A n u a l R e p o r t N a t i o n l C e r f

October 2008 Annual Report

o r October 2008 T h e o r

Annual Report National Center for Theoretical Sciences e t i c a l S n s

National Center for Theoretical Sciences

101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013 O c t o b e r 2 0 8 Mathematics Division Physics Division Tel: 886-3-5728263 Tel: 886-3-5734969 Fax: 886-3-5728161 Fax: 886-3-5735086 e-mail: [email protected] e-mail: [email protected] http://www.math.cts.nthu.edu.twl http://phys.cts.nthu.edu.tw I. Words from the Director ----- 1

II. Mathematics Division ------2 Report of the Division Head ------3 Executive Committee Members ------5 Academic Committee Members ------6 Highlights of the Programs ------7 Activities of Onsite Scientists ------50 Preprints ------61 Appendix ------69 I. Visiting Mathematicians ------69 II. Conference, Workshop & School ------79

III. Physics Division ------85

Report of the Division Head ------86 Highlights of Programs ------92 Focus Group Complex System ------92 Condensed Matter Physics ------95 Particles and Fields ------107 Interdisciplinary Fields ------126 Working Group Plasma Science ------134 Softmatter and Nonlinear Physics ------138 Research Activities of Individuals ------144 Introducing New Members ------183

Annual Report Publisher: Editors: National Center for Theoretical Sciences Jing Yu Mandy Chen(Mathematics Division) October 2008 Sherry Pang(Physics Division) Words from the Director

he second phase of interdisciplinary researches NCTS operation in theoretical sciences. starts from January 2004 till Besides Mathematical December 2008. This is the Biology, Bioinformatics, and last year. National Science Biological Physics in which Council (NSC) has focus programs are actively conducted an on-site review going on, a new initiative of NCTS this January. this year is in the direction Basing on the report of the of theoretical Statistics. In review committee, and the the subproject at NCKU, a suggestion of the steering program on Statistics committee of NCTS, the methods including NSC made the decision in Biostatistics has been July, to continue supporting implemented and well NCTS with a third phase received. In 2009, further operation, from January 2009 to December interdisciplinary program relating to 2014. The basic operating framework remains theoretical Statistics are expected to be the same, with main project at Hsinchu, incorporated into the main project. We cohosted by NTHU, NCTU, and NCU, one anticipate that new international research team subproject at Taipei hosted by NTU, and in this direction will also be formed in the near another subproject in southern Taiwan future. cohosted by NCKU and NSYSU. The detailed When NCTS started its operation 11 years proposal for the 3rd phase is being worked out ago, one of its mission in our mind is to by all participating parts at this moment. modify the landscape of theoretical sciences This year we enjoyed the newly expanded research in Taiwan. On the international and renovated space of the headquarter of stages, there were important research areas in NCTS at the campus of NTHU. Located on which Taiwanese scientists didn't take part. We the 4-th and 5-th floor of the 3rd general made efforts and we now see some changes. building, this expanded space puts the Physics Mathematical Physics is one such area. Division and the Mathematics Division under Dynamical Systems is another. In the direction one roof, working more closely together. The of interdisciplinary researches, theoretical new 1st guest house of NTHU, after one year sciences relating to Biology is also becoming running, also was highly acclaimed by all our an important trend in Taiwan. New research visitors. There is yet another new guest house groups started to form, existed research groups of TCTU nearby. Thus as far as hardware is become more established, as the on-site concerned, we are ready to enter into the 3rd review committee remarked in January. We phase of NCTS. look forward to another 10 years of NCTS with success. We continue our efforts of promoting

1 ‹‹- Words from the Director Mathematics Division Report of the Division Head

his is the last year of the 2nd phase (Canada) and Arizona Arithmetic Geometry operation of NCTS. We are now Center this year, we also supported two planning a detailed proposal for the 3rd phase advanced students to do research abroad for of NCTS, 2009-2014, and looking forward to three months, one at Max-Planck Institute further develop the roles play by NCTS in the (Bonn), the other one at Fields Intitute (with global mathematics research. On the one hand, local expenses supported by Fields). Another we are searching for the new division head to initiative this year is a Taiwan-Tohoku lead NCTS. On the other hand, we are workshop supported by NCTS in April, considering new strategies and initiatives which can bring us to new grounds. organized by E. Yanagida (Tohoku U.), and Jann-Long Chen (NCU), with two Ph.D. There was an on-site review of NCTS students from Taiwan visiting Tohoku, conducted by an international committee in interacting with Ph.D. students on differential January 2008. The report of this committee on equations in Tohoku U. The second round will the mathematics division is very positive and be in Jan. 2009, to be held at NCTS, with 6 encouraging. Japanese Ph.D. students coming interacting In the main project, the three hosting with our Ph.D. students of differential universities now offers 15 center scientists equations. These are a bilateral activities, each positions for the mathematics division. In side pays their own air tickets. 2008, we have five from NCTU, three from Papers from NCTS Math Preprint Series NTHU, and two from NCU. Among them, one of previous years continue to appear in in Algebraic Geometry, one in Algebraic important international journals. We are happy Topology, one in Classical Analysis, three in to report, in particular, the paper: Elliptic Dynamical Systems, two in Number Theory, Functions, Green Function, and the Mean Field and one in Scientific Computation. Equation on Tori, by Chang-Shou Lin and We have committed firmly to the Chin-Lung Wang had recently been accepted cultivation and support of young generations. by Annals of Math. This paper was singled out In last decade the summer internship program in 2006 NCTS report as important at NCTS grows steadily, those undergraduate breakthrough. It is also the third paper from interns of past years now studies in top NCTS in two years accepted by the prestigious graduate schools of the States, Europe, as well Ann. Math. Mathematics papers usually take a as in Taiwan. Past research assistants (one year longer period for refereeing than papers from position at NCTS) are becoming post doctors other fields, for a preprint to appear in print or young faculties in Taiwan after getting their one may need more than two years after it is Ph. D. degrees from great universities abroad. submitted. Submitting to top journals usually Besides (partially) supporting graduate take more time. On the other hand, students to attend important international mathematics works also need more years to summer/winter schools, e.g. Fields Institute have its impact fully come out. The AMS

3 ‹‹- Report of the Division Head Math SciNet therefore keeps track a record of range of pure and applied mathematics. NCTS all the important math journals, counting is happily cooperating with all these university citations of five years, as contrast to the SCI institutions, working together for the common impact factors which count citations only in goal of developing theoretical sciences in two years. Taiwan. However, the role of NCTS is also distinct from and complement to these In the on-site review report this year, the university institutions. The population of following research contributions were mathematicians in Taiwan as compared to the highlighted : total population, is still far below the (a) A sharp bound for the pluri-canonical map developed countries, such as Japan, France, to be rational for threefolds which are U.S. etc. As a result, we dont have enough either of general type or Fano. critical mass in any theoretical science (b) Invariance of the quantum cohomology research field. In order to have research man ring after analytic continuation on the power in a particular field comparable to, say Kähler moduli. Tokyo University which has 60 permanent (c) An important result on the three body faculties in mathematical science, we actually problem by the variational method. have to group all the work forces of several (d) Determined all algebraic relations among universities. NCTS is for such a purpose. special zeta values and gamma values in Under topical program of NCTS, local positive characteristic. mathematicians in the same field are pulled together for going out to various international Since the five year five million project of stages. We can win together. the Ministry of Education started two years ago, the leading research universities in Finally, the Young Theorists Award of Taiwan have put more resources into basic NCTS enters its 2nd year, with three theoretical sciences. This is very encouraging. mathematicians receiving this award : Guan- At National Taiwan University, the Taida Yu Chen (NCTU), Ming-Yi Lee (NCU), and Institute of Mathematical Sciences TIMS was Jyh-Haur Teh (NCTU). G.-Y. Chen specializes established, with Chang-Shou Lin, previous in probability theory and related topics, with director of NCTS, as director. At National degrees from both Cornell U. and NCTU. M.- Tsing Hua University, CMS, a Center for Y. Li is analyst graduated from NCU, and now Mathematical Sciences founded with Sze-Bi works also on certain PDE. J.-H. Teh works on Hsu as director, and at National Central algebraic geometry and topology, had his University, also a Center for Mathematics and degree from Stony Brook. These recipients Theoretical Sciences was set up, with Y. R. were selected by our executive committee Lin-Liu as director. TIMS with fully support basing on evaluation of all the applicants by from NTU is particularly active, with many international experts. seminars, courses going on, covering a wide

Report of the Division Head -›› 4 Executive Committee Members

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

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

Committees Affiliation Jung-Kai Chen National Taiwan University Shun-Jen Cheng Academia Sinica Sze-Bi Hsu National Tsing-Hua University Jonq Juang National Chiao Tung University Yng-Ing Lee National Taiwan University Song-Sun Lin National Chiao Tung University Tai-Chia Lin National Taiwan University Dong-Ho Tsai National Tsing Hua University Julie Tzu-Yueh Wang Academia Sinica Wei-Cheng Wang National Tsing Hua University Soon-Yi Wu National Cheng Kung University Jing Yu National Tsing Hua University Xuding Zhu National Sun Yat-sen University

Executive Committee Members -›› 6 Highlights of the Programs

D.1 Algebra

Coordinators: Shun-Jen Cheng (Academia Sinica) Meng-Kiat Chuah (National Tsing Hua University)

his research group focuses on various Vyjayanthi Chari (University of California - aspects of Lie theory and their related Riverside), Minoru Wakimoto (Kyushu applications. They include Lie University), Jun Morita (University of superalgebra representations, group Tsukuba), Catharina Stroppel (University of representations, vertex operator algebras, finite Glasgow), Yun Gao (University of York), groups, quantum groups, and related Seok-Jin Kang (Seoul National University). combinatorial structures. Most of the scholars of this topic reside in three major research Hsinchu centers (Academia Sinica, National Tsing Hua Jing-Song Huang (Hong Kong University University and National Cheng Kung of Science and Technology), Kyo Nishiyama University). They form a close connection and (Kyoto University), Hiroshi Yamashita support the activities organized by these (Hokkaido University), Cheng-Bo Zhu centers. (National University of Singapore).

D.1.1 Local Algebra Group (in Tainan alphabetical order) Kyo Nishiyama (Kyoto), Hiroyuki Ochiai Shun-Jen Cheng (AS), Meng-Kiat Chuah (Nagoya), Ruibin Zhang (Sydney), Hiroshi (NTHU), Chu-Chin Hu (NTNU), Po Yi Huang Yamauchi ( Aichi), Gerald Hohn ( Kansas (NCKU), Wen Fong Ke (NCKU), Ching Hung State), Toshiyuki Abe ( Ehime), Hiroki Lam (NCKU), Ngau Lam (NCKU), Chufeng Shimakura (Aichi), Christian E. Lomp (Univ. Nien (NCKU), Shu-Yen Pan (NTHU), Chian- do Porto), Koichi Betsumiya (Jobu), Robert Jen Wang (NCTS), Yi-Fan Yang (NCTU). Griess (Michigan), Gunter Pilz (Linz), Hubert Kiechle (Hamburg). D.1.2 Visitors D.1.3 Seminars Academia Sinica A student seminar is held in Academia Jae-Hoon Kwon (University of Seoul), Sinica approximately 4-6 times every month. Alistair Savage (University of Ottawa), Guanglian Zhang (Shanghai Jiaotung Students are given reading assignments and University), Motoko Kotani (Tohoku are then asked to present them in class. University), Jie Xiao (Tsinghua University), Sometimes faculty members also give talks in Jonathan Brundan (University of Oregon), this seminar. Topics include representation Alexander Kleshchev (University of Oregon), theory of the general linear group in George Lusztig (MIT), Nicolai Reshetikhin characteristic p following Zelevinsky, the (University of California - Berkeley), classification of TDS of semisimple Lie

7 ‹‹- Highlights of the Programs algebra following Kostant, the theory of Oregon), George Lusztig (MIT), Nicolai translation functors following Jantzen, Reshetikhin (University of California - representation theory of Yangian following Berkeley), Vyjayanthi Chari (University of Molev, the determination of the Shapovalov California - Riverside), Minoru Wakimoto determinant for the generalized Verma (Kyushu University), Jun Morita (University modules following Jantzen etc. of Tsukuba), Catharina Stroppel (University of Glasgow), Yun Gao (University of York), During July and August 2008, two student Seok-Jin Kang (Seoul National University) seminars are organized at Hsinchu for the NCTS summer interns. Meng-Kiat Chuah runs NCTS Winter Workshop on a student seminar on Lie algebras, and Shu- Representation Theory, January 23-27, Yen Pan runs a student seminar on prime 2008 at NCTS (Hsinchu) numbers. Subject: Representation theory of Lie groups A regular seminar is run weekly at NCKU: by four visitors from Hong Kong, Japan and including lectures given by visitors and given Singapore, as well as topics in Lie theory by by the local group members. The main theme four local scholars. is on the representation theory. The topics include the representations of algebraic groups, Speakers: Shun-Jen Cheng (Academia Sinica), Lie super algebras, vertex operator algebras Meng-Kiat Chuah (National Tsing Hua etc. University), Jing-Song Huang (Hong Kong University of Science and Technology), Ching A student seminar is also run by Wen Fong Hung Lam (National Cheng Kung University), Ke and Ching Hung Lam at weekly basis at Kyo Nishiyama (Kyoto University), Shu-Yen Tainan. This seminar primarily aims at Pan (National Tsing Hua University), Hiroshi graduate students. The main subjects are Yamashita (Hokkaido University), Cheng-Bo Young diagrams and representations of Zhu (National University of Singapore). symmetric groups in 2007/2008. Organizers: Meng-Kiat Chuah and Jing-Song D.1.4 Workshops Huang. Workshop on Algebraic Aspects of Lie Workshop on Combinatorics and Theory, December 20-23, 2007 in Algebras. July 4-July 7, 2008 at NCKU Academia Sinica (sponsored by grants from Subjects: Parking functions, finite calculus, Academia Sinica) graphs Subject: Recent developments in Speakers: Jun Ma, Y-N. Yeh, X. Chu. representation theory, including Organizer: Po Yi Huang representations of quantum groups, e.g. the theory of canonical basis and crystal basis, finite W-algebras, Khovanov algebras, and Summer School on Lie Theory at Tainan, their connections with representation theory of Aug. 11-Aug. 19, 2008 Lie superalgebras. Further topics include Subjects: Representations of Lie groups, Lie representations of affine superalgebras and super algebras and quantum groups toroidal algebras and vertex operator algebras. Speakers: Shun-Jen Cheng (Academia Sinica), Speakers: Chin-Hung Lam (National Cheng- Meng-Kiat Chuah (NTHU), Kyo Nishiyama Kung University), Shu-Yen Pan (National (Kyoto), Hiroyuki Ochiai (Nagoya ), Ruibin Tsinghua University), Jie Xiao (Tsinghua Zhang (Sydney). University), Jonathan Brundan (University of Organizer: Ngau Lam Oregon), Alexander Kleshchev (University of

Highlights of the Programs -›› 8 NCTS/Academia Sinica Winter School in topics include representations of real Lie Representation Theory in NCTS/ TPE groups and vertex operator algebras. from December 18-December 27, 2008 Speakers include: Meng-Kiat Chuah (National The winter school is aimed at graduate Tsinghua University), Tomoyuki Arakawa students and researchers in representation (Nara Women's University, Japan) , Jae-Hoon theory and includes two 10-hour lecture series Kwon (University of Seoul, Korea), Zongzhu by given Raphael Rouquier (Oxford Lin (Kansas State University, USA), Masahiko University) and Shrawan Kumar (University of Miyamoto (University of Tsukuba, Japan), North Carolina Ð Chapel Hill). Liangang Peng (Sichuan University, China), Alexander Premet (University of Manchester, Lie Theory Workshop in Academia Sinica, UK), Raphael Rouquier (Oxford University, from December 28 to December 30, 2008 UK), Vera Serganova (University of Subject: Topics include representations theory California, Berkeley, USA), Eric Sommers of Lie superalgebras, Hecke algebras, finite W- (University of Massachusetts, Amherst, USA), algebras, and geometrical and homological Weiqiang Wang (University of Virginia, USA) methods in representation theory. Further

D.2 Algebraic Geometry

Coordinators: Hui-Wen Lin (National Taiwan University)

fter the workshop on Higher study of invariance of Gromov-Witten Dimensional Algebraic Geometry and theory under a simple flop during the winter the summer school on the latest development and spring visiting of Y.-P. Lee at NCU. of higher dimensional Minimal Model The breakthrough in this work is to achieve Program held in 2007, the year 2008 is a the higher genus invariance by combining practice year for local algebraic geometry their prior result on invariance of big researchers to carry out their works. quantum cohomology ring with C. Teleman's very recent result on In this period, although there are no big classifications of semi-simple Frobenius conferences or workshops on Algebraic structures. Lee, Lin and Wang also found a Geometry as in the previous years, many local complete proof to the invariance of algebraic geometers do make great progresses quantum rings under a splitting flop which in their researches through private research is an ordinary flop with the exceptional set seminars and oversea visiting programs. being a splitting projective bundle over the Besides, the weekly student seminar and general base. This was done during the the summer courses are still designed to summer visiting of Y.-P. Lee at NCTS. The provide students enough background for major achievement in this work is to carry advanced study on the latest development of out completely a case of ordinary flops with Algebraic Geometry. general base. D.2.1 Accomplishments 2. In this period, Jungkai. A. Chen at NTU had visited Chritopher Hacon at University 1. The NCTS frequent visitor Y.-P. Lee at of Utah. Chen and his coworkers study the Utah continues his collaboration with H.-W. basket of singularities introduced by M. Lin and C.-L. Wang. They completed the Reid in a more systematical way and

9 ‹‹- Highlights of the Programs obtained various results including: 1. Student Seminars on MMP (1.) Non-vanishing of plurigenera (resp. There are two weekly based programs antiplurigenera) for three-folds of general toward the MMP: type (resp. weak Q-Fano threefolds), (1) One is organized by C.-L. Wang and H.-W. (2.) Lower bound of canonical volume (resp. Lin and held at NCU from February 2008 anti-canonical volume) for threefolds of to June 2008. The main contributors general type (resp. weak Q-Fano include two students of NCU. Bin-Je Hung threefolds), reported the construction of Hilbert scheme and Mori's theorem on the (3.) Effective birationality of pluricanonical existence of rational curves by using the map for threefolds of general type.The Bend and Break technique. Jian-Nan Yang breakthrough of his recent work is to reported some fundamental materials in describe the relation between flips and complex geometry. "unpacking", which provide another viewpoint to attack the termination (2) The other one is organized by J.-C. Chen problem of flips. and held at NCTS from September 2007 to June 2008. The main contributors include 3. The frequent visiting graduate student three NCTS research assistants Chih-Chi Chen-Yu Chi at Harvard University and his Chou, Sung Yih and Wei-Liang Liu. advisor Professor Shing-Tung Yau, who is During the fall of 2007 they reported on also the Chair of NCTS Scientific Advisory fundamental material in algebraic Committee, have initiated a new geometric geometry as in Hartshorne's text. In the approach to problems in birational spring of 2008 they reported on the book geometry recently. By using this new by Kollar and Mori on birational algebraic approach, they provided a beautiful analytic geometry, especially on the MMP. criterion for birational equivalence between smooth varieties of general type via 2. Student Seminars on Complex checking only one pluricanonical system. Chi announced their results and gave the Geometry detailed report in two NCTS Seminars in It is a weekly based program organized by Algebraic Geometry in June 2008. C.-L. Wang and held at NCTS from March to July 2008. The main contributors include three 4. The center scientist J.-C. Chen visited NCTS research assistants Chih-Chi Chou, Kawakita at RIMS, Fujino at Nagoya Sung Yih and Wei-Liang Liu. The major focus University, Jason Starr at Stony Brook, is on Hormander's book on complex Lawrence Ein and Mihnea Popa at manifolds, especially on the L2 estimate of d- University of Illinois. His current results are bar equation. They end up with an introduction the following: to the multiplier ideal sheaves and the proof of (1.) If a variety X has only quotient Nadel's vanishing theorem. singularities and the pseudo index i > n/2 +1, then Pic(X) = 1. 3. NCTS Summer School on Algebra and (2.) Let X be a 3-dimensional smooth Algebraic Geometry Deligne-Mumford stack. Chen and his It is organized by Jyh-Haur Teh from coauthor H.-H. Tseng constructed a 2008/6/30 to 2008/8/31. This course is moduli space and proved that it is a designed for freshmen and sophomores. The crepant resolution of the coarse moduli main texts are Abstract algebra by Ash and space of X. They are trying to extend this Elementary geometry of algebraic curves by to other moduli spaces associated to X. Gibson. In the first month they run through groups, rings and fields. In the second month, D.2.2 Student Programs they study some fundamental facts of algebraic curves.

Highlights of the Programs -›› 10 D.3 Differential Geometry & Geometric Analysis

Coordinators: Chiung-Jue Sung (National Tsing Hua University)

he subject matter of Riemannian harmonic and geometric analysis. geometry has multiple faucets. NCTS We are going to cover the following topics. has held various programs and workshops in related subject areas since the year 2004, 1. The Hilbert transform and the Cauchy focusing on various aspects of geometry and integral geometric analysis. The covered topics include 2. Homogeneous distributions in Rn Conformal Geometry, Special Lagrangian Submanifolds and Mirror Symmetry, Function 3. Lp theory of singular integral operators (if Theory, Geometric Elliptic and Parabolic we have time, we will also cover basic Hp Equations, Mathematical Physics, Geometric theory) Evolution Equations, and Mathematical 4. Lp estimates on pseudo-differential operators Aspects of General Relativity. The programs and workshops brought together graduate 5. Parametricies and extimates for elliptic students, recent Ph. Ds and well-established operators mathematicians, while the short-courses 6. Cauchy-Szego integral and the Heisenberg provided necessary background material for group the related workshops. The programs and Ð 7. The ∂b-complex on the Heisenberg group workshops also involved both short and longer term visitors to NCTS. 8. Geometric mechanics on the Heisenberg group and its generalizations Ð D.3.1 Advanced Courses and 9. The ∂-Neumann problem Workshops 10. The heat kernel and Riemann zeta function I. Course / Summer & Winter Programs associate to the sub-Laplacian on the unit n (I) NCTS & NTHU Joint Course on Singular sphere in C . Integral Operators, Pseudo-differential (II) NCTS Summer 2008 Program: Mini Operators and Analysis on Homogeneous Lecture Series and Student Seminar Groups, May 8 ~ July 28, 2008 Time: July 4, July 11, July 18, July 24, Instructor : Prof. Der-Chen Chang 2008 PM2:00-4:00 (Georgetown Univ. & NCTS) Topic: Introduction to the Maximum Prof. Chiung-Jue Sung Principle for Parabolic Equations (National Tsing Hua University) Speaker: Prof. Dong-Ho Tsai (NTHU) Course Description and Requirements: The course is aimed at concisely presenting II. Workshop: the basic concepts and principles of Fourier (I) 2008 NCTS Workshop on Harmonic and analysis as well as its applications on nilpotent Complex Analysis, May 19-20, 2008 Lie groups, such as Euclidean spaces, Organizers: Prof. Der-Chen Chang Heisenberg groups to graduate or senior (Georgetown Univ. & NCTS) undergraduate students in mathematics. It Prof. Chiung-Jue Sung includes some recent results that can be taught (National Tsing Hua University) at an elementary level and anable students to reach quickly the frontiers of current Invited Speakers: mathematical research along the direction of • Methods and techniques for finding heat

11 ‹‹- Highlights of the Programs kernels, Der-Chen Chang (Georgetown Jun-Muk Hwang (KIAS) University, USA) • Uniqueness and Algebraic Dependence of • The boundedness of operators on weighted Holomorphic Curves into Abelian Varieties, Hardy spaces, Ming-Yi Lee (National Min Ru (University of Houston) Central University) • Limit Set of the Harmonic Map Heat Flows, • Module of horizontal vector measures on Chiung-Jue Sung (National Tsing Hua Carnot groups, Irina Markina (University of University) Bergen, Norway) • Improved Estimate for Lojasiewicz • Universal sampling of band-limited signals, Inequality and Related Results, Wing-Keung Alexander Olevskii (Tel Aviv University, To (National Singapore University) Israel) • Evolving a Convex Closed Curve to Another • Operators on Manifolds with Corners, B.- One via a Length-preserving Linear Flow, Wolfgang Schulze (University Postdam, Dong-Ho Tsai (National Tsing Hua Germany) University) • The inverse of the sub-Laplacian on the • Fake Projective Planes, Geography of weight spaces, Jingzhi Tie (University of Surfaces and Fake Hermitian Symmetric Georgia, USA) Spaces, Sai Kee Yeung (Purdue University) • Boundary behaviour of conformal maps and angular derivatives, Alexander Vasil'ev D.3.2 Seminars (University of Bergen, Norway) Speakers include: Ching-Hung Lam (National Cheng Kung University), Hui-Wen (II) 2008 NCTS Workshop on Geometric Lin (National Central University), Kuo-Chang Analysis and Several Complex Variables, Chen (National Tsing-Hua University), Cheng- June 24 & 25, 2008 Hsiung Hsu (National Central University), K. Organizers: Prof. Der-Chen Chang Stempak (Politechnika Wroclawska, Poland), (Georgetown Univ. & NCTS) Chin-Cheng Lin (National Central University), Prof. Chiung-Jue Sung ( ), Jui-Tang Ray Chen (National Tsing Hua University) (National Tsing-Hua University), Alexander Invited Speakers: Vasiliev (Univ. of Bergen), Irina Markina (Univ. of Bergen), Chiung-Ju Liu (National • Finding Heat Kernels Using Geometrical Cheng Kung University), Alexander Olevskii Mechanics, Path Integrals and Other (Tel Aviv University, Israel), B.-Wolfgang Methods, Ovidiu Calin (Eastern Michigan Schulze (University Postdam, Germany), University) Ovidiu Calin (Eastern Michigan University), • Geometric Analysis on the Unit Three Duy-Minh Nhieu (San Diego Christian Sphere, Der-Chen Chang (Georgetown College) University, USA) D.3.3 Student Seminars • Isolated Complex Singularities and Their CR Links, Xiaojun Huang (Rutgers University) Topics include: On the pseudo-harmonic heat flow, Geometry of Harmonic Maps, The • On Holomorphic Self-Maps of Fano Harmonic Map Heat Flow, The Existence of Manifolds with Second Betti Number One, Blackhole due to Condensation of Matter

Highlights of the Programs -›› 12 D.4 Discrete Mathematics

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

D.4.1 Background and activities in and Professor Pavol Hell from Simon Fraser the program University, Canada. Professors Raspaud, Pecher and Montassier stayed for two weeks and Professor Hell stayed for one month. Both groups have long time collaborations with our iscrete mathematics has seen rapid group. During their visits, we initiated some development in recent decades, both new joint projects. Collaborations continue abroad and in Taiwan, in width and in depth. after their visits. The main focus on the south As a focus group of NCTS, the discrete group is graph colouring. We initiated studies mathematics group has been focused on on adapted graph colouring and some other research in graph coloring, graph labeling, colouring problems. We have written two joint combinatorial optimization, algorithms, papers based on our joint work during and enumerative combinatorics, cluster after their visits. One paper is already accepted combinatorics, combinatorial number theory. by European Journal of Combinatorics, and the In the past year, through seminars, workshops other is under revision. The visit also made the and hosting visitors, the project has helped arrangement t have a newly graduated Ph.D. to local focus group, especially young researchers do one year post doc. research in Bordeaux. in the group, to establish collaborations with Some other collaborations with earlier researchers abroad, develop links with experts visitors are also working well. Dr. Serguei abroad, and start their research in the frontier Norine visited our group in March of 2007. of related fields. Joint work on consecutive circular list Discrete mathematics program in NCTS colourings were initiated during the visit. We has two teams, one in north which is organized continue our joint work on this subject after his by Gerad Jennhwa Chang at National Taiwan return. Up to now, members from our group University, the other in south which is have written three joint papers with him. organized by Xuding Zhu at National Sun Yat- During this period, our group members also sen University. Each semester, the discrete visited other institutions. Li-Da Tong visited mathematics groups in north and south have Bordeaux for two weeks in 2007, and Xuding series of seminars. Some of the seminar talks Zhu visited University of Victoria for two are given by visitors and some talks from weeks in 2008, and visited Charles university group members, post doctors and students. in Prague for two weeks in the summer of During the past year, the discrete 2008. Joint works initiated during these visits mathematics group in north has invited 8 are carried out. visitors. As we do not have budge for post doctors, we use personal NSC projects of Local focus group Gerard Jennhwa Chang to hire a post doctor, North: Gerard Jennhwa Chang (NTU), Ko- Jiaojiao Wu, joining the program. Wei Lih (AS), Jing-Ho Yan (Aletheia), Hsun- Wen Chang (Tatung), Chiang Lin (NCU), In the past year, the group in south has Hong-Gwa Yeh (NCU), Sheng-Chyang Liaw invited 4 visitors. Professor Andre Raspaud, (NCU), Roger Kwan-Ching Yeh (Feng-Chia), Professor Arnaud Pecher and Professor David Kuo (NDHU), post doctors and Mickael Montassier from Bordeaux, France graduated students.

13 ‹‹- Highlights of the Programs South: Xuding Zhu (NSYSU), Meng-Na Lo domination numbers of graphs, Europ. J. (NSYSU), Tsai-Lien Wong (NSYSU), Li-Da Combin. 29 (2008) 1333-1336. Tong (NSYSU), Mei-Hui Guo (NSYSU), [6] B.-J. Li and G. J. Chang, Clique coverings Zhishi Pan (NSYSU), Sen-Peng Eu (NUK), and partitions of line graphs, Discrete Szu-En Cheng (NUK), Hong-Gwa Yeh (NCU), Math. 308 (2008) 2075-2079. plus 5 Ph.D. students. [7] J. S.-T. Juan and G. J. Chang, Adaptive group testing for consecutive positives, Visitors Discrete Math. 308 (2008) 1124-1129. Khee Meng Koh (National University of [8] G. J. Chang, S.-P. Eu and C.-H. Yeh, On Singapore), Frank Kwang-Ming Hwang the (n, t)-antipodal Gray codes, Theore. (National Chiao Tung University), Silvia Comput. Sci. 374 (2007) 82-90. Heubach (California State University), Wen- Jie He (Hebei University of Technology), Kai- [9] J.-J. Chen and G. J. Chang, Distance Shun Wang (Beijing Normal University), Wai- graphs on R^n with 1-norm, J. Combin. Hong Chen (Hong Kong Baptist University), Optimization 14 (2007) 267-274. Rong-Quan Feng (Peking University), Daphne [10] G.-Y. Chang, G.-H. Chen and G. J. Liu (California State University, Los Angeles), Chang, (t, k)-Diagnosis for matching Wensong Lin (South-East University, composition networks under MM* model, Nanjing), Pavol Hell (Simon Fraser IEEE Trans. Computers 56 (2007) 73-79. University), Andre Raspaud (Laboratoire de [11] R.-Y. Wu, G.-H. Chen, Y.-L. Kuo and G. Recherche), Arnaud Pecher (Laboratoire de J. Chang, Node-disjoint paths on Recherche), Mickael Montassier (LaBRI hierarchical hypercube networks, Inform. Laboratoire Bordelais) Sciences 177 (2007) 4200-4207. As for the south, publications of the local Conferences group are as below: 2007 International Conference on Graph [1] D. Yang andX. Zhu, Activation strategy Theory and Combinatorics & Fourth Corss- for asymmetric marking games, European strait Conference on Graph Theory and Journal of Combinatorics, to appear. Combinatorics (2007.6.24-2007.6.29). Plenary speakers: G. Fan, F. K. Hwang, Y.-N. Yeh, X. [2] T. Wong and X. Zhu, Distinguishing Yu, X. Zhu. There are 56 contribution talks. number of group actions, Discrete Mathematics, to appear. D.4.2 The accomplishment [3] H. Chang and X. Zhu, Colouring games on outerplanar graphs and trees, Discrete In the north, publications are listed below. Mathematics, to appear. [1] R.-Y. Wu, G.-H. Chen, J.-S. Fu and Gerard [4] M. Montassier, A. Raaaspaud and X. Zhu, J. Chang, Finding cycles in hierarchical Adaptive choosability of graphs and hypercube networks, Inform. Process. orientations, European Journal of Letters (accepted). Combinatorics, to appear. [2] L.-H. Huang and G. J. Chang, L(h, k)- [5] A. Guan and X., Zhu, Adaptable labelings of Hamming graphs, Disc. Math. choosability of planar graphs with sparse (accepted). short cycles, submitted. [3] G. J. Chang, L.-H. Huang and H.-G. Yeh, [6] X. Zhu, Bipartite density of triangle-free On the rank of a cograph, Linear Algebra subcubic graphs, Discrete Applied Appl. 429 (2008) 601-605. Mathematics, to appear. [4] H. Lai, G. J. Chang and K.-W. Lih, On [7] X. Zhu, Bipartite subgraphs of triangle-free fully orientability of 2-degenerate graphs, subcubic graphs, Journal of Combinatorial Inform. Process. Letters 105 (2008) 177- Theory Ser. B, to appear. 181. [8] S. Norine, T. Wong and X. Zhu, Circular [5] G. J. Chang, Upper bound on k-tuple

Highlights of the Programs -›› 14 Choosability via Combinatorial Taiwanese Journal of Mathematics, to Nullstellensatz, Journal of Graph Theory, appear. to appear. [10] D. Liu, S. Norine, Z. Pan and X.Zhu, [9] W. Lin, D. Yang and X. Zhu, Circular Circular consecutive choosability of k- consecutive choosability of graphs, choosable graphs, submitted.

D.5 Dynamical Systems

Coordinators: Kuo-Chang Chen (National Tsing Hua University) Chi-Wen Shih (National Chiao Tung University)

ynamical Systems is a major and Organizers: Kuo-Chang Chen: active field of research in [email protected] mathematical science. In the topical program Cheng-Hsiung Hsu: of dynamical systems, we organize related [email protected] activities to broaden the spectrum of current Contents: The conference talks consist of two research in Taiwan, to promote the mini courses, with a total of six hours lectures, collaboration with international scholars, and plus nine invited one-hour talks. Mini courses to enhance the training of graduate students. and two of the one-hour talks were delivered Such activities include weekly seminar, an by established scholars overseas, other talks annual workshop, and several mini courses. were given by researchers in Taiwan. Topics We also cooperate with the people in the covered are: topical program of mathematical biology and scientific computation on some applications 1. Mini Courses: and computational aspects of dynamical systems. These activities are listed in the (1). Speacker: Masato Tsujii (Kyushu following. University) Title: Quasi-Compactness of Transfer D.5.1 Dynamical System Seminar: Operators for Contact Anosov Flows The weekly seminar is primarily organized (2). Speacker: Weishi Liu (Kansas University) by Kuo-Chang Chen (National Tsing Hua Title: Invariant Manifolds and Geometric University) and Min-Chia Li (National Chiao Singular Perturbations Tung University). About half of them are student seminars given by graduate students, 2. One-Hour Talks: among them there were a series of talks on KAM theory, and a series of talks on calculus (1). Speaker: Ken Palmer (National Taiwan of variations. A listing of all the seminar talks University) are available at: http://www.math.cts.nthu. Title: Homoclinic Orbits in Singularly edu.tw/actnews/actnews.php?class=102 Perturbed Systems (2). Speaker: Shih-Feng Shieh ( National D.5.2 Conference and Workshop: Taiwan Normal University) CTS Workshop on Dynamical Systems, Title: Horseshoes for Coupled Discrete May 23 - 25, 2008 Nonlinear Schrödinger Equations

15 ‹‹- Highlights of the Programs (3). Speaker: Yi-Chiuan Chen (Academia (2). Speaker: Wen-Chiao Cheng (Chinese Sinica) Culture University) Title: Family of invariant Cantor sets as Title: Introduction to entropy theory orbits of differential equations Time: 2007/8/14, 2007/8/16, 10:00-11:30, (4). Speaker: Ming-Jiea Lyu (National Chiao 13:30-15:00. Tung University) (3). Speaker: Chang-Yuan Cheng (National Title: Continuation of Topological Entropy Pingtung University of Education) for Multidimensional Perturbations of Title: Convergence of dynamics: Theory Snap-Back Repellers and One- and Applications Dimensional Maps Time: 2007/8/21, 2007/8/23, 11:00-12:00, (5). Speaker: Hyung Ju Hwang (POSTECH, 13:30-14:30. Korea) (4). Speaker: Shyan-Shiou Chen (National Title:Recent Results in Kinetic Theory Taiwan Normal University) (6). Speaker: Jaeyoung Byeon (POSTECH, Title: Introduction to Marotto's chaos and Korea) LaSalle's invariant principle. Title: Standing Waves for Nonlinear Time: 2007/8/28, 10:00-11:30, 13:30- Schrödinger Equations 15:00. (7). Speaker: Je-Chiang Tsai ( National Chung (5) Speaker: Kuo-Chang Chen (National Cheng University) Tsing-Hua University) Title: Traveling Waves in the Discrete Fast Title: Recurrence in dynamical systems, 8 Buffered Bistable System hours lectures (8). Speaker: Suh-Yuh Yang (National Central Time: 15:00-17:00 on July11, 18, 22, 24, University) 2008 Title: Global Exponential Synchronization Abstract: This mini course is a short and Coupling Topology introduction to the concept of recurrence in dynamical systems. We introduce the (9). Speaker: Jung-Chao Ban ( National Poincaré and Birkhoff recurrence Hualien University of Education) theorems, their generalizations, the concept Title: The Dimension of Non-Conformal of ergodic and mixing transformations, and Repeller and Average Conformal Repeller some interesting applications. In particular, we show some applications of the D.5.3 NCTS Summer Course on recurrence theorems to the combinatorial Dynamical Systems number theory, namely the Van der (1). Speaker: Kuo-Chang Chen (National Waerden theorem and the Szemerédi Tsing-Hua University) theorem. Some of the topics are briefly outlined in the mini course and details are Title: Introduction to ergodic theorems. left to the student seminar. Time: 2007/8/7, 2007/8/9, 10:00-11:30, 13:30-15:00.

Highlights of the Programs -›› 16 D.6 Mathematical Biology

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

he purpose of the topical program in We study the following subjects: Mathematical Biology is to promote (i) Fitness Landscapes and sequence spaces the interdisciplinary interactions between mathematicians, physicists, computer scientists (ii) Prisoners of the Dilemma and biologists. In the past one year, we held (iii) Games in finite populations two biweekly seminars in Neutral Theory of Biodiversity and in Evolutionary Biology ; two (iv) Spatial Games intensive courses in Stochastic Process and (v) HIV infection Stochastic Differential Equations ; one intensive course in Monotone Dynamical (vi) Evolution of Virulence Systems with Applications to Reaction- (vii) Evolutionary Dynamics of Cancer Diffusion Equations and several invited talks. There are stated in the followings. III. An intensive course in Monotone Dynamical Systems with Application I. Biweekly seminar in Neutral Theory of to Reaction-Diffusion Equations, Biodiversity and Biogeography, December 5, 2007 - Jan. 3, 2008 September 28 - November 30, 2007 Organizer : Sze-Bi Hsu (Tsing-Hua University) Organizers: Sze-Bi Hsu (Tsing-Hua University) Speaker : Professor Jifa Jiang and Yi-Yun Chen (NCTS) (Tongi University, Shanghai, PRC) In this seminar we study the book "The Professor Jiang gave two hours weekly Unified Neutral Theory of Biodiversity and lectures on his work on Monotone Dynamical Biogeography" by Stephen Hubbell. Neutral Systems with Application to Reaction- Theory is used to explain the biodiversity in Diffusion Equations and Mathematical the community ecology in recent years. The Biology. advantage is that the theory fit many data. We study the following subjects: IV. An intensive course in Stochastic (i) Dynamical Models of the Relative Process and Stochastic Differential Abundance of Species, Equations in Mathematical Biology (ii) Local Community Dynamics under Organizer: Sze-Bi Hsu (Tsing-Hua University) Ecological Drift, Speaker: Professor Linda Allen (iii) Metacommunity Dynamics and the (Texas Tech. University, USA) Unified Theory, Date: Aug. 5, 7, 12, 14, 2008 AM10:00-12:00 (iv) The Unified Theory and Dynamical Part I: Discrete-Time Markov Chains - DTMC Species-Area Relationship. ¥ Theory II. Biweekly seminar in Evolutionary ¥ Applications to Random Walks, Dynamics, Feb. 29 - May 30, 2008 Populations, and Epidemics Organizers: Sze-Bi Hsu (Tsing-Hua University) Part II: Branching Processes and Yi-Yun Chen (NCTS) ¥ Theory In this seminar we study the book ¥ Applications to Cellular Processes, "Evolutionary Dynamics" by Martin Nowak. Network Theory, and Populations

17 ‹‹- Highlights of the Programs Part III: Continuous-Time Markov Chains - Part III: A procedure is explained for deriving CTMC accurate SDE models. SDEs are derived for several problems in ¥ Theory biology, physics, and finance. ¥ Applications to Populations and Epidemics Part IV: The derivation procedure is extended to stochastic partial differential Part IV: Stochastic Differential Equations - equations (SPDEs). SPDEs are SDE derived for several problems in ¥ Comparisons to Other Stochastic physics and biology. Processes, DTMC and CTMC ¥ Applications to Populations and VI. Several invited talks Epidemics (i) Topics:The Interface of Developmental Cell Biology and Mathematical V. An intensive course in modeling Modeling, Nov. 1, 2007 techniques and numerical methods for Stochastic Differential equations. Speaker: Prof. Jui-Chou Hsu (Life Science, NTHU) Organizer: Sze-Bi Hsu (Tsing-Hua University) (ii) Topics: Protein Wrapping: An insight into Speaker: Professor Edward Allen watertied molecular design, June (Texas Tech. University) 16, 2008 Date: Aug. 5, 7, 12, 14, 2008 PM2:00-4:00 Speaker: Professor Ariel Fernandez, Rice Part I: Random variables and stochastic University, USA processes are reviewed and stochastic (iii) Topics: Anatomically Accurate Modeling integrals are introduced. in Cardiac Electrophysiology, July 23, 2008 Part II: The theory and approximation of Itˆo stochastic differential equations (SDEs) Speaker: Professor A.V.Panfilov, Utrecht are studied. University

D.7 Number Theory

Coordinators: Jing Yu (NTHU & NCTS) and J. Tze-Yue Wang (Academia Sinica)

umber Theory at NCTS is understood Diophantine approximations in a broad sense, including traditional Diophantine geometry algebraic number theory, arithmetic geometry and automorphic representations. Modular curves Diophantine geometry and arithmetic of Representation of p-adic groups algebraic function fields are also among the Transcendence theory in positive main interests. characteristic Main Research Focus of the working D.7.1 Local focus group group J. Yu (NCTS Center Scientist and NTHU),

Highlights of the Programs -›› 18 C.-Y. Chang (Post doc), Y.-M. J. Chen (NCU), Winter School on Number Theory and W.-C. Chi (NTNU), L.-C. Hsia (NCU), A. Li Arithmetic Geometry at Aspire Park Feb. (Fu Jen U.), S.-Y. Pan (NTHU), A. Schweizer 12-Feb. 15, 2008. (NCTS), C.-J. Wang (Post Doc), J. T.-Y. Wang Subject: Motives, l-adic representations, Class (Academia Sinica), W.-C. Yao (TMUE), Y. Field Theory, Algebraic Inde pendence Yang (NCTU), C.-F. Yu (Academia Sinica), Y.- Measures. J. Yu (Post Doc). Presently there are also 15 Ph.D. students in this group, from NTHU, Speakers: Jing Yu (NCTS & NTHU), Hui-Wen NCU, and NCTU. Lin (NCU), Wen-Chen Chi (NTNU), Chieh-Yu Chang (NCTS) and graduate students. The short term visitors this year are : Min Ru (U. Houston), J. Tilouine (U. Paris Nord). Summer School on Algebra and Number D.7.2 Seminars and Courses Theory at Aspire Park, June 24-June 28, 2008 NCTS Number Theory Seminar Subject: Chow Forms, Diophantine Geometry, This is regular weekly number theory Geometric Invariant Theory, Deformations of seminar during the academic year. It includes Galois Representations, Representations of talks given by visitors to Taiwan from abroad Semisimple groups. and reports on research results obtained by Speakers: Jing Yu (NCTS & NTHU), Min Ru number theory group at NCTS. (U. Houston), J. Tze-Yue Wang (Academia Sinica), Ment-Kiat Chuah (NTHU), Yih-Jeng Course on Abelian Varieties Yu (Academia Sinica) and graduate students. This Fall 2008 course is given by Jing Yu. Contents : elliptic curves, Abelian varieties, D.7.4 Summer Program for Students theorems of the cube and the square, dual The 2008 summer program on algebra is abelian varieties, polarizations, Rosati organized by Jing Yu, Shu-Yen Pan and Jyh- involution, Riemann forms, Poincare divisors, Haur Teh. Topics include prime numbers, theta divisors, Jacobian. algebraic curves, simple algebras over local and global fields (reciprocity, Hasse- Course on Function Field Arithmetic Minkowski principle, and Hilbert symbols), Another 2008 Fall course given by A. and de Rham cohomology. Schweizer. Content: Riemann-Roch the-orem, -functions, Drinfeld modules, cyclotomic D.7.5 Accomplishments function fields, analogy between number fields [1] T. T. H. An, W. Cherry and J. T.-Y. Wang, and function fields. Algebraic degeneracy of non- Archimedean analytic maps, preprint NCTS Student's Seminar on Algebra and 2008. Number Theory [2] T. T. H. An, J. T.-Y. Wang and P. Wong, This seminar during academic year aims at Non-archimedean analytic curves in the Ph.D. students, with students from NTHU, complements of divisors, Journal of NCU and NCTU join. Sometimes it is Number Theory 128 (2008), 22752281. proceeded using video conference facilities [3] C.-Y. Chang, A note on a refined version among these universities. Topics discussed of Anderson-Brownawell-Papanikolas including transcendence problems, criterion, to appear in Journal of Number Diophantine problems, complex Theory, 2008. multiplications, etc. [4] C.-Y. Chang and M. Papanikolas, Algebraic relations among periods and D.7.3 Advanced Schools and loga-rithms of rank 2 Drinfeld modules, Workshops preprint 2008.

19 ‹‹- Highlights of the Programs [5] C.-Y. Chang, M. Papanikolas, D. Thakur fields in the function field case, preprint and J. Yu, Algebraic independence of 2008. arithmetic gamma values and Carlitz zeta [18] Y. Yang, Modular Units and cuspidal values, preprint 2008. divisor class groups of X1(N), preprint [6] C.-Y. Chang, M. Papanikolas and Yu, 2008. Frobenius difference equations and [19] Y. Yang and J.-D. Yu, Structure of the algebraic independence of equal cuspidal rational torsion subgroup of characteristic zeta values, preprint 2008. n J1(p ), preprint 2008. [7] Y.-H. Chen, Y. Yang and N. Yui, [20] Y. Yang and W. Zudilin, An Sp4 Monodromy of Picard-Fuchs differential modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds, J. equations for Calabi-Yau threefolds, reine angew. Math. 616 (2008), 167-203. preprint 2008. [8] Y.-M. Chen and J. Yu, On class number relations in characteristic two, Math. Zeit. D.7.6 Exchange programs and 259 2008, 197-216. international cooperations [9] Y.-M. Chen, Averaging class numbers in Besides individual visits by members of our characteristic 2, to appear in Journal of focus group to centers and universities in Number Theory, 2008. Canada, China, France, Germany, Hongkong, [10] S. Fukurara and Y. Yang, Period Japan, Korea, U.S.A., highlights of 2008 polynomials and explicit formulas for international cooperations include :

Hecke operators on Γ0(2), to appear in Canada. July 2008 J. Yu was invited to CNTA Math. Proc. Cambridge Philosophical conference at Waterloo University, together Society. with C.-Y. Chang and 3 students. This [11] L.-C. Hsia, On the reduction of a non- conference was held immediately after the torsion point of a Drinfeld module, to Fields Institute Summer School which these appear in Journal of Number Theory, students enrolled in. Fall 2008, L.-C. Hsia, J. 2008. T.-Y. Wang and J. Yu are also invited to the [12] L.-C. Hsia and J. Silverman, On a Fields Institute program on Arithmetic dynamic Brauer-Manin obstruction, Geometry and Hyperbolic Geometry. In Fall preprint 2008. 2007, Y. Yang visited Queens University, with his student Y.-H. Chen, and collaborated with [13] M.-H. Kang, W.-C. Li and C.-J. Wang, N, Yui on arithmetic of Picard-Fuch equations. The zeta functions of complexes from PGL(3) : a representation theoretic France. July 2008, L.-C. Hsia visited Luminy approach, preprint 2008. center for one month (research in pairs [14] S.-Y. Pan, L-functoriality for local theta program), works on arithmetic Dynamics. correspondences with unipotent reduction Germany. Spring 2008, Y. Yang visited Max- for unitary groups, preprint 2008. Planck Institute in Bonn, with his student Y.-H. [15] S.-Y. Pan, L-functoriality for local theta Chen (supported by NCTS). correspondences with unipotent reduction Japan. October 2007, Jing Yu and his student for symplectic and even orthogonal F.-T. Wei were invited to conference on Galois groups, preprint 2008. theory and related topics at Yamagata. [16] M. Papanikolas, Tannakian duality for Korea. Jan. 2008, J. Yu, L.-C. Hsia, Y.-J. Yu, Anderson-Drinfeld motives and algebraic Y. Yang, K.-S. Tan were invited to KAIST, independence of Carlitz logarithms, joining East Asian Number Theory Conference Invent. Math. 171 (2008), 123174. as invited speakers. [17] Fu-Tsun Wei and J. Yu, On the independence of Heegner points USA. Jan. 2008, L.-C. Hsia was invited to associated to distinct quadratic imaginary AIM workshop on arithmetic dynamics. March

Highlights of the Programs -›› 20 2008, J. Yu was invited to Arizona Winter We have also supported travels of Ph.D. school AWS as NSF observer. C.-Y. Chang students to join selected summer/winter was invited as post doctor assisting that schools, or workshops abroad in 2008 : 1 school. Later on Chang visited Texas A & M student to the Arizona arithmetic geometry University cooperating with M. Papanikolas on winter school taking part in its student project, transcendence theory in positive characteristic. 1 post doctor and 1 student to the annual algebraic number theory workshop at Waseda D.7.7 Student's activities and schools University, 3 students to the Fields institute Since 2004 each year we have one week summer school. There is 1 student joining Fall winter school and one week summer school on program (3 months) of the Fields Institute. All various topics in number theory for graduate these students applied (and received) local students, sponsored by Minister of Education support from the organizers of these grant (national chair in science) and NCTS, international organizations. usually this is taken place at a conference site outside NCTS.

