Yuan, Phys. Rev. D76, energy phenomenology. The unparticle with a 055003 (2007). scale dimension dU can be interpreted as a

169 ‹‹- Research Activities of Individuals Research Activities on Cosmic Acceleration and Dark Energy

Je-An Gu (email: [email protected]) Assistant research scholar, 2006/8/1~present

y research is focused on the cosmic dark energy) which by assumption is acceleration and dark energy. The responsible for the cosmic acceleration. cosmic acceleration at the present epoch is one of the most mysterious phenomena. Its existence was first suggested in 1998 by type I. Inhomogeneity Ia supernova (SN Ia) data, and was further reinforced recently by updated SN Ia data and In this topic I try to answer two WMAP measurement of cosmic microwave fundamental questions: 1. Is the FLRW background (CMB). Most of the explanations cosmology a good approximation? 2. Can for this mysterious phenomenon invoke some inhomogeneity generate acceleration? exotic energy source, as generally called "dark Regarding the first fundamental question, energy", which provides significant negative via perturbative analysis it was shown by pressure and repulsive gravity to drive the Ishibashi and Wald in 2005 that the correction expansion to accelerate. However, both the on the Einstein equations contributed from the existence of the cosmic acceleration and the perturbations to the background RW metric is need to invoke dark energy as the origin are negligible under some conditions for the model dependent and should be seriously perturbations, and therefore FLRW is a good questioned and carefully investigated. approximation. However, regarding long-time, Our current knowledge about the cosmic large-scale phenomena such as the cosmic acceleration is very limited. We just realize evolution, the validity of perturbative analysis that the current observational results indicate is doubtful and whether the conditions invoked the present universe is undergoing an therein fit the real situation of our universe accelerating expansion which is defined in the needs further check. FLRW cosmology, a simplified cosmological In my work I followed the same model. In reality, i.e., regarding the real perturbative approach while keeping several situation of our universe, we do not know terms involving time and spatial derivatives. I whether the observational results really found that, opposite to the result mentioned suggest the existence of the cosmic above, the contributions from the perturbations acceleration, corresponding to which the may be significant when the perturbations vary definition of acceleration for the evolution of a violently in space-time (i.e. with regard to space is an essential issue. In addition, we do high-frequency or large-wave-number modes). not know in our real universe whether the inhomogeneities can generate the cosmic Regarding the second question, we found acceleration and explain the observational examples of accelerating expansion based on results (in particular, the SN Ia data), or the Lemaitre-Tolman-Bondi (LTB) solution, introducing dark energy (or other exotic which is an exact solution of the Einstein sources) is necessary. equations for a spherically symmetric dust fluid. These examples illustrate the strong In my research, in one way I investigate the correlation between acceleration and possibility of generating accelerating inhomogeneity. These results strongly support expansion via inhomogeneities, and in the the suggestion that inhomogeneity can induce other way I study possible natural ways of acceleration. These counter-intuitive generating small cosmological constant (or acceleration examples also give us a hint about

Research Activities of Individuals -›› 170 how our understanding of the interplay of This surprising numerical coincidence gravity and the space-time evolution between these two energy gaps prompts us to (including the cosmic evolution) may go the wonder whether these two hierarchy wrong. They open a new perspective for problems are indeed related (in a fundamental understanding the cosmic evolution. way). In our work we suggest that the same Randall-Sundrum (RS) brane-world setup to address the hierarchy problem about the weakness of gravity (i.e. why M >> M ) may II. Dark Energy and Hierarchy Pl SM also address the smallness problem of the Recent observations imply that dark energy cosmological constant. Relying on this is likely to be a cosmological constant with connection as our guidance, we explore the –3 4 vacuum energy density ρDE~ (10 eV) . If dark possibility of interpreting the Casimir energy energy is indeed a cosmological constant density induced in a SUSY-breaking brane which never changes in space-time, then it world as the cosmological constant, with the must be a fundamental property of the space- observed value of dark energy as a reference. time. This would then introduce a new energy Invoking the RS warp geometry and Higgs- –3 scale, 10 eV, which is 15 orders of magnitude gravitino coupling on smaller than the Standard Model scale, MSM ~ the TeV brane for TeV. SUSY-breaking, we There has been another long-standing demonstrate that the hierarchy problem in physics, i.e., the 4D Casimir energy on existence of a huge gap between the Planck the brane indeed 19 2 scale MPl of quantum gravity at 10 GeV and scales as TeV / MPl, that of the standard model gauge interactions remarkably, just right at TeV, by a factor ~ 1016, which is roughly at for the dark energy. the same order of the above-mentioned hierarchy.

171 ‹‹- Research Activities of Individuals Research Activities on Atomic Physics

Hung-Cheuk Ho (email: [email protected]) Postdoctoral researcher, 2006/5/16~present

y current interest is mainly in the As shown in the table, the two set of many-body perturbation theory experimental hfs constants a and b differ, but (MBPT) calculation of atomic structure of the constants c agree within uncertainty. The heavy atoms. Ongoing projects include theoretical values are also in disagreement relativistic third-order MBPT calculation of with measurement. The calculation of a in Ref. the hyperfine structure (hfs) constants of [2] is a third-order one, while those of Ref. [4] Cesium-133. is an all-order single-double with partial triple

2 (SDpT) one. The 5% difference between these Experimentally, the 6 P3/2 state hf splitting of 133Cs has been measured accurate to five two values is probably due to the different significant figures by Gerginov et al. [1] This nuclear charge distributions used, and the fact accuracy enabled the first determination of a that gauge-invariant RPA matrix elements are non-zero magnetic octupole moment of 133Cs in used in Ref. [2], but not in Ref. [4]. 2003. Ref. [1] is a combined experimental and Precise hfs calculations for heavy alkali- 2 theoretical study of hfs of the 6 P3/2 state of metal atoms are of particular interest, as they 133Cs. Its calculation is based on an all-order provide a check for the accuracy of atomic method. And to our knowledge, this is the only wavefunctions. Highly accurate wavefunctions relativistic many-body calculation of the hfs are required for atomic parity nonconservation constant c reported for this case. In this regard, (PNC) calculations. Our group's work on PNC it would be very interesting to perform a is in progress. different hfs calculation to compare with both their measurement and computation. We are extending our previous work of hfs References: studies of 133Cs. [2] In that work, we evaluated [1] V. Gerginov, A. Derevianko, and C.E the off-diagonal hfs matrix element between Tanner, Phys. Rev. Lett. 91, 072501 2 2 the 6 P1/2 and 6 P3/2 states, and the constant a (2003). 2 for the 6 P3/2 state. Now, we calculate the hfs [2] W.R. Johnson, H.C. Ho, and C.E Tanner, constants b and c for the electric quadrupole Phys. Rev. A, 70, 014501 (2004). and magnetic octupole couplings. Particular [3] D. Das and V. Natarajan, Europhys. Lett. care has to be taken for the nuclear charge 72, 740 (2005). distribution, because the constant c is very [4] M.S. Safronova, W.R. Johnson, and A. sensitive to the charge distribution (the radial Derevianko, Phys. Rev. A, 60, 4476 integrand in c depends on r-4). Therefore, the (1999). more sophisticated Fermi nuclear distribution [5] R.K. Chaudhuri and C. Sur, arXiv: is used. physics/0406083 The following table shows a comparison of v1 (2004). 133 2 recent reported values of Cs 6 P 3/2 hfs constants in MHz:

a b c 50.28827(23) [1] -0.4934(17) [1] 0.00056( 7) [1] 50.28163(86) [3] -0.5266(57) [3] 0.00087(32) [3] 48.51 [4] 139Q (b)* [1] 0.00068Ω (bxµN)[1] 51.09 [2] -0.559 [5]

* The value of the nuclear quadrupole moment Q used to obtain b is not specified.