D.8 Partial Differential Equations

Coordinators: Chiun-Chuan Chen, Tai-Chia Lin, Jenn-Nan Wang (National Taiwan University), Jong-Shenq Guo (National Taiwan Normal University)

D.8.1 Background and activities in Short Term Visitors: the program Yoshihito Oshita, Yokihiro Seki, Ken-Ichi Nakamura, Yoshihito Morita, Hirokazu Ninomiya, Gen Nakamura, Yoshihiro he activities Nonlinear PDE at NCTS- Tonegawa, Reika Fukuizumi (Japan), Dongho TPE in the program include regular Chae, Hyeonbae Kang, Namkwon Kim PDE seminars, courses, workshops/ (Korea), Juncheng Wei (HongKong), Philipppe conferences, and international cooperation. Souplet (France), Gunther Uhlmann (USA), Gennady El (United Kingdom), Anatoly Local focus group : Mikhajlovich Kamchatnov (Russia). Jong-Shenq Guo (NTNU), I-Liang Chern (NTU), Chang-Shou Lin (NTU), Chiun-Chuan Courses Chen (NTU), Tai-Chia Lin (NTU), Jenn-Nan ¥ Basic theory of ODEs and its applications, Wang (NTU), Chun-Chi Lin (NTNU), Huey- July 16-August 22, 2008, organized by Jong- Er Lin (NTNU), Jenn-Long Chern (NCU), Je- Shenq Guo: This summer course has been Chiang Tsai (CCU), Sheng-Chen Fu (NCCU), organized twice. In the first three weeks, Mao-Sheng Chang (Fujen U), Chung-Tsun basic theory of ODE such as existence and Shieh (Tamkang U), Dong-Ho Tsai (NTHU), uniqueness theory for IVP, theory of Chi-Kun Lin (NCTU), Chao-Nien Chen continuation of solution, continuous (NCUE), Chun-Kong Law (NSYSU), Ching- dependence on initial value and/or parameter, Lung Lin (NCKU) comparison principle, shooting, etc are introduced. Also, some recent results on

21 ‹‹- Highlights of the Programs traveling waves are given. These lectures are researcher of L. D. Landau Institute for given by Professors S.-C. Fu (NCCU), J-C. Theoretical Physics, Russian Academy of Tsai (CCU), and C.-C. Wu (NCTU). In the Sciences, Russia), Oleg I. Mokhov (Centre fourth week, some special solutions, such as for Nonlinear Studies, Landau Institute for stationary solution, self-similar solution, Theoretical Physics, Russian Academy of traveling wave solution, spiral wave solution, Sciences, Russia), Tsarev Sergey, etc, of some PDE problems are introduced by Krasnoyarsk State Pedagogical University, Guo. There are 10 students selected. 3 of Russia), Anatoly Mikhajlovich Kamchatnov them are to be senior and 6 are to be first year in graduate program of NTU, and 1 is to (Principal Researcher and Deputy-head of be in NCTU. In the final two weeks, these Theoretical Department, Institute of students are assigned some papers related to Spectroscopy, Russian Academy of Sciences, some special solutions of PDE to read and Troitsk, Moscow Reg., Russia), Gennady El present. This year, these students are quite (Department of Mathematical Sciences, excellent. Loughborough University, United Kingdom), ¥ Minicourse on Inverse Problems, March ( ) 19-21, 2008, NTU, organized by Jenn-Nan ¥ Workshop of Nonlinear Partial Wang. This minicourse were given by three Differential Equations Related to Physical prominent mathematicians in the field of Models, May 30-31, 2008, organized by Tai- inverse problems. Chia Lin. Professor Hyeonbae Kang (Korea), Small Speakers: Jun-cheng Wei (Chinese Volume Imaging University of Hong Kong), Liping Wang Professor Gen Nakmura (Japan), (Chinese University of Hong Kong), Reconstruction methods for inverse problems Wei Yao (Chinese University of Hong Professor Gunther Uhlmann (USA), Kong), Yoshihisa Morita (Ryukoku Invisibility University), Yoshihiro Tonegawa ( Hokkaido University), Reika Fukuizumi Conferences and Workshops (Hokkaido University), Namkwon ¥ France-Taiwan Joint Conference on Kim (Chosun University), Dongho Chae Nonlinear PDEs, March 25-28, 2008 at (University of Chicago), Shusen Yan (The CIRM, Marseille, France. Organizers: University of New England), Je-Chiang Tsai Thierry Gallay, Jong-Shenq Guo, Francois (ational Chung Cheng University) Hamel, Jean-Michel Roquejoffre D.8.2 The accomplished and the Speakers: Jung-Chao Ban, Chiao-Nien Chen, anticipations Kuo-Chang Chen, Jong-Shenq Guo, John Selected publications of the local focus group Meng-Kai Hong, Sze-Bi Hsu, Chang-Shou during 2008: Lin, Chun-Chi Lin, Jenn-Nan Wang from Taiwan. Guy Barles, Karine Beauchard, [1] Chiun-Chuan Chen, Robert M. Strain, Henri Berestycki, Yann Brenier, Didier Horng-Tzer Yau, and Tai-Peng Tsai, Bresch, Anne de Bouard, Albert Fathi, Lower bound on the blow-up rate of the Isabelle Gallagher, Michel Ledoux, axisymmetric Navier-Stokes equations, Int. Math. Res. Notices (2008) Vol. 2008, Emmanuel Russ, Laure Saint-Raymond, Eric article ID rnn016, 31 pages. Sere from France. [2] Chiun-Chuan Chen and Chang-Shou Lin, ¥ Workshop of Dispersive PDE and Topological degree of a Liouville type Integrable Systems, March 28, 2008, at equation with singular source, 2008. NTU. Organizers: Tai-Chia Lin, Jyh-Hao Lee [3] Jong-Shenq Guo and Bei Hu, Blowup rate Speakers: Leonid V. Bogdanov (Seniour estimates for the heat equation with a

Highlights of the Programs -›› 22 nonlinear gradient source term, Discrete been published in a top-ranked journal, Int. and Continuous Dynamical Systems 20 Math. Res. Notices. (2008), 927-937. In [2], C.-C. Chen and C.-S. Lin studied a [4] Xinfu Chen, Jong-Shenq Guo, and Chin- Liouville type equation arises from prescribing Chin Wu, Traveling waves in discrete Gauss curvature problem, the mean field limit periodic media for bistable dynamics, of vortices in Euler flows, chemotaxis models Archive Rational Mech. Anal. 189 (2008), in bioscience, and Chern-Simons-Higgs 189-236. models. In recent years, the study on the [5] Gunther Uhlmann and Jenn-Nan Wang, Liouville type equation has reached another Reconstructing discontinuities using stage with efforts of many well-known complex geometrical optics solutions, mathematicians. Ding-Yost-Li-Wang and SIAM J. Appl. Math., Vol 68 (2008), Tarantello-Struwe applied mini-max methods 1026-1044. to prove the existence of solutions when the [6] Horst Heck, Xiaosheng Li, and Jenn-Nan total mass is in some range between 8π and Wang, Identification of viscosity in an 16π. Walensky-Wang-Wei and Prajapat- incompressible fluid, Indiana Univ. Math. Tarantello classified the ground state solutions J., Vol 56 (2007), 2489-2510. for the single-equation case with singular data. Chen-Lin calculated the Leray-Schauder [7] Chiun-Chang Lee and Tai-Chia Lin, degree of solutions. Wang and Jost studied the Incompressible and compressible limits of blowing-up behavior and classified the ground two-component Gross-Pitaevskii equations state solutions for the Toda system. Much of with rotating fields and trap potentials, J. these work relied on the careful study of the Math. Phys. 49, 043517 (2008). phenomenon of energy concentration. The [8] Lin, T.-C. and Wei, J., Orbital stability of limiting case of the Chern-Simons model bound states of semiclassical nonlinear proposed by Hong, Kim and Pac can be Schrodinger equations with critical described by the Liouville type equation with nonlinearity, SIAM J.Math.Anal. Vol. 40 delta functions in the source term. These delta No.1 (2008) 365-381. functions make the study of the equation much more difficult. In [3], Chen-Lin obtained an In [1], C.C. Chen, R. Strain, H.T. Yau and explicit degree formula through combinatorical T.P. Tsai studied the regularity of axi- methods for this case. This degree formula will symmetric incompressible Navier-Stokes have many applications, including the proofs equations. The incompressible Navier-Stokes of the existence of the Bogomol'nyi system in equations are one of the most basic and the electroweak theory of Glashow-Salam- important systems in describing the behavior Weinberg and the existence of the Toda system of fluid. The regularity of existence of of Liouville type equations. solutions of these equations in two dimensions In [3], J.-S. Guo and B. Hu studied an has been solved while this problem in three initial boundary value problem for the heat dimensions still remains as a big challenge. equation with a nonlinear gradient source term. The axi-symmetric case of the Navier-Stokes It was shown that the blowup rate will never equations can be considered as a two match that of the self-similar variables. In the dimensional problem with possible one space dimensional case with assumptions singularities on the axis of symmetry, and is on the initial data so that the solution is under extensive studies among other problems. monotonically increasing in time, the exact This research proved that a solution of the axi- blowup rate is found. This answer an open symmetric incompressible Navier-Stokes problem proposed in the second Euro-Japanese Equations cannot blow up if it is bounded by a conference on blow-up in Spain in 2006. self-similar scaling proposed by Leray. This In [4], X. Chen, J.-S. Guo, C.-C. Wu result "Lower bound on the blow-up rate of the studied the traveling fronts in discrete periodic axisymmetric Navier-Stokes equations" has

23 ‹‹- Highlights of the Programs media with bistable nonlinearity. We show that measurements. nonzero-speed traveling fronts are unique up to In [7], we study the incompressible limit of a time translation and are globally two-component systems of GPEs with initial exponentially stable. The main tools used to data having a large number of vortices and an prove the uniqueness and asymptotic stability interface. The incompressible limit may of traveling fronts are the comparison provide the relaxation of turbulence such that principle, spectrum analysis, and constructions the turbulent flow can be self-organized into of super/subsolutions. To prove the existence vortex crystals. Recently, a rich variety of of traveling fronts, the system is converted to dynamical phenomena ranging from shock- an integral equation which is common in the wave formation to anisotropic sound study of monostable dynamics but quite rare in propagation has been observed in rotating the study of bistable dynamics. The main BECs. To see the dynamical phenomena of difficulty here is the lack of spatial (grid) rotating two-component BECs, we study the translation invariance. Introducing a compressible limit of two-component systems transformation with moving coordinates, we of GPEs. The compressible limit may describe have introduced in this paper a general geostrophic flow and provide rich dynamical framework for the study of traveling fronts in phenomena in rotating twocomponent BECs. discrete periodic media. In [8], we consider the orbital stability of In [5], in this paper we provide a single-spike bound states of semiclassical framework for constructing general complex nonlinear Schrodinger equations with critical geometrical optics solutions for several nonlinearity and a trap potential. Due to the systems of two variables that can be reduced to effect of the trap potential, we derive the a system with the Laplacian as the leading asymptotic expansion formulas and obtain the order term. We apply these special solutions to necessary conditions for orbital stability and the problem of reconstructing inclusions inside instability of single-spike bound states. Our of a domain filled with known conductivity argument is applied to two-component systems from local boundary measurements. of nonlinear Schrodinger equations with a Computational results demonstrate the common trap potential, cubic nonlinearity in versatility of these solutions to determine two spatial dimensions. The orbital stability of electrical inclusions. bound states with spikes of these systems is In [6], in this work we prove a global investigated. Our results show the existence of identifiability of the viscosity parameter in an stable spikes in two-dimensional Bose-Einstein incompressible fluid by boundary condensates.

Highlights of the Programs -›› 24 D.9 Probability Theory

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

D.9.1 Quantitative Studies for Markov and deduced an equivalent condition on the Processes existence of L2-cutoffs . For an illustration, they applied their method to the family of Ehrenfest chains and obtained a simple he qualitative behavior of Markov condition on the L^2-cutoff and an explicit processes has been analyzed in many formula for the L^2-mixing time. This reveals aspects and the stability of time homogeneous a possibility on the determination of the L^2- processes as time tends to infinity has been cutoff for Markov chains with orthogonal discovered for many decades. This observation polynomials as the eigenvectors. Moreover, makes it possible to compute the average of a they studied the relationship between the first function under a probability measure using and the second non-trivial eigenvectors and Markov processes. Such a method, which is acquired a sufficient condition on the total named as Markov chain Monte Carlo (or variation cutoff. briefly MCMC), has wide applications in many other disciplines including statistic D.9.2 Branching Processes and its physics, computer science, biology and etc. In Ramifications statistic physics, it is common to have to Branching processes in discrete time, also estimate the average configuration or entropy called Galton-Watson processes, first appeared of a dynamical mechanism. In biology, the as a discrete-time stochastic process to model question could concern the position of the last the extinction of British peerage. Its common ancestor of two related species in the continuous-state and continuous-time history of evolution or the expected spatial generalization has received attentions ever structure of a protein. From the perspective of since the first half of 20th century. In order to the MCMC method, this is achieved by capture the number of offspring in each simulating a Markov process with desired generation and to record the positions of the limiting distribution and choosing the state at a individuals, one considers a measure-valued certain time T as a random sample. However, process. A superprocess is a continuous limit knowing the qualitative behavior of of such measure-valued processes and it has convergence is not sufficient to determine the been studied extensively since the end of the sampling time T. A quantitative understanding eighties. Important researchers in this area of the mixing time is essential for theoretical include Watanabe, Dynkin, Dawson , Le Gall results. In practice, various heuristics are used and others. While its theory is intriguing in to choose T. itself, it also plays an important role in the Professor Guan-Yu Chen(AM, NCTU) has study of, for example, nonlinear partial worked with Laurent Saloff-Coste(Cornell differential equations and that of fractal University) on the exploration of the cutoff geometry. phenomenon for families of Markov processes The idea to study the genealogical since 2003. Recently, during his visit to structures of branching processes by random Cornell University, Guan-Yu Chen and his host tress is to construct a probability measure on Laurent Saloff-Coste discussed the L^2-cutoff the set of all the genealogical trees. While the for families of reversible Markov processes. construction of discrete random tree is They obtained a spectral representation for the apparent, it is not the same case for continuous L2-mixing time using spectral decomposition random trees until the sequence of seminal

25 ‹‹- Highlights of the Programs papers by Aldous. A Brownian snake is a path- regulatory networks of yeast as a model for valued process which combines the eukaryotic cells. These researches are genealogical structure of the continuous conducted with the collaborations with Wen- random trees with spatial random motions. It Hsiung Li at the University of Chicago, Lei Li turns out that the Brownian snake is a powerful at the University of South California, Huai- tool in the study of super-Brownian motion. Kuang Tsai, Jengnan Tzeng, and others at On the other hand, some recent study also Acdemia Sinica. showed the possibility of applications of continuous random trees to many other fields (I) Summer Course on Probabilistic and (stochastic coalescence and fragmentation Statistic Methods in Bioinformatics processes, statistical mechanics, (Every Tuesday, July 5 - July 26, 2007, combinatorics, to name just a few.) 10:00 - 12:00 and 13:00 - 15:00) From Dec.26, 2007 to Jan.10, 2008, This short course introduced the basic Professor Jean-Fran\c{c}ois Delmas techniques of probabilistic and statistic (CERMICS, Univ.Paris-EST) visited NCTS methods in bioinformatics. These techniques and gave a series of talks in NCTS, NCTU and will provide the foundation of advanced Academia Sinica. The research work of studied of bioinformatics in the post-genomics Professor Delmas encompasses the era. The course ended with special lectures aforementioned perspectives of branching given by Professor Wen-Hsiung Li (GRC, AS, processes. In the first talk in Academia Sinica and the University of Chicago.) he demonstrated the fragmentation processes Topics: associated with continuous random trees and how, as in his recent work, to take into account 1. The analysis of one DNA sequence (Prof. the notion of mutation in the genealogy of Chung-Chin Lu, EE, NTHU) random trees by pruning random trees. In the 2. The analysis of multiple DNA or protein remaining talks in NCTU and NCTS, he sequence( Prof. Wen-Ping Hsieh, IS, introduced the idea of coalescent processes and NTHU) detection of cellular aging. His recent work in coalescence is related to the length of 3. Blast (Prof. Henry Horng-Shing Lu, IS, coalescent time, that is the time to find two NCTU) most common recent ancestors of two 4. Gene expression, microarrays, and multiple individuals on the tree, and its asymptotic testing (Prof. Wun-Yi Shu, IS, NTHU) behavior when the family size tends to infinity. 5. Evolution models (Dr. Yun-Huei Tzeng, D.9.3 Probability with Biological GRC, AS) Applications 6. Phylogenetic tree estimation (Dr. Yun-Huei The foundation of scientific applications of Tzeng, GRC, AS) probability and statistics is the main theme for a series of studies in this focus group. (II) Student's seminars and courses Between 2004 and 2007, we had focused on Starting from the summer studies in 2008, the studies of graphical models. The we will start the on-going investigation of mathematical structure of network and systems biology and bioinformatics. In pathway analysis (which is one of the most summer, we will introduce and review research challenging problems in the era of functional topics related to systems biology and genomics) is related to graphic models and bioinformatics based on the references in their probabilistic properties. The theoretic literature. These studies will provide the properties for reconstruction of regulatory foundation for advanced studies of systems networks have been explored by the biology and bioinformatics in the post- perspectives of probability and statistics. genomic era that will be addressed by During the past year, we investigated the researchers in this field. Also we will continue

Highlights of the Programs -›› 26 the group studies at NCTS to the coming (1) Prof. Szu-Lang Liao( semesters and years. There will be more academic activities held by this study group at On the Valuation of CDO and Subprime NCTS that include seminars, workshops and Financial Crisis summer courses. Moreover, there will be (2) Dr. Hongbing Su( support courses in future semesters for ) students to learn. For instance, Professor Bor- Pricing and Risk-Managing Libor Exotics Sen Chen will teach a course of system in Practice biology at NTHU in the fall semester, 2008. Professor Yuan-Chung Sheu will teach a (3) Prof. Cheng-Der Fuh ( course of stochastic control and Professor / ) Henry Horng-Shing Lu will teach a course of The Pricing of Risk and Sentiment: A statistical learning at NCTU in the fall Study of Executive Stock Options semester, 2008. (4) Prof. Chii-Ruey Hwang( ) D.9.4 Workshop on Stochastics and An Empirical Invariance of Stock Price and Finance (April 21, 2008) Related Problems This workshop was organized by Prof. (5) Prof. Jun Sekine (Institute of Economic Chuan-Hsiang Han(NTHU), Prof. Yuan-Chung Research, Kyoto University , Japan) Sheu(NCTU) and Prof. Ching-Tang Wu On Risk-Premium Process in An (NCTU). Equilibrium

D.10 Scientific Computation

Coordinator: I-Liang Chern (National Taiwan University)

D.10.1 Background and Description science, etc. The funding of NCTS provided opportunities to bring researchers from different disciplines together. In the year 2007/8-2008/7, we focus on three he rapid growth of high performance interdisciplinary topics: (1) core algorithms, computers has transformed the (2) computational fluid dynamics, and (3) methodology of scientific investigation. computational nano-optics. Core algorithm Computing is nowadays joined experiment and focuses on interface problems, especially on theory as one of the fundamental tools of computing surface plasmon polariton appeared investigation. It is safe and cheap. Further, in in nano-optics. many cases, it can go beyond experiments or We also introduce multiscale computational observation, as those in astrophysics or methods by organizing short courses. meteorology, etc. Computational fluid dynamics focuese on CFD The development of computational science code implementation on PC-cluster, multi-grid needs integration of researchers from different and multi-level, preconditioner designs for disciplines: mathematics, physics, chemistry, flow solver. Application of CFD technique to biology, geoscience, engineering, computer computational medicine and industrial

27 ‹‹- Highlights of the Programs problems. Nano-optics focuses on Southampton, UK), K. Macdonald (U. of investigating the topics of optical responses in Southampton, UK), N. Papasimakis (U. of nanometer scale and the resultant intriguing Southampton, UK), R. Bakker (Purdue phenomena such as surface plasmon University, USA), M. Thoreson (Purdue resonances, plasmonic band gaps, and University, USA), Z. X. Shen (Nanyang anomalous light propagation in meta-materials. Technological University, Singapore), A. Through these programs, we integrate Fedyanin (Moscow State Univeristy, Russia), researchers from mathematics, physics and V. Panov (Moscow State Univeristy, Russia), engineering. Regular joint seminars and short X. Zhang (U. of Berkely, USA), T. Tanaka courses have been organized. We also held (Riken, Japan), H. Jackson (U. of Cincinnati, several international workshops on scientific USA), P. C. Yeh (U. of California, Santa computing to bring international researches Barbara, USA). and local researchers together. D.10.4 Seminars, short courses and D.10.2 Local focus group workshops (1) Core algorithms: I-Liang Chern (NTU), Chien-Cheng Chang (Academic Sinica and Regular seminars: There are 47 seminars NTU), Yu-Chen Shu (Academic Sinica), in 2007/8-2008/7 Wei-Chung Wang (NTU) (1) Biweekly seminar on scientific computing and Applied Mathematics (2) Computational Fluid Dynamics: Tony W. H. Sheu (NTU), K. M. Shyue (NTU), J. Y. (2) Computation and Simulation Monthly Yang (NTU), D. L. Yang (NTU), M. J. Seminars on Nano-photonics Huang (NTU), J. H. Lee (NTU), C. C. Yen (Fu-Jen), S. F. Tsai (NTOC) Short courses (3) Computational Nano-optics: Din Ping Tsai (1) France-Taiwan Exchange Program (NTU), Pui-Tak Leung (NTU), Railing Modeling & Simulations of Physiological Chang (NTOU), Hai-Pang Chiang flows, by Marc Thiriet. May 27-June 17, (NTOU), Pi-Gang Luan (NCU), I-Liang 2008 (36-hour course) Chern (NTU), Guang-Yu Guo (NTU), (2) Short course on image processing: Tutorial, Shen-Chung Chen (FEC), Yung-Chiang Jan. 2, 2008, I-L Chern, A Unified Tight Lan (NCKU), Chien-Cheng Chang (NTU), Frame Approach for Missing Data Ruey-Lin Chern (NTU), Chien Liu Chang Recovery in Images, Jan. 3, 4, 2008, (NTU), Yuan Fong Chau (LIT), Tai Huei Raymond Chan (Chinese University of Wei (NCCU), Wei-Chih Liu (NTNU), Jia- Hong Kong). Han Li (NTU), Sy-Hann Chen (NCYU), Bing-Hung Chen (NDHU), He-Nan Lin (3) Short course on Multi-scale Modeling, (NTHU), Ru-Shi Liu (NTU), Kuo-Pin Chiu Analysis and Simulation for Solid (NTU), Yuan-Hsing Fu (NTU), Chih-Ming Materials by Ping Lin (University of Wang (NDHU) Dundee, UK), 3/28, 4/1, 2008. (4) Frontier Nano-photonic Workshop, D.10.3 Short Term Visitors Semiconductor Quantum Dots, Nanowires, 2007/8-2008/7 and Nanobelts: Optical Imaging of New Nanostructures, by Prof. Howard Jackson Richard Y-H Tsai (Univ. of Taxes - Austin), (Department of Physics, University of Chiu-Yen Kao (Ohio State Univ.), Olof Cincinnati, Cincinnati, Ohio, USA), Runborg (KTH, Sweden), Raymond Chan September 05 (Wed.), 2007. (Chinese Univ. of Hong Kong), Ping Lin (University of Dundee, UK), B. Wakeham (U. (5) Workshop on Nanophotonics: Numerical of Southampton, UK), N. Zheludev (U. of Computations and Simulations, Metal- Southampton, UK), D. Hewak (U. of Dielectric Composite Superlenses, by Mark

Highlights of the Programs -›› 28 Thoreson (Photonics and Spectroscopy Science, NTU), Lab, Purdue University, USA). Optical I-Liang Chern (Taiwan University), nanoantennae: Initial design and Keh-Ming Shyue (Taiwan University), characterization with an eye towards device Weichung Wang (Taiwan University), development, by Reuben Bakker Tsung-Min Huang (Taiwan Normal (Photonics and Spectroscopy Lab, Purdue University), University, USA). January 04 (Fri.), 2008 Ming-Chih Lai (Chiao Tung University), at NTU. Chin-Tien Wu (Chiao Tung University), Yin-Tzer Shih (Chung-Hsing University), Workshops Ren-Chuen Chen (Kaohsiung Normal (1) Mini-workshop on strongly nonlinear wave University) equations, Aug. 6, 2008 (4) 2007 International Workshop on Modeling Roberto Camassa, University of North & Simulation in Health, Oct. 22-25, 2007 Carolina, USA Day 1:Tutorial course Long Lee, University of Wyoming, USA Day 2:Theoretical modeling and numerical Juan-Ming Yuan, Providence University, simulations & Modeling and Taiwan scientific computing applied to health problems (2) Mini-workshop on Multiscale computations: Jan. 31, 2008 Day 3:Medical image acquisition and processing 3D reconstruction and Heterogeneous multiscale methods with meshing application to the wave equation by Olof Runborg (KTH, Sweden) Day 4:Modeling, simulation and validation Wavelet-based Numerical Homogenization (5) Workshop on Nanophotonics: Numerical by Olof Runborg (KTH, Sweden) Computations and Simulations, January 04, 2008 at NTU A Numerical Multiscale Method for Highly Oscillatory ODEs by Richard Tsai, UT- Metal-Dielectric Composite Superlenses, Austin. by Mark Thoreson (Photonics and Spectroscopy Lab, Purdue University, (3) 2007 Taiwan-Japan Joint workshop on USA) Numerical Analysis and Scientific Computation, Nov. 30 (Fri.) to Dec. 2 Optical nanoantennae: Initial design and (Sun.), 2007 characterization with an eye towards device development, by Reuben Bakker (Photonics Hiroshi Fujiwara (Kyoto University), and Spectroscopy Lab, Purdue University, Yasushi Hataya (Yamaguchi University), USA) Hitoshi Imai (Tokushima University), Yuusuke Iso (Kyoto University), (6) The 5th International Workshop on Takayuki Kitamura (Kyoto University), Nanophotonics, December 04, 2007. The Tatsuyuki Nakaki (Hiroshima University), content of this course include a broad Yoshimasa Nakamura (Kyoto University), introduction to the topic of plasmonic Mitsuhiro T. Nakao (Kyushu University), nanophotonics. Its aim is to discuss the Yoshihiro Otani (Kyoto University), newly developed metamaterial Shigeru Takata (Kyoto University), nanostructures and their future applications Kenji Tomoeda (Osaka Institute of to nanophotonics. The theme of this Technology), workshop and speakers invited are Prof. Yoshitaka Watanabe (Kyushu University), Min Gu (Swinburne University of Yu-Chen Shu (Center for Research on Technology, Australia) "Femtosecond Applied Sciences, Academia Sinica, Laser Lights Optical Microscopy", Prof. Ze interface problems) Xiang Shen (Nanyang Technological Tony Wen-Hann Sheu (Engineering University, Singapore) "Femtosecond

29 ‹‹- Highlights of the Programs Laser Lights Optical Microscopy: Ultra- D.10.5 Select publications of the local high resolution Raman imaging by focus group optically trapped dielectric microsphere", [1] Chern, I-Liang and Yu-Chen Shu, Prof. Heh Nan Lin (National Tsing Hua Coupling interface method for elliptic University, Taiwan) "Metal and Metal interface problems, Journal of Oxide Nanowires for Nanophotonics", Computational Physics, no. 225 (2007) Prof. Ming Wen Chu (National Taiwan 2138-2174.(SCI) University, Taiwan) "Probing Bright and Dark Surface Plasmon Modes in Individual [2] Chang, C.C., Y-C Shu and I-L. Chern, and Coupled Au Nanoparticles Using a Solving guided wave modes in plasmonic Fast Electron Beam", Prof. Ta Jen Yen crystals, Phys, Rev. B, 78, 035133 (2008) (National Tsing Hua University, Taiwan) (SCI) "Magnetic and Two-handed [3] C. M. Ho, S. F. Tsai, R. K. Lin, P. C. metamaterials", Prof. Shi Wei Chu Liang, Tony W. H. Sheu, R. H. Hu, P. H. (National Taiwan University, Taiwan) Lee (2007), Computer simulation of "Molecular structure probed by optical hemodynamic changes after right nonlinear scattering" lobectomy in a liver with intrahepatic portal vein aneurysm, Journal of the (7) The 6th International Workshop on Formosan Medical Association, Vol. 106, Nanophotonics, March 11, 2008. The issue 8, pp. 617-623 (SCI) content of this course include a broad introduction to the topic of plasmonic [4] Tony W. H. Sheu, V. C. Huang (2008), nanophotonics. Its aim is to discuss the Development of an electro-osmotic flow newly developed metamaterial model to study the dynamic behavior in nanostructures and their future applications human meridian, International Journal for to nanophotonics. The theme of this Numerical Methods in Fluids, Vol. 56, pp. workshop and speakers invited are Prof. 739-751 (SCI) Nikolay Zheludev (University of [5] Tony W. H. Sheu, H. F. Ting, R. K. Lin Southampton, UK) "Coherent Meta- (2008), An immersed boundary method for Materials and the Lasing Spaser", Prof. the incompressible Navier-Stokes Dan Hewak (University of Southampton, equations in complex geometry, UK) "Through Thick and Thin: Our Work International Journal for Numerical with Chalcogenide Materials, Films and Methods in Fluids, Vol. 56, pp. 877-898 Devices", Prof. Ruey Lin Chern (National (SCI) Taiwan University, Taiwan) "LC and [6] P. H. Chiu, Tony W. H. Sheu, R. K. Lin Surface Plasmon Resonances for Split Ring (2008), An effective explicit pressure Structures" Prof. Shangjr (Felix) Gwo gradient scheme implemented in the two- (National Tsinghua University, Taiwan) level non-staggered grids for "Nanoparticle-based Plasmonics: Status incompressible Navier-Stokes equations, and Prospects", Prof. Yung Chiang Lan Journal of Computational Physics, Vol. (National Cheng Kung University, Taiwan) 227, pp. 4018-4037 (SCI) "Cavity-Modulated Resonant Tunneling [7] Tony W. H. Sheu, H. P. Rani, T. C. Tan, S. Effects Caused by Surface Plasmon F. Tsai (2008), Multiple states, topology Excitation", Dr. Kevin Macdonald and bifurcations of natural convection in a (University of Southampton, UK) "Long cubical cavity, Computers and Fluids, Vol. Pulse Delays; A Planar Metamaterial 37, pp. 1011-1028 (SCI) Analog of EIT", Dr. Nikitas Papasimakis [8] Tony W. H. Sheu, C. F. Chen, L. W. Hsieh (University of Southampton, UK) (2008), Development of a three-point "Nanophotonics Under the Electron sixth-order compact Helmholtz scheme for Microscope" scattering wave propagation, Journal of Computational Acoustics (accepted) (SCI)

Highlights of the Programs -›› 30 [9] V. C. Huang, Tony W. H. Sheu (2008), [12] Y. F. Chau, D. P. Tsai, L. F. Shen, T. J. Tissue fluids in microchannel subjected to Yang, Y. S. Sun, "The Plasmon and an externally applied electric potential, distribution effects between incident light

International Journal of Numerical Method and active layer in PtOx-type super- for Heat and Fluid Flow (accepted) (SCI) resolution near-field structure, "Optics [10] Harry Y. H. Chen, Tony W. H. Sheu Communication 281, 1293-1299 (2008). (2008), Development of a monotonic [13] K.P. Chiu, T.S. Kao, D.P. Tsai, upwind convection-diffusion finite "Evanescent field enhancement due to element model in two dimensions, plasmonic resonances of a metamaterial International Journal for Numerical slab, " Journal of Microscopy 269, 313- Methods in Fluids (in press) (SCI) 319 (2008). [11] V. C. Huang, Tony W. H. Sheu (2008), [14] T. S. Kao, Y. H. Fu, H. W. Hsu, D. P. Tsai, Heat transfer involved in acupuncture "Study of the optical response of phase- with burning moxibustion on the top of change recording layer with zinc oxide the handel of the acupuncture needle, nanostructured thin film, " Journal of Acupuncture & Electro-Therapeutics Microscopy 229, 561 Research (accepted)

D.11 Regional Programs in Hsinchu D.11.1 Matrix Computation Coordinator: Wen-Wei Lin (National Tsing Hua University/National Chiao Tung University)

n view of the potential of the real- researchers to offer some short courses and to world applications, without doubt, conduct cooperative research with our Scientific Computation (SC) becomes a community. A summary of our activities lists rapidly growing multidisciplinary research below. area. Based on the support of NCTS in the past years, the SC group gets blooming. The SC I. International Workshop program at NCTS has been getting cooperation with the PDE, Mathematical Biology, and Recent Advances in Numerical Methods Dynamical Systems programs in Mathematics for Eigenvalue Problems Division. (RANMEP2008), January 4-8, 2008 In this academic year (2007/9~2008/8), SC The purpose of the workshop is to provide group at NCTS particularly strengthened the a forum for numerical analysts, application frontier topic on the structured eigenvalue scientists and engineers to present the latest problems which usually arise from the progress on numerical methods for solving applications of vibration analysis of high- eigenvalue problems and discuss some of the speed train, surface acoustic wave filter, and challenges they are facing. Topics of the molecular biology etc. We now report the workshop include (i) methods for solving activities of SC group in this year. We have large-scale eigenvalue problems, (ii) structure- organized one international workshop and a preserving methods for the structured one-semester graduate course. Meanwhile, we eigenvalue problems, (iii) eigenvalue also have invited a number of distinguished applications in control, quantum physics and

31 ‹‹- Highlights of the Programs chemistry, and accelerator design etc. 1. Jacobi-Davidson Method for Large Sparse Eigenvalue Problems, The workshop brings some of the world's leading experts in these fields together and 2. Structure-Preserving Doubling Algorithms, aims at (1) providing an opportunity for direct 3. Structure Algorithms for Palindromic communication and exchange of ideas; (2) Quadratic Eigenvalue Problems: Vibration promoting interaction and collaboration of of Fast Trains, local and international scholars. The workshop included 14 foreign invited speakers, Peter 4. Jacobi-Davidson Method for Polynomial Arbenz (ETH Zurich, Switzerland), Peter Eigenvalue Problems, Benner (Chemnitz University of Technology, 5. Numerical Simulation of Jacobi-Davidson Gremany), Zhaojun Bai (University of Methods, California, USA), Francois Gygi (University of California Davis, USA), Do-Young Kwak 6. Projection-Free Jacobi-Davidson Methods (Korea Advanced Institute of Science and for Maxwell Equation, Technology, Korea), Fong Yin Lim (National 7. Finite Element Modelling of Fast Train University of Singapore, Singapore), Volker Rails, Palindromic Eigenvalue Problem, Mehrmann (Technische Universitat Berlin, Gremany), Axel Ruhe (Royal Institue of 8. Numerical Computation of Maxwell Technology, Sweden), Tetsuya Sakurai Equations, (University of Tsukuba, Japan), Danny 9. Fast Fourier Transformation. Sorensen (Rice University, USA), Yangfeng Su (Fudan University, China), Heinrich Voss III. Short Term Visitors (Hamburg University of technology, Gremany), Qiang Ye (University of Kentucky, 1. Professor Alastair Spence (University of Canada), Zhonggang Zeng (Northeastern Bath, United Kingdom) Illinois University, USA), and total number of Nov. 27 - Nov. 30, 2007 participant is 100 roughly. 2. Professor Ren-Cang Li (University of II. Autumn Graduate Course Texas at Arlington, USA) Jun. 5 - Jul. 4, 2008 NCTS & NTHU Topical Program in Prof. Li visited NCTS one month in this Structured Matrix Computation, summer and presented three talks: September - December 2007 1. Structure-Preserving Model Reduction. The purpose of the course is to introduce real application problems and the potential 2. Analysis for Nonlinear Dimensionality numerical methods to the researchers and Reduction Algorithms. graduate students who are working on SC. The 3. Vandermonde Matrices with problems and numerical methods include Applications to Convergence Analysis of especially, polynomial eigenvalue problems, CG and Lanczos Algorithms. palindromic quadratic eigenvalue problems, Maxwell equation in numerical computations In addition, he finished one paper with and structure-preserving algorithms for Wen-Wei Lin and Chern-Shuh Wang. vibration of fast trains or electrics problems, etc. Seven lecturers, Wen-Wei Lin (NTHU), 3. Professor Yuen-Cheng Kuo (National Tsung-Min Hwang (NTNU), Wei-Cheng Wang University of Kaohsiung) (NTHU), Chin-Tien Wu (NCTU), Yin-Liang Jun. 19 - Sep. 18, 2008 Huang (NTHU), Chern Shuh Wang (NCKU), Prof. Kuo visited NCTS two months in this Weichung Wang (NTU), share the course summer and focused on "palindromic which consists of several different topics eigenvalue problem" to develop a more related to eigenvalue problems and numerical effective transformation rather than S+S-1- methods. transformation. In addition, he also completed

Highlights of the Programs -›› 32 a joint work related to nonlinear Schrodinger our group. In the mean time, he completed two equations. joint works. 1. "A Hyperplane-Constrained 1. "On the *-Sylvester Equation AX ± Continuation Method for Bound States of X*B*= C", Chun-Yueh Chiang, Eric Coupled Nonlinear Schrodinger King-Wah Chu and Wen-Wei Lin. Equations", Yuen-Cheng Kuo, Wen-Wei 2. "Convergence Analysis of the Doubling Lin, Shih-Feng Shieh and Weichung Algorithm for Several Nonlinear Matrix Wang. Equations in the Critical Case", Chun- Yueh Chiang, Eric King-Wah Chu, 4. Professor Tsung-Min Hwang (National Chun-Hua Guo, Tsung-Ming Huang, Taiwan Normal University) Wen-Wei Lin and Shu-Fang Xu Jun. 20 - Sep. 19, 2008 Prof. Hwang visited NCTS about two 7. Professor Ting-Hui Yang (Tamkang months in this summer and finished three joint University) papers with the fellows of SC group. Jul. 15 - Sep. 15, 2008 1. "Structured Algorithms for Palindromic Prof. Yang visited NCTS two months this Quadratic Eigenvalue Problems Arising summer and finished two papers as follows. in Vibration of Fast Trains", Tsung-Min 1. "Viscous standing asymptotic states of Hwang, Wen-Wei Lin and Jiang Qian. transonic flows through a nozzle of 2. "Convergence Analysis of the Doubling varying area", John M. Hong, Ting-Hui Algorithm for Several Nonlinear Matrix Yang and Weishi Liu. Equations in the Critical Case", Chun- 2. "Diversity of traveling waves in Yueh Chiang, Eric King-Wah Chu, FitzHugh-Nagumo type equations", Chun-Hua Guo, Tsung-Ming Huang, Cheng-Hsiung Hsu, Ting-Hui Yang and Wen-Wei Lin and Shu-Fang Xu. Chi-Ru Yang. 3. "Structured doubling algorithms for solving g-palindromic quadratic 8. Professor Edward Allen (Texas Tech. eigenvalue problems", Eric King-wah University) Chu, Tsung-Ming Huang and Wen-Wei Aug. 1 - Aug. 14, 2008 Lin. Although Prof. Allen visited NCTS only two weeks, he provided us a short course 5. Professor Chern Shuh Wang (NCKU) entitled "Modeling Techniques and Numerical Jul. 1 - Sep. 15, 2008 Methods for Stochastic Differential Equations" Prof. Wang introduced some his recent which introduce some state of the art modeling results on the structure-preserving algorithm techniques in the world. After his series talks, and then he finished a joint work with Ren- he also gave us a 350-page lecture note. Cang Li and Wen-Wei Lin. 1. "Structured Backward Error for 9. Professor Chun-Hua Guo (University Palindromic Polynomial Eigenvalue of Regina, Canada) Problems", Ren-Cang Li, Wen-Wei Lin Mar. 1 - Jun. 30, 2009 and Chern-Shuh Wang. Prof. Guo plans to visit NCTS in next spring. However, he is already an active 6. Professor Eric Chu (Monash University, collaborator with our group. Recently he Australia) cooperated with Wen-Wei Lin to finish a paper Jul. 3 - Aug. 2, 2008 as follows. "Convergence Rate of the Cyclic Prof. Chu visited NCTS one month this Reduction Algorithm for Null Recurrent year and continued doing further work with Quasi-Birth-Death Problems", Chun-Hua Guo and Wen-Wei. Lin.

33 ‹‹- Highlights of the Programs D.11 Regional Programs in Hsinchu D.11.2 Nonlinear Partial Differential Equations Coordinators: Chern Jann-Long (National Central University, CTS) Tai-Chia Lin (National Taiwan University)

I. Activity of Visiting Scholars Title: TBA (3) Junping Shi, College of Willian and Mary, USA

s follows are the contents of lectures Title: Standing Pulse solution of a reaction- and activities of our visiting scholars. diffusion equation of logistic growth ¥ Emilio Acerbi (University of Parma, Italy) (4) Tai-Chia Lin, Taiwan University, Taiwan 2007/09/20-2007/10/03: Calculus of Title: Orbital stability of bound states of Variations, Parabolic PDE semi-classical nonlinear Schrodinger ¥ J. Bao (North Carolina UNCC) 2007/12/2- equations with critical nonlinearity 2007/12/23: PDE (5) Jann-Long Chern, Central University, ¥ Jann-Long Chern (National Central Taiwan University) 2007/08-2008/07: Elliptic PDE Title: Uniqueness of Topological Solutions ¥ G. El (Loughborough University, United and the Structure of Solutions for the Kingdom) 2008/03/19-2008/04/01: Nonlinear Chern-Simons Equations with Two Higgs waves, Solitons, Fluid dynamics Particles Other visitors include: Chi-Hun Lin Taiwan-Tohoku Seminar on Differential (National Chiao Tung University), Y. Morita Equations, April 15, 2008 (Ryukoku University), Juncheng Wei (The Organizer: Jann-Long Chern (National Central Chinese University of HongKong), LieJune University, NCTS, Taiwan) Shiau (University of Houston), Tien-Tsan Eiji Yanagida (Tohoku University, Shieh (University of Arizona) Japan) II. Conferences Place: Tohoku University, Godo-To 802 Invite Speakers: Partial Differential Equations Day, November 28 (Wednesday), 2007 (1) Shota Sato (Tohoku University) Organizer: Jann-Long Chern (National Central Title: Solutions with Moving Singularties University, NCTS) for a Semilinear Parabolic Equation Tai-Chia Lin (National Taiwan (2) Zhi-You Chen (National Central University) University) Invite Speakers: Title: the Classification of Standing Wave (1) Eiji Yanagida, Tohoku University, Japan Solutions for the Schrodinger Equation Title: Singular solutions of the Fujita-type (3) Masaki Hoshino (Tohoku University) equation Title: Rate of Approach of Two Solutions (2) Kunimochi Sakamato, Hiroshima for a Semilinear Parabolic Equation with University, Japan Power Nonlinearity

Highlights of the Programs -›› 34 (4) Yong-Li Tang (National Central Instructor: Junging Shi ( ) University) (Department of Mathematics, College of Title: The Structure of Tadial Solutions for William and Mary, Virginia, USA) Elliptic Equations Arising from the Time: F2, F3, F4 ( 9:00 - 12:00), spherical Onsager Vortex 96 9 14 (5) Tatsuki Kawakami (Tohoku University) Place: Room 631 (6) Jann-Long Chern (National Central : MATH 610100 University) Title: On the Uniqueness and Structures of NCTS& NTHU Joint Course on Solutions for the Self-Dual Chern-Simons Nonlinear Analysis and Semilinear Model Elliptic Problems III. Courses , 2008/02-2008/06 NTHU & CMS & NCTS Joint Course on Instructor: Jann-Long Chern Bifurcation theory in Banach space and ( ) application to semilinear elliptic equations and systems Time: F2, F3, F4 ( 9:00 - 12:00), 97 2 22 Place: Room 734, , 2007/09-2008/01 : MATH 657400

D.12 Regional Programs in Taipei D.12.1 Algebraic Geometry--Three dimensional birational geometry Coordinator: Jung-Kai Chen (National Taiwan University)

I. Research achievements furthermore. Its geometric realization, and some more applications was discovered. More precisely, the behavior of baskets under elementary birational maps is studied. It inimal model program is one of the turns out that one can prove an effective main stream in the research of algebraic termination of flips in dimension three as an geometry. Even though there is a satisfactory application. Moreover, one can obtained an theory in dimension three, there are still many application in classification of weak Q-Fano interesting and important problems remaining. threefold, where the sharp lower bound for In this past year, Meng Chen and Jungkai Chen anti-canonical volume is proven to be 1/330. developed a systematical way of studying These works solved many open problems in three-dimensional singularities. It was first the birational geometry of threefolds. One can introduced to solve the problem on also expect these works have some more pluricanonical maps of general type. In the applications, especially in some effectiveness past year, we developed the theory of baskets or finiteness problems in dimension three.

35 ‹‹- Highlights of the Programs Professor Kollár (Princeton University) had 0704.1702 invited us to present an announcement, which J. A. Chen, M. Chen, An optimal was published in the prestigious journal Elec. boundedness on weak $\bQ$-Fano threefolds, Res. Announc. Math. Sci., 14, 69-73, (2007). Adv. Math., to appear. arXiv 0712.4356 II. Publications related to this topic J. A. Chen, M. Chen, Explicit birational in recent years geometry of threefolds of general type, submitted. arXiv 0706.2987 F. Campana, J. A. Chen, T. Peternell, On strictly nef divisors, Math. Ann., to appear. J. A. Chen, C. D. Hacon, On Ueno's arXiv 0511042 Conjecture K, submitted. arXiv 0802.1060. J.A. Chen, M. Chen, The canonical volume J. A. Chen, C. D. Hacon, On the geography of threefolds of general type with X<1, J. of threefolds of general type, submitted. arXiv London Math. Soc., to appear. arXiv 0802.0884.

D.12 Regional Programs in Taipei D.12.2 Arithmetic Geometry and Representation Theory Coordinator: Chia-Fu Yu (Academia Sinica)

I. Seminars 2008-04-24, 04-28, and 05-02, at AS. ¥ Professor David Harari (University Paris- Sud) is going togive a series of 4 lectures on local-global principles in this December, at eminar on Arithmetic Geometry and AS. Representation Theory at NCTS, Taipei office, and Seminar on Number Theory II. Courses at Academia Sinica are two main activities related Number Theory in Taipei. 2007/8 NCTS Course on Representation From September of 2007 to August of 2008 Theory there are 20 talks scheduled in Taipei. Besides, This course is offered by Chia-Fu Yu every the following series of lectures have been Tuesday 9:00-12:00 from October 16 of 2007 organized in this period. to January 22 of 2008, and from Frubary 26 to May 13 of 2008. The scopes and topics of this ¥ Mr. Kai-Wen Lan (Harvard University), one year course are as follows. Arithmetic compactification of Shimura varieties of PEL-type (1)-(4), on 2008-01-02 The motivation of giving such a course is and 2008-01-03, at AS. the mostly visualized international development in the theory of automorphic ¥ Mr. Ming-Lun Hsieh (Columbia University), forms and their arithmetic applications. On the Eisensetien Series and p-adic L functions (1)- other hand, it is the serious lack of these (4), on 2008-01-07 and 2008-01-09, at AS. knowledge even for local admissible ¥ Professor Antoine Ducos (University of representations. This was the lecturer's attempt Nice), Berkovich Analytic Spaces (1)-(6), on

Highlights of the Programs -›› 36 to begin from completely zero to little and it is III. Student summer research our belief that after more than 10 years of program invest, there should be something there and In the summer of 2008, the student research these will grow up from little to a little, and program -"Algebraic Theory of Quadratic from a little to some in Taipei. Form" is organized by Chia-Fu Yu from July The goal of this course is to work out 14 to August 22. Two students are selected. In systematically the classification of irreducible the program we discuss the algebraic theory of smooth representations of GL(2) over non- quadratic forms. The goal is to introduce Archimedean local fields. We use the book by students the theory of quadratic forms over Bushnell and Henniart: The local Langlands local fields and more generally over the ring of conjecture for GL(2), Springer-Verlag, 2006. integers. The theory has a long history but In order to maintain the learning flow, in a part contrarily seldom delivered in graduate of this course students are also invited to courses in Taiwan. Lectures given and present and discuss. discussion organized by the organizing There are 4 students participating this professor every Tuesday morning from 9:30 to course, none of them even have basic 12:30. We cover Chapter VI of Serre's book A representation theory background. Fortunately, course in Arithmetic, and 2 thirds of the paper they are serious on this course. They oragnize by Jacobowitz "Hermitian Forms Over Local some meetings outside the class for some more Fields" Amer. J. Math. 84 (1962), 441-465. detailed discussion, sometimes simply for a Due to the limit background and time of single statement or a sentence of the book. students, this time we did not have the chance to work out some problems, as we plan. In Fall of 2007, we cover the first three chapters of the book and cover the next three IV. Publication chapters in the 2008 Spring. Overall, we cover [1] U.Görtz and C.-F. Yu, Supersingular the classification of irreducible smooth Kottwitz-Rapoport strata and Deligne- representations of GL(2) and the theory of Lusztig varieties, preprint 2008. types. Although the group we are working on is GL(2), the theory and methods help to [2] U. Görtz and C.-F. Yu, On the understand more general groups. We did not supersingular locus in Siegel modular have enough time to discuss the local varieties with Iwahori level structure, Langlands correspondence, which is one of preprint 2008. most importance topics. If these students [3] C.-F. Yu, Irreducibility and p-adic would stay in the next year, we would be able monodromies on Siegel modular varieties to cover all the main topics of the book. Adv. Math 218 (2008), 1253-1285. However, this is still a problem running [4] C.-F. Yu, Irreducibilities of the Hilbert- activities at Taipei - very good students would Blumenthal moduli spaces with parahoric not stay in Taipei long. level structure, to appear in J. reine angew. Most participating students grew-up from Math. 2008. these courses and went to abroad afterwards: [5] C.-F. Yu, An exact geometric mass Ms Pei-Yu Tsai entered Harvard University as formula. Preprint arXiv:0706.3474. a graduate student with full fellowship in Fall [6] J.-D. Yu, Variation of the unit root along of 2008. Ms Yueh-Yi Huang went to Padova the Dwork family of Calabi-Yau varieties, University as a graduate student with full to appear in Math. Ann., 2008. fellowship in Fall of 2008, in the second year [7] J.-D. Yu and N. Yui, K 3 surfaces of finite 2009-2010 she will come to University Paris hight over finite field, to appear in J. Sud with fellowship. Math. Kyoto Univ., 2008.

37‹‹- Highlights of the Programs D.12 Regional Programs in Taipei D.12.3 Functional Identities and Polynomial Identities Coordinator: Tsiu-Kwen Lee (National Taiwan University)

I. Participanting researchers 11, 23]. (organized by Tsiu-Kwen Lee) (4) In [16] Y. Zhou and T.-K. Lee obtained a complete characterization of Algebraic prime subalgebras in simple Artinian algebras. After this paper, we studied the hen-Lian Chuang (NTU), Pjek-Hwee irreducible and transitive subalgebras in Lee (NTU), Tsiu-Kwen Lee (NTU), matrix algebras (see [6]). Tsong-Chen Lee (SU), Chia-Hsin Liu (NTNU), Wen-Kwei Shiue (Dan Han), Ching- IV. Publications related to this topic Yueh Pan (Tunghai), Cheng-Kai Liu (NCUE). in recent years (2007-2008) (2008) II. Visitors related to this topic M. A. Chebotar (December2008) [1] M. A. Chebotar, P.-H. Lee, $\scr L$-prime rings need not be primary, Comm. Edmund R. Puczylowski (August 15- Algebra, 36 (3) (2008), 893--904. September 11, 2008) [2] M. Chebotar, W.-F. Ke, Wen-Fong and V. Di-Ming Luu (April 12- April 20, 2008) Lomonosov, Transitivity of Jordan Yiqiang Zhou (January 9- Feburary 5, algebras of linear operators: on two 2008) questions by Grünenfelder, Omladic and Radjavi. Integral Equations and Operator III. Research achievements: In this Theory, to appear. year we focus the following [3] T.-K. Lee and C.-K. Liu, Partially defined (1) Kothe conjecture: P.-H. Lee and Edmund $\sigma$-derivations on semisimple R. Puczylowskifinished a paper on Behrens Banach algebras, Studia Math., accepted. radical of matrix rings, which is related to [4] C.-L. Chuang, T.-K. Lee, C.-K. Liu and the famous Kothe conjecture. Y.-T. Tsai, Higher Derivations of Ore (2) Skew derivations: In this year we continue Extensions, Israel J. Math., accepted. to study the theory od algebraic skew [5] T.-K. Lee and Y. Zhou, A class of derivations. The papers [4, 10, 12] are exchange rings, Glasgow Math. J., related to this topic. In particular, in [12] accepted. we published the paper: The kernel and [6] T.-K. Lee and Y. Zhou, On irreducible and range inclusions of integral derivations in transitive subalgebras in matrix algebras, semiprime rings. This paper gives a Linear and Multilinear Algebra, accepted. complete solution concerning the problem of kernel and range inclusions. Following [7] C.-L. Chuang and T.-K. Lee, Density of this paper, we am studying the involution polynomial maps, Canad. Math. Bull., on differential polynomials. accepted. [8] T.-K. Lee and Y. Zhou, A theorem on unit- (3) Morphic and quasi-morphic rings: This regular rings, Canad. Math. Bull., topic is a meaningful generalization of accepted. regular rings and unit regular rings. Y. Zhou and T.-K. Lee have obtained some [9] C.-L. Chuang and T.-K. Lee and C.-K. substantial achievement. See the papers [8, Liu, Quotient rings and $f$-radical

Highlights of the Programs -›› 38 extensions of rings, Comm. Algebra, [14] T.-K. Lee and Y. Zhou, A unified accepted. approach to the Armendariz property of [10] C.-L. Chuang, T.-K. Lee and Y. Zhou, polynomial rings and power series rings, Constants of algebraic derivations in Colloq. Math., 113 (2008), 151-168. prime rings, Comm. Algebra, accepted. [15] T.-K. Lee, Z. Yi and Y. Zhou, An example [11] T.-K. Lee and Y. Zhou, Regurality and of Bergman's and the extension problem morphic property of rings, J. Algebra, for clean rings, Comm. Algebra 36(4) second review. (2008), 1413--1418. [12] C.-L. Chuang, T.-K. Lee and T.-L.Wong, [16] T.-K. Lee and Y. Zhou, Algebraic prime The kernel and range inclusions of subalgebras in simple Artinian algebras, integral derivations in semiprime rings, J. Linear Algebra Appl., 428 (2008), 881-- Algebra 320(7) (2008) 2643--2658. 889. [13] P.-H. Leee and E.R. Puczylowski, On the [17] J.-S. Lin and C.-K. Liu, Strong Behrens radical of matrix rings and commutativity preserving maps on Lie polynomial rings, J. Pure Applied ideals. Linear Algebra Appl. 428 (7) Algebra.212, 2163-2169. (2008), 1601--1609.

D.12 Regional Programs in Taipei D.12.4 P-minimizers in the Heisenberg Group and Integrable Systems Coordinator: Jih-Hsin Cheng (Academia Sinica)

I. Research achievements again to modify the details. Derchyi Wu generalizes the results of Villarroel, Fokas and Ioannidou, Dai, Terng and Uhlenbeck, to study the inverse scattering problem of the Ward n this year, Jenn-Fang Hwang and I equation with non-small data and solve the have been continuing the study of C1 Cauchy problem of the Ward equation with a smooth surfaces of prescribed p-mean non-small purely continuous scattering data. curvature in the Heisenberg group. We obtained more regularity results. In studying II. Visitors related to this topic: the singular set, we discovered an ordinary Andrea Malchiodi (Dec. 2007; March, differential equation of the p-area element 2008);Paul Yang (March, 2008); Weimin along characteristic curves. The behavior of Nhieu (July, 2008) the solution to this O.D.E. near the singular set is closely related to the configuration of the singular set. For the moment, we are writing III. Conferences and foreign visits up the results that have been obtained (see th [CHMY1]). During this year our regularity The 4 Pacific Rim Conference (City U., paper has been accepted for publication (see Hong Kong, Dec. 2007, Heisenberg geometry [CHY1]). The results about the existence of session organizer); Annual Meeting of Taiwan BV solutions and general first and second Math. Soc. (Academia Sinica, Dec. 2007, variation formulas have been written down Geometry and Analysis session organizer); th (see [CH1]) and we need some time to go over The 4 ICCM (Dec. 2007, invited speaker- supported by NCTS/TPE); Visit Kamishima

39 ‹‹- Highlights of the Programs at Tokyo Metropolitan Univ., Jan. 2008; Visit [CHMY1] Cheng, J.-H., Hwang, J.-F., Andrea Malchiodi at SISSA, June, 2008. Malchiodi, A., and Yang, P., The singular set of C1 smooth surfaces with prescribed p-mean IV. Publications related to this topic curvature in the Heisenberg group, in in recent years preparation. [C] Cheng, J.-H., Surfaces of prescribed p- [CHY1] Cheng, J.-H., Hwang, J.-F., and mean curvature in the Heisenberg group, Yang, P., Regularity of C1 smooth surfaces Proceedings of the 4th ICCM, Dec.17-22, with prescribed p-mean curvature in the 2007, Hangzhou, China, Vol II, 40-58. Heisenberg group, to appear in Math. Annalen [CH1] Cheng, J.-H. and Hwang, J.-F., (NCTS/TPE 2008-017). Variations of generalized area functionals and [W] D. Wu, The Cauchy problem of the P-area minimizers of bounded variation in the Ward equation, Journal of Functional Analysis Heisenberg group, manuscript. (2008), doi:10.1016/j.jfa.2008.06.009.

D.12 Regional Programs in Taipei D.12.5 Probability and Related Analysis Coordinator: Narn-Ruieh Shieh (National Taiwan University), cooperated by Lung-Chi Chen (Fu Jen University)

I. The activities of this topic in II. Accomplished papers 2007.08-2008.07 proceed as By Narn-Rueih Shieh follows (2008A) Hausdorff dimension of the contours of symmetric additive Levy processes. Probability Theory and Related Fields 140, 129-167. Joint work with D. 1. wo visitors Yimin Xiao Khoshnevisan and Y.M. Xiao. (Michigan State University) and Adrian P.C. Lim (Vandelbilt University) (2008A) The exact packing measure of visit NTU-Math at 2008.04 and 2008.06 Brownian double points. To appear in respectively. Probability Theory and Related Fields. Online at DOI 0.1007/s00440-007-0122-x . Joint work 2. Two one-day workshops at NTU-TIMS at with P. Morters. 2008.01.31 and 2008.07.10, jointly with TIMS, and NTU-Math. (2008B) Dilation-stable-like processes on fractals. In Proceedings of German-Japan 3. Irregular seminar at Wed afternoon; it Symposium at RIMS Kyoto University, pp 213- becomes a regular one since 2008.08, 219, ed. M. Fukushima and I. Shigekawa. faculty/students mixing talks. RIMS Research Notes Series Special Volume 4. Lung-Chi Chen is offered a full Tze-Zer (RIMS KΛokyΛuroku Bessatsu B6), 2008. Scholarship for a long-term visitor of (2008B) Operator semi-selfsimilar U.B.C. processes induced by multi-dimensional random walks in multi-dimensional random

Highlights of the Programs -›› 40 scenery. In Infinite Divisible Processes and ¥ (with Shu-Chiuan Chang) "Dimer-Monomer Related Topics (12). ISM (Tokyo, Japan) Model on the Sierpinski Gasket", Physica A, Cooperative Research Report 213. Joint work 387 (2008),1551-1566. with T. Saigo and H. Takahashi. ¥ (with Shu-Chiuan Chang) "Dimer Coverings (2007C) Multifractality of products of on the Sierpinski Gasket", Journal of geometric Ornstein-Uhlenbeck type process. Statistical Physics, 131 No. 4 (2008) 631- 650. Submitted. Joint work with V. Anh and N.N. Leonenko. ¥ (with Akira Sakai) "Critical behavior and the limit distribution for long-range oriented (2007B) Dimensions for images and percolation", Probab. Theory Related Fields, contours of additive L evy processes. In 142(2008) 151-188. Infinite Divisible Processes and Related Topics (11). ISM (Tokyo, Japan) Cooperative ¥ (with Shu-Chiuan Chang) "Spanning Forests Research Report 195. Joint work with Y.M. on the Sierpinski Gasket", Discrete Xiao. Mathematics and Theoretical Computer Science, 10:2 (2008), 55-76. By Lung-Chi Chen ¥ (with Akira Sakai) " Critical behavior and the ¥ (with Shu-Chiuan Chang andWei-Shih Yang) limit distribution for long-rang oriented "Spanning Tree on Sierpinski Gasket", percolation. II: Spatial correlation", accepted Journal of Statistical Physics, 126 No. 3 by Probab. Theory Related Fields. (2007) 649-667.

D.12 Regional Programs in Taipei 12.6 Semi- and Nonparametric Statistical Models for Biomedical and Financial Data Coordinator: Ming-Yen Cheng (National Taiwan University)

I. Local Focus Group (i) Train and guild potential students. (ii) Help the young colleagues develop their research work.

hu-Hui Chang (National Taiwan (iii) Develop state-of-art work on the topic. University), Hsiu-His Chen (National Taiwan University), Ming-Yen Cheng III. Activities (National Taiwan University), Chiou Jeng-Min (i) Seminars. We have weekly student (Academia Sinica. Statistics), Chih-Kang Chu seminars and talks given by colleagues and (National Dong Hwa University), Ruey-Ching visitors since the fall semester of 2004. The Hwang (National Dong Hwa University), John student seminars cover topics on Jen Tai (National Taiwan University), Jyh- nonparametric regression, nonparametric Shyang Wu (Tamkang University) modeling, semiparametric modeling, and so on. II. Goals (ii) Visitors. 2007-2008, Jeff C.F. Wu (Georgia

41‹‹- Highlights of the Programs Institute of Technology), Susan R. Wilson V. A list of Publications by Some (Australian National University), Marc Members of the Focus Group Raimondo (University of Sydney), 1. Cheng, M.-Y., Peng, L. and Wu, J.-S. Wenyang Zhang (University of Bath). As a (2007). Variance reduction in univariate result of these visits, several papers have smoothing. Annals of Statistics, 35, 522-- been published in prestigious journals such 542. as the Annals of Statistics and the Journal of the American Statistical Association, 2. Cheng, M.-Y. and Raimondo, M. (2008). and the local participants and students have Kernel methods for optimal change-points built connections with international estimation in derivatives. Journal of researchers. Computational and Graphical Statistics, 17, 56--75. IV. Achievement 3. Chen, L.-H., Cheng, M.-Y. and Peng, L. Enhance collaboration among the local people (2008). Conditional variance estimation in and international visitors. heteroscedastic regression models. Journal Introduce frontier topics in statistics to young of Statistical Planning and Inference, to mathematicians. appear. Encourage talented students to advanced study. 4. Cheng, M.-Y., Zhang, W. and Chen, L.-H. Students are supported to international (2008). Statistical estimation in workshops and conferences. generalized multiparameter likelihood models. Submitted.

D.12 Regional Programs in Taipei D.12.7 Stochastic Analysis and Mathematical Finance Coordinator: Shuenn-Jyi Sheu (Academia Sinica)

I. Local Focus Group II. Overview of Research on Probability Theory (i) Probability community is small

eng-Rung Hu (N. Taichung College There are about 20 people who are still Education), Ching-Tang Wu (N. Chiao active in research. Tung Univ.), Chun-Hsian Han ((N. Tsing-Hua I do not count people whose research is Univ.), Tai-Ho Wang (N. Chung Cheng Univ.), related to statistics. Hui-Ming Pei (N. Taipei Univ.), Chii-Ruey 9 people are young (in 5 years of PhD). Hwangz (Academia Sinica, Math.), Tzuu-Shuh Chiang (Academia Sinica, Math.), Yunshyong 4 people whose research relates to Chow (Academia Sinica, Math.), Shuenn-Jyi mathematical finance Sheu (Academia Sinica. Math. ), I-Ching Yiao (ii) The community grows slowly (Academia Sinica. Statistics ), Cheng-Der Fuh (N. Central Univ.) There are few courses on probability for undergraduate students.

Highlights of the Programs -›› 42 Most people enter probability theory by small amount of grant from National Science chance. Council. The NCTS supports are very helpful to their research in this regard. In the past few (iii) Research topics are diversified years, most of them got support from NCTS. (iv) There are three groups running some The research of Wang, Tai-Ho started from activities a visit to Courant Institute. Chiao Tung- Tsing Hua 6 people Chun-Hsian Han invited a student from UC Taiwan Univ. 2 people Santa Barbara a month to work. He used the Academia Sinica 4 people grant to attend a conference in UK. (ii) Train Our Students III. What We Hope to Achieve Senior members work with students by Since we have small group, this is a modest organizing study seminars for them or by project. We are more focus on stochastic doing research project. As a result, there are analysis related to mathematical finance. We now three students in PhD program in USA, are also interested in stochastic analysis in Shang-Yuan Shiu (University of Utah), general. In addition to the research works that I will briefly describe later, we hope to use the Hong,Jyy-I (Iowa State Univ.), project to achieve the following goal. (Brown University). (i) Help our young colleagues to grow in their One will enter University of California this research work. coming fall. We now also have two very good research assistants who will go abroad to enter (ii) Help to organize regular seminars for PhD program. We also help to run a study people to meet and discuss seminar on stochastic calculus for PhD (iii) Senior member can continue their research students from Management Department of and help to train good students NTU. IV. What We Have Achieved V. Visitors (i) Research Works of Our Young Members Hiroyuki Matsumoto, Oct 3-11 Toshio Mikami, Oct 25-Nov 2 Most of the young members in the focus Takahiko Fujita, Dec 2-10 group are all working on subjects related to Xunyu Zhou, Dec 3-5 mathematical finance. They often need to visit Jean-Francois Delmas, Dec 29-31 foreign countries to attend conference to learn , Dec. 23- Jan.1 new ideas or work with international scholars. Hui-Hsiung Kuo, Dec. 27, Jan. 2 For young colleagues, normally they only get

43 ‹‹- Highlights of the Programs D.13 Regional Programs in South D.13.1 Algebra and Geometry

I. Algebra Program A student seminar is also run by Wen Fong Coordinator: Ching Hung Lam Ke and Ching Hung Lam at weekly basis at Tainan. This seminar primarily aims at graduate students. The main subjects are Young diagrams and representations of symmetric groups in 2007/2008. here are three main research directions in algebra and representation theory. Workshops: One is the research leading by Ching Hung Workshop on Combinatorics and Algebras. Lam on the structures and representations of July 4-July 7, 2008 at NCKU. vertex operator algebras and their applications to finite group theory and other fields. Another Subjects: Parking functions, finite calculus, direction is on the representations of Lie super graphs algebras and their relations to various quantum Speaker: Jun Ma, Y-N. Yeh, X. Chu. groups leaded by Ngau Lam. The third topic is on the study of combinatorial structures related Organizer: Po Yi Huang to representation theory, jointly organized by Wen Fong Ke, Po Yi Huang and Ching Hung Summer/Winter Schools: Lam. Summer School on Lie Theory at Tainan, Aug. 11-Aug. 19, 2008 Local algebra group: Ching Hung Lam (NCKU), Ngau Lam (NCKU), Wen Fong Ke Subjects: Representations of Lie groups, Lie (NCKU), Po Yi Huang (NCKU), Chufeng super algebras and quantum groups Nien (NCKU). Speakers: Shun-Jen Cheng (Academia Sinica), Visitors in 2007/2008: Kyo Nishiyama Meng-Kiat Chuah ( NTHU ), Kyo Nishiyama ( (Kyoto), Hiroyuki Ochiai (Nagoya), Ruibin Kyoto), Hiroyuki Ochiai (Nagoya ), Ruibin Zhang (Sydney), Hiroshi Yamauchi ( Aichi), Zhang ( Sydney ) Gerald Hohn ( Kansas State), Toshiyuki Abe ( Organizer: Ngau Lam Ehime), Hiroki Shimakura (Aichi), Christian E. Lomp (Univ. do Porto), Koichi Betsumiya II. Geometry (Jobu), Robert Griess (Michigan), Gunter Pilz (Linz), Hubert Kiechle (Hamburg). Coordinator: Eugene Xia The Geometry group sponsored many Seminars in 2007/2008 visitors and research activities, ranging from Algebra Seminar: algebraic geometry to symplectic geometry to mathematical physics to algebraic topology A regular seminar is run weekly at NCKU: during the 2007-2008 academic year. Visitors including lectures given by visitors and given include: Hua-Liang Chang (SISSA), Siye Wu by the local group members. The main theme (University of Hong Kong), Mikhail Chebator is on the representation theory. The topics (Kent State University), Cheol-Hyun Cho include the representations of algebraic groups, (Seoul National University), Yang Su (Chinese Lie super algebras, vertex operator algebras Academy of Science) etc. Student's Seminar on Algebra: Seminar

Highlights of the Programs -›› 44 Speakers include: Hua Liang Chang us again in mid-September 2008. We also (SISSA, Italy), Siye Wu (University of Hong have plans to invite Professor Ser Peow Tan of Kong), Cheol-Hyun Cho (Seoul National the National University for a return visit. University), Yang Su (Chinese Academy of Starting in the Fall of 2008, the Geometry Sciences, China) group plans to run a semi-regular seminars on de Rham cohomology, compact Lie groups and Future Activities intersection cohomology. Dr. Hua-Liang Chang is scheduled to visit

D.13 Regional Programs in South D.13.2 Analysis and Application

I. Optimization to be held in Taiwan. In the conference, 2 Coordinator: Soon-Yi Wu keynote talks and 15 plenary talks are given by outstanding researchers in various areas of optimization. Speaker: Ivar Ekeland (University of British Columbia), Tien-Yien Li (Michigan ur main goal in 2008 is to joint some State University), Zhi-Quan Luo (University common research project among of Minnesota), Liqun Qi (The Hong Kong members and to learn some new topics. Polytechnic University), Alexander Shapiro The activities for our program from Sept. (Georgia Institute of Technology), Jie Sun 2007 to Aug. 2008 are as follows: (National University of Singapore), Kim Toh Chuan (National University of Singapore), 1. Visitors Kok Lay Teo (Curtin University of There were 7 visitors from Sept. 2007 - Technology), Tetsuzo Tanino (Osaka Aug. 2008. Visitors include : Marco Lopez University), Ya-Xiang Yuan (Chinese (University of Alicante), Jie Sun (National Academy of Sciences), Shu-Zhong Zhang (The University of Singapore), Miguel A. Goberna Chinese University of Hong Kong), Satoru (University of Alicante), Kok Lay Teo (Curtin Fujishige (Kyoto University), Masao University of Technology), Alexander Shapiro Fukushima (Kyoto University), Toshihide (Georgia Institute of Technology), XiaJiao Ibaraki (Kwansei Gakuin University), Tong (Changsha Univ. of Science & Masakazu Kojima (Tokyo Institute of Technology), Shunsuke Hayashi (Kyoto Technology), Shinji Mizuno (Tokyo Institute University) of Technology)

2. Conference II. Nonlinear Analysis We organize an international conference Coordinator: Jen-Chih Yao "Sino-Japanese Optimization Meeting (SJOM Professor Chong Li from the Department of 2008)". The SJOM 2008 will be held in NCTS, Mathematics, Zhejiang University visited the Tainan, Taiwan during August 27-31, 2008. Department of Applied Mathematics, NSYSU This is the first time for the SJOM conference and Professor Jen-Chih Yao from December 3

45 ‹‹- Highlights of the Programs to December 8, 2007. During the period of his Professor Nguyen Manh Hung (Department visit, he and Professor Yao had joint research of Mathematics, Hanoi National University of work on well-posdeness of perturbed Education) will visit the Department of optimization problems and one joint paper has Applied Mathematics, NSYSU and Professor been finished and has been submitted to Jen-Chih Yao from 2008/08/10 to 2008/09/10. Journal of mathematical Analysis and During the period of his visit, Professor Hung Applications for possible publication. Please will give 6 talks and does some joint research see the attached file. with Professor jen-Chih Yao.

D.13 Regional Programs in South D.13.3 Applied Mathematics

I. Discrete Mathematics engaged in discussions with our group. Coordinator: Xuding Zhu Besides those formal talks listed below, they also give some informal talks for our graduate students. There are a few preprints

2. Seminar Talks he research of the group is focused on Speakers include: Eiji Yanagida (Tohoku graph colourings, including game University), Yung-Sze Choi (University of coloring, adapted colouring, circular colouring Connecticut), Songying Li (University of and circular list colouring. We hosted four Irvine), V. Pyvovarchyk (South-Ukrainian visitors in January, 2008: Professor Hell State Pedagogical University, Odessa), Shin- (Canada), Professor Raspaud (France), Hwa Wang (National Tsinghua University) Professor Pecher (France) and Professor Montassier (France), and have fruitful III. Statistics Program collaborations. We plan to have a workshop on (Organizer: Tiee-Jian Wu) graph theory in Jan. 2009. II. Differential Equations 1. Overview The statistics program started its operation Coordinators: Chun-Kong in mid-March, 2008. It is only five months old and is at its initial stage. We have invited six 1. Overview academicians of Academia Sinica to serve as During this past year, we have invited the advisory members of our program. They several excellent scholars in differential are Y.-S. Chow ( ), George Tiao( equations to visit our Center. They are E. ), Jeff Wu( ), T.-L. Yanagida (Tohoku University), Yung-Sze Choi Lai( ), K.-Y. Liang( ) (University of Connecticut), Songying Li and R. Tsay( ). We have also (University of Irvine), V. Pyvovarchyk (South- formed the Academic Executive Committee Ukrainian State Pedagogical University, that currently includes T.-J. Wu ( ) of Odessa) Department of Statistics, NCKU, W.-J. During their visit, they were actively Huang( ) of Department of Applied

Highlights of the Programs -›› 46 Mathematics, NUK and M.-H. Guo( ) of Until now our program has already invited Department of Applied Mathematics, NSYSU. totally seven short-term visiting scholars (one This committee will be expanded as our of them is an academician of the Chinese program develops further in the future. National Academy of Science), held eight seminar talks (one by ), sponsored The focus group this year is classified as (i) the 2008 Probability workshop (about eighty Probability and Statistical Methods and (ii) participants) and co-sponsored the 2008 Applied Statistics, while the latter includes Statistics Conference of Southern Taiwan Biostatistics & Bioinformatics and Financial (about three hundred participants). Statistics & Time Series. Furthermore, we have already supported five The focus group on industrial statistics will young scholars to go abroad for research start its activities in 2009. The NCTS (South) collaborations and/or international plans to sponsor a machine learning workshop conferences. Among them there are two in 2009 and invite professor Jeff Wu( assistant professors, one from NCKU and one ) to the center to give a workshop or mini- NUK; and three PhD candidates, one from course, among others. NCKU and two NSYSC (see Appendix).

D.13 Regional Programs in South D.13.4 Probability and Statistical Methods

I. Probability Program Normal University, while lecture (iii) was Coordinator: Wen-Jang Huang given by Y.-S. Chow ( ). 2. Visitor There was one visitor M-F Chen ( ) from June 18, 2008 to July 4, 2008. He ur main goal is to generate some visited NCKU, NSYSU, NUK, NDHU common research interest among (Hualien), and Academia Sinica. In addition to members and to learn some new topics. those activities described in the I. Seminar The activities since March, 2008 are as above and the III Workshop below, he follows: attended the 2008 Statistics Conference of Southern Taiwan (held from June 27, 2008 to 1. Seminar June 28, 2008 at NDHU) and gave a special lecture in that conference. Totally, there were There were three seminar talks. They were: about three hundred participants. (i) "Starting from the first eigenvalue" (2008/6/24 at NSYSU), (ii) "Eigenvalues, inequalities and ergodic theory" (2008/6/25 at 3. Workshop NUK), and (iii) "Milestones of the The "2008 Probability Workshop" was held development of modern probability" on June 19, 2008 at NCKU. There were two (2008/6/12 at NCKU). Lectures (i) and (ii) lectures: (i) "Some Interactions of Probability were given by M-F Chen ( ), and Other Subjects", given by M-F Chen ( academician of Chinese Academy of Science ), and (ii) "Inference on Long- and School of Mathematical Sciences, Beijing Memory Stochastic Volatility Models-A Martingale Decomposition Approach", given

47 ‹‹- Highlights of the Programs by H-C Ho ( ) of Institute of Statistical of the academic year 2008. Sciences, Academia Sinica. Totally, there were about eighty participants. III. Biostatistics and Bioinformatics Coordinator: Tiee-Jian Wu II. Statistical Methods The activities since March, 2008 are as Coordinator: Tiee-Jian Wu follows: The activities since March, 2008 are as follows: 1. Seminar Professor Agnes Hsiung ( ) of Institute 1. Seminar os Biostatistics and Bioinformatics, NHRI Professor Y-J Chen ( ) of Institute of gave a lecture entitled:"Profiling time course Statistics, National Chung-Cheng University expression of virus genes-an illustration of gave a lecture entitles:"A generalized Bayesian inference under shape restrictions" correlation coefficient with applications to the on June 18, 2008 at NCKU. general two-treatment crossover design" on April 17, 2008 at NCKU. 2. Visitor Professor S.-H. Lo ( ) of Department 2. Visitors of Statistics, Columbia University visited our Professor P-Y. Chen ( )of center from July 7 to July 9, 2008. During his Department of Mathematics, Syracuse visit, we had many discussions on micro- University visited NCTS (South) from arrays and statistics in genetics. He gave a 6/25/2008 to 6/27/2008 and gave a talk speech on July 8 at NCKU. The title of the entitled: "A statistical aspect of signal speech made by him is the following: "Genetic processing". He has also discussed a joint methods in Bioinformatics". research work with Tiee-Jian Wu on "Model order selection for multivariate multiple 3. Short course and Symposium regression". A manuscript on this subject will Professor T.-L. Lai ( ) is be completed soon. scheduled to visit our center from Jan. 8 to Jan. Professor Baiqi Miao ( ) of 10, 2009. He will give a two and a half hours Department of and Finance and Statistics, short course in adaptive designs and sequential University of Science and Technology of analysis in clinical trials at NCKU and conduct China visited NCTS (South) from 8/11/2008 to a symposium in biostatistics/clinical trials at 8/26/2008. He gave three talks entitled: NUK. Professor Agnes Hsiung ( )of NHRI "Assessment theory and empirical methods for will also be invited to give a talk in that panel data" (8/13, NCKU),"The chance and symposium. challenge of modern statistics"(8/20, NUK), We plan to invite W-H Lee ( ) and "Limiting behavior of recursive M- to our center to give a mini-workshop in estimators in multivariate linear regression Bioinformatics in November or December, models and their asymptotic efficiencies"(8/22, 2008. NSYSU). Moreover, he has discussed and completed a joint work with Tiee-Jian Wu. The IV. Financial Statistics and Time paper entitled:" On asymptotic approximation Series of inverse moments of nonnegative random Coordinator: Mei-Hui Guo variables" is submitted to Statistics and Probability Letters. The activities for our group since March, 2008 are as follows: There is a plan to invite professor Grace Yang of the University of Maryland, College park to visit NCTS (south) in the Fall semester 1. Seminar Professor DL Yuen ( ) of Institute of

Highlights of the Programs -›› 48 Economics of North Eastern University, Japan lecture in applications of time series method visited our center and gave a speech entitled: and discuss possible statistical methodology in "Statistical analysis of the stock markets" studying the ozone hole problem. (May 27, 2008 at NCKU). Professor Wolfgang Haerdle of Humboldt- Universitat Zu, Berlin is scheduled to visit our 2. Visitor center from September 29 to October 5, 2008. Professor George Tiao ( ) is He will give two lectures (one in NCKU, one scheduled to visit our center from September in NSYSC) and discuss research ideas in 26 to September 29, 2008. He will give a financial mathematics and statistics.

49 ‹‹- Highlights of the Programs Activities of Onsite Scientists

TitleName Field Period Probability Guan-Yu Chen Stochastic Processes 2007/08/01-2009/07/31 Jiun-Cheng Chen Algebraic Geometry 2006/08/01-2009/07/31 Kuo-Chang Chen Dynamical Systems 2007/08/01-2008/07/31 Meng-Kiat Chuah Algebra 2007/08/01-2008/07/31 Cheng-Hsiung Hsu Dynamical Systems 2008/0801-2009/07/31 Ming-Chia Li Dynamical Systems 2007/08/01-2008/07/31 Center Scientists Chin-Cheng Lin Analysis 2008/0801-2009/07/31 Song-Sun Lin Dynamical Systems 2004/08/01-2008/12/31 Wen-Hsiung Lin Algebraic Topology 2007/08/01-2009/07/31 Dong-Ho Tsai Partial Differential Equations 2006/08/01-2008/07/31 Chin-Lung Wang Algebraic Geometry 2004/01/01-2008/12/31 Jing Yu Number Theory 2004/01/01-2009/07/31 Visiting Professor Der-Chen Chang Geometric Analysis 2008/05/01-2008/07/31 Visiting Associate Andreas Schweizer Number Theory 2008/08/01-2009/07/31 Professor Chieh-Yu Chang Number Theory 2007/10/22-2011/08/31 Postdoctoral Yu-Yun Chen Mathematical Biolog 2007/08/01-2009/07/31 Fellow Yan-Hsiou Cheng Dynamical Systems 2007/03/01-2008/07/31 Chian-Jen Wang Number Theory 2006/08/01-2008/07/31

.1 Center Scientists Southern Taiwan Statistical Conference, invited speaker. I. Guan-Yu Chen ¥ Taipei (July 10, 2008): TIMS "One-day Workshop on Probability and Finance, National Chiao Tung University, Assistant invited speaker. Professor – Japan – Conferences ¥ Kyoto (July 28-August 8, 2008): 1st MSJ-SI – Taiwan – Workshop "Probabilistic Approach to ¥ Hualien, (June 27-28, 2008): "The 17th Geometry at Kyoto University.

Activities of onsite Scientists -›› 50 Visits ¥ University of Illinois at Chicago (November, 2007): visiting Prof. Lawrence Ein a – USA – ¥ Department of Mathematics, Cornell ¥ Italy School and Workshop on Aspects of University (May 19-June 1, 2008): Host: Moduli (June 15-28, 2008, Pisa) Laurent Saloff-Coste NCTS Activities NCTS Activities ¥ NCTS Student Seminar in Algebraic ¥ NCTS Probability Seminar: Speakers Geometry, organizer. (November 13, 20 in 2007) (September 2007-June, 2008)

Publications Research Works ¥ Guan-Yu Chen and Laurent Saloff-Coste, ¥ A note on derived McKay correspondence, The cutoff phenomenon for ergodic Markov (with H.-H. Tseng), Mathematical Research processes. Electronic Journal of Probability, Letter 2008. 13 (2008), 26--78 ¥ Cone Theorem via Deligne-Mumford stacks, ¥ Guan-Yu Chen and Laurent Saloff-Coste, (with H.-H Tseng) submitted to Math Ann. The cutoff phenomenon for randomized riffle ¥ On Derived Mckay correspondence and shuffle. Random Structures Algorithms 32 moduli spaces for Deligne-Mumford stacks, (2008), no. 3, 346--374 in preparation. ¥ Guan-Yu Chen and Laurent Saloff-Coste, On ¥ On Picard number for Fano orbifolds, in 2 the L -cutoff for normal Markov processes. preparation. In preparation.

III. Kuo-Chang Chen II. Jiun-Cheng Chen National Tsing Hua University, Associate National Tsing Hua University, Assistant Professor Professor Invited Conference Talks Conferences and Visiting – Canada – – Japan – ¥ Workshop on Singularities, Hamiltonian and ¥ Kyoto and Nagoya (January, 2008): visiting gradient flows (May 2008, Montreal) Prof. Kawakita at RIMS and Prof. Fujino at Nagoya University. – China – ¥ International Congress of Chinese – Korea – Mathematicians (December 2007, ¥ KIAS(May, 2008): visiting Prof. J. -M. Hangzhou) Hwang. – France – – Hong Kong – ¥ Workshop on Mathematical Aspects of ¥ Chinese University of Hong Kong (August, Celestial Mechanics (December 2007, Paris) 2007): Lecture Series on the Minimal Model Program and Derived Category. ¥ Taiwan-France Joint Conference on Nonlinear Partial Differential Equations –United States – (March 2008, Marseille) ¥ Stony Brook (November, 2007): visiting Prof. Jason Starr. – Japan – ¥ Kyoto Dynamics Days 7 Ð Related Topics ¥ University of Wisconsin at Madison (June 2008, Kyoto) (November, 2007): Algebraic geometry Seminar. – Korea –

51 ‹‹- Activities of onsite Scientists ¥ Young Asian Conference on Partial ¥ NCTS Workshop on Symplectic and Differential Equations (January 2008, Complex Geometry, March 2008, Organizer. Pohang) ¥ NCTS Summer Student Seminar, ¥ International Workshop on Harmonic Introduction to Lie Algebras, July 2008, Analysis and PDE (February 2008, Seoul) Organizer.

– Philippine – Recent Publications ¥ Sino-Philippine Symposium in Mathematics (October 2007, Manila) ¥ Geometric quantization and Zuckerman models of semisimple Lie groups, Forum – Taiwan – Math. 19 (2007), 823-850. th ¥ The 16 Conference on Differential ¥ A quick proof on the equivalence classes of Equations (January 2008, NCTU) extended Vogan diagrams (with C. C. Hu), J. Algebra 313 (2007), 824-827. NCTS Activities ¥ Regular principal models of split semisimple ¥ NCTS 10th Anniversary, 1 lecture Lie groups, J. Reine Angew. Math., to (September 3, 2007) appear. ¥ NCTS Workshop on Dynamical Systems, co-organizer (May 23-25, 2008) ¥ NCTS Mini Course on Dynamical Systems, V. Ming-Chia Li "Recurrence in dynamical systems, 8 hours National Chiao-Tung University, lectures (July11-24, 2008) Professor ¥ NCTS Student Seminar on Dynamical Conferences and Visitings Systems, organizer (July–August, 2008) – Russia – Publications International Conference: Differential Equations and Topology (dedicated to the ¥ Existence and minimizing properties of centennial anniversary of L.S. Pontryagin, retrograde orbits to the three-body problem Steklov Mathematical Institute of the Russia with various choices of masses. Annals of Academy of Science, Lomonosov Moscow Math. 167, 325-348 (2008). State University, Moscow, June 17-22, 2008. ¥ On the mass center of the tent map. (with X. Dong). Preprint. Publications ¥ Variational constructions for some satellite ¥ Chaotic difference equations in two orbits in periodic gravitational force fields. variables and their multidimensional Preprint. perturbations, Nonlinearity, 21 (2008), 1019- 1040. (with J. Juang and M. Malkin) ¥ Chaotic dynamics in a monetary economy IV. Meng-Kiat Chuah with habit persistence, Journal of Economic National Tsing Hua University, Professor Behavior and Organization, 65(2008), 245- 260. (with H.-J. Chen) Conferences and Visitings ¥ Invited speaker, 4th International Congress ¥ An index changing bifurcation creating of Chinese Mathematicians. heterodimensional cycles, preprint, 2008. Hangzhou, China. December 2007. (with S. Kiriki and H. Kokubu)

NCTS Activities ¥ NCTS Winter Workshop on Representation Theory, January 2008, Organizer.

Activities of onsite Scientists -›› 52 VI. Song-Sun Lin 459-496. ( NSC Report, NSC94-2115-M- National Chiao-Tung University, 007-005) Chair Professor of National Chiao-Tung ¥ W. H. Lin, "The Kervaire invariant in 126, University. Part I: A homology theory in the Steenrod algebra, NSC Midterm Report, Conferences and Visitings NSC96-2115-M-007-004-MY2(2008). – U.S.A. – University of Florida, Miami, March 2008. VIII. Dong-Ho Tsai Publications National Tsing Hua University, Professor ¥ Patterns generation and spatial entropy in Recent Invited Talks two-dimensional lattice models, Asian ¥ International Congress of Chinese Journal of Mathematics, vol. 11, no. 3, 497- Mathematicians (45-minute talk), December 534. (2007). (with J.-C. Ban and Y.-H. Lin). 17-22, 2007, Zhejiang, China. ¥ Three-dimensional cellular neural networks ¥ Workshop on Geometric Analysis and and patterns generation problems, Several Complex Variables (50-minute talk), International Journal of Bifurcation and held at NCTS, June 24-25, 2008, Hsinchu, Chaos, vol. 18, No. 4, 957-984. (2008). Taiwan. (with J.-C. Ban and Y.-H. Lin). ¥ Workshop on Geometric Analysis (one hour ¥ Spatial complexity in multi-layer cellular talk), held at East China Normal University, neural networks, to appear in J. Differential July 27-31, 2008, Shanghai, China. Equation (2008) (with Jung-Chao Ban, Chih-Hung Chang and Yin-Heng Lin). Recent Publications ¥ Lin, T. C., Poon, C. C., Tsai, D. H. (2008) VII. Wen-Hsiung Lin Expanding Convex Immersed Closed Curves, to appear in Calculus of Variations National Tsing Hua University, Professor and PDEs. Conferences and visiting ¥ Lin, Yu-Chu, Tsai, D. H. (2008) On a Simple ¥ Visiting Beijing Tsing Hua University, China Maximum Principle Technique Applied to (part of a program of communications Equations on the Circle, to appear in Journal between the two "Tsing Hua Math. Depts" of of Differential Equations. the Taiwan Strait). ¥ Dates: Nov. 2, 2007-Nov. 6, 2007. IX. Chin-Lung Wang ¥ Title of the talk: A homology theory in the Steenrod algebra. National Taiwan University, Professor ¥ Projected participation of a conference to (since August 1, 2008) celebrate the 60th birthday of Professor National Central University, Professor (up Shing-Tung Yau at Harvard University. to July 31, 2008) ¥ Dates: Aug. 27, 2008-Sept. 1, 2008. National Center for Theoretic Sciences, ¥ Topic of the conference: Geometric Shiing-shen Chern Fellow (03 to 08) Analysis, Present and Future. Conferences and Visiting Recent Publications – France – 4,* 5,* ¥ W. H. Lin, "ExtA (Z/2,Z/2/) and ExtA ¥ Universitie Nantes (April): Laboratorie de (Z/2,Z/2/)", Topology and its Mathematiques Jean Leray. applications,Volume 155, Issue 5 (2008),

53 ‹‹- Activities of onsite Scientists – USA – ¥ International Conference on Geometric ¥ Harvard University (August): Geometric Analysis for Yau 60 Analysis, Present and Future. – Canada – ¥ An international conference to celebrate the ¥ Waterloo University(July 2008) 59 birthday of Shing-Tung Yau. Invited ¥ Canadian Number Theory Association speaker. Meeting – Taiwan – (forthcoming event) ¥ (Invited Speaker) ¥ National Tsing-Hua University (December): ¥ Fields Institute (October 2008) ¥ Annual meeting of the Taiwan Mathematical ¥ Workshop on Arithmetic Geometry Society 2008 Plenary speaker. – China – NCTS Activities ¥ (December 2007) ¥ NCTS Student Seminar in Complex ¥ The fourth ICCM Geometry, organizer. (FebruaryÐJune) ¥ (Invited Speaker) ¥ Research meeting with Y.-P. Lee (Utah) and – Japan – H.-W. Lin (NCU). (May at NCU, JuneÐJuly ¥ Yamagata (October, 2007) at NCTS) ¥ Galois theory and related Topics Conference Research Works ¥ (Invited Speaker) ¥ Elliptic functions, Green functions and the – Korea – mean field equations on tori, (with C.-S. ¥ Kaist (January 2008) Lin), Annals of Mathematics, accepted 2008. ¥ East Asian Number Theory Conference ¥ Motivic and quantum invariance under ¥ (Invited Speaker) stratified Mukai flops, (with B. Fu), J. – HongKong – Differential Geometry, accepted 2008. ¥ City University (December 2007) ¥ Invariance of Gromov-Witten theory under ¥ Pacific Rim Conference on Mathematics simple flops, (with Y. Iwao, Y.-P. Lee and ¥ (Invited Speaker) H.-W. Lin), submitted to Duke I. of Math. 2008. Visit ¥ Invariance of quantum rings under ordinary – HongKong – flops, (with Y.-P. Lee and H.-W. Lin), ¥ Department of Mathematics, HKUST(Sept. preprint 2008. 2007), Host : Jian-Shu Li.

Number Theory Seminar/Workshop X. Jing Yu – Taiwan – National Tsing-Hua University ¥ Summer School on Algebra and Number National Chair professor in Science Theory National Central University, ¥ (June 2008, Aspire Park), 1 lecture Adjunct Professor of Mathematics ¥ NCTS Number Theory Seminar ¥ (March through June 2008), 5 lectures Conferences ¥ Introduction to Langlands Program – United States– ¥ (June 2008, TIMS), 2 lectures ¥ Tucson (March 2008) ¥ Winter School on Algebra and Number ¥ Arizona Winter School Theory ¥ (NSF Observer) ¥ (February 2008, Aspire Park), 1 lecture ¥ Harvard University(August 2008) ¥ NCTS Number Theory Seminar

Activities of onsite Scientists -›› 54 ¥ (October through November 2007), 4 Tie from University of Georgia and Professor lectures Der-Chen Chang from Georgetown University, USA; Professor Ming-Yi Lee from National Publications Central University, Taiwan. All speakers gave ¥ On class number relations in characteristic very nice talks on different topics in sub- two (with Y.-M. J. Chen), Math. Zeit. 259 elliptic partial differential equations, sub- (2008), 197-216. Riemannian geometry, Fourier Analysis on band-limit functions, pseudo-differential ¥ Determination of algebraic relations among operator and its applications to Mathematical special Gamma values and Zeta values in Physics. positive characteristic (with C.-Y. Chang, and M. A. Papanikolas), preprint 2008. I also organized the "2008 FuJen Forum on Analysis" with Professor Nanping Yang at Fu ¥ Algebraic Independence of arithmetic Jen Catholic University on May 23, 2008. gamma values and Carlitz zeta values (with Professor Alexander Vasiliev, Professor Irina C.-Y. Chang, D. S. Thakur and M. A. Markina, Professor Alexander Olevskii and I Papanikolas), preprint 2008. gave talks at the Forum. Many faculty ¥ Frobenius difference equations and algebraic members and graduate students of Fu Jen independence of zeta values in positive attended this one day conference. This equal characteristic (with C.-Y. Chang, and opportunity provided an opportunity for M. A. Papanikolas), preprint 2008. mathematicians at Fu Jen University to exchange ideas in mathematics with foreign visitors. E.2 Visiting Professor The second workshop I organized with Professor Chiung-Jue Sung from National Name: Der-Chen Chang Tsing Hua University was the "2008 NCTS Georgetown University and NCTS Workshop on Geometric Analysis and Several Complex Variables" which was held Activities Participation: at NCTS and CTS from June 24 to 25, 2008. During my visit at NCTS, I gave a series of The invited speakers are Professor Min Ru lectures on "Singular Integrals, Pseudo- from University of Houston, Professor Sai Kee differential Operators and Analysis on Yeung from Purdue University Professor, Homoegeneous Groups" at NCTS and CTS. Professor Der-Chen Chang from Georgetown There were more than 12 students from University, Profesor Ovidiu Calin from Eastern National Tsing Hua University, National Michigan University, Professor Jun-Muk Chung-Cheng University and National Central Hwang from KIAS, Korea, Professor Wing- University plus several research assistants Keung To from National Singapore University, from NCTS to attend my lectures. Professor Chiung-Jue Sung and Professor I co-organized two Workshops with Dong-Ho Tsai from National Tsing Hua Professor Chiung-Jue Sung from National University. The workshop was quite Tsing Hua University. The first was "2008 successful. Speakers introduced their update NCTS Workshop on Harmonic Analysis research projects to audiences. and Complex Analysis" which was held at Besides that, I was invited to give NCTS and CTS from May 19 to 20, 2008. colloquium talks at many universities which The speakers were Professor Alexander including Academia Sinica, National Chung- Vasiliev and Professor Irina Markina from Cheng University and National Sun-Yat Sen University of Bergen, Norway; Professor W. University. These activities give me Schulez from Universite of Postdam, opportunities to exchange ideas in Germany; Professor Alexander Olevskii from mathematics with colleagues in Taiwan. Tel Avia University, Israel; Professor Jingzhi

55 ‹‹- Activities of onsite Scientists Current Projects: Calculus and Paneitz Operator I am working on subRiemannian geometry on the Heisenberg Group" induced by subelliptic partial differential 2008-1-002: Ovidiu Calin and Der-Chen equations which arise especially from several Chang "The Heat Kernel for complex variables. During my visit at NCTS, I Gravitational Potential have chances to discuss a joint project with Operators in One and Two Professor Shu-Cheng Chang at Tsing Hua Variables" University and Professor Hsuan-Pei Lee and 2008-3-001: Der-Chen Chang and Ming-Yi Chin Huei Chang at the Academia Sinica. We Lee "Generalized Calderón- are going to finish a paper on "Laguerre Zygmund Operators on calculus and Paneitz operator on the Homogeneous Groups and Heisenberg group". Applications" I finished a joint paper with Professor 2008-5-004: Der-Chen Chang, Dachun Yang Ming-Yee Lee from National Central and Yuan Zhou "Boundedness of University on "Estimates of generalized Sublinear Operators on Calder\'on-Zygmund operators in weighted Product Hardy Spaces and Its spaces". This paper will appear in Applicable Application" Analysis. 2008-5-005: Der-Chen Chang, Irina Markina During my visit at NCTS, I had finished a and Alexander Vasil'ev book with Professor Ovidiu Calin from Eastern "Modified Action and Michigan University (who visited NCTS Differential Operators on the 3- during the summe of 2006 also) on: D Sub-Riemannian Sphere" "SubRiemannian Geometry: General Theory and Exampls" which will publish by 2008-7-001: Der-Chen Chang and Wayne Eby Cambridge University Press. I also finished "Pompeiu Problem for Sets of two papers with another two visitors: Professor Higher Codimension, in Alexander Vasiliev and Professor Irina Euclidean and Heisenberg Markina on "Generalized Hamilton-Jacobi Settings" equation and heat kernel on step two nilpotent Lie groups" which will appear in "Analysis and Mathematical Physics", Trends in Mathematics, Birkh\"auser, 2009 and "Sub- E.3 Report of Post Doctors Lorentzian Geometry on Anti-De Sitter Space" Name: Chieh-Yu Chang which was appeared in J. Math. Pures Appl., 90, 82-110, (2008). We are working on a new Research: project which related to subRiemannian My research is concerned with geometry on the 3-dimensional unit sphere. transcendence theory over function fields in positive characteristic. Since 1980's, a series CTS Preprints: function field analogies of beautiful results in 2007-10-002: Der-Chen Chang and Bao Qin Li the classical transcendence theory have been "On Eiconal Type Partial developed by Yu. However, in 80's and 90's Differential Equations in C2" most results are about transcendence of single special value and linear independence. 2007-11-006: Der-Chen Chang, Irina Markina and Alexander Vasil'ev "Sub- By the work of Anderson-Brownawell- Lorentzian Geometry on Anti- Papanikolas [Ann. Math. 2004] and De Sitter Space" Papanikolas [Invent. Math. 2008], motivic methods have been introduced in this setting 2008-1-001: Der-Chen Chang, Shu-Cheng and make it possible from linear independence Chang and Jingzhi Tie "Laguerre to algebraic independence. This program can

Activities of onsite Scientists -›› 56 be regarded as an analogue of the classical Arithmetic of Function Fields in Positive Grothendieck's conjecture on periods of Characteristic (France), June 19-21 abelian varieties. That is, using motivic Canadian Number Theory Association X (algebraic) Galois groups to realize all the Meeting, Waterloo, July 13-18 algebraic relations among special values in question. According to Papanikolas' theory, Visiting: many problems related to algebraic Texas A&M University (March 1~July 31 independence in positive characteristic can be 2008) reduced to calculating the dimension of the Paris 6th University (June 12~June 18 2008) associated motivic Galois group. However, calculating such motivic Galois groups can be Publication and Preprint: very difficult. [1] C.-Y. Chang and J. Yu, Determination of My current research project is to show algebraic relations among special zeta algebraic independence concerning interesting values in positive characteristic, Advances special values, for example, the zeta values, in Mathematics 216 (2007), p321-345. gamma values and logarithms of algebraic [2] C.-Y Chang, A note on a refined version functions etc. For the joint work with Yu, we of Anderson-Brownawell-Papanikolas have carried out all the algebraic relations criterion, preprint, 2008. among special zeta values and further show [3] C.-Y. Chang, M. A. Papanikolas and J. Yu, that no extra algebraic relations among them as Algebraic independence of Carlitz zeta the constant fields vary (with Papanikolas and values with varying constant fields, Yu). We also work out the algebraic preprint, 2008. independence of special geometric gamma values and zeta values put together. We further [4] C.-Y. Chang, M. A. Papanikolas, D. S. work out the algebraic independence of special Thakur and J. Yu, Algebraic independence arithmetic gamma values and zeta values put of arithmetic gamma values and Carlitz together (with Papanikolas, Thakur and Yu). zeta values, preprint, 2008. [5] C.-Y. Chang and M. A. Papanikolas, After one-year work with Papanikolas, we Algebraic relations among periods and have shown the algebraic independence of logarithms of rank 2 Drinfeld modules, periods and quasi-periods for rank 2 Drinfeld preprint, 2008. modules without CM in the case of odd characteristic. In this situation, we also prove [6] C.-Y. Chang, M. A. Papanikolas and J. Yu, that among the logarithms of algebraic Determination of algebraic relations functions, the linear relations over the CM among special Gamma values and Zeta field of the Drinfeld module in question values in positive characteristic, preprint, account for all the algebraic relations. The case 2008. of higher rank Drinfeld module will be a challenge since the associated motivic Galois Name: Yu-Yun Chen group is much bigger and more complicated. My future plan is to finish this story. Research: My research interest is in ecology, Seminar/Workshop /Conference: especially on the subjects of forest dynamics NCTS Number Theory Seminar and evolution of forest phenology. These topics have been studies both empirically and NCTS Working Seminar on t-motives theoretically. My interest in the theoretical NCTS Winter School on Arithmetic Geometry work is to build evolutionary models for Number Theory Seminar in Texas A&M phenology divergence. The resource budget University model proposed from previous study is a Arizona Winter School, March 15-19 plausible model yet considered too few factors. Improving the model to include more plant-