Research Activities of Individuals -›› 172 Research Activities on Condensed Matter Physics

Wen-Hsuen Kuan (email: [email protected]) Postdoctoral researcher, 2006/2/1~present

ecently, my research interests are structure is described by a macroscopic mainly focusing on two fields: Bose- envelope function, which can be obtained by Einstein Condensation and Spin-Orbit Effect solving the effective-mass-Gross-Pitaevskii on Low Dimensional Semiconductor Quantum equation. By applying small perturbations on Structures. The main research results achieved the system, the dynamics of the condensate is during this year are as follows: investigated via the exploration of collective excitation spectrum. Different from analyses in I. Analysis of instabilities and the Niu's works,2 we provide an unified theory of breakdown of superfluidity of Landau and dynamical instabilities in optical Bose-Einstein condensates in lattices.3 In addition to the phonon excitation, optical lattices our theory shows that the generation of low energy antiphonons plays the crucial role on The observation of superfluid flow in the the dissipation of superfluid.4 It can be weakly interacting Bose gas has the system understood as follows: In the unidirectional served as an ideal paradigm for understanding flow, the counter-motion of phonons and superfluidity. The existence of a critical antiphonons should be governed by the velocity in BEC cloud also verifies Landau's Doppler effect such that the contributions on argument on the phonon generation and the the excitation spectrum differ quantitatively. onset of instabilities in the superfluid He-4. Such a loss of superfluidity was investigated The numerical simulation within Landau experimentally by studying the dynamics of instability regime fits quite well with the BECs in a periodic optical potential.1 Burger experimental results in Ref. 2. However, the et. al. showed that when the velocity of the consistency close to the dynamical instability condensate is lager than the sound velocity, the regime is still lacking. To revise the fraction of atoms remaining in the superfluid discrepancy, we propose to consider part decreases, showing the evidence of the perturbations on the condensate with negative onset of Landau instability. The superfluid effective mass. We expect a power-low like diminishes when the condensate travels faster deduction of the fraction of superfluid atoms and interacts strongly with the lattice. We can be reached if the life time of the unstable claim that the condensate might enter into the condensate is long enough to be observed. dynamical instability regime where the Before the collapse of the superfluid number of quasiparticles grows exponentially condensate, cold atoms may have the thus to impart energy into the flow and destroy possibility to locate at a metastable state if the superfluid. In this regime, Bogaliubou de there is a local minimum in the potential Gennes approach to the description of energy functional. Otherwise, the condensate superfluid dynamics breaks down. may undergo a macroscopic quantum To confirm our arguments and demonstrate tunneling5 to the dense state where the two- the collective flow of BECs, we simulate the body dipolar collision and three-body inelastic dynamics of BECs in a quasi-1D shallow collision occur frequently. We apply the optical lattice. Atoms in the superfluid part instaton technique and variational method to traveling with the group velocity via k.p investigate the decay mechanism. By using approximation. The group velocity that sum rules in the estimation of collective deduced from the dispersion of the band modes, the bounce exponent shows a five-

173 ‹‹- Research Activities of Individuals fourth power relation to the condensate profile is highly anisotropic. We expect that number. Evaluations and competitions on the dipolar Gross-Pitaevskii equation can be decay rates of the mentioned routes are also exactly solved in a fully numerical calculation. taken at finite temperatures. 6 We propose to use the Monte Carlo integration method in dealing with a many-dimensional II. Dipolar Bose-Einstein calculation. Eventually, the optimal set of Condensation beyond Born parameters of trial wave functions can be approximation determined via the variational method in the sort of the lowest energy solution. Recently attained BEC gas of highly magnetic chromium atoms shows a signature of dipolar interactions.7 This opens a door for III. Rashba and Dresselhaus spin- investigations on the dynamics of cold atoms orbit interactions on the spectral in strong electric field under which the long properties, magneto-optical range dipole-dipole interaction may have excitations, and generation of dc profound effect. Moreover, it provides a better spin currents in low dimensional understanding on the formation of the BEC semiconductor quantum molecules and the mechanism in BEC-BCS structures phase transition. Recently, applications on spin-orbit Yi and You8 first introduced a interaction (SOI) originated from the breaking pseudopotential approach for describing of inversion symmetry that gives rise to slowly moving particles interacting via short- intrinsic spin splitting in semiconductor range contact potential and the long-range systems open a field of spintronics. It was dipolar force. However, their approach based pointed out that the quantum transport of on first Born approximation (FBA) that valid electrons in a spin-polarized system differs only in the low energy scattering regime. The greatly from that in a spin-degenerate device. weak interaction assumption breaks down near The success of dc front-gate control for the scattering resonances. Therefore, it is crucial measurement of Rashba coupling strength to develop a full many-body theory for dipole inspires proposals for spin current generation beyond FBA. by nonmagnetic means. These proposals include adiabatic quantum pumping in a In the recent work of Wang,9 the first quantum dot with static SOI interfaced with a effective many-body theory that is capable to time-dependent barrier and a spatially describe bosonic dipolar condensates even separated Rashba SOI region, and an ac-biased near the shape resonance (SR) or in the Rashba-type two-dimensional (2D) disorder strongly interacting regime has been derived. system or quantum channel. It is known that Using the scattering matrix elements the translational invariance is broken in the calculated by Deb et. al.10 the dipolar effect channel direction due to a spatially localized near SR is found to be significantly time-dependent potential, thus allowing us to renormalized so that the system becomes more explore coherent resonant inelastic scattering stable than what is predicted using simple and time-modulated quasi-bound state FBA. Moreover, the elementary excitation of features.11 the 2D condensate behaves as q in the long wavelength limit, showing the same low In one work, we have studied magnetic- energy physics as 2D charge bosons with optical transitions in a semiconductor double Coulomb interactions. ring in the presence of Rashba spin-orbit coupling and the magnetic flux.12 First, based The effective Hamiltonian beyond FBA in on accurate numerical calculations we obtain 3D has been derived, and the ground state SOI-accompanied Aharonov-Bohm energy energy is calculated by using the Gaussian spectra and corresponding eigenstates. The type trial wave function. However, it is presence of the SOI has important influences inadequate to do so while the condensate on the occurrence of level crossings showing

Research Activities of Individuals -›› 174 the evidence both for the periodic orbital device is achievable using a single ac-biased motion and spin flips. We have also studied gate, and should be achievable within recent the temporal evolution processes in a two-level fabrication capability. and two three-level models. The interaction between external fields and the electron results in the successive stimulating absorption and References emission of a photon and turn out as the [1] S. Burger, F. S. Cataliotti, C. Fort, F. effective Rabi oscillators. In the two-level Minardi, and M. Inguscio, Phys. Rev. Lett. model, we demonstrate an alternative 86, 4447 (2001). manipulation of electrons transiting between [2] B. Wu and Q. Niu, Phys. Rev. A 61, two rings. Moreover, by short pulse excitations 023402 (2000); B. Wu and Q. Niu, Phys. we also demonstrate the possibility on optimal Rev. Lett. 89, 088901 (2002). control of selective and direct signals. Finally, [3] W. H. Kuan and S. C. Cheng (preprint PRA we have explored the photon-assisted 2007). tunneling in the -type model. In addition to λ [4] W. H. Kuan and S. C. Cheng (preprint PRL generation of ROs also we give the criterion of 2007). the most efficient transfer via the mediated- [5] M. Ueda and A. J. Leggett, Phys. Rev. Lett. indirect-tunneling paths. Further, by 80, 1576 (1998). successive pulse irradiations the well control [6] W. H. Kuan and S. C. Cheng (preprint PRA on pulse delay results in the time prolongation 2007). on state populations. We should also [7] J. Stuhler, A. Griesmaier, and T. Koch et. emphasize that in the -type scheme the λ al., Phys. Rev. Lett. 95, 150406 (2005). minimization of the intermediate-level [8] S. Yi and L. You, Phys. Rev. A 61, 041604 population is achieved which is an important (2000); ibid. 63, 053607 (2001). and practical strategy in device realization. [9] Daw Wei Wang, cond-mat 07043868 Further, we investigate non-adiabatically (2007). how the dc spin current is generated under the [10] B. Deb and L. You, Phys. Rev. A 64, mechanism of SOI using a dynamical all 022717 (2001). electrical control on a split-gate-confined [11] L. Y. Wang, C. S. Tang, and C. S. Chu, narrow channel.13 We have demonstrated Phys. Rev. B 73, 085304 (2006). nontrivial features concerning the spin current [12] W. H. Kuan, C. S. Tang, and C. H. Chang, generation mechanism caused by different Phys. Rev. B 75, 155326 (2007). strength of Dresselhaus spin-orbit coupling. [13] C. S. Tang, W. H. Kuan, and Y. C. Chang These results provide a robust manner of (preprint PRB 2007). generating spin current without accompanying charge current. The spin current generating features have been demonstrated and illustrated in detail. It has been found that the Dresselhaus spin-orbit coupling intends to suppress the efficiency of spin current generation in the low kinetic energy regime, while the Dresselhaus effect can enhance the pumped spin current in the high kinetic energy regime. Unlike the parametric quantum pumping, in which two pumping potentials with a phase difference is needed. Our proposed spin current generating

175 ‹‹- Research Activities of Individuals Research Activities on Spin Physics

Yung-Chang Lee (Physics Department, University at Buffalo, SUNY, Amherst, NY 14260; email: [email protected]) Visiting professor, 2007/3/15~2007/7/31

his must have been my 10th or 11th instrumental to the development and visit to Taiwan, since my first formulation of science, and physics in sabbatical leave which was spent at Physics particular. Department, Tsing Hua University for two Overall, I am happy and excited to see semesters during the academic year of 1971- science in bloom, much more so than in the 1972. These visits were all sponsored by the past decades. The leadership of the various same government agency, "The National university administrations such as those of Committee of Science". They spanned over a NTHU, NCTU, NTU, NCKU and NSYSU, the period of 36 years, averaging about one visit funding from government agencies and, last every three years. but by no means least, the improved policies I have witnessed the considerable with respect to the independent focus groups continuous growth of science and technology, and their implementation by NCTS have all physics in particular, over more than a third of contributed to the progress of science in a century. It is, therefore, with great pleasure Taiwan. Finally, the very successful and satisfaction, as well as nostalgia that I international symposiums, one on "Two- write this report on probably my last extended dimensional Transport involving the complex visit to Taiwan, now that I am pondering Interplay of Localization and Electron- retirement within two or three years. Electron Interaction Effects", the other on "Twenty years Anniversary of Discovery of Compared to what I saw and experienced in the High-Tc Superconductor YBCO" must be my last sabbatical leave also at Electrophysics counted as the crowning events during my stay Department, NCTU seven years ago, I have in Taiwan. I have benefited greatly from both seen much higher level in quality and quantity events. of creative output from many young faculty members and science workers who have Starting from the second week after arrival, worked independently and also benefited from I gave seminars at different universities, the collaboration, guidance and, more including (i) Institute of Physics, NCTU (ii) importantly, the stimulating atmosphere Physics Department, National Taiwan created by the more senior members of the University (iii) Physics Department, NCKU physics community. In particular, Professors and (iv) Physics Department, National Sun D. S. Chuu, Chon-Saar Chu in NCTU, among Yat-sen University. many others, had successfully guided Interestingly, the titles evolved over time numerous Ph. D and M.S. students, post- from "Macroscopic Quantum Interference doctoral fellows, young Assistant Professors without Cold Temperatures" to "Quantum who have matured into independent Entanglement and Macroscopic Quantum researchers. Similar achievements by other Interference without Cold Temperatures" to members in the academic community all over the final title "Quantum Engagement and Taiwan are too many to be listed. It must also Microscopic Interferences en masse in a be mentioned that the participation of leading Coherently Mixed Bose Gas". This reflected foreign experts from Russia, Japan such as the work being in progress as these talks were Professor A. G. Mal'shukov etc., on short or given. Eventually it was published as last titled long term basis have provided innovative in J. Phys.: Condens. Matter 19 (2007) ideas, vision, and wisdom that are so 376214. We believe it contains a totally new

Research Activities of Individuals -›› 176 concept, namely, "quantum engagement" that spin-Hall effect" was supervised by Prof. C.S. is akin to but more than the familiar concept of Chu. This thesis will soon be published jointly quantum entanglement. While the latter is a by Chen, Chu, and Mal'shukov as an article in purely quantum mechanical correlation, the Physical Review B. former is intrinsically a quantum statistical This series of seminars continued almost correlation for bosons not in physical space weekly (except for national holidays) until late but rather in spin space. In the last section of June when (a) I got stuck, and (b) my wife acknowledgement of this paper, "One of the succumbed to the hot and humid weather authors (YCL) would like to thank Professor coupled with highly polluted air in Hsinchu. C. S. Chu of the National Center for She developed a health (allergy) problem so Theoretical Sciences, National Chiao Tung bad that the physicians strongly advised us to University (Taiwan) for hosting his visit ..." go back to our home base in the US as soon as Another series of seminars on "High we can. Temperature Superconductivity" was started To conclude this report I would be remiss if since the end of March, 2007, given I did not express my deepest gratitude to exclusively in Electrophysics Department, NCTS, and particularly to Professor Chon- NCTU. From the very beginning of this series, Saar Chu of the focus group. Had it not been it was announced that "this would be in the for his participation as well as his most able nature of a progress report on my own work in leadership of the group, consisting of several topics related to high Tc superconductivity. I would strive to give one such seminar every faculty members and six or seven graduate week. However, it would be interrupted if I get students in various stages of research toward stuck and have nothing meaningful to report Ph. D or M.S degree, the seminar series would on until further notice..." The titles of the talks lose all its vitality. He was the center of these ranged from the Generalization of the lively physics activities and discussions, not Hohenberg Theorem; the Broken symmetry; only because of his insights in almost all the application of the Hubbard model; the aspects of condensed-matter physics, but also competition between the effects of because of his innate cordiality and Dimensionality on Superconductivity and friendliness. Without exception, every body Antiferromagnetism; an elementary Review of likes him because he is so genuinely nice to Magnetism; the Spin in Dirac equation for a every body. You might say it stems from his two-band Semiconductor; and First order (v/c) Christian faith, but I'd say it is much more. Relativistic Effect (i.e., without spin-orbit Professors J. F. Jiang, Y. J. Lin, B. L. Yang, coupling) in Spintronics. The last two topics and, of course, my dear old friend of forty were conceived and developed after serving on years, Prof. Der-San Chuu who is venerated by the Master degree oral defense committee of all, provided the magic that jelled the Mr. K. Y. Chen, whose thesis "Resonant ingredients of the seminars together. generation of spin dipole by a gate-induced

177 ‹‹- Research Activities of Individuals Research Activities on Spintronics

Hsiu-Hau Lin (Department of Physics, National Tsing Hua University; email: [email protected]) Center scientist, 2006/2/1~2008/1/31

Spintronics at Nanoscale exchange coupling varies with junction width. It is rather remarkable that the trend of the non-collinear exchange coupling depends on the Fermi surface topology of the itinerant n the past year (2006-2007), I have carriers. For instance, a "wedding cake" been working on various aspects of topology favors the known RKKY-like spintronics at nanoscale. Extending our interaction while a "donut" shape change the previous work on spin-wave theory, we tried to trends to spiral, which is more useful for spin develop a self-consistent Green's function manipulations at nanoscale. (description for diluted magnetic) semiconductors [see Phys. Rev. Lett. 86, 5637 (2001)]. Treating both localized and itinerant spins on equal footing, we go beyond previous studies on thermodynamics and discover interesting trends of spin-wave dynamics [see Appl. Phys. Lett. 89, 072101 (2006)]. We predicted that the spin-wave relaxation in diluted magnetic semiconductors would decrease first and eventually increase again when temperature increases. This is completely opposite to our understanding in conventional magnetic materials.