57 ‹‹- Activities of onsite Scientists animal interactions is one of my research year: goals. This work is underway with a (1) Seminar in mathematical biology: the collaboration with Dr. Sze-Bi Hsu from the Unified Neutral theory for Diversity and Mathematics Department of Tsing Hua Ecology University and Dr. Shu-Ming Chang from the Applied Mathematics Department at the (2) Seminar in mathematical biology: National Chao-Tung University. To test the Evolutionary biology result of our theoretical work, I collaborate with Drs. I-Fang Sun from Tunghai University, 2. Talks given outside NCTS in the past Stephen P. Hubbell from UCLA, and Dr. S. year: Joseph Wright from the Smithsonian Tropical (1) Departmental seminar at the Institute of Research Institute on data collecting in the oceanology, National Taiwan University field. Field work covers forests in Taiwan as (2) Departmental seminar at the Applied well as in Southeast Asia. Mathematics Department, National Chao- In extending my interest on plant Tung University reproductive phenology, I plan to build a (3) Departmental seminar at the Institute of different evolutionary model for phenological Biophysics, National Chun-Hsin University divergence. In a discussion with Dr. Linda Allen from Texas Technology University, a (4) Symposium at the 2007 annual meeting of light was shed on a new model from the angle the Society of Botany from stochastic process. I intent to develop this (5) Weekly seminar at the Taida Mathematics idea and construct a community level model to center, National Taiwan University answer the question of phenological diversity. (6) Symposium at the 2007 annual meeting of Finally, I would like to develop skills on the Association for Tropical Biology and modeling of forest dynamics. This requires Conservation, Asia Chapter at Kuching skills to construct models and analytical technique for seeking answers. This would be 3. Workshop a challenging task for me yet I expect to benefit form obtaining these skills and to (1) Workshop on quantitative ecology, held by produce interesting and useful result from Academia Sinica and Tunghai University mathematical models for forest ecology. in Fushan Botanical Garden, August 2007. (2) Workshop on establishment of forest Seminar/Workshop/Conference: dynamics plots, held by the Center for In the last year, I co-hosted two seminar Tropical Forest Science, Smithsonian series on mathematical biology with Dr. Hsu in Institute, May 2008. the Center. These series were to introduce ecological ideas to mathematicians and to Future plans: demonstrate mathematical analyses for certain My short-term goal is to complete the topics. I was also invited to departmental modified resource budget model and to seminars in several universities, workshops, construct the new community level and conferences. In these occasions, I not only evolutionary model for forest phenological presented ideas from my previous and current patterns. My long-term goal is to apply studies but also exchanged ideas with methods of modeling and mathematic analysis participants of these meetings and started to various studies of ecology, especially on collaborations with them. Here I list the subjects of forest dynamics and related meetings I have attended both within and subjects. outside the Center:

1. Seminar series in NCTS in the past Name: Yan-Hsiou Cheng My research works include two portions,

Activities of onsite Scientists -›› 58 the nodal problem and the spectral theory. The solve the inverse problem. second course, the spectral theory, is the topic I 2. On the other hand, I hope that some am studying in the seminar held by Processor interesting problems will be discussed in the C.L. Shen in NTHU. Last year, we studied the seminar with Processor C.L. Shen. isoperimetric inequalities and membrane Additionally, I wish to learn more technique problems. Recently we discuss the properties and knowledge about my research. of the laplace operator defined on the sphere. We hope that the technique derived from 2- Papers: dimensional domains can be applied on the sphere and obtain similar results. 1. Y.H. Cheng , Reconstruction of the Sturm- Liouville operator on a p-star-shaped graph The research of the nodal problem is a joint with nodal data, to appear. work with Professor C.K. Law in National Sun Yat-sen University. I have went to NSYSU about every two months and discuss with Name: Chian-Jen Wang Professor C.K. Law. We hope to apply the inverse nodal theory to some other eigenvalue Research: problems. Recently, I discuss the Schrodinger My work this year includes two projects. operator defined on the star-shaped graph with The first one focuses on global automorphic general boundary conditions. I found that the representations, while the second one deals potential functions can be uniquely determined mainly with local p-adic representations. using only one set of nodal points. I gave the The first project is a continuation of my asymptotic expansion of the eigenvalues and study on distinguished metaplectic nodal points, and derive a procedure to representations on the covers of general linear reconstruct the potential functions and groups. These distinguished representations boundary conditions. generalize the concepts of famous theta During the past period in NCTS, I have functions. I am finishing up a paper on the participated in the following academic existence of cuspidal distinguished activities. representations on the four-fold cover of GL(4) which are constructed from Hecke characters. Seminar/Talks: Meanwhile, I am studying a related question concerning the distinguished representations 1. I joint the seminar held by Processor C.L. on the two-fold cover of GL(4). What is Shen in NTHU. We discuss the spectral interesting about this new case is that the problem of the Schrodinger operator and distinguished representations now are expected also read some papers and books. to be obtained from cuspidal automorphic 2. The Inverse Nodal Theory of Differential representations of GL(2). I hope similar Equations, Oct. 3, 2007, Tung-Hai technique as in the four-fold case can be University. applied to show the existence of such 3. Inverse Nodal Problems for Sturm-Liouville fascinating representations. operators, Oct. 16, 2007, Tamkang My second project is a joint work with University. Prof. Winnie Li and her Ph.D. student Ming- 4. Reconstruction formulas using nodal points Husan Kang concerning zeta functions of in Schrodinger equation, March 12, 2008, complexes arising from PGL(3). Using National Chung Cheng University. combinatorial method, Prof. Li and Kang obtained a closed form expression for such Future plans: zeta functions, which is analogous to Ihara's formula for graph zeta functions. 1. The Schrodinger operator defined on the general graph are also interesting. I wish to Our joint work uses representation- obtain some properties of the spectrum and theoretic method to obtain this closed form

59 ‹‹- Activities of onsite Scientists expression, which provides a different point of mirabolic subgroups of GL(n) including their view to understand these important zeta applications and one lecture on the local functions. The future goal is to extend our converse theorem at NCTS/TPE. While results to PGL(4) or even PGL(n) in general. visiting Penn State University, I delivered a seminar talk on metaplectic forms and the Seminar/Conference/NCTS Activity: converse theorem. At NCTS, we have number Last summer, I participated in the theory seminar every Wednesday, which I conference "on certain L-functions" attended regularly. I also participated in the (7/30/2007 Ð 8/3/2007) in honor of Shahidi's NCTS winter school on number theory and 60th birthday held at Purdue University. In arithmetic geometry taking place at the Aspire Fall, I visited Prof. Winnie Li and her research Park. I learned a great deal from attending group at Penn State University for three weeks these activities. (11/19/2007 Ð 12/7/2007). These are valuable experiences to me. I appreciate the generous Preprint: travel support from NCTS and the warm 1. (with Ming-Hsuan Kang, and Wen-Ching hospitality of Prof. Li. Winnie Li) The Zeta functions of complexes from PGL(3): a representation-theoretic During this year, I was invited to give a approach, preprint colloquium talk at NTNU on Langlands functoriality conjecture. I gave 3 lectures on

Activities of onsite Scientists -›› 60 Preprints

Series I Title and Author

Evolution of CR Yamabe Constant Under the Cartan Flow on a CR 2008-1-01 3-Manifold Chin-Tung Wu

On Eiconal Type Partial Differential Equations in C2 2008-1-02 Der-Chen Chang and Bao Qin Li

Motivic and Quantum Invariance under Stratified Mukai Flops 2008-1-03 Baohua Fu and Chin-Lung Wang

Convergence Rate of the Cyclic Recuction Algorithm for Null 2008-1-04 Recurrent QUASI-BIRTH-DEATH Problems Chun-Hua Guo and Wen-Wei Lin

Atomic Decomposition and Boundedness of Operators on Weighted 2008-1-05 Hardy Spaces Yongsheng Han, Ming-Yi Lee and Chin-Cheng Lin

Block Analysis on Spaces of Homogeneous Type and the T1 Theorem 2008-1-06 Yongsheng Han, Chin-Cheng Lin and Kunchuan Wang

Local Hardy-Littlewood Maximal Function 2008-1-07 Chin-Cheng Lin and Krzysztof Stempak

A Note on Derived McKay Correspondence 2008-1-08 Jiun-Cheng Chen, Hsian-Hua Tseng

Characterizing Projective Spaces for Varieties with at Most Quotient 2008-1-09 Singularities Jiun-Cheng Chen

Sub-Lorentzian Geometry on Anti-De Sitter Space 2008-1-10 Der-Chen Chang, Irina Markina and Alexander Vasil'ev

Three-dimensional Cellular Neural Networks and Patterns 2008-1-11 Generation Problems Jung-Chao Ban, Song-Sun Lin and Yin-Heng Lin

Least Cost Super Replicating Portfolio in the Boyle-Vorst Model 2008-1-12 with Transaction Costs Guan-Yu Chen, Ken Palmer and Yuan-Chung Sheu

61 ‹‹- Preprints Series I Title and Author

Laguerre Calculus and Paneitz Operator on the Heisenberg Group 2008-1-13 Der-Chen Chang, Shu-Cheng Chang and Jingzhi Tie

The Heat Kernel for Gravitational Potential Operators in One 2008-1-14 and Two Variables Ovidiu Calin and Der-Chen Chang

Structured Algorithms for Palindromic Quadratic Eigenvalue 2008-1-15 Problems Arising in Vibration of Fast Trains Tsung-Min Hwang, Wen-Wei Lin and Jiang Qian

On the -Sylvester Equation AX ± X*B*= C 2008-1-16 Chun-Yueh* Chiang, Eric King-Wah Chu and Wen-Wei Lin

On the Classification of Standing Wave Solutions for the 2008-1-17 Schrödinger Equation Jann-Long Chern, Zhi-You Chen, Jhih-He Chen and Yong-Li Tang

Uniqueness of Topological Solutions and the Structure of Solutions 2008-1-18 for the Chern-Simons System with Two Higgs Particles Jann-Long Chern, Zhi-You Chen and Chang-Shou Lin

On the Mass Center of the Tent Map 2008-1-19 Kuo-Chang Chen and Xun Dong

A Hyperplane-Constrained Continuation Method for Bound States of Coupled Nonlinear Schrödinger Equations 2008-1-20 Yuen-Cheng Kuo , Wen-Wei Lin , Shih-Feng Shieh and Weichung Wang

A Minmax Principle for Nonlinear Eigenproblems Depending 2008-1-21 Continuously on the Eigenparameter Heinrich Voss

Topological Uniqueness of Negatively Curved Surfaces 2008-1-22 Hsungrow Chan

Generalized Calderón-Zygmund Operators on Homogeneous 2008-1-23 Groups and Applications Der-Chen Chang and Ming-Yi Lee

Uniqueness of Finite Total Curvatures and Structure of Radial 2008-1-24 Solutions for Nonlinear Elliptic Equations Jann-Long Chern, Zhi-You Chen and Yong-Li Tang

Preprints -›› 62 Series I Title and Author

Towards a Hyperbolic Dynamics of Three-dimensional Hénon- 2008-1-25 like Maps, Part I Sergey Gonchenko and Ming-Chia Li

Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case 2008-1-26 Chun-Yueh Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung- Ming Huang, Wen-Wei Lin and Shu-Fang Xu

Variational Constructions for Some Satellite Orbits in Periodic 2008-1-27 Gravitational Force Fields Kuo-Chang Chen

Invariance of Gromov-Witten Theory Under a Simple Flop 2008-1-28 Y. Iwao, Y.-P. Lee, H.-W. Lin and C.-L. Wang

Structured Doubling Agorithms for Solving g-palindromic 2008-1-29 Quadratic Eigenvalue Problems Eric King-wah Chu, Tsung-Ming Huang and Wen-Wei Lin

The Linearization and Uniqueness of Solutions for Elliptic Systems 2008-1-30 Zhi-You Chen, Jann-Long Chern, Yong-Li Tang and Chang-Shou Lin

Uniqueness and Structure of Solutions to the Dirichlet Problem for 2008-1-31 an Elliptic System Jann-Long Chern, Zhi-You Chen, Yong-Li Tang and Chang-Shou Lin

The Structure of Radial Solutions for Elliptic Equations Arising 2008-1-32 from the Spherical Onsager Vortex Zhi-You Chen, Jann-Long Chern and Yong-Li Tang

Boundedness of Sublinear Operators on Product Hardy Spaces 2008-1-33 and Its Application Der-Chen Chang, Dachun Yang and Yuan Zhou

Modified Action and Differential Operators on the 3-D Sub- 2008-1-34 Riemannian Sphere Der-Chen Chang, Irina Markina and Alexander Vasil'ev

Non-Periodicity in Chemostat Equations: A Multi-Dimensional 2008-1-35 Negative Bendixson Dulac Criterion Bernold Fiedler and Sze-Bi Hsu

Pompeiu Problem for Sets of Higher Codimension, in Euclidean 2008-1-36 and Heisenberg Settings Der-Chen Chang and Wayne Eby

63 ‹‹- Preprints Series I Title and Author

Structured Backward Error for Palindromic Polynomial 2008-1-37 eigenvalue Problems Ren-Cang Li, Wen-Wei Lin and Chern-Shuh Wang

Microbial Competition for a Single Nutrient with Internal 2008-1-38 Storage in an Unstirred Chemostat Sze-Bi Hsu, Jifa Jiang and Feng-Bin Wang

Regular Principal Models of Split Semisimple Lie Groups 2008-1-39 Meng-Kiat Chuah

Stable Complete Noncompact Hypersurfaces withConstant Mean 2008-1-40 Curvature Jui-Tang Ray Chen

Motivic Integration and Projective Bundle Theorem in Morphic 2008-1-41 Cohomology Jyh-Haur Teh

Algebraic Relations Among Periods and Logarithms of Rank 2 2007-1-42 Drinfeld Modules Chieh-Yu Chang and Matthew A. Papanikolas

The Kervaire Invariant in Dimension 126 Part I: A Homology 2008-1-43 Theory in the Steenrod Algebra Wen-Hsiung Lin

Algebraic Independence of Arithmetic Gamma Values and Carlitz 2008-1-44 Zeta Values Chieh-Yu Chang, Matthew A. Papanikolas, Dinesh S. Thakur and Jing Yu

On a Simple Maximum Principle Technique Applied to 2008-1-45 Equations on the Circle Yu-Chu Lin and Dong-Ho Tsai

A Note on a Refined Version of Anderson-Brownawell- 2008-1-46 Papanikolas Criterion Chieh-Yu Chang

Reconstruction of the Sturm-Liouville Operator on a p-star 2008-1-47 Graph with Nodal Data Y. H. Cheng

Structured Backward Error for Palindromic Polynomial 2008-1-48 Eigenvalue Problems Ren-Cang Li, Wen-Wei Lin and Chern-Shuh Wang

Preprints -›› 64 Series I Title and Author

Diversity of traveling waves in FitzHugh-Nagumo type equations 2008-1-49 Cheng-Hsiung Hsu, Ting-Hui Yang and Chi-Ru Yang

Viscous standing asymptotic states of transonic flows through a 2008-1-50 nozzle of varying area John M. Hong, Ting-Hui Yang and Weishi Liu

The Entropy Formula for the CR Heat Equation on Closed CR 2008-1-51 3-Manifolds Shu-Cheng Chang and Chin Tung Wu

The Bondi-Mass Type Estimate on a Closed CR 3-Manifolds 2008-1-52 with Nonnegatvie Paneitz Operator Shu-Cheng Chang and Chin Tung Wu

Subgradient Estimate and Liouville-Type Theorems for the CR 2008-1-53 Heat Equation on Heisenberg Groups Shu-Cheng Chang Jingzhi Tie and Chin Tung Wu

Uniqueness and Stability of Traveling Waves for Periodic 2008-1-54 Monostable Lattice Dynamical System Jong-Shenq Guo and Chin-Chin Wu

Continuation of Topological Entropy for Multidimensional 2008-1-55 Perturbations of Snap-Back Repellers and One-Dimensional Maps M.-C. Li and P. Zgliczynski

On Stability of Forcing Relations for Multidimensional 2008-1-56 Perturbations of Interval Maps M.-C. Li and P. Zgliczynski

First Exit for Lévy-Type Processes with two-sided Matrix- 2008-1-57 Exponential Jumps from Open Sets Yu-Ting Chen and Yuan-Chung Sheu

A Robust Algorithm for Total Variation Deblurring and 2008-1-58 Denoising Qianshun Chang, Lung-Sheng Chien, Wei-Cheng Wang and Jing Xu

Characterization and Regularity for Axisymmetric Solenoidal 2008-1-59 Vector Fields with Application to Navier-Stokes Equation Jian-Guo Liu and Wei-Cheng Wang

65 ‹‹- Preprints Series II Title and Author The epic journey from Kepler's laws to Newton's law of 2008-2-01 universal gravitation Wu-Yi Hsiang and Hai-Chau Chang Density of polynomial maps 2008-2-02 Chen-Lian Chuang and Tsiu-Kwen Lee A unified approach to the Armendariz property of polynomial rings 2008-2-03 and power series rings Tsiu-Kwen Lee and Yiqiang Zhou Higher derivations of Ore extensions 2008-2-04 Chen-Lian Chuang,Tsiu-Kwen Lee, Cheng-Kai Liu and Yuan-Tsung Tsai On irreduciable and transtive subalgebras in mmatrix algebras 2008-2-05 Tsiu-Kwen Lee and Yiqiang Zhou L-prime rings need not be primary 2008-2-06 Mikhail A. Chebotar, Wen-Fong Ke and Pjek-Hwee Lee A note on polynomial rings over nil rings 2008-2-07 Mikhail A. Chebotar, Wen-Fong Ke, Pjek-Hwee Lee and Edmund R. Puczylowski On the Behrens radical of matrix rings and polynomial rings 2008-2-08 Pjek-Hwee Lee and Edmund R. Puczylowski The kernel and range inclusions of integral derivations in 2008-2-09 semiprime rings Chen-Lian Chuang, Tsiu-Kwen Lee and Tsai-Lien Wong

Adaptive group testing for consecutive positives 2008-2-10 Justie Su-tzu Juan and Gerard J. Chang Clique coverings and partitions of line graphs 2008-2-11 Bo-Jr Li and Gerard J. Chang Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig 2008-2-12 Ulrich Goertz and Chia-Fu Yu The supersingular locus in Siegel modular varieties with Iwahori 2008-2-13 level structure Ulrich Goertz and Chia-Fu Yu L(h,k)-labelings of Hamming graphs 2008-2-14 Lian-Hwao Huang and Gerard J. Chang Upper bound on k-tuple domination numbers of graphs 2008-2-15 Gerard J. Chang A Nonlocal Quenching Problem Arising in Micro-electro 2008-2-16 mechanical System Jong-Shenq Guo, Bei Hu and Chi-Jen Wang Regularity of $C^{1}$ smooth surfaces with prescribed $p$-mean 2008-2-17 curvature in the Heisenberg group Jih-Hsin Cheng, Jenn-Fang Hwang and Paul Yang

Preprints -›› 66 Series III Title and Author

Rootless pairs of EE -lattices 2008-3-01 8 R. L. Griess Jr. and C. H. Lam

+ Ising vectors in the vertex operator algebra VΛ associated with 2008-3-02 the Leech lattice Λ C. H. Lam, H. Shimakura

On the structure of framed vertex operator algebras and their 2008-3-03 pointwise frame stabilizers C. H. Lam and H. Yamauchi

Dihedral groups and Sums of EE8-lattices 2008-3-04 R. L. Griess Jr. and C. H. Lam

u-cohomology Formula for unitarizable modules over general 2008-3-05 linear superalgebras N. Lam and R B. Zhang

Activation strategy for asymmetric marking Games 2008-3-06 D. Yang, X. Zhu

Distinguishing number of group actions 2008-3-07 T. Wong, X. Zhu

Colouring games on outerplanar graphs and trees 2008-3-08 H. Chang, X. Zhu

Adaptive choosability of graphs and orientations 2008-3-09 M. Montassier, A. Raaaspaud, X. Zhu

Adaptable choosability of planar graphs with sparse short cycles 2008-3-10 A. Guan, X. Zhu

Bipartite density of triangle-free subcubic graphs 2008-3-11 X. Zhu

Bipartite subgraphs of triangle-free subcubic graphs 2008-3-12 X. Zhu

Circular Choosability via Combinatorial Nullstellensatz 2008-3-13 S. Norine, T. Wong, X. Zhu

67 ‹‹- Preprints Series III Title and Author

Circular consecutive choosability of graphs 2008-3-14 W. Lin, D. Yang, X. Zhu

Circular consecutive choosability of k-choosable graphs 2008-3-15 D. Liu, S. Norine, Z. Pan,X.Zhu,

A complete solution to the Ambarzumyan problem on graphs 2008-3-16 C. K. Law and E. Yanagida

A note on eigenvalue on forms 2008-3-17 C. K. Law and S. Li

Characteristic functions of quantum graphs 2008-3-18 C. K. Law and V. Pivovarchik

Inverse nodal problems and Ambarzumyan theorems for 2008-3-19 the p-Laplacian C.K. Law, W.C. Lian and W.C. Wang

Canonical Dual Approach to Solving 0-1 Quadratic 2008-3-20 Programming Problems S. C. Fang, David Y. Gao, R. L. Sheu and S. Y. Wu

Well-Posedness for Parametric Vector Equilibrium Problems 2008-3-21 with Applications K. Kimura, Y. C. Liou, S. Y. Wu and J. C. Yao

New Approach for the Nonlinear Programming with Transient 2008-3-22 Stability Constraints Arising from Power Systems X. J. Tong, S. Y. Wu and R. J. Zhou

Gap Functions and Duality for Vector Equilibrium Problems 2008-3-23 S. J. Li, C. R. Chen and S. Y. Wu

Optimality Conditions for Vector Optimization Problems 2008-3-24 N. J. Huang, J. Li and S. Y. Wu

Asymptotic approximation of inverse moments of nonnegative 2008-3-25 random variables Tiee-Jian Wu, Xiaoping Shi and Baiqi Miao

Preprints -›› 68 Visiting Mathematicians 2008

2008

Name Field of Interest Period of Visit Appendix Hubert Kiechle Algebra 2007/09/24 ~ 2007/10/02 (University of Hamburg) Hua-Liang Chang 2007/10/01 ~ 2007/10/25 Geometry (SISSA) 2007/12/08 ~ 2008/01/11 Siye Wu Geometry 2007/10/17 ~ 2007/10/22 (University of Hong Kong) Moshe Rosenfeld (University of Washington, Discrete Mathematics 2007/10/23 ~ 2007/11/01 Tacoma) Nassid Ghoussoub PDE 2007/10/31 ~ 2007/10/31 (Banff Center) Gunter Pilz (Johannes Kepler University, Algebra 2007/11/07 ~ 2007/11/09 Linz) Chi-Song Wong Discrete Mathematics 2007/11/18 ~ 2007/11/23 (University of Windsor) Marco Lopez Applied Mathematics 2007/11/18 ~ 2007/11/24 (University of Alicante) Alastair Spence Scientific Computation 2007/11/27 ~ 2007/11/30 (University of Bath) Jie Sun (National University of Applied Mathematics 2007/12/02 ~ 2007/12/08 Singapore) Chong Li Analysis 2007/12/03 ~ 2007/12/08 (Zhe Jiang University) Prof. Miguel A. Goberna Applied Mathematics 2007/12/05 ~ 2007/12/08 (University of Alicante) Prof. Kok Lay Teo (Curtin University of Applied Mathematics 2007/12/06 ~ 2007/12/08 Technology) Der-Chen Chang Classical Analysis 2007/12/13 ~ 2008/01/13 (Georgetown University) Eiji Yanagida Differential Equations 2007/12/17 ~ 2007/12/21 (Tohoku University) Xun Dong Topological methods in 2007/12/17 ~ 2008/01/14 (University of Miami) combinatorics Hiroshi Yamauchi Algebra 2007/12/24 ~ 2007/12/29 (Aichi University of Education) Koichi Betsumiya Algebra 2007/12/24 ~ 2007/12/30 (Jobu University)

69 ‹‹- Appendix 2008 Name Field of Interest Period of Visit Hiroki Shimakura Algebra 2007/12/24 ~ 2007/12/30

Appendix (Chiba University) Mikhail Chebator Geometry 2007/12/25 ~ 2008/01/01 (Kent State University) Jean-Frangois Delmas Probability 2007/12/26 ~ 2008/01/10 ( ENPS-CERMICS ) Eric K.-W. Chu Scientific Computation 2007/12/30 ~ 2008/02/05 (Monash University) Yung Sze Choi Differential Equations 2008/01/01 ~ 2008/01/07 (University of Connecticut) Yih-Jeng Yu 2008/01/01 ~ 2008/03/31 Number Theory (Universite Paris 13) 2008/08/18 ~ 2008/08/25 Raymond Hon-fu Chan Scientific Computation, (The Chinese University of 2008/01/02 ~ 2008/01/06 Numerical Linear Hong Kong) Richard S. Palais Applied Mathematics 2008/01/03 ~ 2008/01/04 (Professor Emeritus at Brandeis) Peter Arbenz (Universitätsstrasse 6, Scientific Computation 2008/01/04 ~ 2008/01/08 Switzerland) Zhaojun Bai Scientific Computation 2008/01/04 ~ 2008/01/08 (University of California, Davis) Peter Benner (Chemnitz University of Scientific Computation 2008/01/04 ~ 2008/01/08 Technology, Germany) Francois Gygi Scientific Computation 2008/01/04 ~ 2008/01/08 (University of California, Davis) Do Young Kwak Scientific Computation 2008/01/04 ~ 2008/01/08 (KAIST) Fong Yin Lim (National University of Scientific Computation 2008/01/04 ~ 2008/01/08 Singapore) Volker Mehrmann Scientific Computation 2008/01/04 ~ 2008/01/08 (Technische Universität Berlin) Axel Ruhe (Royal Institute of Technology, Scientific Computation 2008/01/04 ~ 2008/01/08 Sweden) Tetsuya Sakurai Scientific Computation 2008/01/04 ~ 2008/01/08 (University of Tsukuba) Danny Sorensen Scientific Computation 2008/01/04 ~ 2008/01/08 (Rice University)

Appendix -›› 70 2008 Name Field of Interest Period of Visit Yangfeng Su Scientific Computation 2008/01/04 ~ 2008/01/08

( ) Appendix Heinrich Voss (Hamburg University of Scientific Computation 2008/01/04 ~ 2008/01/08 Technology) Qiang Ye Scientific Computation 2008/01/04 ~ 2008/01/08 (University of Kentucky) Zhounggang Zeng (Northeastern Illinois Scientific Computation 2008/01/04 ~ 2008/01/08 University) Wing-Lung Lee (Hong Kong University of Geometry 2008/01/08 ~ 2008/01/14 Science and Technology) Yiqiang Zhou Ring Theory and Module (Memorial University of 2008/01/09 ~ 2008/02/05 Theory Newfoundland)

Yuen-Cheng Kuo 2008/01/16 ~ 2008/02/15 Scientific Computation (National University of 2008/06/19 ~ 2008/09/18 Kaohsiung) Frank K. M. Hwang Combinatorial Optimization, (National Chiao Tung Discrete Mathematics, 2008/01/17 ~ 2008/02/02 University) Communication Networks Chern-Shuh Wang 2008/01/21 ~ 2008/02/12 (National Cheng Kung Scientific Computations 2008/07/01 ~ 2008/09/15 University) Shin-Feng Shieh Dynamical System, 2008/01/21 ~ 2008/02/20 (National Taiwan Normal Applied Mathematics 2008/06/19 ~ 2008/09/18 University) Tsung-fang Wu 2008/01/21 ~ 2008/02/20 (National University of Nonlinear PDE 2008/06/19 ~ 2008/09/18 Kaohsiung) Tsung-Min Hwang 2008/01/21 ~ 2008/02/22 (National Taiwan Normal Scientific Computation 2008/06/20 ~ 2008/09/19 University) Olof Runborg (NADA, Royal Institute of Numerical Analysis 2008/01/23 ~ 2008/02/05 Technology(KTH) ) Jing-Song Huang 2008/01/24 ~ 2008/01/30 (Hong Kong University of Representation Theory Science and Technology) 2008/07/16 ~ 2008/07/25 K. Nishiyama Representation Theory 2008/01/24 ~ 2008/01/30 (Kyoto University)

71 ‹‹- Appendix 2008 Name Field of Interest Period of Visit H. Yamashita Representation Theory 2008/01/24 ~ 2008/01/30

Appendix (Hokkaido University) Chengbo Zhu (National University of Scientific Computation 2008/01/24 ~ 2008/01/30 Singapore) Yen-Hsi Richard Tsai (The University of Texas at Scientific Computing 2008/01/24 ~ 2008/02/05 Austin) Piotr Zgliczynski Dynamical Systems 2008/01/30 ~ 2008/02/23 (Jagiellonian University) Songying Li Differential Equations 2008/02/14 ~ 2008/02/27 (University of California, Irvine) Fei Xu Arithmetic Theory of Algebraic (Academy of Mathematics and Groups, Algebraic Number 2008/02/22 ~ 2008/03/28 System Sciences) Theory Cheol-Hyun Cho Geometry 2008/02/24 ~ 2008/02/29 (Seoul National University) Reyer Sjamaar Symplectic Geometry 2008/03/01 ~ 2008/03/08 (Cornell University) Yulii D. Shikhmurzaev Fluid Mechanics 2008/03/14 ~ 2008/03/17 (University of Birmingham) Christian E. Lomp (Universidade do Porto, Algebra 2008/03/14 ~ 2008/03/21 Portugal) Daphne Liu Graph Theory, Discrete (California State University, Los 2008/03/17 ~ 2008/03/21 Mathematics Angeles) Vyacheslav N. Pyvovarchyk (South-Ukrainian State Differential Equations 2008/03/17 ~ 2008/04/05 Pedagogical University) Gennady El Nonlinear Waves, Solitons, 2008/03/19 ~ 2008/04/01 (Loughborough University) Fluid Dynamics Siye Wu Symplectic Geometry 2008/03/22 ~ 2008/03/25 (University of Hong Kong) Susan R. Wilson Statistics 2008/03/24 ~ 2008/04/04 (Australian National University) Ping Lin Numerical Analysis and 2008/03/26 ~ 2008/04/04 (University of Dundee) Scientific Computing

Di-Ming Lu Ring Theory 2008/04/12 ~ 2008/04/20 (Zhejiang University)

Appendix -›› 72 2008 Name Field of Interest Period of Visit Yimin Xiao Probability 2008/04/20 ~ 2008/05/04

(Michigan State University) Appendix

Shin-Chuan Gou Quantum Optics, Statistical (Changhua University of Physics, Low - Temperature 2008/04/28 ~ 2008/05/16 Education) Atomic Physics Alexander Shapiro (Georgia Institute of Applied Mathematics 2008/05/04 ~ 2008/05/17 Technology) Yang Su Geometry 2008/05/05 ~ 2008/05/25 (Chinese Academy of Science) Irene Gamba Caffarelli Applied math 2008/05/06 ~ 2008/05/07 (University of Texas, Austin) Luis A. Caffarelli Differential, Geometry 2008/05/06 ~ 2008/05/07 (University of Texas, Austin) Irina Markina Real Analysis 2008/05/07 ~ 2008/05/30 (University of Bergen) Alexander Vasil'ev Complex and Applied Analysis 2008/05/07 ~ 2008/05/30 (University of Bergen) A.exander Olevskii Analysis 2008/05/08 ~ 2008/05/31 (Tel Aviv University) Hiroki Shimakura Algebra 2008/05/11 ~ 2008/05/17 (Aichi University of Education) Toshiyuki Abe Algebra 2008/05/11 ~ 2008/05/18 (Ehime University) Chi Hin Lau Geometry 2008/05/12 ~ 2008/05/25 (K.I.A.S.) B.-W. Schulze PDE 2008/05/17 ~ 2008/05/31 (Universität Potsdam) Complex Analysis

Weishi Liu (University of Kansas) Dynamical Systems 2008/05/18 ~ 2008/05/24

Chi-Kun Lin PDE, Nonlinear analysis, Fluid (National Chiao Tung 2008/05/21 ~ 2008/05/30 University) mechanics

Jaeyoung Byeon Nonlinear PDE, (Pohang University of Science 2008/05/22 ~ 2008/05/27 and Technology) Dynamical System Hyung Ju Hwang Dynamical System, athematical (Pohang University of Science 2008/05/22 ~ 2008/05/27 and Technology) Biology, Nonlinear PDE

73 ‹‹- Appendix 2008/05/29 ~ 2008/07/10 2008/05/29 ~ 2008/06/01 2008/05/29 ~ 2008/06/02 2008/05/24 ~ 2008/05/31 2008 PDEPath Integrals, Quantization, Stochastic Processes Algebra 2008/05/29 ~ 2008/06/03 ~ 2008/06/05 2008/05/31 PDE, Classical Analysis, Fluid Mechanics Nonlinear PDEs 2008/05/29 ~ 2008/06/02 Bioinformatics 2008/05/29 ~ 2008/06/07 PDEStatisticsNonlinear PDE 2008/06/01 2008/05/26 ~ 2008/05/26 ~ 2008/06/01 2008/05/27 ~ 2008/06/01 Pattern Formation and Dynamics in Reaction Equation and -Diffusion Equation, Ginzburg-Landau Bifurcation Structure of Solutions to Nonlinear Equat Differential Dynamical SystemDynamical EquationsSemi-linear Elliptic 2008/05/22 ~ 2008/06/01 2008/05/22 ~ 2008/05/27 Nonlinear PDE and Algebraic geometry singularity theory 2008/05/22 ~ 2008/06/01 Biofluid and Biomedical 2008/05/25 ~ 2008/06/21 Name of Interest Field Period of Visit Chuan Tai ei Yao oshihiro Tonegawa oshihisa Morita sujii Masato Y (Hokkaido University) Namkwon Kim (Chosun University) Reika Fukuizumi (Hokkaido University) Yu (University of California, San Francisco) Gerald Hohn (Kanasa State University) Dongho Chae (University of Chicago) Marc Raimondo (University of Sydney) Juncheng Wei Y University) (Ryukoku Adrian Poon Chuan Lim University, (Vanderbilt Nashville) (Chinese University of Hong Kong) (Kyushu University) T Liping Wang of (The Chinese University Hong Kong) W Yau Stephen Shing-Toung at (University of Illinois Chicago) Marc Thiriet (French Institute for Research in Computer Science and Control) (The Chinese University of (The Chinese University Hong Kong) 74 -›› Appendix

Appendix 2008 Name Field of Interest Period of Visit Hiroshi Yamauchi Algebra 2008/05/31 ~ 2008/06/06

(Aichi University of Education) Appendix

Zhen-Qing Chen Probability theory, Stochastic 2008/06/01 ~ 2008/06/10 (University of Washington ) analysis

Algebraic Geometry 2008/06/01 ~ 2008/06/30 (Harvard University)

Wen-Ching Winnie Li Automorphic forms, number (The Pennsylvania State theory, coding theory, and 2008/06/03 ~ 2008/06/26 University) spectral graph theory

Ren-Cang Li (University of Texas at Scientific Computation 2008/06/05 ~ 2008/07/04 Arlington)

Ariel Fernández Mathematical Biology 2008/06/15 ~ 2008/06/17 (Rice University)

Ruibin Zhang Lie Theory 2008/06/15 ~ 2008/07/05 (University of Sydney)

Hsiang-Ping Huang Operator Algebras 2008/06/16 ~ 2008/07/15 (University of Utah )

Yuan-Pin Lee Algebraic Geometry 2008/06/16 ~ 2008/07/15 (University of Utah)

Chun-Hsiung Hsia (University of Illinois at Nonlinear PDE 2008/06/16 ~ 2008/07/31 Chicago)

Mu-Fa Chen Statistics 2008/06/18 ~ 2008/07/04 (Chinese Academy of Sciences)

Sun-Yung Alice Chang Geometric Analysis 2008/06/20 ~ 2008/06/30 (Princeton University)

Je-Chiang Tsai (National Chung Cheng PDE 2008/06/20 ~ 2008/06/30 University)

Min Ru Complex Analysis 2008/06/23 ~ 2008/06/29 (Universit of Houston)

Algebraic Geometry, Jun-Muk Hwang Differential Geometry & 2008/06/24 ~ 2008/06/27 (KIAS) Geometric Analysis Wing-Keung To Complex geometry 2008/06/24 ~ 2008/06/27 (National Singapore University)

75 ‹‹- Appendix 2008/07/15 ~ 2008/09/15 2008/07/18 ~ 2008/07/22 2008/08/01 ~ 2008/08/14 2008/06/24 ~ 2008/06/27 2008 Mathematical BiologyDynamical Systems 2008/08/01 ~ 2008/08/14 Representation Theory 2008/08/06 ~ 2008/08/29 2008/08/08 ~ 2008/08/20 Arithmetic GeometryMathematical Biology 2008/07/12 ~ 2008/07/31 Applied Mathematics, Dynamical System, Scientific Computation 2008/07/14 ~ 2008/08/14 Computational Fluid Dynamics: particulate flows, rheology of suspensions and emulsions Stochastic Differential Equation, Scientific Computation Algebraic Geometry, Algebraic & Geometry Differential Geometric Analysis StatisticsAnalysisProbability and StatisticsApplied Mathematics 2008/06/29 ~ 2008/07/04 2008/06/25 ~ 2008/06/27 Scientific Computations 2008/06/26 ~ 2008/07/14 2008/07/01 ~ 2008/07/25 Nonlinear PDEs 2008/07/03 ~ 2008/08/02 StatisticsStatistics 2008/07/06 ~ 2008/07/13 2008/07/06 ~ 2008/07/20 2008/07/07 ~ 2008/07/09 Name of Interest Field Period of Visit enyang Zhang usuke Nishizawa ing-Hui Yang echnology) Xiaofan Li Y Metropolitan University) (Tokyo Kyo Nishiyama (Kyoto University) Linda Allen University) Tech. (Texas (Illinois Institute of Technology) Edward Allen University) Tech. (Texas Mu-Fa Chen Roeger Lih-Ing Wu University) Tech (Texas T University) (Tamkang (Queens University) XiaJiao Tong XiaJiao Tong of Science & (Changsha Univ. T Li Chen Beijing) University, (Tsinghua (Beijing Normal University) Sai Kee Yeung (Purdue University) Pinyuen Chen (Syracuse University) Ovidiu Calin University) (Eastern Michigan Chu Eric K.-W. (Monash University ) W Shaw-hwa Lo (Columbia University) Jeng-Daw Yu (University of Bath) 76 -›› Appendix

Appendix 2008 Name Field of Interest Period of Visit Chiu-Yen Kao Scientific Computing 2008/08/08 ~ 2008/08/25 (The Ohio State University) Appendix Hiroyuki Ochiai Algebraic Analysis 2008/08/10 ~ 2008/08/20 (Nagoya University)

Yong Zhang Dynamical Systems 2008/08/10 ~ 2008/08/31 (Suzhou University)

Yun Zhao Dynamical Systems 2008/08/10 ~ 2008/08/31 (Suzhou University)

Yongluo Cao Dynamical Systems 2008/08/10 ~ 2008/09/08 (Suzhou University) Nguyen Manh Hung (Hanoi National University of Analysis 2008/08/10 ~ 2008/09/10 Education) Bai-Qi Miao (University of Science and Statistics 2008/08/11 ~ 2008/08/26 Technology of China) Shunsuke Hayashi Applied Mathematics 2008/08/11 ~ 2008/09/02 (Kyoto University) Edmund R. Puczylówski Algebra (Ring Theory) 2008/08/15 ~ 2008/09/11 (University of Warsaw) Jacques Tilouine Number Theory 2008/08/19 ~ 2008/08/25 (Unniversité Paris-Sud) Shinji Mizuno Applied Mathematics 2008/08/26 ~ 2008/08/30 (Tokyo Institute of Technology) Toh Kim Chuan (National University of Applied Mathematics 2008/08/26 ~ 2008/09/01 Singapore) Ivar Ekeland Applied Mathematics 2008/08/26 ~ 2008/09/01 (University of British Columbia) Satoru Fujishige Applied Mathematics 2008/08/26 ~ 2008/09/01 (Kyoto University) Masao Fukushima Applied Mathematics 2008/08/26 ~ 2008/09/01 (Kyoto University) Toshihide Ibaraki Applied Mathematics 2008/08/26 ~ 2008/09/01 (Kwansei Gakuin University) Masakazu Kojima Applied Mathematics 2008/08/26 ~ 2008/09/01 (Tokyo Institute of Technology) Tien-Yien Li Applied Mathematics 2008/08/26 ~ 2008/09/01 (Michigan State University)

77 ‹‹- Appendix 2008/09/04 ~ 2008/10/03 2008 PDERing TheoryOperator Theory 2008/12/18 ~ 2009/01/03 2008/12/10 ~ 2008/12/24 2008/12/18 ~ 2009/01/03 Applied MathematicsApplied Mathematics ~ 2008/09/01 2008/08/26 Applied Mathematics ~ 2008/09/01 2008/08/26 Applied Mathematics 2008/08/26 ~ 2008/09/01 Applied Mathematics 2008/08/26 ~ 2008/09/01 Applied Mathematics 2008/08/26 ~ 2008/09/01 Applied Mathematics 2008/08/26 ~ 2008/09/01 Applied Mathematics 2008/08/26 ~ 2008/09/01 PDE 2008/08/26 ~ 2008/09/01 Algebra, Galois Cohomology, Number Algebraic geometry, Theory PDEPDE 2008/09/06 2008/08/31 ~ PDEPDE 2008/12/10 ~ 2008/12/17 2008/12/10 ~ 2008/12/17 2008/12/10 ~ 2008/12/17 2008/12/10 ~ 2008/12/17 i ù Name of Interest Field Period of Visit ictor Lomonosov a-Xiang Yuan oh Iwasa uan Lou echnology) echnology) etsuzo Tanino Mikhail Chebotar (Kent State University) V (Kent State University) Y (Ohio State University) Alexander Shapiro Institute of (Georgia T Kok Lay Teo (Curtin University of T Y (Chinese Academy of Sciences) Boris Kunyavski University) (Bar-Ilan (Osaka University) Jie Sun of (National University Singapore) T Shu-Zhong Zhang (The Chinese University of Hong Kong) Y (Kyushu University) Masayasu Mimura (Meiji University) Sebestian Schreiber (University of California at Davis) Gregory Smith and Mary) (College of William Zhi-Quan Luo Zhi-Quan (University of Minnesota) Liqun Qi Polytechnic (The Hong Kong University) Philippe Souplet (University of Paris-Nord) 78 -›› Appendix

Appendix NCTS 2008 Conference, Workshop & School

Time Conference & Workshop Place Appendix 2007 NCTS Summer School on Lecture Room of NCTS, Automorphic Representation Theory Sept. 4-7, 2007 National Tsing Hua Organizer: University Professor Jing Yu (NCTS & NTHU)

Recent Advances in Numerical Methods for Eigenvalue Problems (RANMEP2008) Lecture Room of NCTS, January 4-8, 2008 Organizers: National Tsing Hua Zhaojun Bai (UCD), Wen-Wei Lin University (NTHU), Chern-Shuh Wang (NCKU), Chao Yang (LBNL)

NCTS Winter Workshop on Representation Theory Lecture Room of NCTS, January 25-29, 2008 Organizers: National Tsing Hua Meng-Kiat Chuah (NTHU), Jing-Song University Huang (HKUST)

Topics in Multiscale Computations Speakers: Room 405, New Olof Runborg (NADA, Royal Institute of Mathematics Building, January 31, 2008 Technology, KTH) National Taiwan Yen-Hsi Richard Tsai (The University of University Texas at Austin, USA)

NCTS 2008 Winter School on Number Theory and Arithmetic Geometry Feb. 12-15, 2008 Aspire Park, Taoyuan Organizer: Jing Yu (NCTS & NTHU)

NCTS Workshop on Symplectic and Lecture Room of NCTS, Complex Geometry March 3-4, 2008 National Tsing Hua Organizer: University Meng-Kiat Chuah (NTHU)

Minicourse on Inverse Problems Speakers: Room 308, New Hyeonbae Kang (Seoul National Mathematics Building, March 19-21, 2008 University) National Taiwan Gen Nakamura (Hokkaido University) University Gunther Uhlmann (University of Washington)

79 ‹‹- Appendix Place Room 308, New Mathematics Building, National Taiwan University Room 405, New Mathematics Building, National Taiwan University Lecture Room of NCTS, Hua National Tsing University Lecture Room of NCTS, Hua National Tsing University Department of Math, National Sun Yat-sen University Lecture Room of NCTS, Hua National Tsing University orkshop of Nonlinear Partial orkshop of Dispersive PDE and of Dispersive PDE orkshop ei Yao (Chinese University of Hong Kong) ei Yao oshihisa Morita (Ryukoku University, Japan) University, oshihisa Morita (Ryukoku Japan) (Hokkaido University, oshihiro Tonegawa sarev Sergey (Krasnoyarsk State Pedagogical (Krasnoyarsk State sarev Sergey Speakers: (Chinese University of Hong Kong) Jun-Cheng Wei (Chinese University of Hong Kong) Liping Wang W Y Y Japan) Reika Fukuizumi (Hokkaido University, Korea) Namkwon Kim (Chosun University, Dongho Chae (University of Chicago, Korea) (The University of New England, Australia) Shusen Yan (National Chung Cheng University) Je-Chiang Tsai Organizers: & Univ. Chang (Georgetown Der-Chen NCTS) and Chiung-Jue Sung (NTHU) on Dynamical 2008 NCTS Workshop Systems Organizers: Kuo-Chang Chen (NTHU) Cheng-Hsiung Hsu (NCU) W Equations Related to Differential Physical Models University, Russia) University, Kamchatnov (Russian Academy Anatoly Mikhajlovich of Sciences) United University, Gennady El (Loughborough Kingdom) Defense University) Jen-Hsu Chang (National 2008 Organizer: Xuding Zhu (National Sun Yat-sen University) on Stochastics and NCTS Workshop Finance Organizers: Chuan-Hsiang Han (NTHU), Yuan-Chung (NCTU) Wu Sheu (NCTU), Ching-Tang on Harmonic and 2008 NCTS Workshop Complex Analysis Speakers: of Sciences) Bogdanov (Russian Academy Leonid V. Academy of Sciences) Oleg I. Mokhov (Russian T W Systems Integrable ime & Workshop Conference T March 30, 2008 May 30-31, 2008 May 23-25, 2008 April 21, 2008 May 19- 20, 2008 March 28, 2008 80 -›› Appendix

Appendix Time Conference & Workshop Place

Workshop on Statistical Methodology of

Microarray Data Appendix Speakers: Yu Chuan Tai (University of California at Room101, New San Francisco) Mathematics Building, June 6, 2008 Hsin-Chou Yang (Academia Sinica) National Taiwan Li-yu D. Liu (National Taiwan University) University Pei-Chun Chen (National Taiwan University) Robert Yuan (Academia Sinica)

2008 NCTS Workshop on Geometric Analysis and Several Complex Variables Lecture Room of NCTS, Organizers: June 24-25, 2008 National Tsing Hua Der-Chen Chang (Georgetown Univ. & University NCTS) Chiung-Jue Sung (NTHU)

2008 NCTS Summer School on Algebra & Number Theory, June 24-28, 2008 Aspire Park, Taoyuan Organizer: Jing Yu (NCTS & NTHU)

Organizers: Chih-Kang Chu (National Dong Hwa University) Mei-Mei Zen (National Cheng Kung University) Tiee-Jian Wu (National Cheng Kung University) Ray-Bing Chen (National Univ. of Kaohsiung) Department of Applied Yuh-Jia Wu (National Univ. of Kaohsiung) June 27-June 28, 2008 Math National Dong Fu-Chuen Chang (National Sun Yat-sen Univ.) Hwa University Mei-Hui Guo (National Sun Yat-sen Univ.) Mong-Na Lo (National Sun Yat-sen Univ.) Yu-Fen Huang (National Chung Cheng Univ.) Kam-Fai Wong (National Univ. of Kaohsiung) Yun-Chan Chi (National Cheng Kung University) Horng-Shing Lu (National Chiao-Tung Univ.)