Meanwhile, combining both analytic and numerical approaches, we found a novel ferromagnetism in the armchair graphene nanoribbons. Our findings highlight the crucial importance of the electron-electron interaction and its subtle interplay with the boundary topology. The resultant magnetic ground state with metallic conductivity is not only surprising from an academic viewpoint, but also has potential applications in spintronics at nanoscale in the future. Our work attracted some attentions in the With the developed spin-wave theory, we international community and I was invited to started to investigate the non-collinear several workshops/conferences to present our exchange coupling [see Appl. Phys. Lett. 89, research results. In the following, I will 2862 (2004)] mediated by itinerant carriers in describe the research results in details. trilayer magnetic junctions. For either Zeeman interaction [Appl. Phys. Lett. 89, 032503 Diluted Magnetic Semiconductors (2006)] or Rashba interaction [Phys. Rev. B Carrier-mediated ferromagnetism, found in 73, 241307 (R) (2006)], we calculated how the

Research Activities of Individuals -›› 178 diluted magnetic semiconductors (DMS) such results go against common intuition. For as III-V semiconductors doped with transition instance, in the RKKY phase, the spin metals, opens up the possibility of electric relaxation actually decreases with increasing manipulations of magnetic and optical temperatures. properties because of the exchange coupling The magnetization curve and the spin between the localized moments of the relaxation rate are closely related. In addition, transition metal and the itinerant spins in the they also sensitively depend on the density semiconducting bands. In recent years, ratio n_h/n_I. This is reminiscent of the experimental progress has stimulated intense interesting differences between as-grown theoretical investigations of DMS which samples and annealed ones. The annealing mainly focus on estimates of the critical process removes interstitial impurities and temperature. Although some experimental data reduces the disorder strength. However, if the is available little theoretical attention has been as-grown sample is already in the diffusive paid to spin dynamics, which is crucially regime, the annealed one can also be described important in understanding the spin coherence. by the virtual crystal approximation. We believe the major difference arises from the increase in carrier density and thus the density ratio n_h/n_I. The annealing process increases n_h/n_I from the strong coupling to the RKKY phase which changes the shape of the magnetization curve. Therefore, it would be exciting to study the spin dynamics for both as-grown and annealed samples and compare the experimental outcomes with our numerical predictions. Note that we did not include the realistic six-band Luttinger model here. In We employ a self-consistent Green's principle, our approach can be generalized to function approach to investigate the spin-wave include more bands by introducing more relaxation Gamma(p) in diluted magnetic Green's functions but the self-consistent semiconductors. We find the trend of the spin- equations will be rather complicated, not fatal wave relaxation strongly depends on the ratio though. However, it is important to emphasize of the itinerant and impurity spin densities. For that the ratio n_h/n_I to enter the RKKY density ratios in the so-called Ruderman- regime is expected to be larger, as compared to Kittel-Kasuya-Yosida phase, Gamma(p) the estimate from the two-band model. decreases even though thermal fluctuations increase. On the other hand, in the strong Carrier-Mediated Non-collinear coupling phase, an interesting peak structure Exchange Coupling appears. The central theme of spintronics is to To analyze how spin waves relax in DMS, manipulate the extra spin degrees of freedom both the itinerant and impurity spins need to be in condensed matter systems as compared with treated on an equal footing. We employ the the traditional electronic devices where only self-consistent Green's function approach that the charge part was utilized. One of the classic retains both spatial and thermal fluctuations, to examples, which merges charge and spin investigate the spin-wave relaxation at finite sectors together in a single device is the spin temperatures. The Green's functions allow us field effect transistor (SFET) proposed by to numerically compute the spin spectral Datta and Das more than a decade ago. It was function and therefore the spin-wave suggested that the Rashba interaction, whose relaxation. One may naively expect a smooth strength is controlled by the gate voltage, increase in the spin-wave relaxation as thermal causes the spins of the itinerant carriers to fluctuations grow. However, our numerical spiral and can be used to modulate the

179 ‹‹- Research Activities of Individuals transport currents. Another more recent rise to the oscillatory RKKY interaction. To proposal, now under the name of spin Hall explore the subtle competition between the effect, explores the possibility to generate spin spiral and the RKKY interactions, one needs to currents (or spin accumulations) by electric integrate over the whole Fermi surfaces by gates via spin-orbital interactions and has numerical approach. received some primitive verification in The outcome is rather surprising -- the experiments. dominance of either spiral or RKKY interactions depends on the topology of the Fermi surface. When the Rashba interaction is weak (compared with the Fermi energy), the Fermi surface consists of two cocentered circles with opposite chiralities. In this regime, the RKKY interaction dominates over the spiral. However, as one gradually increases the strength of the Rashba interaction, the inner Fermi circle shrinks to zero first, reappears On the other hand, it is less explored how again but with the same chirality as the outer the spin-orbital interaction will reshape our circle. The topological change of the Fermi understanding in the more conventional surface magically alters the dominant coupling magnetic junctions. We study the non-collinear from the RKKY to the spiral. Therefore, in the exchange coupling across the F/N/F trilayer strong Rashba limit, the non-collinear magnetic junction (TMJ), where the exchange coupling mainly comes from the intermediate layer consists of semiconductors spiral interaction with minor quantum (such as GaAs) with significant Rashba corrections. It is rather amazing that the interaction. Since the TMJ resembles the transition between different magnetic Datta-Das SFET, one may naively guess that behaviors coincides with the change of the the carrier-mediated exchange coupling can be Fermi surface topology. explained following similar arguments. Within the single-particle picture, Datta and Das had Magnetism in Armchair Graphene demonstrated the spins of the itinerant carriers Nanoribbon undergo precessions due to the Rashba One of graphene's superior properties is its interaction and, therefore, lead to the non- pronounced ambipolar electric field effect. By collinear coupling between the ferromagnetic applying gate voltages, the charge carriers can layers. be tuned between electrons and holes with However, there is a sharp difference concentration up to 1013 cm-2. Making use of between SFET and TMJ. In the SFET, the the sensitivity to the electric field, Son, Cohen time-reversal symmetry is broken (by the and Louie demonstrated zigzag graphene source-drain bais which drives the current) nanoribbons (GNR) can become half metallic while, in the TMJ, the symmetry is preserved and their magnetic properties can be controlled and gives rise to Kramers degeneracy. In fact, by the external electric field. Their results not this non-trivial degeneracy has a profound only show that the electronic spin degrees of influence upon the effective exchange freedom can be manipulated by the electric coupling across the junction. It turns out that fields, but also bring up the possibility to the single-particle picture (with specific explore spintronics at the nanometer scale momentum) employed in Datta-Das' original based on graphene. work fails to explain the magnetic behavior Since open boundaries of GNR play a because the inclusion of the whole Fermi crucial role at nanoscale, we expect the surface is crucially important. For instance, the interplay between Coulomb interaction and the quantum interferences between the Kramers- edge morphology will lead to rich physics. It is degenerate patches of the Fermi surfaces give