81 ‹‹- Appendix Time Conference & Workshop Place

Appendix Organizers: Lecture Room of NCTS, Wen-Fong Ke (National Cheng Kung July. 4- July 7, 2008 National Cheng Kung University) University Po-Yi Huang (National Cheng Kung University)

One-day Workshop on Probability and Finance Speakers: Room 308, New Horng-Tzer Yau (Harvard University) Mathematics Building, July 10, 2008 Chuan-Hsiang Han (National Tsing Hua University) National Taiwan Ching-Tang Wu (National Chiao Tung University) University Guan-Yu Chen (National Chiao Tung University) Narn-Rueih Shieh (National Taiwan University)

Mini-Workshop on Strongly Nonlinear Wave Equations Speakers: Room 308, New Roberto Camassa (University of North Mathematics Building, August 6, 2008 Carolina, USA) National Taiwan Long Lee (University of Wyoning, University Laramie, USA) Juan-Ming Yuan (Providence University, ROC)

Summer School on Lie Theory Lecture Room of NCTS, Organizer: Aug. 11-Aug. 19, 2008 National Cheng Kung Ngau Lam (National Cheng Kung University University)

The 4th Sino-Japanese Optimization Meeting Organizing Committee: Lecture Room of NCTS, M. Fukushima (Kyoto University, Japan) Aug. 27-Aug. 31, 2008 National Cheng Kung L. Qi (Hong Kong Polytechnic University, Hong University Kong) S. Y. Wu (National Cheng Kung University, Taiwan) J. C. Yao (National Sun Yat-sen University, Taiwan)

Appendix -›› 82 Time Conference & Workshop Place

NCTS One-day Workshop for Summer Appendix Students Presentation Organizers: Kuo-Chang Chen (NTHU) Lecture Room of NCTS, Sept. 4, 2008 Meng-Kiat Chuah (NTHU & NCTS) National Tsing Hua Shu-Yen Pan (NTHU) University Jyh-Haur Teh (NTHU) Dong-Ho Tsai (NTHU) Jing Yu (NTHU & NCTS)

The Ninth Pacific Rim Geometry Conference Speakers: Kazuo Akutagawa (Tokyo University of Science, Japan) Robert Bartnik (Monash University, Australia) Shu-Cheng Chang (National Tsing Hua University, Taiwan) Jih-Hsin Cheng (Academic Sinica, Taiwan) Jaigyoung Choe (Korea Institute for Advanced Study, Korean) Mark Haskins (Imperial College London, Room 308, New UK) Mathematics Building, December 10-14, 2008 Yng-Ing Lee (National Taiwan University, National Taiwan Taiwan) University Naichung Conan Leung (The Chinese University of Hong Kong, China) Melissa Liu (Columbia University, USA) Zhiqin Lu (UC Irvine, USA) Richard Schoen (Stanford University, USA) Chiung-Jue Sung (National Tsing Hua University, Taiwan) Chuu-Lian Terng (UC Irvine, USA) Mu-Tao Wang (Columbia University, USA) Chin-Lung Wang (National Taiwan University, Taiwan) Xi-Ping Zhu (Sun Yat-Sen University, China)

83 ‹‹- Appendix Time Conference & Workshop Place

International Workshop on Mathematical Biology: Modeling and Analysis Appendix Speakers: Yoh Iwasa (Kyushu University, Japan) Yuan Lou (Ohio State University, USA) Masayasu Mimura (Meiji University, Japan) Sebestian Schreiber (University of California at Davis, USA) Gregory Smith (College of William and National Taiwan Normal December 15-16, 2008 Mary, USA) University Hsuan-Yi Chen (National Central University) Sze-Bi Hsu (National Tsing-Hua University) Sy-Sang Liaw (National Chung Hsing University) Hsiang-Ning Luk (Taichung Veterans General Hospital) Chih-Wen Shih (National Chiao Tung University)

Appendix -›› 84 Physics Division Report of the Division Head

General Remarks Mathematics Division are supported by the main project. Executive Committee he year 2008 is very special for NCTS The operation of the Physics Division has as the operation of the NCTS in the 2nd been conducted with the help of the executive phase has entered the last year. Except that the committee and PIs for subprojects. Due to main academic program have been operated other commitment in National Science coherently in the same way as before, the Council, Prof. Ching-Ray Chang ( ) Physics Division moved into the more resigned from the leadership for subproject I. I spacious fifth floor of the third General would like to thank Prof. Wei-Shu Hou ( Building at National Tsing Hua University ) for agreeing to lead subproject I. In (NTHU). The new space, when combined with accompany with the above change, there is a third of the space in the fourth floor, enabled also a sight change of Executive Committee in the operation of the Physics and Mathematics 2008. Prof. Xiang-Gang He ( ) of NTU Divisions at the same place in a more coherent joined the committee in replacement of Prof. way. Another key development was the Ching-Ray Chang. Prof. Der-San Chuu ( decision of National Science Council (NSC) to ) resigned from the committee later in this support NCTS for the next phase (2009-2014). year due to his retirement from National Chiao The decision was based on the external Tung University (NCTU). The rest members reviews with on-site review conducted in early are Hai-Yang Cheng ( ) of Academia January of 2008 and has made the future of Sinica (AS), Chon-Saar Chu ( ) of NCTS clear so that many long-terms plans can NCTU, Chung-Yu Mou ( , chairman), be committed. The detailed planning for the Sy-Sang Liaw ( ) of National Chung- next phase is now undertaken. Before we Hsing University, and Wei-Ming Zhang ( describe the on-site review, we shall first ) of NCKU. Members of Executive summarize highlights of academic activities of Committee represent various fields in NCTS Physics Division in 2008. Detailed theoretical physics, providing opinions and reports on each focus group can be found on suggestions based on their expertise, and the NCTS web-site http://phys.cts.nthu.edu.tw/. serving as the second reviewers of applications and recruitments submitted to NCTS. The budget allocation of NCTS in 2008 is approximately the same as those in previous years. About two-ninth and one-ninth of the Scientific Activities NCTS annual budget are channeled through The majority of the NCTS scientific Subproject I at National Taiwan University activities are planned and carried out by the (NTU), and Subproject II at National Cheng NCTS affiliated focus groups. All NCTS Kung University (NCKU), respectively. The sponsored activities have been posted on the rest of the NCTS budget is allocated in the NCTS web-site at http://phys.cts.nthu.edu.tw/ main project. The main project and subprojects as soon as it is planned, and also stayed on the support all activities of focus groups together, web-site afterwards as a future reference. In while the NCTS scientific personnel, and the the past two years, performance evaluation of additional NCTS sponsored functions, such as all focus groups was conducted each year. For the joint programs between Physics and the year 2008, "Softmatter, Biophysics and System Biology" and "Non-linear Phenomena

Report of the Division Head -›› 86 in Physical and Biological Systems" are retardation effect between two quantum dots is suggested to combined into a working group proposed. In particular, it is shown that by "Softmatter and Nonlinear Physics" so that measuring current noises, one is able to inviting international visitors and workshops measure the retardation effect. can be appropriately coordinated. The working In a joint effort of theoretical and group is now a structure that can act as a experimental investigation on the material bridge of two focus groups with overlapped LiCu O which was believed to be quantum participants but different focused directions. 2 2 spin-1/2 chains, Di-Jing Huang ( , In 2008, a number of activities were National Synchrotron Radiation Research performed through international collaborations Center)and Chung-Yu Mou (NCTS) showed with foreign prestigious physics centers. Late that instead of being quasi one-dimensional, in 2007, the Physics Division resumed the the ground state of the material exhibits long- organization of the KITP-type topic program. range 2D-like incommensurate magnetic order. The first topical program was on In particular, it is shown that the spin coupling "Superconductivity and Magnetism at along the c-axis is essential for the recently Nanoscale" and was a joint activity with the observed multiferroic behavior. This work was Argonne National Laboratory. The published in Phys. Rev. Lett. 101, 077205 coordinators are Prof. Baruch Rosenstein of (2008) and was also selected for highlighting NCTU and Prof. Valerii Vinokur of Argonne by Nature Publishing Group in Asia Materials National Laboratory. There were about eight website. outstanding visitors stationing at NCTS during By performing statistical analysis on the the program. The program was finished with a transmission properties of p53 gene with all concluding workshop. In order to enhance the possible point mutations, Chi-Tin Shih ( interaction of visitors with local community, a , Tunghai University) and collaborators host is assigned to each visitor. This program discovered that mutations that would cause sets up an example for the topical program in cancers in general result in weaker changes in the future. In addition to the topical program transmission of charges along DNA molecules. held at the Center, the Physics Division also This result suggests that charge transport may co-sponsored the KITP Program on "Advanced play an important role for repairing DNA and Topics on Flavor Physics" in the summer of has profound implication in understanding 2008 held at the Kavli Institute for Theoretical causes of cancers. The work was published in Physics, China. Six delegates supported by Phys. Rev. Lett. 100, 018105 (2008). NCTS attended the program. During the period of the program, the interaction among Taiwan During the past two years, triggered by the delegates and other foreign participants was work of Howard Georgi at Harvard intensive. In particular, there was a hot debate University, tremendous amount of work has on a recent hot subject: unparticle physics. The been devoted to investigate the presumed scale discussions have inspired all participants and invariant sector (coined as unparticle) with a some project were also initiated. The joint nontrivial infrared fixed point but the higher organization KITP topical program appears to energy scale may describe the real world. be quite useful for NCTS focus groups and Members from focus groups "Collider, will be encouraged in the future. Astroparticle and BSM" and "Particle, Nuclear and Cosmology" were able to catch the Highlights of Research research front and had published important Highlights of research in 2008 include the papers on this subject. In a series of papers, work by the Center Scientist, Prof. Yueh-Nan Kingman Cheung ( , Center Scientist, Chen ( ) of NCKU, and his collaborator NTHU), Tzu Chiang Yuan ( , NCTS) (L. Gilz) that was selected as the cover image and NCTS multi-year senior visitor, Wai-Yee of Applied Physics Letters (Sep. 29, 2008). In Keung ( , U. of Chicago) laid down the this work, a novel way to observe the formalism for calculations and identified

87 ‹‹- Report of the Division Head channels to observe effects due to unparticle at year. Five new members and one visiting high energy colliders. In particular, it was member have joined the Physics Division: Dr. pointed out that a nontrivial phase factor in the Chih-Hao Chen ( ) joined the working propagator would arise and induce interference group "Softmatter and Nonlinear Physics", Dr. with the Standard Model amplitude. These Hiroaki Koyhama joined the focus group works were published in Phys. Rev. Lett. 99, "Particle, Nuclear and Cosmology" at Taipei. 051803 (2007), Phy. Rev. D76, 055003 (2007), Drs. Chih-Wei Wang ( , Particle and Phy. Rev. D77, 097701 (2008) and have Physics and String), Dan Tomino (String received more than 200 citations in SPIRES Theory), Jae-Sik Lee (Particle Physics), and database. Prof. Haranath Ghosh (Visiting Professor, Condensed Matter Physics) joined the Physics For past years, members of the focus group Division at Hsinchu. In addition, through the "Particle, Nuclear and Cosmology" have been Center Scientist program, the Physics Division working closely with high energy has recently made a new appointment to a experimentalists in NTU. The strong string theorist, Prof. Yi Yang. The joining of interaction between theorists and Prof. Yi Yang has enhanced the local research experimentalists has resulted in many activity in string theory and enabled the important works both in theories and formation of a research group on string theory experiments. Recently, the experimental group at the NCTS Physics Division. The in NTU has measured the direct CP violation. appointment of Prof. Hsiu-Hau Lin ( , A large difference in the decay rate asymmetry NTHU), which was first made in early 2006, between charged and neutral B-meson decays - has been renewed at senior level and the (B± ➝ K±π0 versus B0 ➝ K+π− & B0 ➝ K-π+) appointment is demanded by the leadership in was observed. This important work was his research field. published in Nature 452, 332(2008) and is the first Nature paper from Taiwan high energy community. On-Site Review As mentioned at beginning, the second Young Theorist Award and Scientific phase of NCTS will end by this year. Hence it Staff is time to review the Center to determine the best way for its continuation into the next To encourage young colleagues to pursue phase. For this purpose, NSC has invited six excellent theoretical research, Young Theorist mathematicians and six theoretical physicists. Award was established in 2006. The For the physics part, the members include Executive Committee has selected Professors Shih-I Chu ( , NTU), Yia-Chung Chang Horng-Tay Jeng ( ) of AS and Chun- ( , AS), Gordon M. Crippen (University Khiang Chua ( ) of Chung Yuan of Michigan), Bambi Hu ( , University Christian University as the recipients in 2007. of Houston & Hong Kong Baptist University), In 2008, there are seven staff scientists Steven Louie ( , University of departing from the NCTS Physics Division. California at Berkeley), and Chien-Pang Yuan Among the recent departures, four members ( , Michigan State University). have found faculty positions in Taiwan. Dr. Yi The on-site review took place from January Yang ( ) was recruited by NCTU. Dr. Tzu 3 to 5. On the first day, the review began with Chiang Yuan joined the faculty at AS. Others a general report by the NCTS director, Jing Yu, who have accepted faculty positions are Dr. to all review committee members. Then the Wen-Hsuen Kuan ( ) at Taipei Physics and Mathematics committee separated. Municipal University of Education and Dr. Yu- The Physics committee then heard reports Pin Luo ( ) at National Formosa from the Physics Division Head (Chung-Yu University. To expand local supporting Mou), representatives of Center Staff scientific personnel, the Physics Division Scientists and Center Scientists. In the continues to recruit staff scientists in the past afternoon, after hearing brief report from each

Report of the Division Head -›› 88 focus group, the review committee met all Concluding Remarks coordinators and representatives from major The NCTS has entered the 12th year. During universities in Taiwan and heard suggestions the past eleven years, we have enjoyed strong from the physics community of Taiwan. support from the physics community in On the second day, the review committee Taiwan. On the other hand, nationawide conducted the on-site visits to subprojects I programs of the Physics Division have also and II at NTU and NCKU. The visit to NCKU helped in shaping and promoting researches of was in the morning. It started with a brief theoretical physics in Taiwan. We have seen introduction to the NCTS building at NCKU that under the nationawide programs, there is a and then followed by the report from Prof. substantial increase in scientific activities and Wei-Min Zhang. In the afternoon, the review the more focused research directions have been committee visited NTU to review subproject I. developed. The overall productivity of high After briefly visiting related scientific resource quality research works has also been units, the review committee heard general approximately doubled since the establishment reports from Prof. Gerard Chang and had panel of NCTS. For instance, number of theoretical discussions with representatives from Taipei papers published in Physical Review Letters area. has increased from about seven per year to fifteen per year. Although total productivity On the third day, the review committee seems to be saturated in recent years, more and stayed in the Hotel and drafted their reports. more of research works have gained I am grateful to report that committee international attention as one can see that just members are very pleased with the scientific for the year 2008, a number of works have directions and achievements of the Physics been selected by international publishers for Division. In particular, reviewers are pleased highlighting. This is a good sign indicating with the current organization structure: As that NCTS has provided important assistance pointed by reviewers, "We see a significant and helped in promoting our theoretical improvement both in quality and quantity of physics community. I am confident that with research output of theorists in Taiwan as a the recent commitment made by NSC and direct result of the NCTS effort...Having focus support from the physics community in groups has contributed to these results". Taiwan, the NCTS Physics Division will enjoy Reports of the review committee form the another success for the next phase. basis for the decision that NSC made on the next phase operation of NCTS. Chung-Yu Mou ( ) October 2008

A scene in the on-site review, Informal panel discussion with representatives of Taiwanese Physicists.

89 ‹‹- Report of the Division Head

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), Chai-Yu Lin, (National Chung Cheng University) , Ning-Ning Pan (National Taiwan University), Wen-Jer Tzeng (Tamkang University), Ming-Chya Wu (Academia Sinica)

I. Brief Description International Symposium on Statistical Physics on 8-12 July 2008 and a Cross Strait Conference on Statistical Physics on 14-17 July 2008. In each workshop, some 1. he purpose of this focused group visitors from other countries were invited to is to work on various model give a series of talks on topics related to the systems to gain a better understanding of interest of this FG. Some members of our critical phenomena and then apply the FG and researchers in Taiwan were also methods and concepts from such studies to invited to give talks so that related research interdisciplinary problems, especially the problems can be discussed. Some foreign complex systems. The problems being visitors also work with researchers of this studied include: (1) lattice models of FG on join research problems. critical systems (such as Ising, Potts, dimer 3. In 2008, the key active members of this FG models, spin glass, etc), (2) chaos, include Prof. Shu-Chiuan Chang (National synchronization, and non-equilibrium Cheng-Kung University), Prof. Wen-Che process, (3) complex networks and self- Tzeng (Tamkang University), Dr. Ming- organized critical systems (such as sandpile Chya Wu (National Central University), model, gene regulation network), (4) Prof. Hsin-Chang Chi (Department of structure and properties of biological Applied Science, National Hualien macromolecules (such as DNA, RNA, and University of Education), Dr. Jung-Hsin Lin protein), (5) molecular biological evolution (Research Center for Applied Sciences, models, and (6) models for economic and Academia Sinica), Prof. Jui-Ling Yu (Dept. social systems. of Applied Math., Providence University), 2. Since members of this FG scatter in Prof. Ming-Chang Huang (Dept. of Phys., different universities and research institutes, Chung-Yuan Christian Univ.), Prof. Ming- the main academic activities of this FG Chung Ho (Dept of Phys, National include five 2~3 days workshops, one Kaohsiung Normal Univ.), Prof. Chi-Ting

Highlights of Programs -›› 92 Shih (Dept. of Phys., Tunghai Univ.), and data in arbitrary dimensions and published Dr. Yu-Pin Luo (NCTS). the paper in Physical Review E in July 2008.. II. Activities 3. Prof. Hsin-Chang Chi (Deaprtment of 1. From March to August 2008, we have Applied Science, National Hualien organized three 2008 NCTS Workshop on University of Education) visited NCTS Critical Phenomena and Complex Systems. during winter break. He and Prof. K. N. The program of the workshops can be Huang of Academia Sinica used relativistic found at http://www.sinica.edu.tw/ many-body perturbation theory to calculate ~statphys/activities/workshop.html. energy levels and transition probabilities of 2. We had organized the 9th Taiwan molecules. A research paper is under International Symposium on Statistical preparation. Physics on 8-12 July 2008 at Institute of 4. Olga S. Rozanova (Mathematics and Physics, Academia Sinica, Taipei. The Mechanics faculty, Moscow State program of the workshop can be found at University, RUSSIA) visited NCTS during http://www.phys.sinica.edu.tw/~statphys/ac summer break. She and Prof. Jui-Ling Yu tivities/conference/2008/. (Dept. of Applied Math., Providence 3. Our FG sponsored the 4th Cross Strait University, a visitor at Institute of Physics Conference on Statistical Physics at of Academia Sinica and NCTS during National Kaohsiung University and summer break) worked on a model about National Sun-Yat Sen University on 14-17 typhoon trajectories and a manuscript will July 2008. be submitted to a journal for publication in September 2008. 4. We are organizing 2008 NCTS September Workshop on 5 and 6 September. Speakers 5. Prof. Chi-Tin Shih (Physics Department, from USA, Armenia, and Taiwan have been Tanghai University) invited Prof. Rudolf invited to give talks on RNA folding, A. Romer (University of Warwick, UK) to biological evolution, protein folding and visit Taiwan in March-April 2008. Prof. complex systems. Romer gave a series of three talks at 2008 NCTS March Workshop on Critical 5. In December 2008, we will organize Phenomena and Complex Systems. They another workshop. are working together on point mutations effects on charge transfer properties in the III. Visitors and International DNA sequence of tumor-suppressor genes.. Collaborations 6. Dr. N. Sh. Izmailian (Yerevan Institute of 1. Prof. Shu-Chiuan Chang (Physics Physics) visited NCTS in early 2008. He Department, National Cheng Kung and Dr. Chin-Kun Hu finished on boundary University) visited NCTS during winter and conditions and amplitude ratios of finite- summer breaks. He already published two size corrections for a quantum spin model. papers in J. Stat. Phys.: one on exact The paper was submitted to Nuclear partition function of the Potts model for Physics B for publication. strips of the honeycomb lattice (with Professor Robert Shrock at SUNY Stony 7. Zbigniew Struzik (Graduate School of Brook) and another one on dimmer Education, The University of Tokyo) coverings on the Sierpinski gasket (with visited NCTS in December 2007. He, Dr. Prof. Lung-Chi Chen in Department of Ming-Chya Wu (National Central Mathematics, Fu Jen Catholic University). University), and Dr. Chin- Kun Hu finished a paper on the survival probability. They 2. Prof. Tzeng Wen-Jer (Tamkang Univ, Dept found that a particular type of phase Phys) visited NCTS during winter break. distribution has zero survival probability. He finished a paper on parametric fitting of The paper will be sent to a journal for

93 ‹‹- Highlights of Programs publication in September 2008. tend to result in significantly weaker changes of tran smission properties. This IV. Highlights of Research Results suggests that charge transport could play a 1. Prof. Ming-Chang Huang (Dept. Phys., significant role for DNA-repairing Chung-Yuan Christian Univ.) and Yu-Pin deficiency yielding carcinogenesis. Their Luo finished a paper on self-similarity in paper was published in [Phys. Rev. Lett. the classification of finite-size scaling 100, 108015 (2008)]. functions for general toroidal boundary 4. Synchronization in coupled nonlinear conditions. They found a nice way to systems is one of the research topics of this classify universal finite-size scaling FG. and six papers have been published in functions under different parameters for the Phys. Rev. E and Chaos since 2005. The boundary conditions. The paper was most recent paper on paths to globally published in [Phys. Rev. E77, 010101 generalized synchronization in scale-free (2008)] as a Rapid Communications. networks by Yao-Chen Hung, Yu-Ting 2. Under partial support by NCTS, Prof. Huang, Ming-Chung Ho and Chin-Kun Hu David B. Saakian (Yerevan Physics was published in [Phys. Rev. E 77, 016202 Institute) had visited NCTS and Institute of (2008)]. Dr. Chin-Kun Hu has been invited Physics of Academia Sinica several times to give a plenary talk on synchronization in since 2004. He and Dr. Chin-Kun Hu coupled nonlinear systems at Dynamic published several papers at Proc. Natl. Days Asia-Pacific 5 (DDAP5) at Nara, Acad. Sci. USA (PNAS), Phys. Rev. E, and Japan on 9-12 September 2008. J. Stat. Phys.. They extended the studies from asexual evolution models to diploid V. Publication evolution models recently, which take into From January to August 2008, our FG has account the recombination. A paper on this 14 papers published or accepted by SCI problem was published at [Phys. Rev. 77, journals. The SCI journal papers include 1 in 061907 (2008)]. Physical Review Letters, 4 in Physical Review E, 2 in J. Statistical Physics, 1 in J. Chemical 3. Prof. Chi-Tin Shih (Physics Department, Physics, 1 in Proteins., 1 in J. Computational Tanghai University), Stephan Roche (CEA, Cemistry, 1 in BioSystems, 2 in Chaos, France), and Rudolf A. Romer (University Solitons and Fractals, 1 in Int. J. of of Warwick, UK) studied point mutations Bifurcation and Chaos. Our FG has sent 16 effects on charge transfer properties in the papers to journals for publication. Some DNA sequence of the tumor-suppressor p53 published or accepted papers and the pdf files gene. On the basis of effective single-strand of such papers can be found at "Publication" of or double-strand tight-binding models the website of Laboratory of Statistical and which simulate hole propagation along the Computational Physics at Academia Sinica : DNA, a statistical analysis of ch arge http://www.sinica.edu.tw/~statphys/ or http:// transmission modulations associated with http://phys.cts.nthu.edu.tw/research/focus_gro all possible point mutations is performed. up.php?Sn=38 or NCTS. They found that in contrast to non- cancerous mutations, mutation hotspots

Highlights of Programs -›› 94 Highlights of Programs Condensed Matter Physics

Focus Group on Computational Material 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), Chao-Cheng Kuan (Academia Sinica), Ming-Hsien Lee (Tamkang University), Min-Hsien Tsai (National Sun Yat-Sen University), Shiow-Fon Tsay (National Sun Yat-Sen University)

I. Brief Description W. S. Su ( Postdoc. student at CCU ), C. H. Cho ( Ph. D. student at CCU ), C. L. Huang (Sinica), T. R. Chang ( Ph. D. Student at NTHU), and H. L. Huang ( Ph. D. student at he chief purpose of this program is to NTU ) to attend international school. We also enhance the domestic research capacity supported C. Y. Ren (NKNU), J. M. Lu in computational material science especially (NCHC), S. P. Ju (NSYSU), and W. S. Su quantum mechanics-based ab initio electronic (CCU) to visit NCTS this summer in order to structure calculations and molecular dynamics promote the collaboration among local simulations, through promoting exchange and members. The gatherings of this kind have collaboration among local members as well as provided an essential channel for fruitful between Taiwan and foreign members, and also discussions among members of the community, through attracting more young researchers into and in particular, benefit our postgraduate this field. To this end, like previous years, we students and young postdoctoral fellows have organized ab initio methods study group tremendously. meeting, mini-schools with leading The CMR focus group consists of 56 international scientists as main lecturers, and members (33 faculties and 23 Ph. D. students also program-wide annual conference. and postdocs). It is run by a committee from Furthermore, to attract younger researchers as various institutions. The committee members well as experienced ones to the field of CMR are T. C. Leung (Coordinator, CCU), G. Y. Guo and also promote awareness of the important (NTU), M. H. Lee (TKU), C. C. Kuan (Sinica), role in the modern scientific research played by C. Cheng (NCKU), S. F. Tsay (NSYSU), M. H. the computation using present-day computers, Tsai (NSYSU), and C. M. Chang (NDHU). we have also organized spring school The missions of the committee are to allocate (introductory level) and summer school the budget, to initiate research activities, to (advanced level) on first-principles invite the long-term and short-term visitors and computational materials research. We have to recommend candidates (Ph. D. student or encouraged members especially young ones to junior scientist) to attend international school, attend relevant international conferences, conference, or workshop with the financial workshops and schools. Specifically, we support of CMRFG. supported Y. H. Su ( Ph. D. student at NCKU),

95 ‹‹- Highlights of Programs II. Activities eighty participants from all over the country. 1. Mini-Workshop on Quantum Transport 4. The 8th Workshop on First-Principles and Current-Driven Dynamics in Computational Materials Physics Molecular-Scale Electronics The 8th Workshop on First-Principles Inelastic electron tunneling via molecular- Computational Materials Physics, organized by scale junctions can induce a variety of T. C. Leung (CCU), was held on July 1-3, 2008 fascinating dynamical processes in the in Huisun Forest Station. The aim of this molecular moiety. Potential applications of conference is to promote interaction and current-driven dynamics in heterojunctions collaboration among local physicists. The range from new forms of molecular machines Program Committee would also like to take this and new modes of conduction, to new opportunity to hear about interests of the directions in surface nanochemistry and community in order to plan future activities at nanolithography. This mini-workshop is the Center. Like previous years, all participants organized by C. C. Kuan (Sinica) and held in including PhD students and young postdocs, March 7, 2008. Prof. T. Seideman from were encouraged to give a talk in this Northwestern University was invited to give workshop. lectures on this issue. 5. School on First-Principles Computational 2. Mini-School on Computational Material Materials Research Physics : Towards an understanding of The spring school on first-principles surface processes and catalysis using density computational materials research-introductory functional theory calculations level, lectured by T. C. Leung (CCU), is held in It is well known that catalysis plays a very National Center for High-Performance important role in a wide range of scientific and Computing. technological problems. It is virtually The summer school on first-principles impossible to provide an insight into catalysis computational materials research Ð advanced without an understanding of the electronic level, organized by T. C. Leung (CCU), is held structures of catalysts. This mini-school was in NCTS. The purpose of this schools are to organized by M. H. Lee (TKU) and held in offer an introduction to the fundamentals of ab Institute of Atomic and Molecular Sciences in initio density functional theory, of March 29, 2008. Prof. Prof. Peijun Hu from pseudopotentials, and large scale calculations, Queen's University gave four lectures on the as well as a practical hands-on training for following topics. young students and non-specialists. The 1. A simple thermodynamic rule for the rapid response from both young students and non- catalyst search specialist researchers were very positive, there 2. CO oxidation on metal and metal oxide were more than hundred participants in the surfaces spring school and more than fifty participants in the summer school. 3. Towards an understanding of Fischer- Tropsch synthesis 6. OpenMx Study Group Meeting It is well known that the computing time of 3. Summer Workshop on Nanoscale Materials currently popular electronic structure methods To provide opportunities for exchange and based on Density Functional Theory scale like discussion between theoreticians and N2-3, with N being the number of atoms in the experimentalists and also foster collaborations simulation cell. In the last few years, much among them, the Summer Workshop on effort has been devoted to overcome this Nanoscale Materials, organized by Dr. J. M. Lu problem, and a number of methods have been (NCHC), was held in August 21-22 in NCTS. developed with "order Ð N " [O(N)] scaling. Fourteen theroreticians and experimentalists One of the successful order N ab initio were invited to present in this workshop. The computing code is OpenMx (Open source workshop was well attended and more than

Highlights of Programs -›› 96 package for Material eXplorer) developed by compared. How to implement QMC methods Dr. Taisuke Ozaki from National Institute of efficiently is critical. Nowadays, QMC can Advanced Industrial Science and Technology deal with systems up to hundreds of valence in Japan. In order to familiar with the electrons. The aim of this series of study-group principles used in the program and how they meetings is to provide an opportunity of are implemented so that the program can be interactions and experience sharing for those properly applied to the systems we want to who are employing or about to use QMC study, several study group meeting on OpenMx methods in their research, several QMC study were organized by T. C. Leung (CCU) and held group meeting were organized by C. Cheng in NCTS. The key members involved in this (NCKU) and C. M. Wei (Sinica). The key project are C. S. Hsue (NTHU), T. C. Leung members involved in this project are C. Cheng (CCU), Y. C. Hsu (NCKU), G. Y. Guo (NTU), (NCKU), C. M. Wei (Sinica), C. M. Chang C. Y. Ren (NKNU), and B. R. Wu (CGU). (NDHU). 7. Excited State Study Group Meeting III. Collaborative Activities The conventional DFT method fails to give The examples of these collaborations accurate excitation properties, e.g., band gaps, between CMRFG members are listed as excitonic binding energies, of solids. The GW follows : method has been successfully used to predict electronic properties of a variety of different 1. C. M. Chang (NDHU), C. Cheng (NCKU) systems, whereas the linear optical response is and C. M. Wei (Sinica) on the Quantum routinely studied by solving the Bethe-Salpeter Monte Carlo simulation on nanomaterials. Equation (BSE) with comparable success. 2. H. T. Jeng (Sinica) , C. Y. Ren (NKNU) and ABINIT is a package whose main program C. S. Hsue (NTHU) on the Orbital Ordering allows one to study the excited states using the in transition-metal oxides. GW approximation. On the other hand, the EXC is an exciton code which uses the output 4. B. R. Wu (CGU) and T. C. Leung (CCU) on of ABINIT to calculate the dielectric and the electronic and optical properties of optical properties by solving the Bethe-Salpeter ribbon under external electric field. equation. In order to familiar with the 5. G. Y. Guo ( NTU), T. C. Leung (CCU) and principles used in the program and how they H. C. Hsueh (TKU) on the ab initio study on are implemented so that the program can be excited state of nanomaterials. properly applied to the systems we want to study, several exited state study group meeting International collaborations are listed as were organized by G. Y. Guo (NTU) and held follows : in NTU. The key members involved in this 1. N. Nagaosa (Japan) and G. Y. Guo (NTU) project are G. Y. Guo (NTU), T. C. Leung on the intrinsic spin Hall effect. (CCU), H. C. Hsueh (TKU) , M. Hayashi 2. C. T. Chan (Hong Kong) and T. C. Leung (CCMS), C. K. Yang (CGU), H. T. Jeng (CCU) on the optical properties of (Sinica), and B. R. Wu (CGU). nanomaterials. 8. Quantum Monte Carlo Study Group 3. N. Drummond (UK) and C. M. Wei ( Meeting Sinica) on the Quantum Monte Carlo The quantum monte carlo (QMC) method simulation on nanomaterials. based on random walk sampling provides a 4. Steven G. Louie ( USA) and H. C. Hsueh direct treatment of quantum many-particle (TKU) on the quasiparticle excitations in effects, thus making it beyond the reach of nanomaterials. mean-field methods and giving a highly accurate description in electron-electron correlation. QMC provides promising results IV. Highlights of Research Results in the study of real materials and can serve as (1) Intrinsic Spin Hall Effect in Platinum benchmarks for other techniques may be

97 ‹‹- Highlights of Programs G.Y. Guo and his collaborators have studied [6] Y. H. Ho, G. W. Ho, S. C. Chen, J. H. Ho, the Spin Hall effect with first-principles and M. F. Lin, Phys. Rev. B 76, 115422(6) relativistic band calculations for platinum. (2007). They show that intrinsic spin Hall conductivity [7] Y. C. Huang, C. P. Chang, and M. F. Lin, has a peak near the Fermi energy and that the Nanotechnology 18, 495401(8) (2007). vertex correction due to impurity scattering [8] Y. H. Chiu, Y. H. Lai, J. H, Ho, D. S. Chuu, vanishes. They argue that the large SHE and M. F. Lin, Phys. Rev. B 77, 045407(6) observed experimentally in platinum is of (2008). intrinsic nature [14]. [9] C. M. Chang, C. Cheng, C. M. Wei, J. (2) Au/Si(111)-(5x2) surface reconstruction Chem. Phys., Vol.128, 124710 (2008) F. C. Chuang and his collaborators have [10] Chung-Yuan Ren, Shiow-Fon Tsay, and studied the models with a honeycomb chain Feng-Chuan Chuang, Phys. Rev. B 76, feature for the Au/Si(111)-(5x2) surface 75414(2007). reconstruction using. Their calculation shows [11] F.C. Chuang, Chia-Hsiu Hsu, C.-Z. Wang, that one of these models has a lower surface and K.-M. Ho, Phys. Rev. B, 77 153409 energy than the previously proposed models. (2008) This newly identified model also reproduces [12] F.C. Chuang, Y.Y. Hsieh, C.C. Hsu, and certain key features in the angle-resolved M.A. Albao, J. Chem. Phys. 127, 144313, photoemission measurement and experimental (2007). scanning tunneling microscopy images[11]. [13] Pao-An Lin, Horng-Tay Jeng, and Chen- (3) Work function of Carbon Nanotubes Shiung Hsue, Phys. Rev. B 77, 085118 T. C. Leung and his collaborators have (2008). investigated the work functions of various [14] G. Y. Guo, S. Murakami, T. W. Chen and forms of small radius carbon nanotubes and N. Nagaosa, Phys. Rev. Lett. 100, 096401 their derivatives by density functional (2008). calculations. They found that the work function [15] S. Ju and G. Y. Guo, Appl. Phys. Lett. 92, can exhibit significant variations depending on 202504 (2008). the length of the tubes and the way they are [16] I. J. Wu and G. Y. Guo , Phys. Rev. B 78, arranged. It is interesting to see that for isolated 035447 (2008). tubes, the tip dipole does not affect the work function, but the density and the sign of the [17] I. J. Wu and G.Y. Guo, Phys. Rev. B 76, dipole become the crucial factor when the tubes 035343 (2007). form a bundle [22]. [18] J. C. Tung and G.Y. Guo, Phys. Rev. B 76, 094413 ( 2007) [19] S. Ju, T.Y. Cai, G.Y. Guo, Z.Y. Li, Phys. V. References Rev. B 75, 064419 (2007) [1] R. B. Chen, C. H. Lee, C. P. Chang, and M. [20] G.Y. Guo, S. Ishibashi, T. Tamura and K. F. Lin, Nanotechnology 18, 075704(7) Terakura, Phys. Rev. B 75, 245403 (2007) (2007). [21] Y. -H. Tang and M. -H. Tsai, Phys. Rev. B [2] R. F. Liu and C. Cheng, Phys. Rev. B, 75 113404 (2007). Vol76, 014405 (2007) [22] W. S. Su, T. C. Leung, Bin Li, C. T. Chan, [3] C. M. Chang, C. Cheng, and C. M. Wei, J. Appl. Phys. Lett. 90, 163103 (2007). Chem. Phys. 128, 124710 (2008). [23] W.S. Su, T.C. Leung, C. T. Chan, Phys. [4] M. C. Lin and R. F. Jao, Optics Express 15, Rev. B 76, 235413 (2007). 207 (2007). [24] Chih-Kai Yang, Letters to the Editor / [5] T. S. Li and M. F. Lin, Phys. Rev. B 76, Carbon 45 (2007) 2445¡V2458 073409(8) (2007) [25] Chih-Kai Yang, Appl. Phys. Lett. 92, 033103 (2008)

Highlights of Programs -›› 98 Focus Group on Mesoscopic and Spin Physics

Coordinators: Chung-Hou Chung (National Chiao Tung University; email: [email protected]) , Shun-Jen Cheng (National Chiao Tung University; email: [email protected]) Committee members: Yu-Chang Chen (National Chiao Tung University), Shun-Jen Cheng (National Chiao Tung University), Chon-Saar Chu (National Chiao Tung University), Chong-Der Hu (National Taiwan University), Chao-Cheng Kuan (Academia Sinica), Juhn-Jong Lin (National Chiao Tung University)

I. Brief Description quantum criticality in coupled quantum dots and in cold atoms (C.H. Chung). II. Activities oals: International Mini-Workshop on Mesoscopic To understand and discover interesting and Spin Physics, NCTU, Jan., 2008: new phenomena on electronic and spin We hosted a focused mini-workshop on two transport in nanostructures. frontier topics: quantum transport in quantum dots and graphene physics. Each of the three Core members: Chong-Der Hu (NTU), Yu- major foreign invited visitors gave two Chang Chen (NCTU), Jung-Jong Lin intensive talks on their expertise, which allows (experimentalist , NCTU). the participants to gain a deeper understanding. Active members:Cheng-Hung Chang (NCTU, We also arranged more time for discussions. NCTS), Cheng-Chung Chen (experimentalist, Participants all benefited a lot in the workshop. NTHU), Yi-Ping Lin (experimentalist, In particular, J.J. Lin and C.H. Chung have NTHU), Kuan-Ming Hung (NKUAS, benefited from the discussions with Prof. Hans Kaohsiung) Kroha (Boon U.) in detail about the 2-channel Research topics: Kondo physics in nano-wires. This can lead to future collaborations. Prof. Antonio Castro ¥ Electronic transport in semiconductor Neto (Boston U.) gave an excellent review of nanostructures. Topics include: quantum the current interesting topics in graphene, phase transition and non-equilibrium which inspired many of the participamnts. transport in quantum dots associated with PhD. Student S.S. Yeh presented his Kondo effect (C.H. Chung), transport in experimental work on the Kondo physics in nano-junction devices (Y.C. Chen, C.C. nanowires. These two students had benefited Kuan, and C.H. Chung), dephasing and from comments and suggestions from Prof. decoherence in disordered nano-wires/nano- Kroha. junctions (J.J. Lin), Optical excitations in quantum dots (S.J. Cheng, K.M. Hung) Seminars and regular discussions: ¥ Spintronics in nanostructures. Topics We have had a number of interesting include: novel magnetic properties in diluted Monday seminars in our Focus group on magnetic semiconductor (H.H. Lin), spin various spin-related transport and magnetic transport and spin Hall effect in Rashba-type properties. The goals are to develop new ideas, 2-D electron gas (2DEG) (C.S. Chu, C.H. to encourage new collaborations, to educate Chang, and C.D. Hu), spin-characteristic students/postdocs and to invite people from charged excitons in self-assembled quantum institutions with relatively limited resources to dots (S.J. Cheng). participate. These talks have inspired us, in various degrees, in our research interests. Such ¥ Strongly correlated effects in nanostructures. examples include: Topics include: edge states and magnetic properties of carbon nanotubes (H.H. Lin), ¥ New projects/ ideas were developed: (i).The

99 ‹‹- Highlights of Programs interesting results in the National Sun Yat- nonequilibrium quantum transport in Sen University research group (Prof. I.K. Lo dissipative quantum dots. and Prof. J.C. Chiang), seminar given by Mr. ¥ Weidong Sheng (Fudan U., China) + S.J. Wang, on the wurtzite structure causes us to Cheng on the optical excitation in quantum ponder the spin-Hall effect in the diffusive dots. regime. (ii). Among J.J. Lin (experimentalist) C.H. Chung and Chi-Tong ¥ Peter Woelfle, Gergely Zarand (Budapest, Chen (Academia Sinica) on the transport Hungary) + C.H. Chung on coupled through quantum dots coupled to nanowires. quantum dots in Kondo regime. Matthias (ii) Between J.J. Lin's experimental group Vojta, Pascal Simon (Grenoble, France), and C.H. Chung on Kondo effect in transport Kevin Ingresent (U. Florida) on quantum through nanowires. The recent experimental phase transitions in dissipative quantum results done by Lin's group can be explained dots. very well by the 2-impurity Kondo model. ¥ Dr. Dmytro Luzhbin, (National Academy of (iii) Among C.S. Chu, C.D. Hu and C.H. Sciences of Ukraine), Prof. Tamar Seideman, Chung in the spin transport in multi-ferroics. (Department of Chemistry, Northwestern (iv) Between S.J. Cheng and K.M. Hung on U.), Prof. Hong Guo, (McGill U.) + C.C. excitons in semiconductors. Kuan on transport in molecular nano-juction. ¥ Participants from institutions with less ¥ Dr. G. Sun (U. of Massachusetts at resource: Shih-Jye Sun (Kauhsiung U.), Boston)+K.M. Hung on semiconductor Kuan-Ming Hung (National Kaohsiung quantum processes and semiconductor opto- University of Applied Sciences). electronics and plasmonics. Training and Education for young generation physicists: IV. Highlights of Research Results (i). The mini-workshop on Mesoscopic and • Chon Saar Chu Spin physics in Jan. 2008 was proved to be (i). We have demonstrated that spin-orbit very successful in providing training for interaction (SOI) arising from an in-plane students and young physicists. The lecture potential gradient in a 2D microstructure series given by Prof. Kroha, Castro Neto can result in significant spin accumulations and Prof. Kanda (U. Tsukuba, Janpan) in its vicinity: in the resonant scattering were all very inspiring and were attracted a regime and in the presence of a driven large audience. electric field. The sign of the non- (ii). A one-day PhD students workshop equilibrium spin accumulation can be organized by master Dr. Lu Yao Wang, reversed by monitoring the chemical and Ph.D. students Jeng-Cheng Wu in the potential µ. Focus group is to be held on Sept. 6, (ii). We have demonstrated that the usually 2008. This is intended to be a meeting for neglected SOI term in a 2DEG due to the these young physicists to discuss, to vanishing of , the averaging over the share, and to collaborate. thickness, has restored its SOI effect when a flux of unpolarized electrons are III. Visitors and International allowed to tunnel across the thickness of Collaborations the 2DEG. ¥ G. Mal'shukov (NCTS visiting professor (iii). We have demonstrated that the from Moscow) + C.S. Chu on the spin-Hall asymmetries in intrinsic spin-Hall effect effects and other spin physics in 2DEG in in low in-plane magnetic field can be both the diffusive and the mesoscopic utilized for the probing of the underlying regimes.. SOI in sample within the diffusive ¥ Karyn Le Hur (Yale U.), Peter Woelfle regime. (Karlsruhe, Germany), Matthias Vojta (iv). We have studied the spin-Hall effects in a (Koeln U., Germany) + C.H. Chung on diffusive Dresselhaus SOI 2DEG

Highlights of Programs -›› 100 sandwiched between two quantum size effects improve the stability of superconductors [submitted]. The ferromagnetic magnetic polarons. The carrier- supercurrent that passes through the mediated spin interactions between magnetic 2DEG drives the spin-Hall effect: causes ions result in the enhancement of magnetism. in it a bulk in-plane polarization and out- By contrast, the ground states of NCs of-plane spin accumulation at transverse containing short ranged Mn clusters undergo a edges. series of magnetic phase transitions from antiferromagnetism to ferromagnetism, with • Chung-Hou Chung decreasing size of NC. An analysis based on a (i). We found a new type of quantum phase simplified constant interaction model, transition between localized and supported by the numerical calculations of delocalized phases in a dissipative quantum local mean field theory, is presented for the dot within the spinless Anderson impurity magnetic NCs with many magnetic ions over a model. We developed a new epsilon- wide range of Mn concentration and NC size. expansion in field-theoretical Accordingly, we derive the condition for the Renormalization Group (RG) approach and formation of magnetic polaron and predict the applied the newly developed Numerical observable signatures of the magnetic phases RG calculations. Both approaches reach an in magnetization measurements. excellent agreement. C.H. Chung was invited by the Kavli Institute for • Yu-Chang Chen Nanoscience, TU Delft, The Netherlands, We discuss how the shot noise in quantum and the Neils Bohr Institute, Denmark in channels is affected by the quantum nature of Feb., 2008 to present this work. the transverse momenta K in ballistic regime. We demonstrate, from first principle (ii). We investigated the quantum phase calculations that the Fano factor may increase transition associated with the Kondo linearly with the number of well-separated breakdown mechanism due to the parallel wires by the interference effects prominence of extra fluctuations in a through the reservoirs. This is in sharp contrast tunable surrounding environment, e.g., to the case of mesoscopic system, where the the zero-point fluctuations. We found a Fano factor is independent of the number of new scaling behavior for a dissipative well-separated parallel wires because of the quantum dot coupled to Luttinger-liquid restoration of quantized parallel channels. leads close to the localized-delocalized quantum transition. This is the first • Chao-Cheng Kuan systematic study on the new subject-- We calculate the conductance of Au- non-equilibrium quantum criticality. We alkanedithiol-Au molecular junctions from clarify the different role played by the first-principles, finding agreement with temperature and the bias voltage. C.H. measured data [Science 301, 1221 (2003)] for Chung was invited in an international junctions where the terminal S-atoms are workshop in quantum information and attached to top sites of the gold electrodes. A nanoscience in ICTP, Trieste in May 2008 major effect of the contact geometry on the to present this work and it has attracted conduction properties is found, whose origin is much attention. C.H. Chung traced to the symmetry and spatial localization acknowledges the general support from of the interface states. The implications of our the NCTS. Its activities play an important finding to ongoing experiments are noted. This role in carrying out the above-mentioned work was presented as invited talks in the work. following workshops: "The 10th Asian • Shun-Jen Cheng Workshop on First-Principles Electronic Structure Calculations", Hiroshima U., Japan, We present a theoretical investigation of Oct. 2007. and "2008 Taiwan (NSC) Ð US magnetism in II-VI diluted magnetic (NSF) Workshop on Simulation Based semiconductor nanocrystals (NCs). For NCs Engineering & Science (SBE&S) on containing long range interacting Mn ions, the Biomedicine, Energy, Enabling Materials, and

101 ‹‹- Highlights of Programs Micro-Nanotechnology", NCKU, Taiwan, tunneling electrons", Physical Review B, Feb., 2008. 76, 245326 (2007). • Kuan-Ming Hung [3] Chung-Hou Chung, Gergely Zarand, and Peter Woelfle, "Two-stage Kondo effect in We have developed the theory of exciton double quantum dots: Perturbation theory dynamics in quantum dots (QDs) and and Numerical Renormalization Group quantum-dot molecules (QDMs) based on analysis", Phys. Rev. B 77, 035120 (2008); equation of motion approach. The interactions selected for publication for the January 28, of exciton with photon and LO-phonon are 2008 issue of Virtual Journal of Nanoscale considered in QD/QDM systems. Our results Science and Technology. show that resonant-round trips of the exciton [4] Chung-Hou Chung, Matthew Glossop, between the ground (bright) and excited (dark Lars Fritz, Marijana Kircan, Kiven or bright) states, mediated by the LO-phonon, Ingersent, and Matthias Vojta. "Quantum alter the decay time and yield the Rabi phase transitions in a resonant-level model oscillation. The initial distributions of the with dissipation: Renormalization-group population in the ground and the excited states studies", Phys. Rev. B 76, 235103 (2007). dominate the oscillating amplitude and frequency. This property provides a detectable [5] Shun-Jen Cheng, "Spin characteristics of signature to the information that is stored in a excitonic absorption in multiply charged qubit that is made from QD or QDM, over a quantum dots" Phys. Rev. B 76, 075329 wide range of temperatures T. The results also (2007). provide a reasonable explanation to the [6] S.J. Cheng and P. Hawrylak, "Controlling anomaly of T-dependent decay in self- magnetism of semi-magnetic quantum dots assembled InGaAs/GaAs QDMs, which has with odd-even exciton numbers", recently been experimentally identified. Europhys. Lett. 81, 37005 (2008). Comments/suggestions of our focus group [7] Shun-Jen Cheng, "Theory of magnetism in diluted magnetic semiconductor In the previous years, the workshops, nanocrystals", Phys. Rev. B 77, 115310 seminars, and visitors in the Focus Group have (2008). broadened our exposure in the recent frontier [8]. Wen-Hao Chang, Hsuan Lin, Sheng-Yun research activities in the fields of spin related Wang, Chia-Hsien Lin, Shun-Jen Cheng, physics. Long term international collaboration and Ming-Chih Lee, Wen-Yen Chen, Tzu- has been established between our group and Min Hsu, Tung-Po Hsieh and Jen-Inn various internationally well-known physicists. Chy, "Nonresonant carrier transfer in Other activities have inspired research ideas single InGaAs/GaAs quantum dot which impact upon our research output will be molecules", Phys. Rev. B 77, 245314 shown in our future publications. We have also (2008). improved significantly our domestic connections by inviting new members in many [9] C.-C. Kaun and T. Seideman, different universities in Taiwan. We expect to "Conductance, contacts and interface be benefited significantly in our research by states in single alkanedithiol molecular this new development. junctions", Phys. Rev. B 77, 033414 (2008). V. References [10] K.-M. Hung, J. Appl. Phys. 102, 023111 (for more details, please go to our webpage) (2007); this paper was selected for Aug 2007 issue of V. J. Nano-Scale Science [1] K.Y. Chen, C.S. Chu, and A.G. and Tech. and Aug 2007 issue of V. J. Mal'shukov, "Resonant spin dipole Quantum Information. induced by an in-plane potential gradient [11] Sujit Sarkar and C. D. Hu, "Quantum spin-orbit interaction", Physical Review B, spin pump in fractionally quantized 76, 153304 (2007). magnetization states with competing [2] A.G. Mal'shukov and C,.S. Chu "Spin exchange interaction" Phys. Rev. B 77, orientation and spin-Hall effect induced by 064413 (2008).