Research Activities of Individuals -›› 180 As a result, the magnetic properties of armchair GNR sensitively depend on the doping and thus can be manipulated by the external electric fields. Besides its potential applications to spintronics at nanoscale, the ferromagnetic ground state in the armchair GNR also reveals a new type of flat-band ferromagnetism, different from those proposed by Mielke and Tasaki. The key to Mielke-Tasaki ferromagnetism is the finite overlap of then interesting to study GNR with armchair adjacent Wannier orbitals in the flat band. edges. Note that the edges are hydrogenated so Once the so-called local connectivity condition that the dangling sigma bonds are saturated is achieved, the finite overlaps generate and only the pi bands remain active in low exchange coupling among these orbitals, energy. By combining analytic weak-coupling leading to flat-band ferromagnetism. However, analysis, numerical density matrix the Wannier orbital in armchair GNR has zero renormalization-group (DMRG) method, and overlap with its adjacent neighbors. The flat the first-principles calculations, we show that band alone only accounts for the existence of armchair GNR exhibits novel carrier-mediated the magnetic moments and the ferromagnetic ferromagnetism upon appropriate doping. order sets in only when itinerant carriers are present. Even though only pi bands are active in low-energy, in appropriate doping regimes, the armchair edges give rise to both itinerant Bloch and localized Wannier orbitals. As will be explained later, these localized orbitals are direct consequences of quantum interferences in armchair GNR and form flat bands with zero velocity. The carrier-mediated ferromagnetism can thus be understood in two steps: Electronic correlations in the flat band generate intrinsic magnetic moments first, then the itinerant Bloch electrons mediate ferromagnetic exchange coupling among them.

181 ‹‹- Research Activities of Individuals Research Activities on Spin Physics

Kao-Chin Lin (email: [email protected]) Postdoctoral researcher, 2006/12/1~present

y last research topics before I was which the Kondo effect interacting quasi- offered the postdoctorship from the particle is scattered by the EPAUT and in NCTS is the electron-photon interaction the form of the direct product of the associated with the uncertainty based EPAUT coupling energy and Green tunneling (EPAUT). During the earlier period function of Kondo effect. as the postdoctor in NCTS, my main project is (2) The characteristic temperature is to continue my previous research. The interdot calculated. There are three regions of Coulomb interaction and the Kondo effect are temperature. When the detuning factor is considered. larger than the characteristic temperature, I considered the electron interacting with the characteristic temperature decreases the detuning photon field quantum exponentially with the incensement of mechanically in a parallel coupling double detuning factor. When the detuning factor quantum dot(DQD) system. In the DQD is in order of or smaller than the system, each QD is coupled to the lead and characteristic temperature, the EPAUT is becomes a subsystem. I employed the detuning dominated by the thermal effect and the photon field to open an energy-time characteristic temperature is insensible of uncertainty for electron tunneling between QD the detuning factor. and lead. The process in which electron (3) Besides the detuning factor, the EPAUT tunnels between the QD and the lead via the effective electron-photon coupling strength energy-time uncertainty is called electron- is tunable via tuning the Fermi energy of photon associated uncertainty based tunneling the lead. The strength of the EPAUT and (EPAUT) in my research. electronic current via the EPAUT channel Some new results are pointed out as are maximum when the energy difference follows. between the energy levels of QDs and the energy difference (1) Unlike the Kondo effect in which the between the Ferm Coulomb interaction is the necessary energy of the condition and is a two particle problem, the subsystems are EPAUT is arised even the situation in equal. which one electron is considered or the Coulomb interaction is ignored. I Should These results have emphasized that the EPAUT is not equal to been submitted to PRB the Kondo effect. This factor is reflected on and Journal of physics : the EPATU corresponding self-energy in Condensation matter.

Research Activities of Individuals -›› 182 Research Activities on Accelerated Detector - Quantum Field System

Shih-Yuin Lin (email: [email protected]) Assistant research scholar, 2006/8/1~present

y research is mainly on theories of from the initial ground state over an infinitely quantum particles or atoms coupled long duration of interaction derived from time- with quantum fields. I have been working on dependent perturbation theory is existent in the this topic in collaboration with Prof. Bei-Lok exact solution only in transient under special Hu at University of Maryland since 2004. We limiting conditions corresponding to the are looking at the properties of the vacuum, Markovian regime. Furthermore, the detector the response of the accelerated particle to the at late times never sees an exact Boltzmann vacuum, the radiation emitted by the distribution over the energy eigen-states of the accelerated particle, and the radiation reaction free detector, thus in the non-Markovian to the particle in curved space. regime covering a wider range of parameters the Unruh temperature cannot be identified We had worked out a complete, exact inside the detector. evolution of the Unruh-DeWitt detector theory in (3+1) dimensional Minkowski space [1], While we have broadened the research on which can be related to quantum Brownian the Unruh effect to the realm of non- motion of harmonic oscillators. The radiation equilibrium statistical physics, we are emitted by the detector and observed at the currently focusing on the modern quantum null infinity of Minkowski space has been information issues in the Unruh-DeWitt obtained from initial transient to final steady detector theory. Using our non-perturbative state. results we are able to look at the quantum decoherence and recoherence processes in a Applying the non-perturbative results we single detector as well as the quantum obtained in Heisenberg picture, we expressed entanglement between two accelerated the reduced density matrix in terms of two- detectors over the whole parameter range. We point functions to study the quantum statistical expect that our results can help to answer the property of the detector. We discovered new questions of the entropy and information features in the dynamical evolution of the raised in black hole physics and quantum detector's internal degree of freedom, and gravity. identified the Unruh effect derived originally from time-dependent perturbation theory as operative in the ultra-weak coupling and ultra- high acceleration limits [2,3]. The mutual interaction between the detector and the field References [1] S.-Y. Lin and B. L. Hu, Phys. Rev. D 73, engenders entanglement between them, and 124018 (2006) [gr-qc/0507054]. tracing out the field leads to a mixed state of the detector even for a detector at rest in [2] S.-Y. Lin and B. Minkowski vacuum. Different from those L. Hu, Found. conventional results in which the quantum Phys. 37, 480 field's back-reaction is ignored, our findings (2007) [gr- based on the exact solution shows clearly that qc/0610024]. the detector no longer behaves like a perfect [3] S.-Y. Lin and B. thermometer. From a calculation of the L. Hu, Phys. Rev. evolution of the reduced density matrix of the D 76, 064008 [gr- detector, we find that the transition probability qc/0611062].

183 ‹‹- Research Activities of Individuals Research Activities on Spin Transport in Semiconductors