Highlights of Programs -›› 102 Focus Group on Novel Quantum Phenomena in Condensed Matter

Coordinators: Ying-Jer Kao (National Taiwan University; email: [email protected]), Hsiu-Hau Lin (National Tsing Hua University; email: [email protected]) Committee Members: Yung-Chung Chen (Tunghai University), Chung-Hou Chung (National Chiao Tung University), Chang-Ming Ho (Tamkang University), Di-Jing Huang (National Synchrotron Radiation Research Center), Horng-Tay Jeng (Academia Sinica), Jiunn-Yuan Lin (National Chiao Tung University), Chien-Hua Pao (National Chung Cheng University), Wen-Chin Wu (National Taiwan Normal University)

I. Brief Description condensed matter, Dec14, 2007 (Hsin-Chu, Taiwan) (2) Workshop on Multiferroic Physics, May 29, 2008 (Taipei, Taiwan) he "Novel Quantum Phenomena in Condensed Matter" (NQPCM) focus (3) CMP2008: The First NCTS Condensed group is formed to provide a platform for Matter Summer Workshop, June 27-30, condensed matter theories in Taiwan to 2008 (Hua-Lien, Taiwan) facilitate the interaction and collaboration (4) Taiwan International Conference on among each other. In addition, activities and Superconductivity (TICS08), July 7-10, visitor programs are designed to provide 2008 (Puli, Taiwan) opportunities for researchers to establish (5) NCTS Summer School for TICS08, July 3- international collaborations. In addition, travel 5, 2008 (Hsinchu, Taiwan) funds are available for students and junior researches to attend international conferences. (6) Student Journal Clubs (Taipei & Hsin-Chu, An executive committee of ten members from Taiwan) major institutes is formed to coordinate these Activities (1) & (2) are one-day workshops activities and oversee the usage of the fund. on special topics in condensed matter physics, In addition to the executive committee, where international speakers and local there are twenty-two active faculty members researchers exchange ideas and establish future and twenty junior members (postdocs and collaborations. They also provide a useful senior graduate students). The focus research platform for experimentalists and theorists to topics are (1) Superconductors, share their own research. Activity (3) is the Multiferroics and Oxides, (2) Spintronics, (3) first attempt to establish an informal workshop Supersolidity in lattice boson models, (4) among experts. We aim to create a stage where Numerical Methods in strongly correlated people can concentrate on a specific topic in systems, (5) Non-equilibrium quantum phase physics for several days with an informal transition, and (6) Quantum Information. atmosphere, so the initiation of collaborations can be facilitated. Activity (4) is one of the II. Activities important international conferences hosted in During the past one-year period, our focus Taiwan, and our focus group helped part of the group organized or sponsored following organization. Activity (5) is designed to activities, educate graduate students to familiarize them with necessary techniques and background. (1) Mini-workshop on strong correlations in The summer school also serves as a platform

103 ‹‹- Highlights of Programs for students from different universities to (Koeln) on nonequilibrium quantum phase interact with each other. Activity (6) is a new transition. activity, specially designed for postdocs and ¥ Chien-Hua Pao (CCU) + Mark Jarrell students. Seminars are held biweekly in both (Cincinnati) on DCA studies of BCS-BEC Taipei and Hsin-Chu with participants from crossover. institutes in the area. This informal seminar is intended to motivate junior researchers to ¥ Horng-Tay Jeng (AS) + M.A.van Hove identify and discuss on research topics. (Hong-Kong), Xiao Hu, Toshiya Hikihara (Japan), and H. Berger (Switzerland). III. Visitors and International Collaborations IV. Highlights of Research Result (1) International Visitors: (Dec 07-Aug 08) (1) Superconductors, Multiferroics and Oxides Jer-Lai Kuo(Singapore), Hae Young Kee (Toronto), Yong Baek Kim (Toronto), Wen-Chin Wu (NTNU) and collaborators Krishnandu Sengupta (India), Robert Joynt have calculated the point-contact spectroscopy (Wisconsin), Anders Sandvik (Boston), Ka-Di to explore the possible coexistence of an AF Zhu (Shang-Hai), Yaowen Liu (Shang-Hai), order and the d-wave superconducting order Nai-Chang Yeh (Caltech). parameter in electron-doped cuprate superconductors [1]. More recently, they (2) International Collaborations: extend the calculation to investigate the ¥ Hsiu-Hau Lin (NTHU)+Toshiya Hikihara phenomena exhibited in a ferromagnetic (Hokkaido): on the flat-band ferromagnetism metal/AF+dSC junction. Ting-Kuo Lee (AS) in armchair graphene nanoribbon. and his collaborators show that the presence of the cluster glass state, recently observed in ¥ Hsiu-Hau Lin (NTHU)+Masaki Oshikawa BSCO, is actually an inherent nature of the t-J (Tokyo): on the quantization of magnetic model [submitted]. moment near the edge of carbon nanotube. Chung-Yu Mou (NTHU) and Di-Jing ¥ Hsiu-Hau Lin (NTHU)+Sung-Ik Lee Huang (NSRRC) have collaborated on the (APCTP): on the concurrent magnetic and theoretical and experimental studies of metal-insulator transitions in EuB6 . LiCu2O 2. Based on resonant soft x-ray ¥ Ming-Che Chang (NTNU) + Qian Niu magnetic scattering and theoretical analysis of (Austin) on non-canonical dynamics with correlation length versus temperature, they

Berry phase effects. find that LiCu2O2 exhibits a large inter-chain ¥ Chung-Hou Chung (NCTU), Yong-Chung coupling which suppresses quantum Chen (THU) + Yong Baek Kim (Toronto) on fluctuations along spin chains, and a quasi-2D incommensurate supersolid. short-range magnetic order prevails at temperatures above the magnetic transition. ¥ Ying-Jer Kao (NTU) + Roger Melko These observations unravel that the ground (Waterloo) on shortloop QMC algorithm. state of LiCu2O2 has a long-range 2D-like ¥ Ying-Jer Kao (NTU) + Anders Sandvik incommensurate magnetic order rather than (Boston) on numerical approaches based on being a gapped spin liquid expected from the tensor networks for frustrated systems. nature of quantum spin-1/2 chains, as previously believed. They also show that the ¥ Wen-Chin Wu (NTNU) + Robert Joynt spin coupling along the c-axis is essential for (Wisconsin) on the coexistence of the observed multiferroic behavior [2]. Chong- antiferromagnetism and superconductivity in Der Hu (NTU) studies the microscopic Hg-based multilayer cuprate mechanism of multiferroics, in particular, with superconductors. the "spin current" mode starting from a system ¥ Chung-Hou Chung + Karyn Le Hur (Yale), with helical spin configuration. The relation Peter Woelfle (Karlsruhe), Matthias Vojta between ferroelectricity and Dzyaloshinskii-

Highlights of Programs -›› 104 Moriya interaction is thus clearly established Chen and their collaborators showed the [3]. existence of supersolid phase in the hardcore Bose-Hubbard model on the anisotropic Horng-Tay Jeng (AS) and collaborators triangular lattice over a wide range of investigated the electronic structures of parameters, and the supersolid phase has SrRu Ti O using the generalized gradient 1-x x 3 "quasi-incommensurate" density-density approximation (GGA) as well as the GGA+U correlations [submitted]. scheme. It is found that the Ti substitutions significantly affect the orbital ordering patterns (4) Numerical Methods in strongly correlated on the Ru sublattices. They show that the systems experimentally observed metal-insulator Ying-Jer Kao and collaborator developed a transition upon Ti doping is driven by the on- new algorithmic framework for a variant of the site Coulomb repulsion U [4]. QMC loop algorithm, in which non-local loop (2) Spintronics or cluster constructs in the d+1 dimensional simulation cell close in a way which makes Hsiu-Hau Lin (NTHU) in collaboration each individual loop smaller. The algorithm is with experimentalists demonstrates, for the designed to increase simulation efficiency in first time, that the transition-metal doped cases where conventional loops become very amorphous Si films exhibit ferromagnetic large [9]. Yung-Chung Chen, Ming-Fong Yang order and anomalous Hall effect. The (THU) and their collaborators use the fidelity measured magnetization fits the theoretical approach to the Gaussian transitions in spin- prediction rather well [5]. Ming-Che Chang one XXZ spin chains with different values of and collaborator establish a novel quantization Ising-type anisotropy by density matrix procedure for non-canonical dynamics with renormalization group (DMRG). They find Berry phase effects, generalizing the venerable that, despite the success in some cases, the Peierls substitution rule. This new rule, when fidelity susceptibility fails to detect some of applied to semiconductor bands, gives new the Gaussian transitions. Their results insight to various effective interactions [6]. demonstrate the limitation of the fidelity (3) Supersolidity in lattice boson models susceptibility in characterizing quantum phase Ying-Jer Kao (NTU) and collaborators transitions [10]. study the ground state phase diagram of the (5) Non-equilibrium quantum phase hard-core extended boson Hubbard model on transition the square lattice with both nearest-(nn) and Chung-Hou Chung (NCTU) and next-nearest-neighbor (nnn) hopping and collaborators study the AC conductance repulsion. They observe the formation of through a side-coupled two-dot system. The supersolid states with checkerboard, striped, side-coupled RKKY interaction gives rise to a and quarter-filled crystal structures, when the "two-stage Kondo effect'' where the two spins system is doped away from commensurate are screened by two consecutive Kondo effects fillings [7]. Kao was invited to present this [11]. This paper was selected for publication work at KITP, Santa Barbara and ISSP, Tokyo. for the January 28, 2008 issue of Virtual In a similar study, Yung-Chung Chen and Journal of Nanoscale Science and Technology. Kwai-Kuang Ng (THU) performed a They also study the Anderson impurity model comprehensive numerical study of the same with dissipation, and they show this model has model without the nnn hopping. In addition to a phase transition between localized and the quantum solid and superfluid phases, they delocalized phases. They are able to provide an report the existence of a striped supersolid and overall picture of how dissipation interferes the three-quarter (quarter-filled) supersolid at charge transport of a quantum dot [12]. Chung commensurate density ρ‚=0.75 (0.25) [8]. was invited to present his work at Kavli Both studies find the transition between two Institute for Nanoscience, TU Delft and Neils supersolids with different symmetries to be Bohr Institute. first order. Chung-Hou Chung, Yung-Chung

105 ‹‹- Highlights of Programs (6) Quantum Information [7] K. K. Ng and Yung-Chung Chen, Phys. Rev. B 77, 52506 (2008). Using time-dependent DMRG, Chung-Yu Mou and Po-Chung Chen (NTHU) study the [8] Ying-Jer Kao and Roger G. Melko, Phys. reduced dynamics of qubit(s) coupled to an Rev. E 77, 036708(2008). interacting quantum spin bath, and they find [9] Yu-Chin Tzeng, Hsiang-Hsuan Hung, both decoherence and entanglement depend Yung-Chung Chen, and Min-Fong Yang, strongly on the phase of the underlying spin Phys. Rev. A 77, 62321 (2008). bath. They show that spin baths can induce [10] Chung-Hou Chung, Gergely Zarand, and entanglement for an initially disentangled pair Peter Woelfle, Phys. Rev. B 77, 035120 of qubits [13]. (2008). [11] Chung-Hou Chung, Matthew Glossop, Lars Fritz, Marijana Kircan, Kiven Ingersent, and Matthias Vojta, Phys. Rev. V. Selected Publications B 76, 235103 (2007). [12] Cheng-Yan Lai, Jo-Tzu Hung, Chung-Yu (*) acknowledgement to NCTS missing Mou, Pochung Chen, Phys. Rev. B 77, [1] C.S. Liu and W.C. Wu, Phys. Rev. B 76, 205419 (2008). 220504(R) (2007). [13] J. E. Bunder and Hsiu-Hau Lin Phys. [2] S. W. Huang, D. J. Huang, C.-Y. Mou, et Rev. B 78, 035401 (2008). al., to appear in Phys. Rev. Lett.(2008) [14] Wen-Min Huang, Hsin-Hua Lai, Cheng- [3] C. D. Hu, Phys. Rev. B 77, 174418 (2008). Hung Chang and Hsiu-Hau Lin, Int. J. [4] Pao-An Lin, Horng-Tay Jeng, and Chen- Mod. Phys. B 22, 88 (2008) (invited). Shiung Hsue, Phys. Rev. B 77, 085118 [15] X. Z. Yuan, K. D. Zhu and Hsi-Sheng (2008). Goan, Euro. Phys. J. D 46, 375 (2008).(*) [5] Jia-Hsien Yao, Hsiu-Hau Lin and Tsung- [16] Shih-Jye Sun, Phys. Lett. A. 372, 1890 Shune, Appl. Phys. Lett. 92, (2008); ibid., 3493(2008). 242501(2008). [17] C. L. Huang, J.-Y. Lin, Y.T. Chang, C.P. [6] M.C. Chang and Q. Niu, J. Phys.: Sun, H.Y. Shen, C.C. Chou, H. Berger, Condens. Matter 20, 193202 (2008).(*)Yu- T.K. Lee and?H.D. Yang, Phys. Rev. B Chun Chen, Roger G. Melko, Stefan 76, 212504 (2007). Wessel, and Ying-Jer Kao, Phys. Rev. B [18] Horng-Tay Jeng and Ding-Sheng Wang, 77, 014524 (2008). J. Magn. Magn. Mater. 317, 46 (2007).

Highlights of Programs -›› 106 Highlights of Programs Particles and Fields

Focus Group on Collider, Astroparticle and BSM

Coordinator: Kingman Cheung (National Tsing Hua University/ National Center for Theoretical Sciences; email: [email protected]) Committee members: We-Fu-Chang (National Tsing Hua University), Chuan-Hung Chen (National Cheng Kung University), Cheng-Wei Chiang (National Central University), Chun-Khiang Chua (Chung Yuan Christian University), Wei-Shu Hou (National Taiwan University), Tzu-Chiang Yuan (Academia Sinica)

I. Brief Description Higgs boson and supersymmetry and on "unparticle", which will be described later. II. Major activities held in 2007/8 - e focus on collider phenomenology 2008/8 and astroparticle physics, in relation to (i) Regular journal-club meetings in new physics beyond the standard model (SM). NCTS/NTHU have been held during Participants include postdocs and research Tuesday lunch time; and also regular HEP students in NCTS, NTHU, and NCTU. They seminars in NTHU. come to seminars and journal-club meetings on (ii) Regular HEP seminars in CYCU. regular basis. Researchers from NCU often come to our activities. This focus group also (iii) "Challenges and Opportunities at the supports the seminars at CYCU coordinated by LHC'' from January 8th to January 12th Chun-Khiang Chua. 2008. Most of us believe that the new physics (iv) Support of students to attend international should come in in the TeV scale. Many new conferences. Feng-Yin Chang of NCTU to models predict new particles or new dynamics attend the SLAC Summer Institute, at TeV scale so as to halt the gauge hierarchy. Stanford; Dmitry Zhuridov of NTHU to There is a hope that the upcoming LHC is the attend the AFCA workshop in Tohoku place for the next big discovery. Together with University, Sendai, Japan. other planned cosmology experiments, testing new ideas will be the major activities in the III. Visitors and International next ten years. Our activities concentrate on Collaborations the particle physics phenomenology, which International visitors include Koji Harada links up the theory and experiments. We have (Kyushu University), Xiao-Hong Wu (KIAS), accomplished a number of interesting Jeonghyeon Song (Konkuk), Pyungwon Ko published works, which are the consequence of (KIAS), Taeil Hur (KIAS), Shigeki Matsumoto our group activities. (Toyama), Nobuchika Okada (KEK), David This year we have continued efforts on Mateos (UCSB), Mei Huang (IHEP), Michael Ramsey-Musolf (UW-Madison), Wai-Yee

107 ‹‹- Highlights of Programs Keung (UIC), Chung Kao (OKU),C.P Yuan Recently, perceived by Georgi a scale (MSU), Takeo Inami (Chuo U.), Shie invariant sector (coined unparticle) with a non- Minakami (Ochanomizu U.), Yasuyuki trivial infrared fixed point at a higher energy Katsumata (Chuo U.), Youji Koyama (Chuo scale may actually describe the real world at U.), Youji Koyama (Chuo U.), Kentarou high energy. So he visualized what kind of Mawatari (KIAS), Hoang Ngoc Long physics that such a sector can induce in high (Vietnam). energy phenomenology. The unparticle with a scale dimension d can be interpreted as a Kingman has established a long term U collection of d invisible massless particles, collaboration with Jeonghyeon Song and S.Y. U which can be unveiled by measurements of Choi of Korea. They have been working on a various energy distributions in the processes project of BMSSM. Kingman, Tzu-Chiang Z➝fføU and e-e+➝ γ U at e-e+ colliders, as well Yuan, and Wai-Yee Keung have been long as mono-jet production at hadron colliders. term collaborators. With visit of Wai-Yee in the Summer kingman and Tzu-Chiang have Our first two papers not only discovered the established a couple of well-defined projects novel propagator effect of the unparticle but on "quirks" and on "using tau-polarization to also laid down the formalism for calculations test properties of the staus", which also and identified the important channels to involves Chung Kao. observe unparticle effects at high energy colliders. The novel features, induced by scale Qi-Shu Yan, Yi Yang, and Mei Huang have invariance, include effective 4-fermion established collaboration on AdS/QCD. They interactions and a nontrivial phase factor, have finished one work, and have more to which interferes with the SM amplitudes in an come. interesting manner The spectacular phase factor exp(-i d ) associated with the IV. Highlights of Research Results U π propagator in s-channel can give rise to non- (i) Unparticle Stuff trivial behavior in a number of processes. This has been an exciting topic in particle In a work [3] with Li from Peking physics. We finished two important papers on University, we worked out the decay of the this subject in 2007 [1,2]. One was published standard model Higgs boson into a single in Physical Review Letters and the other one in photon and a vector unparticle through a one- Physical Review. They received more than loop process is studied. For an intermediate 200 citations in SPIRES database. The latter mass Higgs boson, this single photon plus contains the formalism, derivations, and the unparticle mode can have a branching ratio results for important phenomenology of comparable with the two-photon discovery unparticle. The paper is well cited and useful mode. The emitted photon has a continuous to others. We continued to work on a few energy spectrum encoding the nature of the more interesting phenomena in unparticle recoil unparticle. It can be measured in stuff, and published three more papers on the precision studies of the Higgs boson after its subject in 2008. discovery. The subject is about the scale invariance or, In another work [4], we study the decay of in broader terminology, conformal invariance. the standard model Z boson into unparticle Our existing particle theory is not conformal plus a single photon through a one-loop invariant, as the invariance is obviously broken process. As in the anomaly type decay, only by all the discrete masses of particles. Banks the axial-vector part of the Z coupling and Zaks in the 80s showed that a number of matching with the vector unparticle and/or the supersymmetric field theories contain a vector part of the £I coupling matching with conformal window such that the theories can the axial-vector unparticle can give a nonzero develop IR fixed points, where the scale is contribution to the decay. We show that the invariant. photon spectrum terminates at the end point in

Highlights of Programs -›› 108 accord with Yang's theorem. Existing data on not only the gauge-Higgs sector but also the single photon production at LEP I is used to pure gauge sector. constrain the Photon-photon can occur in the We finished the first paper on this subject. standard model only via loop diagrams and is It is still under review when this report is naturally suppressed. written. We have working on the second paper Unparticle can induce tree-level photon- and almost ready to finish. It also involves Dr. ab photon scattering through the operator Fab F Yu-Kuo Hsiao of Sinica. c ab OU for spin-0 unparticle or Fac F b O U for spin- 2 unparticle. Due to the peculiar CP- V. Publications conserving phase exp(-i dU π)associated with [1] K. Cheung, W.Y. Keung and T.C. Yuan, the time-like unparticle propagator for non- "Collider signals of unparticle physics," integral scaling dimension dU, the interference Phys. Rev. Lett. 99, 051803 (2007). effects of the s-channel amplitude with the t- [2] K. Cheung, W.Y. Keung and T.C. Yuan, and u-channels ones on the total cross sections "Collider Phenomenology of Unparticle as well as the angulardistributions are found to Physics,'' Phys. Rev. D76, 055003 be of some significance [5]. In addition, we (2007). show that the cross sections via unparticle exchange can be substantially larger than the [3] K. Cheung, C.S. Li and T.C. Yuan, "Higgs standard model contribution. Boson Decays into Single Photon plus Unparticle,'' Phys. Rev. D77, 097701 (ii) Higgs Physics (2008). The ultimate goal of the LHC is hunt for [4] K. Cheung, T.W. Kephart, W.Y. Keung and the Higgs boson, which is responsible for T.C. Yuan, "Decay of Z Boson into Photon electroweak symmetry breaking and mass and Unparticle," Phys. Lett. B662, 436 generation. We discuss a likely scenario at the (2008). LHC [8]. What if only a light Higgs boson is [5] C.F. Chang, K. Cheung and T.C. Yuan, discovered at the CERN LHC? Conventional "Unparticle effects in photon-photon wisdom tells us that the scattering of scattering,'' Phys. Lett. B664, 291 (2008). longitudinal weak gauge bosons would not [6] K. Cheung, W.Y. Keung and T.C. Yuan, grow strong at high energies. However this is "Bottomed Analog of Z+(4433),'' Phys. generally not true. In some composite models Rev. D76, 117501 (2007). or general two-Higgs-doublet models, the presence of a light Higgs boson does not [7] K. Cheung, X.H. Wu and Q.S. Yan, guarantee complete unitarization of the WW "Spectra, triple and quartic gauge scattering. After partial unitarization by the couplings in a Higgsless model,'' Phys. light Higgs boson, the WW scattering becomes Rev. D76, 116006 (2007). strongly interacting until it hits one or more [8] K. Cheung, C.W. Chiang and T.C. Yuan, heavier Higgs bosons or other strong "Partially Strong WW Scattering,'' dynamics. We analyze how LHC experiments arXiv:0803.2661 [hep-ph]. can reveal this interesting possibility of [9] K. Cheung, J. Song, P. Tseng and Q.S. partially strong WW scattering. Yan, "Production and decays of the light Our key result is that even if the coupling pseudoscalar boson η at the LHC in the simplest little Higgs model,'' ghWW deviates by a mere 5% from the SM arXiv:0806.4411 [hep-ph]. value, the WL WL scattering will indicate a dramatic change in the invariant mass [10] C.W. Chiang and E. Senaha, "Update distribution. If ghWW deviates by 30%, just by analysis of two-body charmed B meson counting the event rates one can tell the decays,'' Phys. Rev. D75, 074021 (2007). difference from the SM. This is of immense [11] C.W. Chiang, J. Jiang, T. Li and Y.R. interests for LHC experiments. Furthermore, Wang, "Top Hypercharge,'' JHEP 0712, we point out that the WL WL scattering probes 001 (2007).

109 ‹‹- Highlights of Programs [12] C.H. Chen, C.Q. Geng and C.W. Kao, production in exclusive B decays", Phys. "U-boson and the HyperCP exotic Lett. B650, 379 (2007). events", Phys. Lett. B663, 400 (2008). [15] C.H. Chen, C.Q. Geng and T.C. Yuan, [13] C.H. Chen and C.Q. Geng, "Flavors and "D-\bar D mixing and rare D decays in Phases in Unparticle Physics", Phys. Lett. the Littlest Higgs model with non- B661, 118 (2008) unitarity matrix", Phys. Lett. B655, 50 [14] C.H. Chen and T.C. Yuan, "f0 (1710) (2007).

Highlights of Programs -›› 110 Focus Group on Gravitation, Cosmology and Quantum Gravity

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

l. Brief Description School/Workshop on Cosmology and Gravitation, 7th Ð 10th January, 2008, Nation Taitung University, Taitung, Taiwan, http://phys.cts.nthu.edu.tw/ his is a year of harvesting the works actnews/actnews.php?Sn=94243 and efforts of various collaborative (2) 5th Italian-Sino Workshop on Relativistic forces established among the focus group Astrophysics -- Lights of the Dark members in the past two years. On top of the Universe, May 28 - June 1, 2008, Taipei, important results obtained previously, like, Hualien, Taiwan, http://www.phys. proving black holes are elementary particles in sinica.edu.tw/~si5/ superspace, obtaining the most stringent limit on the parity violating coupling of Dark Another special efforts of our focus group energy,…etc, the major research achievements is to create opportunities for postdocs and of this year are: graduate students to visit and to collaborate with prestige research institutes overseas like, (1) unexpectedly found that some University of Maryland, Perimeter Institute, cosmological models have negative energy, Yukawa Institute, Institute of Applied (2) quantum states with the negative energy Mathematics, Academia Sinica, Beijing…etc. density in some spacetime region may These will prove to help not only to sharpen exhibit quantum anti-correlations, which the ability of individual junior researcher but likely can cancel the effects of fluctuations also to broaden their spectrum of views. on the coupled microscopic object and will Major members of our focus group are: find important applications to LIGO experiments, ¥ Chiang-Mei Chen (NCU) on gravitation and string theories, (3) obtained full knowledge of a single Unruh- DeWitt detector uniformly accelerated in a ¥ Hing-Tong Cho (TKU) on gravitation and quantum field. black holes Through joint international school / ¥ Chung-Hsein Chouh (NCKU) on quantum workshops, we have not only reinforced the gravity and quantum mechanics collaborative force in the Asia-Pacific areas ¥ Da-Shin Lee (NDHU) on non-equilibrium but have also identified cutting edge research physics and cosmology problems to further sharpen the training of our ¥ Wo-Lung Lee (NTNU) on large scale younger generation in gravitation and structure of Universe cosmology research. The major joint international school/workshop hosted by our ¥ James M. Nester (NCU) on gravitation and focus group were: Quasi-local energy (1) Second 2008 Taitung International ¥ Kin-Wang Ng (Academia Sinica) on

111 ‹‹- Highlights of Programs cosmology and data analysis Nation Taitung University, Taitung: ¥ Chopin Soo (NCKU) on quantizing gravity This was the second joint international and cosmology school/workshop of the sort in Cosmology and ¥ Hwei-Jang Yo (NCKU) on numerical general Gravitation researched in Taiwan and was relativity sponsored by NCTS, Institute of Physics, Academia Sinica and APCTP of Korea. The ¥ Hoi-Lai Yu (Academia Sinica) on quantizing sponsorship from APCTP not only made the gravity and cosmology meeting helpful in reinforcing collaborative Frequent visitors are: research activities among Asia Pacific area within a flight distance of two hours but also in ¥ Bei-Lok Hu (University of Maryland); attracting talented young researchers to ¥ Roh-Suan Tung (Shanghai Normal contribute. The main purpose of this meeting is University); to introduce to students and researchers the latest developments in cosmology, semi- ¥ Yun-Kau Lau (Applied Mathematics classical and quantum gravity. Institute, Academia Sinica, Beijing); We have about 80 graduate students, ¥ Larry H. Ford (Tufts University); postdocs, local faculties, and faculties from the ¥ Misao Sasaki (Kyoto University); Asia Pacific area, Europe and the United States participating in the meeting. Major lectures ¥ Ray Rivers (University of London). were delivered by researchers from overseas: ¥ The purposes of this focus group are: Larry Ford (Tufts U.), Bei-Lok Hu (Maryland (1) To generate a long-term collective force in U.), Misao Sasaki (Kyoto U.), Yangmin Cho Cosmology and Gravity research among (Seoul National U.), Sean Hayward (Shanghai the local communities and the Asia-Pacific Normal U.) and Sang Pyo Kim (Gusan area; National U.). Several collaborative works on the topics of black hole entropy, negative (2) Using non-equilibrium field theories and energy cosmologies and negative energy General Relativity as tools and keys to density states were kicked off after the generate interdisciplinary and cutting-edge meeting. research activities in cosmology, classical and quantum gravity, LIGO experiments Three special scholarships were awarded to and quantum information science; the best graduate student presentations during the workshop session. The awarding of (3) To train and create opportunities for scholarships had generated enthusiastic talented graduate students and postdocs to discussions among the participating students make major contributions by helping them and postdocs which will certainly help the to identify hot and important students not only to grasp and sharpen the interdisciplinary problems in the area of lecture materials effectively but will help them cosmology, gravitation and quantum to generate friendship and collaboration after gravity research. the school/workshop. ll. Activities The highlights of the meeting were: The following major activities were carried (A) the surprising and unexpected results on out last year on top of our regular/irregular negative energy cosmology was journal club meetings at the Institute of announced for the first time to the world Physics, Academia Sinica and Department of by Prof. Nester's group, Physics, National Central University. (B) the quantum anti-correlation of negative (1) Second 2008 Taitung International energy density states to cancel effects of School/Workshop on Cosmology and fluctuations on the coupled microscopic Gravitation, 7th – 10th January, 2008, object and its application to LIGO

Highlights of Programs -›› 112 experiments were discussed for the first gravitation workshop at the Institute of time in the meeting by Profs. Larry Ford Applied Mathematics, Academia Sinica, and D.S. Lee's group. Beijing and to participate in related research programs during the summer (2) 5th Italian-Sino Workshop on Relativistic annually in the last three years. Astrophysics -- Lights of the Dark Universe May 28 - June 1, 2008, Taipei- (3) Joint School/Workshop in Gravity & Hualien, Taiwan Cosmology rotates between Taiwan, China, Korea and Japan. The aim of this workshop is to provide a platform for information and ideals interchange between Sino and Italian IV. Highlights of Research Results researchers on recent advances in modern (1) Identified an energy for homogeneous astrophysics. The main topics were focused on cosmologies, unexpectedly found that some dark energy, large scale structures, gamma ray models have negative energy; J.M. Nester, bursts, supernovae, as well as first stars. The L. L. So and T. Vargas, "Energy of meeting was successful, not only in the aspect homogeneous cosmologies" (accepted for of fruitfulness of contributions, but the first publication in Phys. Rev. D). time of the meeting outside Italy in Taiwan. (2) Studies on the nature of quantum states A total number of 65 researcher joined the with the negative energy density. In meeting with 32 coming from abroad and 33 particular, these states may exhibit from local institutions. 33 talks on the cutting quantum anti-correlations, which likely can edge developments on astrophysics and large cancel the effects of fluctuations on the scale cosmologies were presented. coupled microscopic object. The goal of Mechanisms on gamma ray bursts through this study is for a better control on the macroscopic nuclei under gravitation collapses quantum noise in order to improve the and its effects in cosmologies were discussed. accuracy of the measurement on the state Chances and collaborations from recently of the microscopic object, especially in the installed Large Sky Area Multi-Object Fiber laser interferometer gravitational wave Spectroscopy Telescope (LAMOST) were also detection; J. T. Hsiang, T.H. Wu and D.S. discussed enthusiastically during the meeting. Lee "Stochastic Lorentz forces on a point We expect another fruitful harvest of the charge moving near the conducting plate", meeting will be materialized in the years to Phys.Rev.D77:105021, 2008. This provides come. a successful example of cross-discipline works from cosmology, gravitation and III. Visitors and International fundamentals of quantum mechanics. Collaborations (3) Obtained the full knowledge about a single (1) With the help of Prof. L. Ford and B.L. Hu Unruh-DeWitt detector uniformly our postdocs (S.Y. Lin, C.S. Chou and C.H. accelerated in a quantum field and the Wu) were arranged to visit and conduct extension to the case of the single inertial research at Princeton University, University detector; S.-Y. Lin and B. L. Hu, of Maryland , Tuft University, International "Backreaction and Unruh Effect: New Center for Gravitation Research at Insights from Exact Solutions of University of Pennsylvania and Perimeter Uniformly Accelerated Detectors", Phys. Institute, Canada. Several important papers Rev. D 76, 064008 (2007) (selected for the (see the highlights and publication list September 2007 issue of Virtual Journal of below) in the cutting edge were published Quantum Information). This is a during these activities. successful example of combing efforts from various institutes and techniques (2) With the help of Prof. Y.K. Lau, more than developed from gravitation and non- 12 graduate students (from NCU, NDHU equilibrium field theories. and NCKU) were arrange to attend the

113 ‹‹- Highlights of Programs (4) Higher dimensional bulk fermion Hawking [7] J. M. Nester, J. Phys. A: Math. Theor. 40, emission lead to the interesting conclusion 2751(2007). that for d>5 the emission dominates over [8] K.F. Shie, J.M. Nester, H.J. Yo, Phys. Rev. the brane-localized one. This is an example D78, 023522 (2008). contrary to the conjecture that "black holes [9] H.J. Yo, J.M. Nester, Mod. Phys. Lett. 22, radiate mainly on the brane"; H. T. Cho, A. 2057 (2007). S. Cornell, J. Doukas, and W. Naylor, "Bulk Dominated Fermion Emission on a [10] C.P. Soo, Class. Quantum Grav. 24, Schwarzschild Background" Phys. Rev. 1547-1555 (2007). D77, 016004 (2008). [11] C.H. Chou, C.P. Soo and H.L. Yu, Phys. Rev. D76, 084004 (2007). [12] C.H.Chou, B.L. Hu and T. Yu, Physica A 387, 432 (2008). [13] C.H.Chou, B.L. Hu and T. Yu, Phys. Rev. V. References E 77, 011112 (2008). [1] H. T. Cho, A. S. Cornell, Phys. Rev. D77, [14] I. C. Wang and K.W. Ng, Phys. Rev. D 016004 (2008). 77, 083501 (2008). [2] H. T. Cho, A. S. Cornell, J. Doukas, and [15] S.Y. Lin and B. L. Hu, Class. Quantum W. Naylor, Phys. Rev. D77, 041502 Grav. 25, 154004 (2008). (2008). [16] C.H. Wu, K.W. Ng and L.H. Ford, Phys. [3] H.-T. Cho and C.-L. Ho, J. Phys. A41, Rev. D75, 103502 (2007). 172002 (2008). [17] C.H. Wu, K.W. Ng, W. Lee, D.S. Lee and [4] H.-T. Cho and C.-L. Ho, J. Phys. A41, Y. Y. Charng, JCAP 0702006 (2007). 255308 (2008). [18] A. Bouchareb, C.M. Chen, G. Clement, [5] J. T. Hsiang, T.H. Wu and D.S. Lee, D. Gal'tsov, N. Scherbluk and T. Wolf, Phys.Rev.D77, 105021, (2008). Phys. Rev. D 76, 104032 (2007). [6] J.M. Nester, L. L. So, T. Vargas, "Energy of homogeneous cosmologies" (to appear in Phys. Rev. D).

Highlights of Programs -›› 114 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 http://twcp3.phys.ntu.edu.tw/lqcdjc/. Among them, (4) is a new activity which has started since March 2007. These weekly activities are crucial for the successes of High Energy he main theme of PNC focus group is Physics in Taiwan. In particular, (1) has played to tackle the important physics within a pivotal role to bring HEP experimentalists the Standard Model (SM), as well as to and theorists together, which is crucial for the identify any signals which may suggest new advancements of the NTU Belle group as well physics beyond the SM. To achieve this goal, as our B-physics phenomenologists. In fact, we call for the collective efforts of theorists many new ideas and insights were initiated at and experimentalists. The topics under active (1), through intensive discussions among investigations are: (1) Phenomenologies of several participants, and also between Strong and Electroweak Interactions, (2) experimentalists and theorists. Flavor physics and CP violation, (3) Grand During 2008, Prof. C.P. Yuan was visiting unification, (4) Supersymmetry, (5) Models Academia Sinica, thus a working class for the beyond the SM, (6) Hadron physics, (7) LHC phenomenology was organized: LHC Effective Field Theory of QCD, (8) Lattice Working class on LHC phenomenology (Feb. QCD, (9) Baryon asymmetry in the universe, 28-Mar. 28, Jun. 9-Aug. 6) (10) Accelerating universe and CMB effects. http://www.phys.sinica.edu.tw Even though our projects appear to cover a /~heptheory/LHC_class/LHC_Working_Class. wide range of topics, they are unified under the htm main theme. The salient features of PNC focus group are: Besides the regular weekly seminars and journal clubs, we also held the following ¥ Theorists and experimentalists work together international conferences and schools in 2008: ¥ We have about 40 members, many with ¥ The FPCP08 International Conference on international reputations flavor physics and CP violation (May 5-9) ¥ Young researchers are highly encouraged and http://hep1.phys.ntu.edu.tw/fpcp08/ supported ¥ The 12th Taiwan Nuclear Physics Summer ¥ Extensive international collaborations School (June 20-23) http://phys.cts.ntu.edu.tw/nuclear/2008/ II. Activities * The Summer Institute 2008 (SI2008) Our weekly seminar and journal clubs are: (August 10-17) (1) Particle physics journal club http://phys.cts.ntu.edu.tw/si2008/ https://hep1.phys.ntu.edu.tw/NTUHEP/journal They have provided great opportunities for -club, (2) Theoretical physics seminar, (3) local theorists/experimentalists to interact Cosmology and astrophysics journal club, and among themselves, as well as with foreign (4) Lattice QCD journal club visitors.

115 ‹‹- Highlights of Programs In particular, for the Summer Institute and TWQCD Collaborations. It is well known 2008, we had many distinguished lecturers and that JLQCD Collaboration constitutes an elite participants from Japan, Korean, and US, group of lattice field theorists, who have been including the Director of the newly established playing a vital role in the lattice QCD Institute of Physics and Mathematics of the community. Since 2006, JLQCD has started Universe (IPMU) at Tokyo University, Prof. the project of simulating dynamical overlap Hitoshi Murayama, a famous particle theorist fermion using the IBM BlueGene working at UC Berkeley. The SI2008 is the supercomputer with peak speed ~50 Teraflops. 14th in a series of Summer Institutes in Since 2006, there have been many mutual phenomenology of particle physics started in visits between JLQCD and TWQCD, and now Japan in 1995. This year, the Summer Institute we have worked out several important results was the first time holding in Taiwan. The total (see Sections V and VI). Furthermore, we also number of participants of SI2008 is over 140, encourage local people (faculty and graduate in which about 55 from Japan, 15 from Korea, students) to work on lattice QCD, and to join 70 from Taiwan, and a few from Europe. this international collaboration. This is also Evidently, SI2008 is a very successful summer one of the goals of the journal club on lattice institute in particle physics, in terms of its QCD. scientific merits, impacts, and international In the last year, a new research group in participations. It has triggered many interesting PNC FG has been formed. Namely, the discussions among the participants, which research group led by Prof. Hsiang-Nan Li, have blossomed into new ideas and which have been focusing on QCD for collider collaborations. physics, in view of the turn on of the Large Hadron Collider (LHC) in 2008. III. Visitors and International Collaborations IV. Young Researchers The largest international collaboration in In the PNC focus group, we support young the PNC focus group is the NTU Belle group, researchers with the highest priority. In the incorporating theorists and experimentalists. In following, we outline some of these supports. general, the members of the PNC focus group have a lot of international collaborations as In the summer of 2007, we supported 3 well as domestic ones. For example, Prof. NTU graduate students to attend the INT Hsiang-Nan Li has been collaborating with summer school on lattice QCD at University of many theorists around the world: Satoshi Washington (http://www.int.washington.edu/ Mishima (Institute for Advanced Study, PROGRAMS/07-2b.html). They also received Princeton Univ), Junegone Chay (Korea Univ), supports from the Institute of Nuclear Theory Soumitra Nandi (Univ of Calcutta), Takeshi to cover their local expenses at the summer Kurimoto, (Univ of Toyama), Makiko school. This was the first time our graduate Nagashima (Univ of Montreal), Tony Sanda students attend international summer school (Kanagawa Univ), Yue-Long Shen (Ocean and also receive financial supports from the University of China), besides with the theorists organizing institution. In future, we will in Taiwan: Wei-Shu Hou (National Taiwan encourage more Ph.D. students to participate Univ), Yeo-Yie Charng (Academia Sinica), the renowned summer/winter schools in high and Chuan-Hung Chen (National Cheng-Kung energy physics, e.g., TASI, Les Houches, Univ). Here we do not attempt to list all ERICE, etc. Obviously, these schools do collaborations of all members of the PNC provide excellent trainings to our graduate focus group. Rather, we report the students. Also, their interactions with other international collaboration which has been participants during the schools would be an established recently. invaluable experience to them. During 2006-2007, we have set up an In November 2007, we provided full international collaboration between JLQCD support for a Ph.D student working in

Highlights of Programs -›› 116 astrophysics to give a presentation at the Prize in Experimental Particle Physics. AstroGPU 2007, a workshop held at Princeton In general, the priorities of support for PNC Institute for Advanced Study. Note that it members are: Graduate students (highest), would be extremely difficult for him to get the Postdocs, Junior faculty, Senior faculty necessary support from NSC or MOE, under (lowest). Also, we highly encourage the existing regulations. Thus PNC focus outstanding junior researchers around the group plays a crucial role in supporting the world to visit and/or to collaborate with us. graduate students to participate conferences / schools / workshops which are relevant to their V. Highlights of Research Results Ph.D thesis researches. A. Observation of Direct CP Violation Besides graduate students, the PNC focus group also invests a lot in supporting our In 2007, theorists and experimentalists of outstanding young faculty and postdocs. For NTU HEP group (also members of PNC focus example, in the fall semester 2007, Prof. Jiunn- group) have measured the direct CP violation Wei Chen has received a NSC visiting in B meson decays. Previous work suggested a fellowship (for faculty only) to visit MIT for 3 difference in the decay of charged and neutral months. However, there is no similar NSC particles, but the large uncertainties on these supports for his postdoc Dr. Eiji Nakano. Thus, measurements made it difficult to say whether the PNC focus group has provided a travel and the difference was real. The new study reduced living support for Dr. Eiji Nakano such that he the uncertainty on the charged particle decay can also visit MIT together with Prof. Jiunn- rate asymmetry by a factor of 1.7. Although Wei Chen. Furthermore, PNC focus group has firm conclusions cannot be drawn from this provided additional supports to both of them result, the measurement provides stronger such that they can extend their stay at MIT to evidence for a large deviation in direct CP 4-5 months. violation between charged and neutral B- meson decays and possible new sources of CP In July 2008, we have provided full violation beyond the standard model. This supports for two postdocs to give presentations significant result was published in Nature Vol. th at the 34 International Conference on High 452, No. 7185, (2008) 332 [doi:10.1038 / Energy Physics at Philadelphia. One of them nature06827]. Note that this is the first Nature (Dr. Kai-Feng Chen) was to give a plenary talk paper published by the Belle Collaboration as and also to receive the IUPAP Young Scientist well as the NTU physics department.

FIG. The difference between decay rates of B meson and its anti-particle.

117 ‹‹- Highlights of Programs B. B decay golden mode However, it has not been confirmed by other experimental groups since 2002. B physics has entered the era of precision measurement. The standard model parameter In July 2008, the BABAR Collaboration sin(2\phi_1) can be extracted from tree- (arXiv:0807.1086[hep-ex]) announced the dominated or penguin-dominated modes. observation of the pseudoscalar meson of b- Especially, the tree-dominated B \to J/\psi K bbar, the eta-b(1S), with the mass 9388.9 decay is the so-called golden mode with very {+3.1} {-2.3} (stat) +/- 2.7(syst) MeV. This is small penguin correction. However, how large the lightest meson of b-bbar, which has been the penguin correction is has not yet been sought for a long time by many HEP studied carefully due to the difficulty in experimental groups. Most interestingly, the handling QCD dynamics. Li and Mishima [9] mass of eta-b observed by BABAR is in (JHEP 0703:009,2007) gave the first reliable excellent agreement with the TWQCD calculation of this penguin correction, which is theoretical prediction. This is a triumph of of order 10^{-3}. This calculation is important lattice QCD with exact chiral symmetry. for judging whether different extractions of E. Dubna-Mainz-Taipei (DMT) Dynamical sin(2\phi_1) from different modes can be Model regarded as new physics signals. The work of Li and Mishima [9] has been widely quoted in The completion of DMT (Dubna-Mainz- many conferences on flavor physics. Taipei) dynamical model for pion electromagnetic production up to the first C. Theoretical prediction of a new particle resonance region is Shin-Nan Yang and In a series of papers, Xiao-Gang He and collaborators' remarkable achievement in collaborators studied the experimental data recent years. The model has been from ∑+ -> p µ +µ - anomalous HyperCP result demonstrated to give excellent description of observed at Fermilab a few years ago and the existing pion production data from pointed out several interesting features of the threshold to resonance region. For example, data. These results opened the possibility for the prediction of our model agrees beautifully the existence of a new particle X with unusual with the recent Mainz data for the threshold π0 properties. This work has been published in electroproduction at Q2=0.05 GeV-2, while [Phys. Rev. Lett. 98 (2007) 081802] and ChPT fails badly. The DMT model also has received some international attentions and was been used extensively to extract the NÐ∆ e.m. reported by New Scientist, PhysOrg.com, and transition form factors at low and medium Physicsweb.com. momentum transfer. In short, DMT model is now cited in practically every paper on e.m. D. Theoretical prediction of ηb the lightest pion production, be it a theoretical or pseudoscalar meson of bottomium experimental one. And together with In 2007, TWQCD Collaboration performed Pascalutsa and Vanderhaeghen, we have a theoretical calculation of the spectrum of all finished an invited review article on heavy mesons b-bbar, c-cbar, b-sbar, b-cbar, "Electromagnetic excitation of the ∆(1232)- etc, in the framework of lattice QCD with resonance" [Physics Reports 437, (2007) exact chiral symmetry, "Beauty mesons in 125]. It is expected that this review will lattice QCD with exact chiral symmetry" Phys. become a classic in this field. According to Lett. B651 (2007) 171. In this paper, we have Science Direct (http://top25.sciencedirect.com

predicted that the mass of ηb is 9383(4)(2) /index.php?cat_id=12&subject_area_id=21), it MeV, along with many other predictions. In tops the list of "Top 25 hottest articles in our paper, we also commented that the ALEPH Physics and Astronomy" for the period of Collaboration might not have "determined" the April-June, 2007 and placed second overall in

mass of ηb accurately. Recall that the first science (http://top25.sciencedirect.com/

report of the observation of ηb was by ALEPH, ?cat_id=12). back in 2002, with a mass 9300(28) MeV. F. QCD viscosities

Highlights of Programs -›› 118 Recently, Jiunn-Wei Chen have initiated a [3] "Next-to-leading-order corrections to series of investigations of QCD viscosities in exclusive processes in k(T) factorization", the hadronic phase using chiral perturbation Soumitra Nandi, Hsiang-nan Li. theory. This research has connections to Phys.Rev.D76:034008, 2007. relativistic heavy ion collisions (RHIC), string [4] "Factorization approaches to B meson theories and physics of ultra cold atom. With decays", Hsiang-nan Li. FPCP-2007-011, members of our NTU group (Li, Liu, Nakano, In the Proceedings of 5th Flavor Physics Wang, Yang) and Mei Huang (Beijing), we and CP Violation Conference (FPCP established that shear viscosity to entropy 2007), Bled, Slovenia, 12-16 May 2007. density ratio reaches to its minimum near the arXiv:0707.1294 [hep-ph] phase transition temperature for QCD and one [5] "Possible complex annihilation and B ---> component real scalar field theories K pi direct CP asymmetry", Junegone [ Phys.Lett.B647,371(2007); Chay, Hsiang-nan Li , Satoshi Mishima, Phys.Rev.D76,114011(2007); MIT-CTP-3902. arXiv:0711.2953 [hep- arXiv:0709.3434]. This behavior agrees with ph], accepted for publication in Phys. Rev. those of many other materials (such as water, D. nitrogen, helium and cold atoms in the infinite scattering length limit) with no exceptions [6] "Comment on 'Gauge Invariance and found so far. For bulk viscosity to entropy $k_T$-Factorization of Exclusive density ratio, however, the general behavior is Processes", Hsiang-nan Li . arXiv: less known. In the case with massless quarks, 0808.1526 [hep-ph] we found that its maximum is reached near the [7] "Constraints on Unparticle Interaction phase transition temperature (arXiv: from b ---> s gamma", Xiao-Gang He, 0711.4824). It will be very interesting to see Luhsing Tsai, JHEP 0806:074, 2008. how general this behavior is in other systems [8] "Rare Decays with a Light CP-Odd Higgs and what implications to cosmology it might Boson in the NMSSM", Xiao-Gang He, have. Jusak Tandean, G. Valencia, JHEP 0806:002, 2008. VI. Outlook [9] "Unparticle Induced Baryon Number ¥ To enhance our on-going international Violating Nucleon Decays", Xiao-Gang collaborations, and to initiate new ones He, Sandip Pakvasa. Phys.Lett.B662:259- ¥ To encourage outstanding young researchers 263, 2008. to play a leading role in all PNC activities [10] "Supersymmetric Unparticle Effects on Higgs Boson Mass and Dark Matter", ¥ To invite outstanding young theorists to visit N.G. Deshpande, Xiao-Gang He, Jing NCTS, and to develop long-term and fruitful Jiang, Phys.Lett.B656:91-95, 2007. collaborations [11] "Constraints on unparticle interactions from invisible decays of Z, quarkonia and neutrinos", Shao-Long Chen, Xiao-Gang VII. References He, Ho-Chin Tsai, JHEP 0711:010, 2007. [1] "Fourth generation CP violation effect on [12] "SUSY R-parity violating contributions B ---> K pi, phi K and rho K in NLO to the width differences for D - anti-D PQCD", Wei-Shu Hou , Hsiang-nan Li , and B(d,s) - anti-B(d,s) systems", Shao- Satoshi Mishima , Makiko Nagashima , Long Chen, Xiao-Gang He, A. Phys.Rev.Lett.98:131801, 2007. Hovhannisyan, Ho-Chin Tsai , JHEP [2] "Okubo-Zweig-Iizuka-rule violation and B 0709:044,2007. ---> eta-(prime) K branching ratios", Jen- [13] "Interactions of Unparticles with Feng Hsu, Yeo-Yie Charng, Hsiang-nan Standard Model Particles", Shao-Long Li, Phys.Rev.D78:014020, 2008 Chen, Xiao-Gang He, Phys.Rev.D76: 091702, 2007

119 ‹‹- Highlights of Programs [14] "Spontaneous CP violating phase as the pions", Jiunn-Wei Chen , Juven Wang, CKM matrix phase", Shao-Long Chen, arXiv:0711.4824 [hep-ph]. N.G. Deshpande, Xiao-Gang He, Jing [23] "Phase Transitions and the Perfectness of Jiang, Lu-Hsing Tsai, Eur.Phys.J.C53: Fluids", Jiunn-Wei Chen, Mei Huang, 607-614,2008. Yen-Han Li, Eiji Nakano, Di-Lun Yang, [15] "D - anti-D mixing constraints on FCNC arXiv:0709.3434 [hep-ph]. with a non-universal Z-prime", Xiao- [24] "Universality of mixed action Gang He, German Valencia, Phys.Lett. extrapolation formulae". Jiunn-Wei Chen, B651:135-138, 2007. Donal O'Connell, Andre "Walker-Loud, [16] "Scalar dark matter effects in Higgs and arXiv:0706.0035 [hep-lat]. top quark decays", Xiao-Gang He, Tong [25] "QCD viscosity to entropy density ratio Li, Xue-Qian Li, Ho-Chin Tsai, in the hadronic phase", Jiunn-Wei Chen, Mod.Phys.Lett.A22:2121-2129, 2007 Yen-Han Li, Yen-Fu Liu, Eiji Nakano, [17] "A(4) group and tri-bimaximal neutrino Phys.Rev.D76:114011, 2007. mixing: A Renormalizable model", Xiao- [26] "Generalised parton distributions of the Gang He, Nucl.Phys.Proc.Suppl.168:350- pion in partially-quenched chiral 352, 2007. perturbation theory", Jiunn-Wei Chen, [18] "Does the HyperCP Evidence for the William Detmold, Brian Smigielski, Decay Sigma --> p mu+ mu- Indicate a Phys.Rev.D75:074003, 2007. Light Pseudoscalar Higgs Boson", Xiao- [27] "BEC-BCS Crossover in the Epsilon Gang He, Jusak Tandean, G. Valencia, Expansion", Jiunn-Wei Chen, Eiji Phys.Rev.Lett.98:081802, 2007 Nakano, Phys.Rev.A75:043620, 2007. [19] "Calculation of BR(anti-B0 ---> [28] "Shear viscosity to entropy density ratio Lambda(c)+ + anti-p) in the PQCD of QCD below the deconfinement approach", Xiao-Gang He, Tong Li, Xue- temperature", Jiunn-Wei Chen, Eiji Qian Li, Yu-Ming Wang, Phys.Rev. Nakano, Phys.Lett.B647:371-375, 2007. D75:034011,2007. [29] "Self-Adjoint Extensions of the [20] "Minimal modification to the tri- Hamiltonian Operator with Symmetric bimaximal neutrino mixing", Xiao-Gang Potentials which are Unbounded from He, A. Zee. Phys.Lett.B645:427-431, Below", H.-T. Cho and C.-L. Ho, J. Phys. 2007. A 41,255308, 2008. [21] "Shear Viscosity of a Non-Relativistic [30] "A Novel Quasi-Exactly Solvable Model Conformal Gas in Two Dimensions", with Total Transmission Modes", H.-T. Jiunn-Wei Chen, Wen-Yu Wen, Cho and C.-L. Ho, J. Phys. A 41, 172002, arXiv:0808.0399 [hep-th]. 2008. [22] "Bulk viscosity of a gas of massless

Highlights of Programs -›› 120 Focus Group on Strings

Coordinator: Hsien-chung Kao (National Taiwan Normal University, email:[email protected]) Committee members: Chuan-Tsung Chan (TungHai University), Chiang-Mei Chen (National Central University), Kazuyuki Furuuchi (National Center for Theoretical Sciences), Choon-Lin Ho (Tamkang University), Pei-Ming Ho (National Taiwan University), Jen-Chi Lee (National Chiao Tung University), Feng-Li Lin (National Taiwan Normal University).

I. Brief Description strings. There were about twenty participants. In the past few years, research topics investigated by the group members include AdS/CFT string duality and its applications, here are eleven postdocs members: non-commutative geometry, string cosmology, Pravina Borhade (TungHai string high energy scattering, string black University), Takayuki Hirayama (NCTS), holes, quasi-normal modes in black holes and Peter Matlock (Nat'l Chiao Tung University), quasi exactly solvable models. Toshihiro Matsuo (Nat'l Taiwan Normal University), Makoto Narita (Nat'l Taiwan II. Activities University), Dmitry Orlov (Nat'l Central 1. Weekly string seminars at NTU University), Tomohisa Takimi (NCTS & Nat'l The schedule is announced at Chiao Tung University), Dan Tomino (Nat'l http://web.phys.ntu.edu.tw/string/index.htm. Taiwan Normal University), Wen-Yu Wen The record of past seminars can be found at (Nat'l Taiwan University), Yi Yang (NCTS & http://phys.cts.ntu.edu.tw/fgroup.aspx?mclass= Nat'l Chiao Tung University) and Syoji 4&fclass=2&aclass=7. This is the core Zeze(Nat'l Taiwan University). There are also activities of the group. This series of seminars about six student members. The main purpose was initiated in 1996. It is scheduled in the for this focus group is to enhance the Friday afternoon so that most group members interaction and collaboration among the group can attend. The talks are given either by group members. It is fair to say that so far the string members or by invited visitors from oversea to focus group does live up to our expectation present their recent works. It usually lasts for and most of our members are satisfied with the two hours so that details of the work can be way it is run, thanks to the effort of the explained to some extent and participants have previous coordinators, Pei-Ming Ho and Jen- enough time to ask questions. After the Chi Lee. Currently, we have regular seminars seminar, members would usually stay for at NTU, NTHU and NTNU. If some members further discussion with the speaker or with one are interested in certain specific topics, we another. It is important for generating would also ask our visitors to give review collaborations and bonding the group lectures on these topics. Through these members. activities, we have established a close connection with the Japanese string 2. Biweekly high energy seminar at NTNU community. Last year, we had more than The schedule is announced at twenty visitors from Japan. In addition, many http://home.phy.ntnu.edu.tw/~highenergy/. of our group members were invited to go to This series of seminars includes topics such as Japan to talk about their works. A lot of cosmology and particle physics so that the collaborations have been generated through group members have a chance to interact with these visits. In August, Chuan-Tsung Chan physicists from other fields. Many foreign organized a two-day mini-workshop on little visitors visiting NTU also spend a few days in

121 ‹‹- Highlights of Programs NTNU for giving additional talks or having 1. Choon-Lin Ho is visiting YITP, hosted by further discussion. Prof. Ryu Sasaki, form 6/12 to 9/11 and will visit Tokyo University, hosted by Prof. 3. Biweekly high energy seminar at NTHU Yutaka Matsuo, in September. There are now five faculty and postdocs 2. Kazuyuki Furuuch visited YITP for a members in the Hsinchu area and regular KIAS-YITP joint workshop on String seminars have been arranged since last year. Phenomenology and Cosmology from Kazuyuki Furuuch has been very active in September 24 to 28 and Riken for the Riken inviting visitors who would usually stay in Symposium "String Field Theory 07" from NCTS for a few days. He has also asked October 6 to 7 in 2007. He also visited several of our visitors to give review lectures KEK from October 9 to 12 in 2007. He was in NCTS if some members are interested in hosted by Prof. Yoshihisa Kitazawa and certain specific topics. gave a talk titled "Matrix model for 4. Mini-Workshop on Matrix and String Polyakov loops, string field theory in the Chuan-Tsong Chan organized a two-day temporal gauge, and winding string mini-workshop on August 4 and 5. It is condensation in Anti-de Sitter space" there. announced at http://phys.cts.ntu.edu.tw/data/ 3. Jen-Chi Lee visited Tokyo University, 97.8.4poster.pdf. There are two series of hosted by Prof. Yoneya, from April 9 to lectures: Minimal String Theory and IKKT July 8 in 2007. He is visiting YITP, hosted Model given by three speaker, David Shih by Prof. Sasaki, from July 15 to August 15, (IAS), Hirotaka Irie (NTU) and Dan Tomino 2008. (NCTS). There were about twenty 4. Feng-Li Lin attended Strings 2007 in participants. Mardid. He also went to a String III. Visitors and International cosmology workshop at YITP in September Collaborations of 2007. The string focus group has maintained a IV. Highlights of Research Results steady and close connection with the Japanese 1. Lie 3-Algebra and Multiple M2-branes string community thanks to the effort of Prof. Takeo Inami of Chou University. In the past In the past few months there has been a few years, we have about thirty oversea surge in interest in the Lie three-algebra, which visitors each year. A summary of the lays down the mathematical foundation for information about these visits in last year can understanding multiple M2 and M5 branes. be found at http://phys.cts.ntu.edu.tw/ Pei-Ming Ho and his student Ru-Chuen Hou, fgroup.aspx?mclass=3&dclass=1&fclass=2. collaborating with Japanese string theorists, About two thirds of them are from Japan. have made important contribution on this Many of them even pay for their own airfare topic. Two of their papers (number 2 and 4) and we only need to pay for their local have been cited more than fifty times expanses. That is the reason why we can according to the statistics by Spires. afford to invite many Japanese string theorists References to visit us. In addition, many of our group members have been invited to go to Japan to [1] Pei-Ming Ho, Yosuke Imamura, Yutaka talk about their works. A lot of collaborations Matsuo and Shotaro Shiba, "M5-brane in have been generated through these visits. In three-form flux and multiple M2-branes", the future, we would like to strengthen our arXiv: 0805.2898, JHEP 0808:014, 2008. connection to the string communities in other [2] Pei-Ming Ho, Yosuke Imamura and Asian countries, such as South Korea, India Yutaka Matsuo, "M2 to D2 revisited", and Mainland China. Below is a summary of arXiv: 0805.1202, JHEP 0807:003, 2008. the group members' visits of oversea [3] Pei-Ming Ho and Yutaka Matsuo, "M5 institutions in the past year.

Highlights of Programs -›› 122 from M2", arXiv: 0804.3629, JHEP amplitudes of D-brane", hep-th/0612059, 0806:105, 2008. Phys.Lett.B646, 120 (2007). [4] Pei-Ming Ho, Ru-Chuen Hou and Yutaka [5] Jen-Chi Lee,"Zero-norm states and Matsuo, "Lie 3-Algebra and Multiple M2- superstringy symmetries", hep-th/0610272 branes", arXiv: 0804.2110, JHEP (to be published by World Scientific). 0806:020, 2008. [6] Chuan-Tsung Chan, Jen-Chi Lee and Yi 2. High Energy String Scatterings Yang,"Power-law behavior of strings scattered from domain-wall at high This is a long term project started in 2003. energies and breakdown of their linear It is based on many earlier works of Jen-Chi relations", hep-th/0610219. Lee in 90's. Following a breakthrough of Chuan-Tsung Chan and Jen-Chi Lee in 2003, [7] Chuan-Tsung Chan, Jen-Chi Lee and Yi The Taiwan string group has published more Yang, "Scatterings of massive string states than 15 papers on this single subject and about from D-brane and their linear relations at half of the group members participated in the high energies",hep-th/0610062, Nucl. project. Although these works are not well Phys.B764, 1 (2007). recognized, they are truly initiated in Taiwan. [8] Chuan-Tsung Chan, Jen-Chi Lee and Yi Hopefully they will attract more attention in Yang, "Notes on High energy limit of the near future. In 2006, Chuan-Tsung Chan, Bosonic closed string scattering Jen-Chi Lee and Yi Yang generalized the linear amplitudes", hep-th/0604122, relations (stringy symmetry) to include D- Nucl.Phys.B749, 280 (2006). branes. More importantly, Jen-Chi Lee and Yi [9] Pei-Ming Ho and Xue-Yan Lin, "Linear Yang have shown the coexistence of the linear relations among 4-point functions in the relations and the softer exponential fall-off high energy limit of string theory", behavior of high energy string scattering Phys.Rev.D73, 126007 (2006). amplitudes. They have also discovered some 3. AdS/CFT Duality and Its Applications interesting string scatterings which has an unusual power-law behavior at high energy. AdS/CFT and its possible application to More recently, Jen-Chi Lee and Yi Yang, QCD remains one of the focus in the string together with Prof. Yoneya of Tokyo community. By studying the gravity dual of University, are trying to fit their results to supersymmetric Yang-Mills theories, it is Yoneya's "space time uncertainty relation". hoped that certain non-perturbative aspect of QCD can be understood. Many group References members have published works on this topic. [1] Jen-Chi Lee, Yi Yang, "High-energy References Massive String Scatterings from Orientifold Planes", 0712.4245, [1] Chong-Sun Chu and Pei-Ming Ho, "Time- Nucl.Phys.B798:198-209, 2008. dependent AdS/CFT duality. II. [2] Jen-Chi Lee and Yi Yang,"Power-law Holographic reconstruction of bulk metric Behavior of High Energy String and possible resolution of singularity", Scatterings in Compact Spaces", arXiv: 0710.2640, JHEP 0802:058, 2008. 0709.4657, Phys.Conf.Ser.110:102007, [2] Feng-Li Lin, Toshihiro Matsuo and Dan 2008. Tomino, "Hagedorn Strings and [3] Jen-Chi Lee and Yi Yang, "Linear Correspondence Principle in AdS(3)", Relations and their Breakdown in High arXiv:0705.4514, JHEP 0709:042, 2007. Energy Massive String Scatterings in [3] Koji Hashimoto , Takayuki Hirayama, Compact Spaces", 0705.1872, Feng-Li Lin and Ho-Ung Yee, "Quark Nucl.Phys.B784, 22 (2007). Mass Deformation of Holographic [4] Jen-Chi Lee and Yi Yang,"Linear relations Massless QCD", arXiv: 0803.4192, JHEP of high energy absorption/emission 0807:089, 2008.

123 ‹‹- Highlights of Programs [4] Eiji Nakano and Wen-Yu Wen, "Critical Modes of Schwarzschild Black Holes", magnetic field in a holographic arXiv: 0704.0284, Phys.Rev.D75:124008, superconductor", arXiv: 0804.3180, 2007. Phys.Rev.D78:046004, 2008. 5. International Collaborated Papers [5] Wen-Yu Wen, "2D Heisenberg model from References rotating membrane", arXiv: 0705.263 Nucl.Phys.B791:164-174, 2008. [1] V.R. Khalilov and Choon-Lin Ho, [6] Eiji Nakano, Shunsuke Teraguchi and "Scattering of spin-polarized electron in an Wen-Yu Wen, "Drag force, jet quenching, Aharonov-Bohm potential," arXiv: and AdS/QCD", hep-ph/0608274, 0708.3131, Annals Phys.323:1280-1293, Phys.Rev.D75: 085016, 2007. 2008. [7] Wen-Yu Wen, "Spin chain from marginally [2] Choon-Lin Ho and Ryu Sasaki, "Deformed deformed AdS(3) x S**3," hep- multi-variable Fokker-Planck equations," th/0610147, Phys.Rev.D75: 067901, 2007. cond-mat/0703291, J. Math. Phys. 48:073302, 2007. 4. Gravity and Cosmology [3] N.D. Hari Dass and Peter Matlock, Gravity and cosmology are close related to "Covariant Calculus for Effective String string theories. In particular, understanding Theories," arXiv:0709.1765. black holes is important for making progress in [4] Tsunehide Kuroki and Toshihiro Matsuo, quantum gravity. "Production cross section of rotating References string," arXiv:0712.4062, Nucl.Phys. B798:291-309, 2008. [1] R0ong-Gen Cai, Chiang-Mei Chen , Kei- ichi Maeda, Nobuyoshi Ohta and Da-Wei [5] Pei-Ming Ho, Yosuke Imamura, Yutaka Pang, "Entropy Function and Universality Matsuo and Shotaro Shiba, "M5-brane in of Entropy-Area Relation for Small Black three-form flux and multiple M2-branes", Holes", arXiv:0712.4212, Phys.Rev.D77: arXiv: 0805.2898, JHEP 0808:014, 2008. 064030, 2008. [6] Pei-Ming Ho, Yosuke Imamura and [2] Adel Bouchareb, Gerard Clement, Chiang- Yutaka Matsuo, "M2 to D2 revisited", Mei Chen, Dmitri V. Gal'tsov, Nikolai G. arXiv: 0805.1202, JHEP 0807:003, 2008. Scherbluk and Thomas Wolf, "G(2) [7] Pei-Ming Ho and Yutaka Matsuo, "M5 generating technique for minimal D=5 from M2", arXiv: 0804.3629, JHEP supergravity and black rings", 0806:105, 2008. arXiv:0708.2361, Phys. Rev. D76:104032, [8] Pei-Ming Ho, Ru-Chuen Hou and Yutaka 2007. Matsuo, "Lie 3-Algebra and Multiple M2- [3] Chiang-Mei Chen, Dmitri V. Gal'tsov and branes", arXiv: 0804.2110, JHEP Dmitry G. Orlov, "Extremal black holes in 0806:020, 2008. D=4 Gauss-Bonnet gravity", hep- [9] Chong-Sun Chu and Pei-Ming Ho, "Time- th/0701004, Phys.Rev.D75: 084030, 2007. dependent AdS/CFT duality. II. [4] S.A. Kononogov and D.G. Orlov, Holographic reconstruction of bulk metric "Variation of the gravitational constant in and possible resolution of singularity", S-brane cosmology, "Grav.Cosmol.13:185- arXiv: 0710.2640, JHEP 0802:058, 2008. 190, 2007. [10] Koji Hashimoto , Takayuki Hirayama, [5] Hsien-chung Kao and Dan Tomino, Feng-Li Lin and Ho-Ung Yee, "Quark "Quasinormal Modes of Kerr Black Holes Mass Deformation of Holographic in Four and Higher Dimensions", arXiv: Massless QCD", arXiv: 0803.4192, JHEP 0801.4195, Phys.Rev.D77:127503, 2008. 0807:089, 2008. [6] Hsien-chung Kao, "Second Order [11] Rong-Gen Cai, Chiang-Mei Chen , Kei- Perturbative Calculation of Quasinormal ichi Maeda, Nobuyoshi Ohta and Da-Wei

Highlights of Programs -›› 124 Pang, "Entropy Function and Hermitian and non-Hermitian Universality of Entropy-Area Relation Hamiltonians," Talk given at Conference for Small Black Holes", arXiv: in Honor of C.N. Yang's 85th Birthday: 0712.4212, Phys.Rev.D77: 064030, 2008. Statistical Physics, High Energy, [12] Adel Bouchareb, Gerard Clement, Condensed Matter and Mathematical Chiang-Mei Chen , Dmitri V. Gal'tsov, Physics, Singapore, 31 Oct - 3 Nov 2007. Nikolai G. Scherbluk and Thomas Wolf , arXiv:0801.0944. "G(2) generating technique for minimal [2] Kazuyuki Furuuchi, "Matrix Model For D=5 supergravity and black rings", Polyakov Loops, String Field Theory In arXiv:0708.2361, Phys. Rev. D76: The Temporal Gauge, Winding String 104032, 2007. Condensation In Anti-de Sitter Space And [13] Chiang-Mei Chen, Dmitri V. Gal'tsov and Field Theory Of D-branes," Talk given at Dmitry G. Orlov, "Extremal black holes International Symposium on Cosmology in D=4 Gauss-Bonnet gravity", hep- and Particle Astrophysics (COSPA 2007), th/0701004, Phys.Rev.D75: 084030, Taipei, Taiwan, 13-15 Nov 2007. 2007. arXiv:0806.4800. [14] S.A. Kononogov and D.G. Orlov, [3] Chiang-Mei Chen, "Extremal dilatonic "Variation of the gravitational constant in black holes in 4D Gauss-Bonnet gravity," S-brane cosmology, "Grav.Cosmol. 8th Asia - Pacific International Conference 13:185-190, 2007. on Gravitation and Astrophysics (ICGA8): For the 100th Anniversary of Hideki 6. Talks Presented in International Yukawa and Protomotion of Women Conferences Scientists (ICGA8), Nara, Japan, 29 Aug - References 1 Sep 2007. Prog.Theor.Phys.Suppl. [1] Choon-Lin Ho, "Prepotential approach to 172:161-164, 2008. arXiv:0801.0032. exact and quasi-exact solvabilities of

125 ‹‹- Highlights of Programs Highlights of Programs Interdisciplinary Fields

Focus Group on Atomic, Molecular and Optical Physics

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

I. Brief Description systems before. By combining analytic and numerical methods developed recently, we hope to explore the exotic many-body phases of cold atom systems as well as the roup size: dynamical and finite temperature properties, which can be important to its Active faculty members are about future application of quantum physics. 20, including experimentalists. (2) Weakly interacting Bose gases: A certain Goal: portion of our group members have 1) To encourage more cooperation between developed their own numerical technique faculty in this community, including to study the static as well as the dynamic cooperation between theorists and properties of Bose-Einstein condensation experimentalist. of cold atoms in the mean-field level and beyond. Several analytic works on the 2) To attract more researchers/ students to join transition temperature properties of to form a stable research environment. 3) To interacting bosonic atoms as well as enhance the research quality by actively magnetic dipoles are developed. cooperating with international frontier researchers and concentrating on some (3) Atomic structure theory: We have had a promising projects. good start in atomic structure theory in the past few years when Prof. Tu-Nan Chang Research direction: (USC, USA) was in Taiwan as NCTS Our FG encourages the following four director. We will keep such cooperation on- directions of research: going and encourage more national-wide activities in this subfield. (1) Strongly correlated effects in cold atoms: It is well-known that cold atom systems are (4) Intensive laser and plasma: Although so a very excited systems for studying far there are not many theoretists in this quantum many-body system in a much new field in Taiwan, there has been some controllable methods than any other great progress in the experiments in

Highlights of Programs -›› 126 Academia Sinica and NCU recently. We molecules. hope this group can grow larger and stronger by cooperating with local III. Visitors and International experimentalist as well as some oversea Collaborations researchers, like Chii-Dong Lin (UKS, Visitor in the past year: In the previous year USA), regularly. (Sep. 2007-Aug. 2008), we invited Prof. Tin- Lun (Jason) Ho at Ohio State University to II. Activities visit NCTS from Nov. 18 to 23, 2008. Prof. Summer School: Tin-Lun Ho is a world-famous condensed From 8/26 to 8/29 in 2008, we held the 5th matter theorist, and was awarded the Lars AMO summer school in National Taiwan Onsager Price 2007 for his great achievement University, locally hosted by Prof. Ying-Chen in quantum fluids. During his visit in Taiwan, Cheng in IAMS. This year, we try to include Prof. Ho had intensive discussions with local active local members in the four subfields researchers in the fields of cold atoms. His mentioned above to exchange their research visit enables Prof. D.-W. Wang (NTHU) to results with each other and also introduce the collaborate with Prof. Ho in the quantum phase most frontier development to students. We transition of condensate in optical lattice. hope this could attract more students to the In May 9-18, we also invited Prof. Chris AMO community and different kinds of Greene at JILA to visit IAMS, NCU, and research. We will also have a poster session NCTS-NTHU. Prof. Greene is a well-known and this should be also a good training atomic theorist and has contributed three program for students and/or postdocs. different talks to these three different institutes. Local Workshop: Prof. Greene s visit stimulated a closer collaboration of local researchers in different On 10/22-10/23 in 2008, we will host a subfield of AMO physics (for example the AMO workshop in National Central possible collaboration between Daw-Wei University. We will invite several top Wang and Chien-Nan Liu on polar molecules researchers from both local community and in optical lattice). He also gave some valuable those in China to exchange ideas. The goal of comments/suggestions to some local AMO this workshop is to provide a flexible forum experimentalists. for domestic physicists to exchange ideas as well as research results with colleagues in Visitors in the near future: China. We believe that it will be a good start 1) We also have invited Prof. F. Kh. Abdullaev for our local AMO researchers to have a (Physical-Technical Institute, Uzbekistan) to broader connection. The workshop will be visit NCTS in Oct. 2008. Prof. Abdullaev is coordinated by Prof. Tai-Tsong Yi in NCU. a famous researchers on nonlinear physics International Workshop: and Bose-Einstein condensation. He will stay for one month and have a close We are planning to hold one international collaboration with Prof. Tsing-Fu Jiang, workshop in early of 2009 on some specific Prof. Shih-Chuan Guo, and Prof. Wen-Chin topics of cold atoms (for example, dipolar Wu on the dynamical/numerical problems in atoms/molecules), which are closely related to Bose-Einstein Condensation. the interest of local researchers and main string development. So far, we have invited Prof. 2) Further more, we have invited Prof. John Eugene Demler (Harvard) and Prof. John Bohn Bohn (JILA) and Prof. Eugene Demler (JILA) to join. We may continue to invite other (Harvard) to attend the international speakers, say Prof. L. Pitaeviskii. We believe workshop on cold atoms/molecules in that it can be an important chance for local spring 2009. researchers to be updated with the latest International collaboration: development in cold atoms and/or cold Our group members have active

127 ‹‹- Highlights of Programs international collaboration with frontier unequal concentrations in a harmonic trap researchers. For example, D.-W. Wang using the mean field theory and the local (NTHU) recently has collaboration with Prof. density approximation [4]. This is one of the P. Zoller (Innsbruck) on polar molecules, with most frontier research directions in the cold Prof. T.-L. Ho (Ohio State U.) on the atom field. They found that the system can superfluid to Mott insulator transition in exhibit a superfluid shell structure optical lattice, and with Prof. E. Demler sandwiched by the normal fermions. This (Harvard) on dipolar atoms as well as fermions superfluid shell structure occurs if the mass in optical lattice . Prof. Y.-J. Kao (NTU) ratio is larger then certain critical value cooperated with Prof. A. Sandvik (BU) in the which increases from the weak-coupling development of quantum Monte Carlo BCS region to the strong-coupling BEC calculation. Prof. Chung-Hou Cheng (NCTU) side. In the strong coupling BEC regime, has a close collaboration with Yong Baek Kim the radii of superfluid phase are less (U. Toronto) on the supersolid phase in sensitive to the mass ratios and are similar frustrated system. Prof. T.-K, Fang (FJU) to the case of pairing with equal masses. collaborates with Prof. T.-N. Chang (USC) in C. Supersolid phase in triangular lattice: atomic structure theory. Prof. Chien-Nan Liu Chung-Hou Cheng and his collaborators, (FJU) collaborates with Prof. Shinichi explore supersolid state, an exciting Watanabe and Toru Morishita (University of research topic in following years, by Electro-Communications, Japan) on the applying the Variational Monte-Carlo, the dynamics of Bose-Einstein condensation. Quantum Monte-Carlo approaches combined with the many-body Green's IV. Highlight of Research Results function techniques on a triangular optical Strongly interacting cold atoms/molecules: lattice [5]. Special focus is on the noise A. Exotic quantum phases of polar molecules: correlations in boson density which has D.-W. Wang cooperated with P. Zoller s been proven a useful probe to this phase via group on the development of dipolar lattice time of flight measurement of condensed using polar molecules [1]. They proposed a bosons. This is an important measurable possible system to replace optical lattice by quantity to probe the many-body state in the using the low-dimensional dipolar lattice as traped bosons. a hosted lattice structure. Prof. Wang also Weakly interacting bosonic atoms: developed a complete effective many-body theory for strongly interacting polar Shih-Chuan Guo and his collaborators have molecules [2], and predicted some novel found a new prototype of quatnum turbulence properties in 2D and 3D geometry. This in trapped BEC via the disruption of a single result is beyond the traditionally used Born quantized vortex ring [6,7]. This quantum approximation and can be very relevant for turbulence is well characterized by an energy the study of cold polar molecules in the spectrum following the famous Kolmogorov's experimental regime. Finally, Prof. Wang -5/3 power law in classical turbulence. They and Prof. Pochung Chen (NTHU) found a also have ascertained that the quantum universal spin decoherence mechanism [3] turbulence occuring in a 2D BEC is in a nuclear spin bath, which is important to simultaneously characterized by Kolmlgorov's the semi-conductor-based quantum -5/3 power law and Kraichnan's -3 power law computation and can be also applied to the in the energy spectrum - a very unique feature study of the dynamics of spinful cold atom that belogns to the 2D classical turbulence. mixtures. Currently, they are examining the energy spectrum for quantum turbulence achieved by B. Superfluidity of mixtures of two different various combinations of system parameters. fermions: Sungkit Yip, Shin-Tza Wu and Chien-Hua Pao study the dilute fermion gas Atomic structure and spectroscopy: with pairing between two species and Recently, by using a B-spline-based

Highlights of Programs -›› 128 complex rotation (BSCR) method, Te-Kuai Spin Decoherence in a Nuclear Spin Bath, Fang, Tu-Nan Chang (USC) and their Phys. Rev. B, 77, 174434 (2008). collaborators have successfully included the [4] C.-H. Pao, Shin-Tza Wu, and Sungkit Yip, spin-orbit interaction for the study of atomic Asymmetric Fermi superfluid with photoionization leading to multiple ionization different atomic species in a harmonic channels dominated by doubly excited trap, Phys. Rev. A 76, 053621 (2007). resonances for two-electron and divalent [5] Sergei Isokov, Shiuan-je Shiu, Jian-Jeng atoms. Its application to Mg photoionization Wu, Young-Chung Chen, Chung-Hou gave good agreement between the theoretical Chung, Yong Baek Kim, Krishnendu and the observed singlet-triplet mixed Mg Sengupta, Quasi-imcommensurate spectra [8]. They also have applied the BSCR supersolid phase in the Bose-Hubbard method to investigate the ground-state model on an anisotropic lattice, photoionization for Ca and Sr atoms, where ArXiv:0708.3084 (submitted to Physical more overlapped resonance structures are Review Letters). expected due to a stronger spin-mixing. [6] C.-H. Hsueh, S.-C. Gou, T.-L. Horng and Y.-M. Kao, Vortex-ring solutions of Gross- Pitaevskii equation for an axisymmetrically trapped Bose-Einstein V. References condensate, J. Phys. B: At. Mol. Opt. Phys. 40, 4561 (2007). [1] G. Pupillo, A. Griessner, A. Micheli, M. Ortner, D.-W. Wang, and P. Zoller, Cold [7] T.-L. Horng, C.-H. Hsueh and S.-C. Gou, Atoms and Molecules in Self-Assembled Transition to quantum turbulence in Bose- Dipolar Lattices, Phys. Rev. Lett. 100, Einstein condensate through bending-wave 050402 (2008). instability of a single vortex ring, Physical Review A 77, 063625 (2008). [2] D.-W. Wang, An effective theory of strongly interacting polar molecules, New [8] T. K. Fang and T. N. Chang, B-spline- J. Phys. 10, 053005 (2008). based complex-rotation method with spin- dependent interaction, Phys. Rev. A 76, [3] Yi-Ya Tian, Pochung Chen, and D.-W. 012721 (2007). Wang, Universal Dynamics of Electron

129 ‹‹- Highlights of Programs Focus Group on Quantum Information Science

Coordinators: Yueh-Nan Chen (National Cheng Kung University; email: [email protected]) Hsi-Sheng Goan (National Taiwan University; email: [email protected]) Committee members: Alec Maassen van den Brink (Academia Sinica), Yia-Chung Chang (Academia Sinica), Pochung Chen (National Tsing Hua University), Chi-Yee Cheung (Academia Sinica), Chung-Hsien Chou (National Taiwan 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. Brief Description benefit the QIS community in Taiwan, we have held "The 2nd International Workshop on Solid-State Quantum Computing and Mini-School on Quantum Information he main mission of the QIS focus Science" in Taipei during June 23 ~ 28 group is to build a platform of (2008). Many world-leading researchers, communication and discussion for researchers such as Prof. Milburn, Prof. Martinis, Prof. in this area in Taiwan. In the last few years, we Nori, Prof. Schoen, Prof. Delsing, and Prof. have brought QIS researchers in Taiwan to Tarucha …, were invited to give lectures. work and discuss research together and to hold The workshop attracted many participants, activities, such as scientific seminars, including faculties, postdocs and students. workshops and short-term schools. We have The Proceedings of the workshop and mini- also been seeking to establish links and school will be published by the International exchanges as well as to initiate collaborations Conference Proceedings Series of the with other QIS researchers worldwide. American Institute of Physics (AIP; http://proceedings.aip.org). The printed Focused research topics: Quantum Proceeding book and its online version will decoherence, quantum measurement, quantum have the Volume number in the AIP entanglement and communication. Conference Proceedings Series, ISSN and ISBN, and will be registered at the Library II. Activities and Beneficiaries of Congress. The proceedings are valuable Activities as topical status reports providing quick 1. Winter school on, "The 3rd Winter School access to information before it appears in on Quantum Information Science" at the traditional journal literature. Taitung, Jan. 5 ~ 7 (2008). 2. Ever since Prof. B. L. Hu (Univ. of 2. "The 2nd International Workshop on Solid- Maryland) became the senior multi-year State Quantum Computing and Mini-School visitor of our focus group, one of the major on Quantum Information Science" at NTU, QIS focus group research topics was June 23 ~ 27 (2008). focused on the field of quantum decoherence. The 2008 winter school was 3. Mini-workshops and seminars at NCKU, the third summer school (the previous two NTHU, and NTU. were held in 2006 and 2007) focusing on this particular topic. As a result of these schools, several focus group members have Beneficiaries engaged in the research on Non-Markovian 1. To enhance international visibility and dynamics of qubits and continuous variable

Highlights of Programs -›› 130 systems in external environments. I. Decoherence 3. We also successfully attracted young 1. Induced decoherence by interacting researchers into this field, such as the quantum spin baths: postdoctoral fellow (Dr. Che-Ming Lee) and We study the reduced dynamics of a single graduate students (Mr. W. Y. Tu, Mr. H. B. or two qubits coupled to interacting quantum Chen, Mr. D.B. Tsai, Mr. C.H Li and Mr. spin baths described by a one-dimensional Y.Y. Lai). XXZ Heisenberg Hamiltonian. By using time- Training of young-generation physicists dependent density matrix renormalization 1. Inviting potential young-generation group (TD-DMRG) technology we go beyond physicists as speakers at mini-workshop the uniform coupling central spin model and evaluate nonperturbatively the induced (1) Dr. Tzu-Chieh Wei (Institute for decoherence and entanglement [1]. Quantum Computing, Univ. of Waterloo) 2. Universal dynamics of quantum spin relaxation in a spin bath: (2) Dr. Min-Hsiu Hsieh (Univ. of Southern California, USA) We investigate the universal spin relaxation dynamics of a localized electron due to III. Visitors and International hyperfine interaction with nuclear spins. We prove that (1) the electron spin relaxation Collaborations dynamics can always show universal behavior Visitors if the initial state is composed of sufficient 1. Prof. B. L. Hu, Univ. of Maryland, USA large amount of spin eigenstates. (2) For a (July 2008) given system, the pattern of the universal dynamics is governed by a single initial 2. Prof. Gurvitz, Weizmann Institute (Nov. 6, parameter [2]. 2007 ~Feb. 5, 2008) 3. Quantum Decoherence of Coupled 3. Prof. Daniel Braun, Universite Paul Oscillators in a General Environment Sabatier, France (Jan. 2 ~7, 2008) We study the dynamics of quantum 4. Prof. Xin-Qi Li, Chinese Academy of entanglement between two Unruh-DeWitt Sciences (Dec. 27, 2007 ~Jan. 29, 2008) detectors, one stationary (Alice) and another 5. Dr. Jacob Taylor, Massachusetts Institute of uniformly accelerating (Rob), with no direct Technology (Jan. 4 ~ 8, 2008) interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that International Collaborations for all cases studied the initial entanglement 1. Prof. T. Brandes at Technische Universität between the detectors disappears in a finite Berlin, Germany time (``sudden death"). After the moment of -- A three-year international collaboration total disentanglement the correlations between project with Prof. Y. N. Chen. the two detectors remain nonzero until late times [3,4]. 2. Prof. G. J. Milburn at the University of Queensland and Prof. Xin-Qi Li at the 4. Decoherence of a qubit embedded inside a Chinese Academy of Science suspended phonon cavity -- with Prof. H.-S. Goan on quantum We elucidate the theory of phonon-induced measurement and quantum feedback decoherence of a double dot charge qubit that control of qubits and continuous variable is embedded inside a suspended semiconductor systems. slab. The influences of the lattice temperature, width of the slab, and positions of the dots on IV. Highlights of Research Results the decoherence are analyzed. The decoherence is markedly suppressed by the

131 ‹‹- Highlights of Programs inhibition of the electron-phonon coupling [5]. The proof of the no-go theorem of unconditionally secure quantum bit II. Quantum measurement commitment assumes that the parties involved 1. Shot-noise spectrums of non-Markovian know every detail of the protocol so that no QD excitons secret parameters exist. We extend the We propose to detect non-Markovian decay theorem to cover the cases in which secret of an exciton qubit coupled to multi-mode parameters (secret probabilities) are allowed bosonic reservoir via shot-noise [12]. measurements. Non-equilibrium current noise 4. Minimal classical communication and is calculated for a quantum dot embedded measurement complexity for quantum inside a p-i-n junction [6]. We also propose to information splitting observe the retardation effect between two We present two quantum information quantum dots (via current-noise) in a one- splitting schemes [13] using respectively dimensional waveguide [7]. tripartite GHZ and asymmetric W states as III. Quantum Computation quantum channels. We show that if the secret state is chosen from a special ensemble and is 1. Charge-to-spin conversion of electron known to the sender (Alice), then she can split entangled states and spin interaction free and distribute it to the receivers Bob and solid-state quantum computing: Charlie by performing only a single-qubit We have proposed an implementation of measurement and broadcasting a one-bit scalable spin quantum computation in classical message. No other schemes could semiconductor nanostructure without resorting possibly achieve the same goal with simpler to spin-spin interaction. [8] We can generate a measurement and less classical charge entangled state of two electrons using communication. single electron transition assisted by a semiconductor multiple-quantum-dot structure. IV. Quantum entanglement and communication V. References 1. Generalized Smolin states and their [1] Cheng-Yan Lai and Jo-Tzu Hung and applications Chung-Yu Mou and Pochung Chen, Phys. Rev. B 77, 205419 (2008). We consider the generalized Smolin states [2] Yi-Ya Tian, Pochung Chen, and Daw-Wei with common stabilizers among the mixtures Wang, Phys. Rev. B 77, 174434 (2008). [9]. In particular, we focus on the family of the mixed states that maximally violate Bell-type [3] Chung-Hsien Chou, B.L. Hu, and Ting Yu, inequalities. The Bell-correlated mixed states Physica A 387, 432-444 (2008). can be exploited in the scheme of remote one- [4] Chung-Hsien Chou, Ting Yu, and Bei-Lok qubit information concentration [10]. Hu, Phys. Rev. E 77, 011112 (2008). 2. Entanglement detection and witness [5] Y. Y. Liao, Y. N. Chen, W. C. Chou, and D. S. Chuu. Phys. Rev. B. 77, 033303 We propose the "correlator" as the product (2008). of the two differences of joint probabilities [6] Y. N. Chen and G. Y. Chen, Phys. Rev. B [11]. A necessary condition of quantum 77, 035312 (2008). correlation is proposed. The correlators help construct the entanglement witness and Bell- [7] Yueh-Nan Chen and Lukas Gilz, Appl. type inequalities. Phys. Lett., accepted (2008). [8] Wei-Min Zhang, Yin-Zhong Wu, Chopin 3. Quantum bit commitment with secret Soo, and Mang Feng, Phys. Rev. B 76, parameters 165311 (2007).

Highlights of Programs -›› 132 [9] Li-Yi Hsu, Phys, Rev. A 76, 022322 [13] Z.J. Zhang and C.-Y. Cheung, J. Phys. B (2007). 41, 015503 (2008). [10] Li-Yi Hsu, Phys, Rev. A 76, 032311 [14] X. Z. Yuan, K. D. Zhu and H.-S. Goan, (2007). Eur. Phys. J. D 46, 375 (2008) [11] C. M. Li, L. Y. Hsu, Y. N. Chen, D. S. [15] T.-Y. Huang, C.-T. Liang, G.-H. Kim, C. Chuu, and T. Brandes, Phys, Rev. A 76, F. Huang, C.-P. Huang, J.-Y. Lin, H.-S, 032313 (2007). Goan, and D.A. Ritchie, accepted by [12] C.-Y. Cheung, Int. J. Mod. Phys. B 21, Phys. Rev. B (2008). 4271 (2007).

133 ‹‹- Highlights of Programs Highlights of Programs

Working Group on Plasma Science

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-Chi Liu (National Taiwan Normal University), JyhPyng Wang (Academia Sinica)

I. Brief Description beyond national boundaries. 3. Incubating young generations of plasma scientists.

he NCTS Plasma Science Program I. 2. Guidelines: identifies the following plasma 1. Following the NCTS written guidelines. research frontiers: space and astrophysical 2. Providing the needed administrative plasma, fusion plasma, laser plasma, surface assistances and a flexible and reliable service plasma, coherent radiation, plasma for easy budget access. 3. The NCTS budget applications, low temperature plasma, and should be used efficiently. 4. Suggestions for gluon plasma. The local community has activities and positions are encouraged. 5. research activities in all but the last one. In Proposal and report in written should be brief; fact, it has world-leading research result in in most cases, an email may be enough as long almost every area, although the size of local as key information and justifications included. plasma physics community is still small. 6. The program committee makes the decision Education is essential for this community to only based on the objectives, the guidelines, increase its enabled manpower and future the academic merit, and available budget. 7. prosperity. Plasma researches are often across Activities aiming to stimulating collaboration disciplinary boundaries and important in both and interaction are encouraged and have a scientific frontiers and critical applications. higher priority for budget supporting. 8. The NCTS Plasma Science Program provides Activities aiming to incubating young a forum for the local plasma science generations are encouraged and have a higher community, to achieve the following priority for budget supporting. 9. Sponsored objectives, and to operate under the guidelines foreign visitors should be superior in particular listed below. methodology and knowledge. 10. Local experts and groups are encouraged to offer I. 1. Objectives: tutorial courses, schools, and workshops. 11. 1. Promoting theoretical plasma research in Self-organized working groups across Taiwan. institutions are encouraged. 12. Each working 2. Stimulating research collaborations with group should have focused interest and experimentalists, of inter-disciplinary, and activities, and is encouraged to be bounded with specific experimental concerns. 13. The

Highlights of Programs -›› 134 plasma sub-areas and working groups are II. 3. 2007 and 2008 Laser-Plasma coupled through common interest in Interaction Summer School simulation and theory, such as nonlinear II. 3. A. Purpose dynamics. 14. Anyone in the community is welcome to participate in any of the groups of In Taiwan and possibly many other places his/her interest. in Asia, it is not uncommon to meet a prospective graduate student who is interested II. Activities in experimental sciences but poorly prepared II. 1. Surface Plasma Working Group for laboratory work. Many students can do Meetings textbook exercises well, but do not know how to describe the thread of a screw, or how to Surface plasma on metallic surface is a read the color code of a resister. They cannot newest frontier in plasma research. It is a operate a milling machine or a soldering iron, research area of multi-disciplines, involving or tell the difference between epoxy and physics, mathematic, electro-optics, bio- silicon rubber. The reason is simple: these are medical, electronics, materials, nano- not part of their education or experience. In technology, mechanical, and electrical this summer school held at National Taiwan engineering. This biweekly meeting was University by Jyhping Wang of Academic organized by Professor Y. C. Lan in 2006, Sinica from July 16 to 20 of 2007 and from Professor S. J. Chen in 2007 and Professor H. July 7 to 11 of 2008, respectively, we wish to C. Chui in 2008. At the beginning, the active extend their education in this direction, even participants include five NCKU professors and though it is not possible to provide them a real one professor with Kaoshiang University of laboratory experience. Applied Science and their students. In addition to working group discussion, external II. 3. B. Courses and internal speakers are invited. The purpose Forty hours of lectures that form fourteen is to educate students and to stimulate courses were delivered. The objective is to collaboration. In July 2007, NCKU realized introduce to the participating students a near the importance of a simulation result by the complete set of basic knowledge that is group. A NCKU experimental team supported required in a laser-plasma laboratory. In by the Top University fund is formed and a addition, recognizing computer simulation as a joined biweekly meeting is being held. The form of numerical experiments, the courses number of involved professors has been also cover basic knowledge of computer increased to about fifteen. simulation. The courses are: characteristics and II. 2. Computational Plasmonic Nano- applications of optical components, ultrafast Photonics Meetings optics and high-power lasers, basic laser- plasma interaction, experimental techniques in At nano scale, charge is the most effective laser-plasma interaction, basic numerical media to interact with photons. Thus, for simulation, Particle-in-cell simulation, handy many experts, plasmonic is the most important computation: Introduction to Matlab, area of nano-photonic research. While Mathematica, and Mathcad, working with covering both fundamental physics and electronics, computer control of instruments, applications, this monthly working group introduction to electro-optics instruments, meeting aims to understand the interactions of working with vacuum, data analysis and curve photons and metallic/dielectric structures, and fitting, mechanical design and drafting, data to investigate novel optical phenomena. About plotting and presentation, and using LaTeX for two speakers per month are invited for preparing scientific documents. presentation. It is organized by Professors D. P. Tsai of NTU and W. C. Liu of NTNU. The II. 3. C. Participation organizers and some of its participants have There were 160 and 130 participants successfully landed a National Nano Project. enrolled in year 2007 and 2008, respectively.

135 ‹‹- Highlights of Programs In additional to a few faculties and some full- The Workshop was a community-wide time research assistants, most of them are event and was held at the National Cheng master students, undergraduate students, and Kung University during December 22-23, Ph.D. students. At the end, we had conducted 2007. The Workshop was organized by a poll to see how students evaluate the courses. Professor Frank C. Z. Cheng and is sponsored In the poll we asked students to rate each by the NCTS, Plasma and Space Science course in two scales, one on the level of Center (PSSC) and Department of Physics of difficulty and the other on the pace of National Cheng Kung University and co- lecturing. The cost per participant is about sponsored by Tung Sheng Chang Foundation 1,500NT for this five days intensive school. of Culture and Education. All plasma science areas, from fundamental studies to device II. 4. Particle-in-cell Mini-school applications, are covered. The workshop Particle-in-cell is a first-principle and the served as a forum to promote plasma sciences, most powerful method to simulate plasmas. exchange ideas, foster collaborations, and Aiming to educate students and young plasma encourage student participation. There were scientists in a joined effort, this mini-school three plenary talks, sixteen invited talks, as brings local experts together. It was organized well as some oral and poster presentations. by Professor Y. C. Lan and was held at NCKU There were about 70 participants. on September 29 and 30, 2007. There were about 50 participants including graduate II. 7. A Short Course on the students, postdocs and a few professors. Magnetohydrodynamics (MHD) As a fluid method describing plasma, MHD II. 5. International Workshop on EM is a common methodology in plasma science. Particle-In-Cell Simulation of Plasmas This two days short course is organized by The Workshop was held at Fu Jen Catholic Professor L. N. Hau and J. Y. Hsu, and will be University during January 5-6, 2008. We held at NCKU on August 28 and 29, 2008. specially invited the foreign researchers from Beginning with an introduction and the Plasma Theory and Simulation Group at equilibrium, this short course covers the linear University of California, Berkeley. The focus theory of wave and instability, the nonlinear of this workshop was the electromagnetic theory on shock waves, statistics approach, particle-in-cell simulation of plasmas and it's bifurcation and boundary layer problem, as applications, from fundamental studies to well as computational MHD. The number of device applications. The purposes of this seats was set as forty-five and was filled workshop are the following. The first is to get quickly. together local and foreign researchers to discuss the EM PIC method. The second aims II. 8. The International Workshop on to foster new collaborations between theorists Frontiers In Space and Fusion Energy and experimentalists as well as between local Sciences (FISFES) researchers and foreign visitors. The last, but The International Workshop will be held at not the least, is to attract young generation into the National Cheng Kung University during this revival field, plasmas, to provide them November 6-8, 2008. It is organized by with the opportunities to discuss with each Professor Frank C. Z. Cheng and sponsored by other and with foreign researchers. The the Plasma and Space Science Center of workshop is sponsored by National Science National Cheng Kung University and the Council and Fu Jen Catholic University while NCTS. About fourteen speakers from USA, the Program provides administrative help and Japan, Korea and Canada are invited, in some expenses for the need of local additional to a few from Taiwan. participants. II. 6. The 2007 NCTS Plasma Science III. Visitors and International Workshop Collaborations III. 1. Professor Liu Chen, UC Irvine, USA

Highlights of Programs -›› 136 Professor Liu Chen has been a frequent systems. The spheromak plasma equilibrium visitor. He officially visited NCTS from 11/8- paper while submitted to APS meeting still 26, 2006. He spent the first week in NCU, the needs further effort to finish, however. second week in NCKU, and then in NDHU III. 3. International Speakers of the and NCU. In addition to giving series lectures International Workshop on Frontiers on gyrokinetic theory and toroidal physics, he In Space and Fusion Energy Sciences started the collaboration on the work of (FISFES) relativistic ion cyclotron instability under non- uniform magnetic field with Professor K. R. Daniel N. Baker (University of Colorado at Chen and his student, Mr. T. H. Tsai. After the Boulder, USA), Masaki Fujimoto visit, Mr. Tsai went to UC Irvine from the end (ISAS/JAXA, Japan), Masafumi Hirahara of March 2007 to January 2008 to carry out the (University of Tokyo, Japan), Mitsuru Kikuchi theoretical derivation, under the support of (Japan Atomic Energy Agency, Japan), Gyung- National Science Council. During the Su Lee (National Fusion Research Institute, meantime, Professor Liu Chen has visited Korea), Robert P. Lin (University of California Taiwan twice (one in July and the other in at Berkeley, USA), Neville C. Luhmann, Jr. September) and discussed with Professor K. R. (University of California at Davis, USA), Chen, under the support of NCU with a Chair Atsushi Mase (Kyushu University, Japan), Professorship; the three got together for in- Yasushi Ono (University of Tokyo, Japan), depth discussion in November 2008 during the Hyeon Park (Pohang University of Science and annual meeting of Plasma Physics Division of Technology, Korea), Shigeru Sudo (National American Physical Society, held at Orlando, Institute for Fusion Sciences, Japan), William FL, USA. The discussion continues after Mr. M. Tang (Princeton Plasma Physics Tsai returned; e.g., Professor Liu Chen visited Laboratory, USA) James W. Van Dam us again in March 2008. The result yielded is (University of Texas at Austin, USA), Andrew consistent qualitatively with Particle-in-cell W. Yau (University of Calgary, Canada). The simulation; the quantitative comparison has cost will be covered by the NCKU Plasma and been done. Two papers are being written. Space Science Center. III. 2. Professor C. M. Ryu, Postech, Korea IV. Highlights of Research Results Professor C. M. Ryu visited NCTS from Taiwan's plasma physics community is 6/26 to 7/8, 2007. He is a well rounded relatively small in size as compared with other plasma physicist and has done research in research fields of physics. However, the various areas of plasma physics. He made academic performance is impressive with so presentations on "Magnetic Field Generated by many outstanding research results and the Transport Flow" at both NCKU and NCU. international reputation is high. For example, During the visit, he started collaborative work in the areas of electron cyclotron maser, dusty with Professor J. Y. Hsu on the spheromak plasmas, space plasma, laser plasma, red- plasma equilibrium. He pointed out the Sprite observation, fast ion cyclotron correlation dimension to quantify the fractal instabilities, and recently surface plasma, dimension and one student has implemented a Taiwan's groups are making outstanding numerical code successfully to examine for original contributions and, in fact, are among example the Henon map, and will apply the leaders of the international research same to arc root dynamics, and other stochastic community.

137 ‹‹- Highlights of Programs Working Group on Softmatter and Nonlinear Physics A. Nonlinear Phenomena in Physical and Biological Systems Coordinators: Mingchih Shih (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), Sy-Sang Liaw (National Chung Hsing University), Jiunn-Ren Roan (National Chung Hsing University)

I. Introduction II. Activities (1) Regular meeting Biophysical Journal Club (BJC): Thursday 12:00-13:00 he working group includes several faculty members and Ph. D students Biophysical Journal Club was initiated by from various institutes in central Taiwan. The Prof. Roan since 2004, and it has been key members of this working group are: Sy- continues and thriving successfully with the Sang Liaw(Physics, NCHU); Jiunn-Ren support of this focus group. BJC is well Roan(Physics, NCHU); Kai-Jung Chi(Physics, organized and has attracted broad attendance NCHU); Ming-Chih Shih(Physics, NCHU); I- from various disciplines. The mailing list of Min Tso(Life Science, THU); Chao-Nien Chen BJC continues growing. About 20 to 40 people (Math, NCUE); Chung-Tu Yang(Entomology, attend the Club at each gathering. Details of NCHU); Tzyy-Leng Horng(Applied Math, the BJC activity subjects can be found at FCU). The main theme of the group focuses on http://140.120.11.15/vedio/biophysics/Chinese/ the non-linear phenomena that appear in journal%20club/activity.htm nature, including the biological world. Our Nonlinear phenomena seminar: activities include regular meetings, workshops, Monday 12:00-13:00 and short visits from or to institutes abroad. Nonlinear phenomena seminar was Current projects under intensified organized by Prof. Liaw. The scope of the discussion comprise: seminar includes granular physics, pattern 1. The mechanical responses of spider web formation and econophysics. About 10 to 15 (Biological Materials) people attend the seminar at each gathering. 2. Fluid dynamics of biological sniffers (Fluid (2) Workshops Mechanics) • Biophysics workshop: Biological materials 3. The effect of Pterostigma on insect and Animal Behaviors, Hsin-Hua Forest locomotion (Biomechanics) Station, Tai-Nan, Sep. 5-7, 2008 4. The mechanism of the Brazil nut effect and We focus on the physics of biological its reverse (Granular Physics); materials and animal behaviors in this workshop. Five prestigious speakers are 5. Biological patterns and stability of the invited: Kai-Jung Chi (Physics, NCHU); I-Min Turing equation (Pattern Formation); Tso (Life Science, THU); Chung-Tu Yang 6. Statistical behavior of agents in economics (Entomology, NCHU); Tzen-Yuh Chiang (Life (Econophysics). Science, NCKU) and Hsin-Drow Huang Because of the interdisciplinary nature of (NMNS) will give lectures in this workshop. our topics, we constantly consult with experts Students and Post Docs are also encouraged to from economics and biology departments. contribute. The audience is expected to about 50 people.