Anatoly G. Mal'shukov (Institute of Spectroscopy, Russian Academy of Sciences and Department of Electrophysics, National Chiao Tung University; email: [email protected]) Center scientist, 2007/1/1~2008/6/30

n 2007 my research activity in NCTS of spin polarization directed parallel to the has been focused on spin transport in quantum well has been also predicted. A very semiconductors. Most of the work was on the convenient way to observe these effects is spin-Hall effect (SHE) and related phenomena. STM with a magnetic tip. With some A conventional set up for studying this effect modification our results can be applied to is a 2D quantum well with an electric field metal surfaces carrying surface states with a applied parallel to the heterointerface. This large spin orbit splitting. field drives a spin current in the direction As known, the spin-Hall effect leads to perpendicular to it. Spins in such a current are accumulation of the spin polarization near the oriented along the normal to the quantum well. sample boundaries. The spin density can be Since the spin current consists of two counter also accumulated near impurities. We fluxes of oppositely directed spin considered [2] the nonequilibrium spin density polarizations, the total polarization in the around a potential barrier having the form of a normal direction is zero. At the same time, the mesoscopic 2D ring. The spin orbit interaction spin polarization of 2DEG in the parallel caused by gradients of the potential is strongly direction is not zero due to the so called enhanced due to semiconductor band structure. electric spin orientation effect which is closely We found that the accumulated spin related to SHE. Together with Prof. C. S. Chu polarization has the form of a dipole. from NCTU we considered [1] SHE and the Moreover, the strength and the sign of a dipole electric spin orientation in a set up quite strongly depend on the position of the Fermi different from the conventional one. Instead of level with respect to transmission resonances the planar electric current, which drives SHE of the ring structure. Besides this special and spin orientation, we considered a geometry, we are considering [3] a traditional tunneling current perpendicular to the quantum problem of spin accumulation near boundaries well. A rectangular double barrier system was of a 2D strip with Rashba and Dresselhaus taken as a model. An important distinction interactions plus a magnetic field parallel to from the traditional approach is that one can the quantum well. We found that there is no not consider such a problem using a spin-orbit spin accumulation when only Rashba interaction (SOI) averaged over quantum well interaction takes place, independent on the confinement. To make this distinction more presence or absence of the magnetic field. clear we considered a symmetric quantum well where Rashba SOI is absent after averaging The spin relaxation rate is an important over confinement. In such a situation one parameter for various spintronic applications. should consider the initial SOI associated with In semiconductors at low temperatures the gradients of material parameters across the major mechanism of spin relaxation is the so QW heterointerface. It has been shown that called D'yakonov- Perel' relaxation due to the this SOI, together with the bulk Dresselhaus SOI effect. It has been shown several years interaction, give rise to the electric spin ago that this mechanism is strongly suppressed orientation with polarization directed in systems with restricted geometry. For perpendicular to the quantum well. The current example, a dramatic slowdown of the spin relaxation has been predicted for quantum

Research Activities of Individuals -›› 184 wires. Indeed, such a slowdown has been Resonant spin dipole induced by an in- recently observed in quantum wires. The plane potential gradient in metallic observed behavior, however, does not agree conduction, Phys. Rev. B, accepted well with theoretical predictions, based on the [3] L.Y. Wang, C.S. Chu, A.G. Mal'shukov, in diffusion approach to spin transport. Together preparation with Prof. C. H. Chang [4] we tried to [4] C.H. Chang, A.G. Mal'shukov, understand such a discrepancy using a method Semiclassical path integral approach to of classical trajectories. This method can be spin relaxation in quasi-1D wires, in applied for calculation of the spin relaxation preparation time within a broad range of parameters, including a ballistic case. Now this work is in progress.

References [1] A.G. Mal'shukov, C.S. Chu, Spin orientation and Spin-Hall effect induced by tunneling electrons, submitted to Phys. Rev. B [2] K.Y. Chen, C.S. Chu, A.G. Mal'shukov,

185 ‹‹- Research Activities of Individuals Research Activities on Condensed Matter Physics

Baruch Rosenstein (Department of Electrophysics; email: [email protected]) Center scientist, 2007/1/1~2007/12/31

uring last several years there is a clear research in the area of condensed matter trend in experimental physics to physics in strong magnetic fields. This advance towards construction of facilities overlaps with activities of both the providing magnetic fields in the 100 Tesla Correlated Electron Systems and range. Existing facilities include the NHMFL, Mesoscopic Physics focus group. For this Tallahassee (45T DC), Los Alamos 60 (100 ms several leading physicists should be invited pulse) and just completed Dresden 100T as visitors. (10ms). These facilities are profoundly 2. Organize International workshop on the different from those appearing ten years ago in topic. Japan and elsewhere which could provide only a very short pulse in this range. The new 3. Organize education of graduate student by facilities operate in the DC mode or in the giving a course on physics in magnetic frequency range suitable for condensed matter fields. The field is highly specialized and research. Taiwan is also currently considering separate from other topics (for example, building such a facility. The 50-100T range notoriously dominated by the Landau levels opens a lot of new possibilities for condensed concept, less dissipation, spin's importance). matter physics (as well as for certain material science, biological sciences experiments). Accomplished goals Examples of already existing areas are: 1. I started the research in this field and will Quantum Hall effect (fractional QHE and continue it next half a year. Includes both newer discoveries can be observed only above analytical methods (with help of NCTS 30T), deHaas-van Alfven effect in metals and visitors V. Zhuravlev (Max Planck, superconductors, vortex matter in high Tc Dresden) and D.P. Li (Beijing U) and superconductors (which have Hc2 above numerical. 100T), dephasing in disordered metals and semiconductors, magnetism (phase diagram of 2. Have given a course for both NTHU and manganites extends well into 50T range) and NCTU graduate students on the topic. spin physics. Physically the 100T range 3. Have given a 3 hour lecture at NCTS as part corresponds to magnetic length in the of the "Introduction" course. nanometer range and energy range of 0.1 eV. 4. Started to organize a program and a European Union have already organized workshop in collaboration with Argonne International conference on Theoretical National lab. It includes inviting several Physics in High magnetic fields (Correlated leading experts in the field including Dr. Electrons in HMF, Ein Gedi, Israel, December Vinokur (Argonne) and A. Gurevich 2004 and Recent Trends in Theory of Physical (Magnetic lab., Phenomena in High Magnetic Fields II, Tallahassee). Will Dresden, Germany, October 2006) . The field use the designated definitely requires theoretical support. First money textbook on the physics in high magnetic (200.000$NT) to fields have already appeared (Vagner et al, invite speakers to Springer) the workshop that is planned for My mission was December 2007. 1. To initiate and promote a cutting edge

Research Activities of Individuals -›› 186 Research Activities on Quantum Control of Qubits

Kazuomu Shiokawa (email: [email protected]) Visiting scientist, 2006/4/4~present

uantum information science and analyze. Most common approaches are to technology is currently one of the invoke Born-Markov type approximation. most active fields of research in science. It is However, at low temperature and strong also an interdisciplinary field that overlaps system-bath interactions where many with many different areas in theoretical and experiments in quantum information are experimental sciences including computer performed, this approximation is no longer science, mathematics, engineers, chemistry, valid. Other common methods such as weak physics, etc. Thus it provides a good topic to coupling approximations do not guarantee the be pursued at the institute such as NCTS positivity of quantum state evolution and may which has interdisciplinary themes and not be reliable for the precise analysis of resources. quantum properties sensitive to this issue such In quantum computation, its capability of as quantum entanglement. Therefore the exact providing the solution for certain problems solutions are extremely useful for the faster than classical computer has important fundamental understanding of the nature of practical applications such as communications quantum computing at low temperature. and cryptography. However, actual implementation of quantum information processors requires the precise manipulation of small quantum systems with high precision. The most serious obstacle against the realization of quantum processors is the interaction with its surrounding environment which destroys quantum coherence, the essential resource of fast computation. This physical process is called decoherence. Therefore, it is crucial to understand the precise mechanism of decoherence and invent better and realistic methods to prevent quantum processors from decoherence. Most naïve theories of quantum computing assume a coupled-spin system. This naïve model fails to explain the realistic phenomena in many ways when it comes to the specific implementation. In a recent few years, I have been developing systematic methods to study quantum computation in a general environment. In my previous works [1] and [2], some exact solutions for generalized spin boson models are found and analyzed. The spin-boson model is a standard model Fig. 1 The decay rate of population at T=0 in (a) and at for qubits in a general open quantum T=20 mK in (b). The solid curve is our exact result, environment. Reduced dynamics of this model while the dashed lines are from using the Born- follows nonlinear evolution and is difficult to Markov Apporoximation Ω=1 GHz, γ=0.2 GHz, and Λ=100 GHz.

187 ‹‹- Research Activities of Individuals In Figure 1, the exact evolution of the Fig. 2 (a) Coberence as a function of pulse interval at T=0 decay rate is plotted and compared with the is plotted. t=0.25(ns). Parameter are: ΛUV=100(GHz), ΛIR=1, γ=0.125(GHz) for Ohmic, and Born-Markov result for zero and finite γ=0.005(GHz) for super-Ohmic case. (b) Plots of the temperature. The decay rate under exact first excited state population at T=0 and t=0.15(ns). evolution is strongly time-dependent while it is Other parameter values are: ΛUV=100(GHz), just a constant under Born-Markov Ω=1(GHz), γ=0.1(GHz) for Ohmic, and Λ =100(GHz), Ω=1(GHz), γ=0.5(GHz) for 1/ƒ, approximation. UV ΛUV=50(GHz), Ω=10(GHz), γ=0.01(GHz) for super- With the close solutions for generalized Ohmic case. Parameter values are chosen to fit all the curves in the parameter range in the figure, For spin boson models, it is possible to explore the the same parameter values, while their qulitative external pulse control of quantum bits in more behavior remains similar, the differences in their detail than previously done by other methods values are more striking. under various approximations [5]. In Figure 2, the effects of dynamical In order to protect quantum devices from decoupling pulses are shown. The pure environment-induced decoherence, various dephasing model (a) and exact generalized quantum error correcting codes are invented spin-boson model both show the performance [3]. Dynamical decoupling is an active way of more effective on decoupling 1/f noise and protecting qubits by using a fast control pulse less effective on super Ohmic noise. Important to cancel the net effect of environment before difference is that the former (in (a)) shows the it leads to destroy the coherent evolution of the complete elimination of coherence at the system. It was shown to be extremely effective resonant pulse frequency, who appears to be to eliminate the 1/f noise which is a common disastrous. However, this is not observed in source of decoherence of qubits where the laboratory experiments. Our exact solution (in control is provided by electronic devices [4]. (b)) does not show such behavior and correctly agrees with experiments.

References [1] K. Shiokawa and R. Kapral, J. Chem. Phys. 117, 7852 (2002). [2] K. Shiokawa and B. L. Hu, Phys. Rev. A 70, 062106 (2004). [3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, (2000). [4] K. Shiokawa and D. A. Lidar, Phys. Rev. A 69, 030302 (2004). [5] K. Shiokawa and B. L. Hu, Quantum Information Processing, V. 6, 55 (2007).

Research Activities of Individuals -›› 188 Research Activities on String Theory

Yi Yang (email: [email protected] Assistant Research Scholar, 2006/8/1 – present

y research interesting is on string interesting subject and extended it to the cases theory, and string related theories. of closed string and superstring. The similar During the last year, I have been working linear relations were found. In the last year, we mainly on the study of the relationship further extended our study to the case of between the high energy behavior of string including D-brane. D-brane is a non- scattering amplitudes and the hidden perturbative soliton-like object in string symmetry in string theory. As it is well known, theory; its existence extraordinarily enriches the most important property of string theory is the string backgrounds. We systematically that string theory is a finite theory, i.e. string studied closed strings scattering from a rigid theory does not need renormalization to get a (i.e. no back reaction) D-brane in [1, 2, 3], we physical result. This wonderful property is found that, for most of the D-branes, there are because of the milder high energy behavior of similar linear relations among the high energy string scattering amplitudes comparing to the string scattering amplitudes. While for a conventional quantum field theory (QFT). In domain-wall brane, i.e. a (d-2) dimension D- QFT, the high energy behavior of scattering brane in d dimensional space-time, the linear amplitudes follows a power law. On the other relations break down. We then found that, hand, the high energy behavior of string when the linear relations breaking down, the scattering amplitudes enjoys an exponential exponential-law behavior reduces to a power- law, which decreases much faster than the law behavior at the same time. This is a perfect power law. This faster decrease in ultra-violet anti-example to validate our conjecture that the (UV) leads to the finite results in string theory. symmetry (linear relations) corresponds to the However, in string theory, there are infinity high energy behavior of string scattering massive modes in UV comparing to the finite amplitudes. To clear our point, we recently modes in QFT. Instinctively, people will think studied winding closed strings scattering in a that in the high energy limit, there will be compact space-time in [4]. Another anti- more and more scattering channels contribute example was found in this case, i.e. when we to the amplitudes in string theory and make it move from Gross regime to Mande regime, more divergent than in QFT. Therefore, there some of linear relations break down, and the must be a hidden symmetry in string theory to corresponding high energy scattering induce a cancellation among the infinity amplitudes will be reduced from exponential- channels. This symmetry should be infinity law to a power-law. large. Study this hidden symmetry directly is Recently, I am interesting in studying the so difficult, we therefore turn to study the high called AdS/QCD duality. This is a realistic energy scattering amplitudes for the fixed version of the original AdS/CFT duality in mass levels. In our previous work, we have string theory. In AdS/CFT duality, the type IIB proved that for any fixed mass level in string string theory in an Anti-de-Sitter (AdS) space- theory, the different amplitudes are linear time is conjectured to dual to an N=4 related each other although they have different supersymmetry Yang-Mills field theory, which tensor structures. It is then natural to is a conformal theory (CFT) on the boundary conjecture that these linear relations of AdS space-time. Compatifying a space correspond to the hidden symmetry in string dimension on a circle to break all theory. We continued our study in this supersymmetries, and adding flavor D-branes,

189 ‹‹- Research Activities of Individuals the boundary field theory is conjectured to dual to QCD. Of many AdS/QCD models, Sakai-Sugimoto model is the most promising References one and has been studied extensively during [1] C.T. Chan, J.C. Lee and YY, Scatterings of the last several months. Some meson spectrum Massive String States from D-brane and was calculated by AdS/QCD and the results Their Linear Relations at High Energies, have been compared to the experimental data hep-th/0610062, Nucl.Phys. B764 (2007) and to lattice QCD, a good agreement was 1-14. obtained. In addition, spontaneously chiral [2] C. Chan, J.C. Lee, Y.Y., "Power-law symmetry breaking has been constructed in the Behavior of Strings Scattered from model and Goldstone boson is identified with Domain-wall and Breakdown of Their pion, whose action is consistent with Skyrme High Energy Linear Relations", hep- model. The AdS/QCD at finite temperature th/0610219. has also been studied. Confinement- [3] J.C. Lee, Y.Y., "Linear Relations of disconfinement, S/ SB phase transitions χ χ Absorption/Emission Amplitudes of D- were studied; the results are consistent with brane", hep-th/0612059, Phys.Lett. B646 the ones obtained by lattice QCD. However, (2007) 120-124. there are still many questions remained in the model. Now I am collaborating with the NCTS [4] J.C. Lee, Y.Y., "Linear Relations and their members in phenomenology focus group. We Breakdown in High Energy Massive String are going to systematically study the Scatterings in Compact Spaces", AdS/QCD for different string backgrounds and arXiv:0705.1872, (Accepted by Nucl.Phys. the corresponding "QCD" theories. Hopefully B). we can effectively fixed the parameters and to make some predictions for the coming LHC. During the last year, I have attended two conferences. One is in Vietnam where I given a talk about my work in NCTS. The other is the annual conference of Strings2007 in Spain. I would like to thank NCTS to support me attending the international activities.

Research Activities of Individuals -›› 190 Research Activities on Computational Materials Research

Zizhong Zhu (Department of Physics, Xiamen University; email: [email protected]) Visiting professor, 2007/3/8~2007/9/8

started my visit of Taiwan on March cooperation with Prof. Guo during this 8, 2007, and returned home on visit. September 7, 2007. The duration of my visit is Except for many communications with six months. Under the support of National material scientists in Taiwan, I have also Center for Theoretical Sciences (NCTS), I had attended several mini-schools supported by the the honor to have visited several universities NCTS. I have gained many new ideas and and institutions in Taiwan and discussed with learned a lot of advanced information of many scientists who are experts in the field of modern material physics, which will be of computational material sciences. I benefit a lot great importance in my future studies. The by these discussions and have also created mini-schools are: many opportunities for future cooperation. Here, I present a brief report on my experience (1) March 2007, the "Mini-school on time- and achievement of this visiting. dependent Density Functional Theory", hold at National Taiwan University; (2) May 25-26, On the aspect of academic interactions: 2007, the "Mini-School on Tight Binding (1) I gave a talk of "First-principles, Molecular Simulation of Nanomaterials", hold at Dynamics and EAM potentials: recent National Cheng Kung University; (3) August works in our CMP group" at the Physics 27-28, 2007, the "Mini-School on Fast O(N) Department of National Taiwan University Electronic Structure Calculations: Principles on March 22, 2007, and have discussed and Implementation in the OpenMX package", with Prof. G. Y. Guo and his group hold at National Taiwan University. members as well as the graduate students. On the aspect of scientific research: (2) On April 10, 2007, I presented a talk I have cooperated closely with Prof. G. Y. "Computer Simulations on some Guo of National Taiwan University, and Nanostructures: classical MD and Ab initio carried through the studies on the "Magnetism methods" at the Institute of Physics, of Nanostructured s- and sp-electron Academia Sinica, and discussed with Prof. Elements". The possibilities of elements with Horng-Tay Jeng and other scientists from only s- or sp-valence electrons to exhibit the nanomaterials research group. magnetism under nano-scale structures have (3) May 21-22, 2007, I visited National Chung been explored. We have shown that these Cheng University, and gave a talk on the systems can show magnetism under either "Ab initio method and Classical MD bond elongation or bond compression at one- Simulations on Nanostructures". I have dimensional chain structures. The paper is now also discussed with Prof. T. C. Lueng as in preparation. We have also calculated the well as the graduate students. electronic and structural properties of Li MSiO (M = Mn, (4) On May 28, 2007, I visited National Sun 2 4 Fe, Co, Ni) for the Yat-Sen University, and discussed with modern lithium-ion Prof. Feng-Chuan Chuang on the batteries. The paper computational material physics. has been under (5) On August 23, 2007, I presented a talk at revision. the group of Prof. G. Y. Guo of National Thank you very Taiwan University. The title is "Magnetism much for giving me of Nanostructured s- and sp-electron the opportunity to visit Elements: Ab initio calculations", which is Taiwan. basically a summary report of my research

191 ‹‹- Research Activities of Individuals Introducing New Members

Prof. Chung-Hsien Chou

Center scientist (Ph.D., National Tsing Hua University) email: [email protected]

efore joining the National Center for (1) High energy physics: We need to go Theoretical Sciences, I was a beyond Standard Model physics, but how? postdoctoral researcher at Institute of Physics, What s the nature and properties of dark Academia Sinica from where I started my energy and dark matter? What s the research career after graduating from the origin and nature of the ultra high energy National Tsing-Hua University under the cosmic rays? How to consistently combine supervision of late Prof. Darwin Chang. quantum mechanics and general relativity? During my stay at Academia Sinica, I benefited from the active and stimulative (2) Quantum information science: With a atmosphere and gradually enlarged my scope particle physicist background, my interest of research. Not only particle physics in quantum information science focus on phenomenology, astroparticle physics, the application of field theory techniques to quantum theory of gravity, and quantum examine fundamental issues in quantum information science are all on my list. mechanics such as quantum decoherence, My research interests can be broadly quantum entanglement, quantum characterized in two categories: teleportation, etc.

Dr. Kazuyuki Furuuchi

Staff scientist (Ph.D., Osaka University) e-mail: furuuchi @phys.cts.nthu.edu.tw

research interest is on deeper commutative space, string field theory, matrix understanding of the laws that govern models and black hole thermodynamics via elementary particles and the universe. In the AdS-CFT correspondence. past I have worked on instantons on on-

Introducing New Members -›› 192 Dr. Takayuki Hirayama

Postdoctoral researcher (Ph.D., Kyoto University) email: [email protected]

am a NCTS postdoc starting from Meanwhile I have been applying AdS/CFT for September 2007. My interest in analysing strongly coupled gauge theories and theoretical physics is wide including QCD, for modeling new physics at TeV scale like extra dimensions, SUSY and SUSY breaking, Higgsless models. black holes, AdS/CFT, D-branes and string I like to discuss various topics, model building theory. I have been approaching the physics and phenomenology, field theory, more stringy beyond SM through field theoretical analysis. stuffs and so on.

Prof. C.-J. David Lin

Staff scientist (Ph.D., University of Edinburgh) email: [email protected]

y research hightlight last year of heavy quark spin symmetry breaking in includes: the operators. We also used these results to investigate finite-volume effects in these 1). The investigation of matrix elements of matrix elements, and found that they would neutral B mixing using Heavy Meson be a few percent on currently available Chiral Perturbation Theory: With William lattices. Finite-volume effect in one of the Detmold, we studied the chiral behaviour matrix elements is plotted as a function of of these mtrix elements and discovered that the pion mass in the figure. the light-quark mass dependence of the matrix elements for B mixing beyond the 2). Numerical calculations in lattice gauge Standard Model would be more theory: Since I moved back to Taiwan in complicated than that of the Standard February, I have been setting up facilities Model matrix element. We identified the for numerical calculations in lattice gauge origin of this complication to be the effect theory. These include the purchase of a PC cluster dedicated to such research avenue and the tests of softwares (QMP, QDP and CHROMA) on such a cluster. In the future, I will use these facilities to investigate the role played by strongly-coupled gauge theories in LHC physics. In addition to QCD matrix elements for the LHCb programme, I am also working on topics such as Walking Technicolour and the Banks-Zaks infrared fixed point.

193 ‹‹- Introducing New Members Dr. Yu-Pin Luo

Postdoctoral researcher (Ph.D., Chung-Yuan Christian University) email: [email protected]

n 2005, I got Ph. D. degree in Chung- Ising model on two-dimensional lattices with Yuan Christian University. During the periodic/aperiodic boundary conditions. Then post-graduate study for my Ph.D. degree, I after military service for one year, now I am mainly worked on two directions, one is the postdoctoral research associate in NCTS. protein folding problem and the other is the

Dr. Tzu Chiang Yuan

Assistant research fellow (Ph.D., Northeastern University) email: [email protected]

earned my PhD at 1986 from early universe, CP violation, quarkonium Northeastern University under the physics, QCD corrections to Higgs processes, guidance of professor Pran Nath. My thesis hot QED, etc. work was about low energy phenomenology of In the past two years since I came to minimal supergravity model, including muon NTHU, I had been collaborated with various anomalous magnetic moment, proton decay physicists in different institutions and worked and production of gaugino pair from electron- on various phenomenology topics including positron annihilation. glueball, little Higgs, hidden milli-charged During my various postdoc career at fermion in Stueckelberg Z' model as dark Vanderbilt University, Northwestern matter, etc. My most recent work is about University and University of California at unparticle physics. My research interest is Davis, I had explored other areas of particle mainly in the area of phenomenology beyond physics and had made important contributions. the standard model and its implications in These includes topics in phase transition at collider physics as well as astrophysics.

Introducing New Members -›› 194 101, 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://math.cts.nthu.edu.tw/Mathematics/index.html http://phys.cts.nthu.edu.tw

October 2007