Highlights of Programs -›› 138 • Biophysics workshop: Surface and interface been highlighted by Nature magazine in 2006. physics of biological systems, Huisun Forest Their following research work on the Station, Nautou, Oct 31 ~ Nov 2 (or Nov. 7- oscillatory Turing pattern has also been 9), 2008 published in 2007. Their work on the biological pattern formations is continued. The second workshop of biophysics will focus on the physics of surface and interface 3. Sand flow through a vertical pipe: Liaw, properties in biological systems. The main Liu, Shih, Matsushita speaker will be Dr. Stanislav Gorb from Max- The experiment was proposed by Prof. Planck Institute. Dr. Gorb will give a serie of Matsushita of Chuo University during his visit lectures in the workshop. The audience is to our group in September, 2005. We set up the expected to about 60 people. experiment immediately and have observed (3) Conferences many interesting phenomena since then. We are constructing a model to simulate the Under the support of this focus group, we density flow of the sand in the pipe, and to have sent student to attend international analyze its power law. conferences: • R.T. Liu, J.Y. Wang, F.F. Chung, Hangzhou IV. Highlights of research results and Jinhua, China, 11/12-15, 2007 1. In the study related to econophysics, Prof. The 3rd Cross-strait conference on statistical Liaw used agent-based simulation on the physics. Oral and poster presentations. model of the Minority Game and found some implications about where does the III. International collaborations power law come from in complex systems. 1. Physics of Biological surfaces: Chi, Shih, 2. The Brazil nut effect in granular physics Gorb has puzzled physicists for more than 50 Prof. Chi has great experience on the years. After three years of intense study, mechanical properties of biological systems, Fei-Fang Chung et al have come up with a and she invites Prof. S. Gorb who is the group mechanism that successfully describes a leader of evolutionary biomaterials group at type of horizontal segregation phenomenon the Max-Planck-Institute for a series of very similar to the Brazil nut effect. They biophysics workshop. Together, they tend to are optimistic in solving the long-standing explore the feasibility of study physical puzzle in the coming years. properties of biological surfaces. V. Selected Publications 2. Biological pattern formation: Liaw, Liu, [1] Sy-Sang Liaw, "Frequency Maini distributions of complex systems", J. During the execution of this focus group, Stat. Mech. P05015 (2008). Professor S.S. Liaw and Dr. Ruey-Tarng Liu of [2] Fei Fang Chung, Sy-Sang Liaw*, and NCHU had established a steady research Chia-Yi Ju, "Spiral trajectories in the relationship with Professor P.K. Maini in horizontal Brazil nut effect", Phys. Rev. Oxford. One of the great successes in their E 77, 061304 (2008). collaboration is the joint publication which has

139 ‹‹- Highlights of Programs Working Group on Softmatter and Nonlinear Physics B. Soft-matter, Biophysics & Systems Biology Coordinators: Peilong Chen (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 physics, biophysics and systems biology held at various associated institutions. We have been organizing the weekly "Soft-Bio Matters Seminar/Journal Club" for more than 5 years, he working group of soft-matters, at NCU. This active seminar series has been biophysics and systems biology inviting local and foreign visiting researchers (SBSB) was running from 2006 after on various areas of soft-matter and biophysics combining two previously related focus and it turns out that various research ideas and groups. The SBSB working group contains actual collaborations are indeed come out as participants from diversified fields, especially direct/indirect consequences of this seminar with many more biology background series. In the past year, some topics are more researchers. Academic activities have emphasized in the areas of DNA increased appreciably, especially for conformations, genomic/protenomic analysis, workshops and seminars. In the past year, we evolution theory, nonequilibrium physics in have organized a number of activities to pulling biomolecular bonds, polyelectrolytes; promote collaborations both within Taiwan rheology & pattern formation in complex and internationally. Our purpose is to fluids; excitable bio-systems such as cardiac encourage the use of theoretical means to and neural biophysics; collective motions in investigate the fundamental principles in soft- active organisms; membrane biophysics; matter and bio-related sciences and aiming at dynamics on complex and bio networks; Brain obtaining some quantitative understanding in physics; physics of DNA & proteins, etc. soft materials and biological processes with SBSB working group also supported a emphasis on the more recent hot topics using number of foreign visiting scientists aiming at systems approaches to investigate biological academic interflow of ideas and set up systems. Emphasis is also put on the collaborations. We have both short and long- communications and collaborations with term visitors, delivering lectures and carrying experimentalists, as reflected by the fact that out collaborations. Foreign visitors in the past some of the active members of the are year include: experimentalists also. In recent years, we have encouraged strongly on creating actual Prof. Moira L. Styen-Ross (University of collaboration environment between our local Waikato), Prof. D. Alistair Styen-Ross members and researchers in the Asian-Pacific (University of Waikato), Prof. Takao Otha regions and we are starting to see some (Kyoto University), Prof. Yohannes Shiferaw concrete outcomes. (California State University at Northridge), Dr. Qiuming Yu (University of Washington), Dr. SBSB working group also organizes regular Kuo-Ping Chiu (Genome Institute of and irregularly scheduled seminars, Singapore), Dr. Chia Lin Wei (Genome workshops, conferences on soft-matter Institute of Singapore), Prof. Tony Zee (UC

Highlights of Programs -›› 140 Santa Barbara), Prof. Daniel Figeys (University of Ottawa), Prof. Shao-Chen Lee (Sunnybrook Health Science Center), Prof. Rong-San Huang (Saint Louis University), Dr. Kuan Wang (NIH), Dr. Chia Lin Wei (Genome Institute of Singapore), Dr. Hsinyi Steve Tsang (Johns Hopkines), Dr. Kuan Wang (National Institute of Arthritis and Musculoskeletal and skin Diseases), Prof. Sangsoo Kim (Korea Res. Inst. Of Biosci. & Biotech). II. Activities Continuing our activities from the past year, Biophysics Camp 2007 we organized a number of workshop and schools. We have attracted a number of young and established local researchers, as well as participants from nearby countries. It is worth to mention that these workshop/conferences always attract a good collection of active researchers from various local institutions to participate/organize these activities in an active way. 1. Mini Workshop on Mass Spectrometry- based Proteomics (NCU), Aug. 8, 2007. Mini-Workshop on Neuroscience 2. Biophysics Camp 2007 (NCU), Oct. 27Ð28, 2007 3. Mini-Workshop on Neuroscience (NCU), Dec. 10, 2007 4. Biophysics & Soft-Matter Days 2008 (NCNU), Jan. 21-24, 2008 5. Mini-Workshop on soft matters (NCU), Feb. 19, 2008 6. The 19th Complex Systems Symposium (NCU), May 17-18, 2008 We have long been putting special focus on BioPhysics & Soft-Matter Days 2008 attracting/promoting students to enter into our field by organizing the Biophysics Camp. The response was very positive. Continuing our tradition, the 19th Complex Systems Symposium was formatted to have speakers consisted of solely graduate students. In this two-day symposium, graduate students from various institutions reported their concrete research results. The best two talks given by xxx titled xxx and by xxx titled xxx were awarded with best presentation awards. Students found this to be very stimulating and Mini-Workshop on soft matters (NCU) the positive competition among the students transformed into an enthusiastic atmosphere.

141 ‹‹- Highlights of Programs III. Highlights and Research Results [5] Bell's expression and generalized Garg's In the paper entitled Bell's expression and form for forced dissociation of a generalized Garg's form for forced biomolecular complex, Han-Jou Lin, dissociation of a biomolecular complex [5], it Hsuan-Yi Chen, Yu-Jane Sheng, and is shown that the celebrated Bell expression Heng-Kwong Tsao, Phys. Rev. Lett., 98, provides a good approximation for the bond 088304 (2007) dissociation rate of a biomolecular complex [6] Contact-induced structure transformation under constant force. In the paper Contact- in transmembrane prion propagation, D.- induced structure transformation in M. Ou, C.-C. Chen, and C.-M. Chen, transmembrane prion propagation [6], a Biophys. J. 92, 2704 (2007) theoretical model for the molecular mechanism [7] Driven polymer transport through a of the transmission of prion diseases due to a nanopore controlled by a rotating electric particular transmembrane form is proposed field: Off-lattice computer simulations, Y.- and computer simulation results are obtained. S. Tsai and C.-M. Chen, J. Chem. Phys., In the paper The Rubik's cube problem 126, 144910. (2007) revisited: a statistical thermodynamic [8] The dielectric spectrum of flexible approach [13], the protein folding problem is polyelectrolyte solutions, C.-Y.D. Lu, studied by observing the thermodynamic and Europhysics Letters 80, 67002 (2007) kinetic behavior of a Rubik's cube model. In [9] Ganoderma lucidum polysaccharides in the paper Characterization of microRNA- human monocytic leukemia cells: from Regulated Protein-Protein Interaction Network gene expression to network construction, [16] the topological analysis of global Cheng, K.-C., Huang, H.-C., Chen, J.-H., correlation between microRNA regulation and Hsu, J.-W., Cheng, H.-C., Ou, C.-H., Yang, protein-protein interaction network shows that W.-B., Chen, S.-T., Wong, C.-H., Juan, H.- target genes of individual microRNA tend to F., BMC Genomics 8, 411 (2007) be hubs and bottlenecks in the network. [10] A statistical simulation approach for V. Related Recent Selected early stage thin-film growth from vapor- Publications deposited atoms, Peilong Chen, T. Y. Wang and M. F. Luo, Journal of * The below publications are direct or indirect outcomes of the activities organized by our focus group. However, Chemical Physics 127, 144714 (2007). not all of these publications have shown affiliation with [11] Field-induced columnar structures in a NCTS. quasi-two-dimensional system of dipolar [1] Polymer Turbulent Drag Reduction near particles, Shin-Shing Yeh, Ching Hsueh, the Theta-Point, S.T. Lim, C. A. Kim, H.J. Peilong Chen and Jorge Vinals, Physical Choi , Pik-Yin Lai, and C.K. Chan, Review E 76, 051407 (2007). Europhys.. Lett. 80, 58003 (2007) [12] Elasticity and stability of a helical [2] Spherical vesicles distorted by a grafted filament with spontaneous curvatures and latex bead: An exact solution, J. Benoit isotropic bending rigidity, Zhou, Z; Joos, and A. Saxena, Phys. Rev. E 76, 041912 B; Pik-Yin Lai; Young, YS; Jan, JH, (2007) Mod. Phys. Lett. B 21, p.1895-1913 [3] Lifetime of ligand-receptor clusters under (2008) external force, Yi-Ping Chu, Chih-Chao- [13] The Rubik's cube problem revisited: a Tang, and Hsuan-Yi Chen, Physical statistical thermodynamic approach, Chi- Review E, 76,061905 (2007) Lun Lee and Mu-Chieh Huang, Eur. [4] Influences of Linkage Stiffness on Rupture Phys. J. B 64, 257 (2008) Rate in Single-Molecule Pulling [14] Forced dissociation of a biomolecular Experiments, Han-Jou Lin, Yu-Jane complex under periodic and correlated Sheng, Hsuan-Yi Chen, and Heng-Kwong random forcing, Han-Jou Lin, Yu-Jane Tsao, J. Phys. Chem. B, 111, 6493 (2007) Sheng, Hsuan-Yi Chen, and Heng-

Highlights of Programs -›› 142 Kwong Tsao, J. Chem. Phys., 128, Hsu, C.-W., Juan, H.-F., Huang, H.-C. 084708 (2008) Proteomics 8, 1975-1979 (2008) [15] Non-linear rheology of lamellar liquid [17 MeInfoText: Associated Gene crystals, C.-Y.D. Lu, P. Chen, Y. Ishii, S. Methylation and Cancer Information from Komura, and T. Kato Eur. Phys. J. E 25, Text Mining, Fang, Y.-C., Huang, H.-C.*, 91 (2008) Juan, H.-F., BMC Bioinformatics 9, 22 [16] Characterization of microRNA-Regulated (2008) Protein-Protein Interaction Network,

143 ‹‹- Highlights of Programs Research Activities of Individuals

Research Activities on Interdisciplinary Research

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

y research progress in this year can be ATP-dependent rotation of a rotary motor F1- divided into three disciplines: (I) ATPase. Since the working principle of this biological motors, (II) spintronics, and (III) model is simpler than that of F1-ATPase, it quantum chaos. The results are summarized as provides an easier way to realize a nanoscale follows. rotary motor than artificially reconstructing a F1-ATPase. (I) Biological motors Most proteins have electric dipoles and net (II) Spintronics charges in the structure and their In Ref. [2], we investigate the carrier-mediated conformations are susceptible to the electric exchange coupling between two ferromagnets, and magnetic perturbation. The shape of a cell sandwiching an intermediate thin layer with may also amplify an electric field across its Rashba interaction. The effective exchange plasma membrane. Therefore, a membrane coupling is obtained by integrating out the integral protein such as an ion channel, an ion itinerant carriers. It turns out that the magnetic pump, or a molecular motor, is especially trends depend sensitively upon the topology of amenable to electric perturbation. When an the Fermi surface. As the topology changes alternating electric field or a fluctuating from "wedding cake" to "donut", the mediated electric field is employed to actuate a two-state exchange goes from the oscillatory Ruderman- protein oscillator, the dynamics of the Kittel-Kasuya-Yosida to the non-collinear conformational change of the protein can be spiral interactions accordingly. It is rather synchronized with the applied field. Through surprising that the Fermi surface topology this two-state protein oscillator, we construct a determines which type of magnetic interaction four-state catalytic wheel by coupling an becomes dominant. Finally, we also discuss energy transducer mechanism to the two-state potential applications for carrier-mediated protein oscillator [1]. Analysis shows that the exchange coupling across the junction. catalytic wheel can extract energy from a disordered external energy source, be it (III) Quantum chaos electrical, mechanical, or chemical, and The correspondence principle in quantum convert this stochastic energy source to a mechanics states that in the semiclassical limit usable energy format. The catalytic wheel is h → 0 classical mechanics emerges and tested with the experimental data on the governs quantum mechanical quantities for electric field-stimulated cation pumping of Na, small de Broglie wavelength. One K-ATPase. A dipole ratchet model based on manifestation of this principle is that the the electroconformational coupling concept Wignerfunctions of eigenfunctions converge will also be discussed and compared with the weakly to invariant probability measures on

Research Activities of Individuals -›› 144 phase space, the so-called quantum limits machines, Nano 2, No. 5, 273Ð280 (2007). (QLs). It is one of the big open problems in the [2] Wen-Min Huang, Hsin-Hua Lai, Cheng- field to classify the set of QLs, and it is in Hung Chang, Hsiu-Hau Lin, Carrier- general not known which invariant measures mediated exchange coupling and Fermi can occur as QLs. For ergodic classical surface topology, International Journal of systems, the celebrated quantum ergodicity Modern Physics B, 22, Nos. 1 & 2 88Ð93 theorem states that almost all eigenfunctions (2008). have the ergodic Liouville measure as QL. If all eigenfunctions converge to the Liouville measure, it is called quantum unique [3] Cheng-Hung Chang, Tyll Krueger, Roman ergodicity (QUE). Possible exception for QUE Schubert, Serge Troubetzkoy, is strong scarring, i.e., QLs concentrated on Quantisations of piecewise parabolic maps periodic orbits and mixed classical systems, on the torus and their quantum limits, i.e., the phase space has several invariant Communication in Mathematical Physics components of positive measure. Less is 282, 395Ð418 (2008). known to what extent the quantum mechanical system respects the splitting of the classical system into invariant components. In Ref. [3], we introduce a class of model systems for which the set of QLs can be determined very precisely. This work provides a very rare example that a quantum ergodic map is not QUE.

References [1] Cheng-Hung Chang and Tian-Yow Tsong, Energy transduction in molecular

145 ‹‹- Research Activities of Individuals Research Activities on Quantum Information Science

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 (II) Decoherence of a charge qubit quantum information science. There embedded inside a suspended are four major results in the past year: phonon cavity We elucidate the theory of phonon-induced (I) Proposal for observation of decoherence of a double dot charge qubit that retardation effect between two is embedded inside a suspended semiconductor quantum dots via current noise slab (Fig. 2). The influences of the lattice We propose to observe the retardation temperature, width of the slab, and positions of effect between two quantum dots in a one- the dots on the decoherence are analyzed (Fig. dimensional waveguide. The effect of 3). Numerical results indicate that the retardation is more pronounced comparing to decoherence in the slab system is weaker than that in free space. If the photons are to be that in a bulk environment. In particular, the reflected by a mirror at one of the ends, the decoherence is markedly suppressed by the interference role played by the reflecting inhibition of the electron-phonon coupling. photon is found to be destructive. With the Such a system with low decoherence may be combination of p-i-n junction, the retardation useful for manipulating the qubits.. effect can be read out via current-noise spectrums (Fig. 1).

Fig.2 (a) Schematic view of a DQD embedded in a suspended semiconductor slab with a width of w. The surfaces of the slab are z= ±w/2, and the dots are located at z=0. (b) The top view shows that two identical dots are performed with the dot radii of a and interdot distance of d.

Fig. 1 (a) Schematic view of the two dots embedded in a p-i-n junction, such that the electron and hole can tunnel into QD 2. (b) Current-noise spectrums of the system with(black line)/without(green line) the consideration of retardation. The blue-dashed and red-dashed curves respectively represent the real parts of the memory functions.

Research Activities of Individuals -›› 146 An additional term from non-Markovian effect is obtained in the derivation of noise spectrum. As examples, two practical photonic reservoirs, photon vacuum with the inclusion of cut-off frequency and surface plasmons (Fig. 5), are given to show that the noise may become super-Poissonian due to this non- Markovian effect. Utilizing the property of super-radiance is further suggested to enhance the noise value.

Fig. 3 (a) Quality factor Q as a function of tunneling coupling ∆ for slab and bulk systems (upper inset). Fig. 5 Shot-noise spectra of QD excitons in front of a silver The temperatures are T=20 mK (black solid line), surface. The black, red, and blue lines represent the 200 mK (red dashed line), and 400 mK (blue dotted results of various dot-surface distances: d=0.1, line), respectively. A drastic enhancement of quality 0.045, and 0.03 (in units of /2 = 1423Å), factor is found to be independent of temperature respectively. The inset shows the corresponding (arrow). (b) Dependence of the specific tunneling curves of the imaginary part of A(i ). couplings ∆ for perfect quality factor on the width w. The corresponding period of time-dependent population is shown in the lower inset. (IV) Entanglement detection via the condition of quantum (III) Proposal for detection of non- correlation Markovian decay via current We develop a necessary condition of noise quantum correlation. It is utilized to construct We propose to detect non-Markovian decay a d-level bipartite Bell-type inequality which is of an exciton qubit coupled to multimode strongly resistant to noise and requires only bosonic reservoir via shot noise measurements. analyses of O(d) measurement outcomes Non-equilibrium current noise is calculated for compared to the previous result O(d2). a quantum dot embedded inside a p-i-n Remarkably, a connection between the junction (Fig. 4). arbitrary highdimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized Greenberger- Horne-Zeilinger (GHZ) state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose a robust entanglement witness to detect a four-level tripartite GHZ state with Fig.4 Schematic view of a QD p-i-n junction with its exciton only two local measurement settings. coupled to a bosonic environment.

147 ‹‹- Research Activities of Individuals References [1] Yueh-Nan Chen and Lukas Gilz, Appl. Phys. Lett., accepted (2008). [2] Y. Y. Liao, Y. N. Chen, W. C. Chou, and D. S. Chuu. Phys. Rev. B 77, 033303 (2008). [3] Y. N. Chen and G. Y. Chen, Phys. Rev. B 77, 035312 (2008). [4] C. M. Li, L. Y. Hsu, Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. A 76, 032313 (2007).

Research Activities of Individuals -›› 148 Research Activities on Particle Physics Phenomenology

Kingman Cheung (Department of Physics, National Tsing Hua University; email: [email protected] Center Scientist, 2006/11/1~2008/10/31

joined the Center as a Center the invariant mass spectrum of the 4 b-tagged Scientist on November 2006. I am also jets can beautifully distinguish the Higgs the convener for the focus group on "Collider, signal peak from the continuum background. Astroparticle and BSM". My research area is The result is very important to future search in particle physics phenomenology. for the Higgs boson at the LHC. Since the ultimate goal of the LHC is hunt for the Higgs (I) Introduction boson, which is responsible for electroweak The Large Hadron Collider should have symmetry breaking and mass generation, our started running when this report is published. It work fully establishes the feasibility in will be the place for the next big discovery. searching for the intermediate-mass Higgs ➝ More than half of the resources in high energy boson if h ηη dominates and solves the little community will be put into it. Together with hierarchy problem. other planned cosmology experiments, testing In another work [7], we discuss a likely new ideas beyond the standard model (SM) scenario at the LHC. What if only a light will be the major activities in the next 10-20 Higgs boson is discovered at the CERN LHC? years. My role is to link up theory and Conventional wisdom tells us that the experiments. In past few years, I have scattering of longitudinal weak gauge bosons accomplished a number of works on would not grow strong at high energies. supersymmetry, Higgs physics, unparticles, However this is generally not true. In some and other new physics. In the following, I composite models or general two-Higgs- highlight a few topics that I feel very exciting. doublet models, the presence of a light Higgs boson does not guarantee complete (II) Higgs boson and supersymmetry unitarization of the WW scattering. After ➝ The dominance of h a1a1 decay mode for partial unitarization by the light Higgs boson, the intermediate mass Higgs boson is highly the WW scattering becomes strongly motivated to solve the little hierarchy problem interacting until it hits one or more heavier and to ease the tension with the precision data. Higgs bosons or other strong dynamics. We However, the emergence of analyze how LHC experiments can reveal this h ➝ ηη decay mode has undesirable effects on interesting possibility of partially strong WW - the golden search modes (h➝γγ, bb) of the scattering. Higgs boson at the LHC. This will Little Higgs models are interesting significantly worsen the chance of detecting an alternatives to supersymmetry. A good intermediate-mass Higgs boson at the LHC. example is the SU(3) simplest little Higgs In a Letter [1], we explicitly showed that model, which accommodates a light the associated production of the Higgs boson pseudoscalar boson η with quite different with a W or Z boson can recover the loss of characteristics from those in other multi- sensitivity in the golden modes. With the Higgs-doublet models. We study various Higgs boson decaying into two pseudoscalar phenomenological signatures of the η at the bosons, which further decay into 4 b jets, LHC in a work [8]. In particular, we calculate together with at least a charged lepton from the in details both production and decays in the W or Z boson decay, a significant Higgs boson Drell-Yan type channel qqø ➝ Z/Z' ➝ hη , and signal is observable at the LHC. We found that in the associated production with a t tø pair,

149 ‹‹- Research Activities of Individuals qq(qqø ) ➝ ttøη. We emphasize the τ + τ - decay also laid down the formalism for calculations mode of the boson when its mass is below and identified the important channels to - η the bb threshold. We show that ttøη production observe unparticle effects at high energy is in fact large enough to give a sizable number colliders. The novel features, induced by scale of events while suppressing the backgrounds. invariance, include effective 4-fermion We also comment on the direct gluon fusion interactions and a nontrivial phase factor, process and the indirect decay from the heavy which interferes with the SM amplitudes in an T quark (T➝ tη). interesting manner The spectacular phase

factor exp(ÐidUπ) associated with the (III) Unparticle physics propagator in s-channel can give rise to non- This has been an exciting topic in particle trivial behavior in a number of processes. physics. We finished two important papers on In a work [4] with Li from Peking this subject in 2007 [2,3]. One was published University, we worked out the decay of the in Physical Review Letters and the other one in standard model Higgs boson into a single Physical Review. They received more than 200 photon and a vector unparticle through a one- citations in SPIRES database. The latter loop process is studied. For an intermediate contains the formalism, derivations, and the mass Higgs boson, this single photon plus results for important phenomenology of unparticle mode can have a branching ratio unparticle. The paper is well cited and useful comparable with the two-photon discovery to others. We continued to work on a few more mode. The emitted photon has a continuous interesting phenomena in unparticle stuff, and energy spectrum encoding the nature of the published three more papers on the subject in recoil unparticle. It can be measured in 2008. precision studies of the Higgs boson after its The subject is about the scale invariance or, discovery. in broader terminology, conformal invariance. In another work [5], we study the decay of Our existing particle theory is not conformal the standard model Z boson into unparticle invariant, as the invariance is obviously broken plus a single photon through a one-loop by all the discrete masses of particles. Banks process. As in the anomaly type decay, only and Zaks in the 80s showed that a number of the axial-vector part of the Z coupling supersymmetric field theories contain a matching with the vector unparticle and/or the conformal window such that the theories can vector part of the Z coupling matching with the develop IR fixed points, where the scale is axial-vector unparticle can give a nonzero invariant. contribution to the decay. We show that the Recently, perceived by Georgi a scale photon spectrum terminates at the end point in invariant sector (coined unparticle) with a non- accord with Yang's theorem. Existing data on trivial infrared fixed point at a higher energy single photon production at LEP I is used to scale may actually describe the real world at constrain the high energy. So he visualized what kind of Photon-photon can occur in the standard physics that such a sector can induce in high model only via loop diagrams and is naturally energy phenomenology. The unparticle with a suppressed. Unparticle can induce tree-level scale dimension dU can be interpreted as a photon-photon scattering through the operator collection of dU invisible massless particles, µν α µν Fµν F OU for spin-0 unparticle or Fµα F νO U for which can be unveiled by measurements of spin-2 unparticle. Due to the peculiar CP-

various energy distributions in the processes conserving phase exp(ÐidUπ) associated with Z➝ fføU and e-e+➝ —>γU at e-e+ colliders, as the time-like unparticle propagator for non-

well as mono-jet production at hadron integral scaling dimension dU, the interference colliders. effects of the s-channel amplitude with the t- Our first two papers not only discovered the and u-channels ones on the total cross sections novel propagator effect of the unparticle but as well as the angular distributions are found to

Research Activities of Individuals -›› 150 be of some significance [6]. In addition, we [3] K. Cheung, W.-Y. Keung, and T.-C. Yuan, show that the cross sections via unparticle Phys. Rev. D76, 055003 (2007). exchange can be substantially larger than the [4] K. Cheung, C.S. Li and T.C. Yuan, Phys. standard model contribution. Rev. D 77, 097701 (2008). [5] K. Cheung, T.W. Kephart, W.Y. Keung and (IV) Other topics T.C. Yuan, Phys. Lett. B 662, 436 (2008). I am also interested in some bound states [6] C.F. Chang, K. Cheung and T.C. Yuan, that are recently discovered. The newly Phys. Lett. B664, 291 (2008). observed Z+ (4433) resonance by BELLE is believed to be a tetraquark bound state made [7] K. Cheung, C.W. Chiang and T.C. Yuan, up of (cu)(cødø). We propose [10] the bottomed arXiv:0803.2661 [hep-ph]. analog of this bound state, namely, by [8] K. Cheung, J. Song, P. Tseng and Q.S. replacing one of the charm quarks by a bottom Yan, arXiv:0806.4411 [hep-ph]. 0, ±,±± quark, thus forming Zbc . One of the Zbc is [9] K. Cheung, X.H. Wu and Q.S. Yan, Phys. doubly charged. The predicted mass of Zbc is Rev. D 76, 116006 (2007). around 7.6 GeV. This doubly-charged bound [10] K. Cheung, W.Y. Keung and T.C. Yuan, ± ± state can be detected by its decay into Bc π . Phys. Rev. D 76, 117501 (2007). Similarly, we can also replace both charm quark and antiquark of the Z+ (4433) by bottom quark and antiquark, respectively, thus forming + Zbb the bottomonium analog of Z (4433). The predicted mass of Zbb is about 10.7 GeV.

References [1] K. Cheung, J. Song, and Q.-S. Yan, Phys. Rev. Lett. 99, 031801 (2007). [2] K. Cheung, W.-Y. Keung, and T.-C. Yuan, Phys. Rev. Lett. 99, 051803 (2007).

151 ‹‹- Research Activities of Individuals Research Activities on Quantum Information Science

Chung-Hsien Chou (Department of Physics, National Cheng Kung University; email: [email protected]) Center Scientist, 2007/8/1~2009/7/31

n 2008 my research activity in NCTS harmonic oscillators, one stationary (Alice) has been focused on quantum and another uniformly accelerating (Rob), with information science. Most of the work was on no direct interaction but coupled to a common quantum entanglement dynamics in relativistic quantum field in (3+1)D Minkowski space. motions and macroscopic quantum phenomena These two detectors are set to be entangled (MQP). initially, while the initial state of the field is the Minkowski vacuum. The covariant formalism In an earlier paper [1] we showed the can account for the fully relativistic effects. derivation of an exact master equation for two Our treatment is non-perturbative and with coupled quantum harmonic oscillators back-reaction automatically included in a self- interacting bilinearly with a common consistent way. We also address some of the environment made up of n harmonic oscillators key issues such as "sudden death" and at an arbitrary temperature for a general entanglement revival, entanglement in spectral density function. This equation can be different coordinates, and spatial separation applied to the analysis of model problems in between two detectors. Following this MQP involving two harmonic oscillators, dimension of consideration, we are now either mechanical such as the superposition of studying the issue of decoherence and two mirrors, or one of them of electromagnetic disentanglement in a dynamical background or superconducting flux origin, as in spacetime [3]. nanoelectromechanical (NEM) resonators or SQUID-resonator. For the dynamics of Another important issue is the demarcation quantum entanglement between two qubits between microscopic, mesoscopic and different environmental settings could lead to macroscopic. At the conceptual level we want very different results. to examine the validity of an implicit assumption made in many MQP Most of the discussions on quantum investigations, namely, that the quantum entanglement dynamics are non-relativistic and mechanical behavior of a macroscopic object with an implicit assumption that the like the NEM or a C60 molecule, placed in background spacetime is globally Minkowski. interaction with an environment, behavior such Together with Dr. S.Y. Lin at NCTS and as quantum decoherence, fluctuations and Prof. B.L. Hu from UMD we considered the dissipation, entanglement and teleportation, quantum entanglement dynamics that was can be captured by its centor-of-mass behavior. arising from nontrivial global structure of In an earlier paper [4] in collaboration with spacetime such as the existence of an event Prof. Yu and Prof. B.L. Hu, we took a small horizon, as in the spacetime of a black hole step towards treating the quantum properties of (Schwarzschild) or a uniformly accelerated a mesoscopic or macroscopic object in a detector (UAD) [2]. This is an important general environment by providing the ingredient for the establishment of relativistic technical base for such studies. Now we are quantum information theory. In this work we pursuing further on the micro-to-macro study the dynamics of quantum entanglement transition. between two Unruh-DeWitt (UD) detectors (atoms), which are point-like objects with internal degrees of freedom described by

Research Activities of Individuals -›› 152 [4] C.H. Chou, B.L. Hu, and T. Yu, Quantum References: Brownian motion of a macroscopic object in a general environment, Physica A [1] C.H. Chou, T. Yu, and B.L. Hu, Exact 387,432(2008). master equation and quantum decoherence of two coupled harmonic oscillators in a general environment, Phys. Rev. E 77, 011112(2008). [2] S.Y. Lin, C.H. Chou, and B.L. Hu, Disentanglement of two harmonic oscillators in relativistic motion, arXiv:0803.3995[gr-qc], submitted to Phys. Rev. D. [3] C.H. Chou, S.Y. Lin, and B.L. Hu, in preparation.

153 ‹‹- Research Activities of Individuals Research Activities on String

Kazuyuki Furuuchi (email: [email protected]) Staff Scientist, 2007/8/1~2009/7/31

n this academic year, my research model, and provided a framework to describe activity in NCTS was mainly focused the Hawking-Page transition as condensation on following three subjects in string theory. of winding strings. As a continuation of the above series of (I) Description of thermodynamics of works, in this academic year at NCTS I Yang-Mills theory on three initiated construction of D-branes as solitons in dimensional sphere by effective string field theory. D-branes are regarded as matrix model of Polyakov loops, solitons in closed string field theory and they and black hole thermodynamics in played crucial roles in recent developments of anti-de Sitter space string theory. But in order to really describe D- AdS-CFT correspondence is a conjectural branes as solitons, field theoretical framework equivalence between closed string theories in for closed strings is necessary. However, anti-de Sitter space and conformal field closed string field theory has very complicated theories in lower dimension. The duality can structure and partial success has been made in be "explained" from extrapolation from open- the past. My string field theory constructed closed string duality in perturbative string from effective matrix model of Polyakov loops theory, though rigorous proof is difficult since is a much simpler effective theory, and it is beyond the region of validity of constructing D-branes in this model will help perturbative open or closed string theory. understanding above issue as well as However, evidences found in the past ten years uncovering roles of D-branes in black hole are enormous and it provides us a very strong physics. I found D-brane field in my model is tool to tackle issues in quantum gravity given by fermionization of string field [3]. (gravity is contained in closed string theory). This result is similar to what has been found in Thermodynamics in AdS-CFT correspondence the Hermite matrix models, but the new feature is particularly interesting because one of the here is that the analogue of string length in the most intriguing puzzles about gravity is Hermitian matrix model is winding number in thermodynamical nature of black holes. In the unitary model, but "negative length" in AdS(5)-CFT(4) correspondence (5 and 4 refer Hermitian model has more natural to space-time dimensionality), it has been interpretation in unitary matrix model as argued that the cofinement-deconfinement winding number in opposite direction. This transition in large N N=4 super Yang-Mills feature leads to doubled degrees of freedom of theory is a dual description of Hawking-Page left and right movers in string field and D- transition, a transition from AdS geometry to brane field in the case of unitary matrix model. AdS-black hole geometry. I have pointed out a From discussions with Prof. Fukuma at relation to vortex condensation on the string Kyoto University and Dr. Irie at NTU, I began worldsheet in my past research [1]. The to recognize that these D-branes may be useful thermodynamical phases of Yang-Mills for probing space-time geometry in the above theories on three dimensional sphere are AdS-CFT correspondence at finite governed by effective unitary matrix model of temperature. I hope to clarify this issue in the Polyakov loops. In ref. [2], I have constructed near future. string field theory from the unitary matrix model using the techniques in old matrix

Research Activities of Individuals -›› 154 (II) Space-time supersymmetry shows an advantage of the BLG model. algebra in the model for multiple We are currently working on how the BLG membranes model from can be obtained from covariant M-theory is a hypothetical theory which is M5-brane action. This is the direction expected to provide unified description to five suggested by the result of ref. [4], as I types of ten-dimensional superstring theory. mentioned above. This is important in order to However, only some parts of its structure in understand the relation between the new model some specific limits are currently understood. of multiple membranes and currently One of the expected features of M-theory is understood part of M-theory. that super-membrane is one of the fundamental Discussions with Prof. Pei-Ming Ho at building blocks of the theory. In the case of D- NTU who is one of the leading researchers in branes which played crucial roles in the this field were particularly helpful in this developments in non-perturbative studies of project. string theory in the last ten and some years, Lie algebra structure of multiple D-branes was a (III) Cubic open string field theory in characteristic new feature. From this linear dilaton backgrounds experience, we can expect that if we find characteristic algebraic structure of multiple Recently, there was a rapid progress in membranes, our understanding of M-theory construction of classical solutions in cubic will make progress. From the end of 2006 open string field theory. Cubic open string towards the end of 2007, Bagger and Lambert field theory in linear dilaton backgrounds is constructed a model for multiple super- interesting because 1. light-like linear dilaton membranes which has a novel gauge symmetry backgrounds is one of rare time-dependent based on Lie 3-algebra, a natural extension of exact string backgrounds. 2. The gradient of Lie algebra (also Gustavsson 2007, 2008). dilaton backgrounds induces novel type of After Mukhi and Papageorgakis showed a way classical solutions. With Syoji Zeze who was a to relate it to multiple D2-brane action in type postdoc at NTU and moved to Yokote Seiryo IIA superstring theory, huge interests were high school, we constructed cubic open string attracted on this model. In ref. [4], together field theory in linear dilaton backgrounds, in with Sheng-Yu Darren Shih at NTU and particular, explicit form of three-string- Tomohisa Takimi at NCTU, I studied interaction vertex. From this result we supersymmetry algebra of the Bagger-Lambert naturally obtained the string field theoretical Gustavsson model (BLG model). In particular, version of the field re-definitions used in the we tried to construct space-time paper of Pei-Ming Ho and Sheng-Yu Darren supersymmetry algebra, which does not Shih, who were also our discussion partners. manifestly present in the original model. We also try to construct new solutions in two However, we almost fully obtained space-time dimensional string theory, where comparison superalgebra. This result suggests a relation to with another strong method, matrix model, is some space-time covariant formulation, and possible. this is an interesting direction for future Progress of this project has been slowed investigation. Central charges of the down a little since Dr. Zeze became busy for supersymmetry algebra provide important moving to his new job place, and during that information of BPS objects in the BLG model. period my main research focus was shifted to We found that in order to construct M5-brane the model of multiple membranes mentioned charges, Lie 3-algebra structure is essential. above. However, we hoped to complete this This result provides an explanation for why in project after Dr. Zeze settles down. the matrix model of M-theory, a model based on Lie algebra and conjectured to describe M- theory, M5-brane charge was absent, and

155 ‹‹- Research Activities of Individuals Physics Letters A Special Issue ¡V 2007 References International Symposium on Cosmology and Particle Astrophysics Vol. 23, Nos. [1] Kazuyuki Furuuchi, "From free fields to 17-20 (2008) pp.1565-1576. AdS: Thermal case," Phys. Rev. D72, 066009 (2005); Kazuyuki Furuuchi, [4] Kazuyuki Furuuchi, Sheng-Yu Darren "Confined phase in the real time Shih, Tomohisa Takimi, "M-Theory formalism and the fate of the world behind Superalgebra From Multiple Membranes," the horizon," Phys. Rev. D73, 046004 to appear in JHEP. (2006); Kazuyui Furuuchi, "Lectures on AdS-CFT at weak 't Hooft coupling at finite temperature," arXiv:hep-th/0608181. [2] Kazuyuki Furuuchi, "Matrix model for Polyakov loops, string field theory in the temporal gauge, and winding string condensation in anti-de Sitter space," arXiv:hep-th/0608108. [3] Kazuyuki Furuuchi, "Matrix Model For Polyakov Loops, String Field Theory In The Temporal Gauge, Winding String Condensation In Anti-de Sitter Space And Field Theory Of D-branes," Modern

Research Activities of Individuals -›› 156 Research Activities on Cosmic Acceleration and Dark Energy

Je-An Gu (National Taiwan University Leung Center for Cosmology and Particle Astrophysics; email:[email protected]) Assistant research scholar, 2006/8/1~2008/8/31

y research is focused on the cosmic it is essential to answer two basic questions: acceleration and dark energy: (1) whether dark energy is played by a understanding its behavior and its origin from cosmological constant and (2) whether the both the phenomenological and the theoretical dark energy equation of state changes with point of view. time. In the process of obtaining the dark energy information from data, a suitable The existence of the cosmic acceleration at parametrization is needed, especially when one the present epoch was first discovered in 1998 requires the model independence. It was found via type Ia supernova (SN Ia) observations, that the information one obtains from data and was further reinforced recently by updated could be affected by the choice of the SN Ia data, WMAP measurement of cosmic parametrization. Furthermore, the current microwave background (CMB) and the model-independent parametrizations may be observations of large-scale structures. Many intrinsically incompatible with (thereby explanations for this mysterious phenomenon disfavoring) a significant part of models. invoke some exotic energy source, as generally called "dark energy", which provides (I-1) In the work in collaboration with Mr. significant negative pressure and repulsive Yu-Hsun Lo (master student) and Dr. Qi-Shu gravity to drive the cosmic expansion to Yan at the National Tsing-Hua University accelerate. (NTHU) we proposed a new parametrization (based on the Fourier series expansion) that is The current status is: there exist many dark particularly reasonable and controllable [1]. energy models that the current observations We have tested the efficiency of distinguishing cannot distinguish. Accordingly, from the dark energy models with the use of this phenomenological point of view the most parametrization for analyzing the current and urgent issue at the present stage is to extract the future supernova data. As a result, we dark energy information as much and as found it as good as the so-called "standard efficiently as possible from the current and the parametrization" proposed by Linder even for near future observations and experiments. In the simplest version of our parametrization. In addition, from the theoretical point of view the addition to the goodness in distinguishing naturalness and the link with the fundamental models, we emphasize that it is systematical physics have been two important key issues and controllable to extend our parametrization since the discovery of the cosmic acceleration. with more parameters for accommodating (I) Phenomenological Approach more detailed and more complicated behavior (that is necessary particularly when the data For the phenomenological study I am become much richer and much more accurate interested in extracting physical information in the future). about dark energy from observations, in particular, in a model-independent manner. (I-2) In the work in collaboration with Chien-Wen Chen (Ph.D. student) at the Observations which can map out the National Taiwan University (NTU) and expansion history of the universe, such as the Professor Pisin Chen at the NTU and the distance measurement of type Ia supernovae, Stanford Linear Accelerator Center (SLAC) are crucial probes of dark energy. With regard we proposed a new approach to constraining to the physical information about dark energy, the quintessence models [2], which can also be

157 ‹‹- Research Activities of Individuals extended to other dark energy models. In this (II-1) For the naturalness I explored a approach firstly we reconstruct the mechanism to control the cosmological quintessence potential with observational data constant through a scalar field non-minimally via the model-independent parametrization coupled to gravity [3]. By utilizing non- proposed by Linder. We then compare the minimal phantom or quintessence, the reconstructed potential with those considered cosmological constant can be automatically in quintessence models for the purpose of driven to a value (which, in particular, can be identifying the potential and constraining positive in the phantom case) on the scale of quintessence models. To facilitate this the mass parameter in the comparison, we propose that for each category phantom/quintessence potential V( ). The of quintessence models one introduce a distinct reduction of a large cosmological constant characteristic that bridges observational results involves the weakening of gravity that and the models under consideration. As a therefore may be much stronger initially. I demonstration of the effectiveness of this found the cases where originally gravity is on approach, we examine the power-law potential the TeV scale so that the hierarchy between and the exponential potential. As a result, we gravity and three gauge interactions in the conclude that at the 68% confidence level both standard model of particle physics is bridged at are ruled out, but at the 95% confidence level the beginning. Although the cosmological the power-law potential with a negative power constant can be automatically tuned or largely between -2 and 0 can fit the data, while the reduced under this mechanism, explaining the exponential potential remains disfavored. smallness of the observation-suggested cosmological constant energy density is still a For the future works, the model- difficult mission yet to be completed. independent reconstruction of other dark energy models (in addition to quintessence) (II-2) For both the naturalness and the link from data is worth of investigation. In addition with the fundamental physics I investigated to the model-independent parametrizations, I rapidly oscillating quintessence [4,5]. There plan to explore the model-oriented has been the suggestion that a rapidly parametrizations, i.e., which are optimized for oscillating scalar field can play the role of dark or motivated by certain categories of models, energy. The case of a power-law potential is such as quintessence, phantom, modified particularly intriguing, where the equation of

gravity, etc. For both two kinds of state woq of dark energy is a constant parametrizations, their stability and their determined simply by the power n in the

compatibility with a variety of models are potential through woq = (n-2)/(n+2). In the going to be investigated. recent work I focused on the power-law potential, and investigate the condition for (II) Theoretical Approach oscillation and the constraints from the current For the theoretical study, in the past 8 years observations. For this oscillating quintessence I have been working on many different scenario I found a specific model with much possible explanations of the cosmic less fine tuning, where all of the dimensionful acceleration, involving a variety of scenarios parameters and the period of oscillation are on including cosmological constant, quintessence, the same scale as the energy density of the phantom, extra dimensions, modified gravity present universe. This natural model provides and inhomogeneities of the universe. Recently, a working example that largely increases the I focused on quintessence and phantom. feasibility of oscillating quintessence. Along the direction of addressing the two For the future works, in addition to the key issues mentioned earlier, the naturalness theoretical studies oriented towards the two and the link with the fundamental physics, I key issues mentioned above, I also plan to investigated two models: (1) non-minimally launch the investigations relevant to my coupled phantom and quintessence; (2) current and future phenomenological works oscillating quintessence. mentioned earlier, such as the establishment of

Research Activities of Individuals -›› 158 the model-oriented parametrizations and the [5] Je-An Gu, "Can field excitations play the test of the compatibility of parametrizations role of dark energy?" Mod. Phys. Lett. A with models. 23, 1384 (2008).

References [1] Je-An Gu, Yu-Hsun Lo and Qi-Shu Yan, in preparation. [2] Je-An Gu, Chien-Wen Chen and Pisin Chen, "A New Approach to Constraining Quintessence Models by Observations," submitted for publication, arXiv: 0803.4504 [astro-ph]. [3] Je-An Gu, "Automatic Control over the Cosmological Constant through Non- minimal Phantom and Quintessence," submitted for publication, arXiv: 0801.4737 [hep-th]. [4] Je-An Gu, "Oscillating Quintessence," submitted for publication, arXiv: 0711.3606 [astro-ph].

159 ‹‹- Research Activities of Individuals Activities report on String

Takayuki Hirayama (email: [email protected], [email protected]) Postdoctoral researcher, 2007/9/1~2009/8/31

became a member of NCTS on string theory. We alsocomputed the value of September 2007 and my activities chiral condensate and showed the relation since them are summarized into two topics. between the quark mass and the value of chiral One is the application of so-called AdS/CFT condensate satisfies the Gell-Mann-Oakes- into QCD ( Quantum Chromo Dynamics ) and Renner relation. Now I continue working on the other is a black hole stability in a quantum this direction to compute the quark mass level. I published one paper for each topic, [1] dependenceof mesons and baryons which is and [2]. important when we study hadrons which contain s-quark. The AdS/CFT is a conjecture in string theory which claims the equivalence between a Another work on the black hole stability string theory or supergravity on a curved space was carried out in [2]. Einstein gravity predicts and a quantum field theory without gravity. black holes and the black hole physics is The example which have been studied important in classical and quantum gravity. intensively is the duality between Type IIB Especially the black hole thermodynamics has string theory in a space of 5 dimensional Anti- provided many implications of quantum de Sitter space times 5 dimensional sphere and properties of gravity. Gross, Perry and Yaffe the four dimensional N=4 supersymmetric showed that there is a negative mode around Yang-Mills theory. This duality is a weak- the Schwarzschild black holes which induces a strong duality in a sense that a weak string decay process of hot flat space into nucleation coupling region of Type IIB string theory is of black holes. And there is a general dual to a strong gauge coupling region of expectation that the existence of negative Yang-Mills theory. Therefore this AdS/CFT mode and the instability of black hole as a correspondence offers a quite powerful tool of thermodynamics ( the negative heat capacity in computing a strongly coupled gauge theory the case of Schwarzschild black hole ) are from a weakly coupled gravity theory. QCD ( equal. In fact if we introduce a negative Quantum Chromo Dynamics ) is a gauge cosmological constant and a Schwarzschild theory which describes the strong force in black hole starts showing the thermodynamic nature. The mesons and baryons are stability, the negative mode disappears. String composites made of quarks which are bound theory contains gravity and is a perturbatically by this strong force. Because of strong gauge well defined quantum theory. From studying coupling of QCD, it is quite difficult and the low energy effective theory of string challenging to compute the masses and theory, the low energy effective theory has interactions of mesons and baryons. I have additional higher dimensional terms in challenged to compute the lightest mass state addition to Einstein gravity. Then there is a in QCD which is called the pion by applying natural question that whether the equivalence the AdS/CFT correspondence into QCD. The between the existence of negative mode and dual description of QCD in terms of gravity is the thermodynamic instability holds even there based on so-called D-branes in string theory.In are higher dimensional correction terms [1] I and my collaborators succeeded to realize expected from string theory. I studied this the observed value of pion mass by problem in [2] and found an unexpected result. introducing another D-branes in the model. We For simplicity, I added the so-called Gauss- showed that the pion mass is generated from Bonnet term into Einstein theory which is the the contribution of worldsheet instanton in lowest dimensional term among the

Research Activities of Individuals -›› 160 corrections and studied negative mode(s) around the Schwarzschild type black hole. When the black hole size is small enough so References that the Gauss-Bonnet term becomes relevant, [1] Koji Hashimoto, Takayuki Hirayama, I found the equivalence no longer holds. This Feng-Li Lin, Ho-Ung Yee, Quark Mass is quite unexpected since this equivalence is Deformation of Holographic Massless shown to be satisfied in many different black QCD, published in JHEP 0807:089, 2008. holes in Einstein gravity with matter and gauge [2] Takayuki Hirayama, Negative modes of fields, although there is no proof. At this Schwarzschild black hole in Einstein- moment I have not had physical understanding Gauss-Bonnet Theory, submitted to of my results.Therefore I have continued Classical and Quantum Gravity. working on this project and expect more properties of quantum gravity can be revealed through this project.

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

Wen-Hsuan Kuan (Department of Science, Taipei Municipal University of Education; email: [email protected]) Postdoctoral researcher, 2006/2/1~2008/7/31

y works in 2008 were briefly Together with professor Daw-Wei Wang, summarized as follows: we have derived the effective Hamiltonian beyond FBA in 3D, and the ground state (I) Ground state properties and energy has been calculated by using the collective excitations of a dipolar Gaussian type trial wave function. However, it Bose-Einstein condensate (BEC) is inadequate to do so while the condensate profile is highly anisotropic. To remedy the Recently attained BEC gas of highly flaw, we solved the dipolar Gross-Pitaevskii magnetic chromium atoms shows a signature equation in a fully numerical manner. Also, we of dipolar interactions. This opens a door for directly solved the many-body Hamiltonian. investigations on the dynamics of cold atoms We used the Monte Carlo integration method in strong electric field under which the long in dealing with a many-dimensional range dipole-dipole interaction may have calculation that provided the results all within profound effect. Moreover, it provides a better great accuracy. Eventually, the optimal set of understanding on the formation of the BEC parameters of trial wave functions would be molecules and the mechanism in BEC-BCS determined via the variational method in the phase transition. sort of the lowest energy solution. The Yi and You1 first introduced a program is in progress. Based on our work, the pseudopotential approach for describing further calculation in collective excitations can slowly moving particles interacting via short- provide a comparison with ab initio range contact potential and the long-range calculations and the significance of dipolar dipolar force. However, their approach based effect can be quantitatively confirmed. on first Born approximation (FBA) that is valid only in the low energy scattering regime. (II) Landau-level mixing effect on The weak interaction assumption breaks down rotating BECs with attractive near scattering resonances. Therefore, it is interactions in anharmonic crucial to develop a full many-body theory for trapping potentials dipole beyond FBA. Problems of rotating BECs have attracted In the recent work of Wang2, the first much attention in the past years. In the rotating effective many-body theory that is capable to frame at frequency , BECs feel the Coriolis describe bosonic dipolar condensates even force which is identical to the Lorentz force of near the shape resonance (SR) or in the a charged particle with mass M in a magnetic strongly interacting regime has been derived. field B = 2M . The analogy between the Using the scattering matrix elements motion of charged particles in a magnetic field calculated by Deb et.al., the dipolar effect near and neutral atoms in a rotating frame can SR is found to be significantly renormalized so reveal some interesting solid state phenomena that the system becomes more stable than what such as vortex lattice, quantum Hall liquid and is predicted using simple FBA. Moreover, the Wigner crystal in rotating BECs. elementary excitation of the 2D condensate behaves as q in the long wavelength limit, Repulsive rotating BECs in a harmonic showing the same low energy physics as 2D trapping potential can form a singly quantized charge bosons with Coulomb interactions. vortex above a certain critical rotational frequency. When rotation frequency is close to

Research Activities of Individuals -›› 162 the harmonic trapping frequency, rotating BECs condense into the lowest Landau level (LLL) and form a vortex lattice. The centrifugal force cancels the trapping force, and BECs fall apart if rotational frequency is equal to the harmonic trapping frequency. It is interesting to know whether vortices can also exist for attractive BECs even attractive BECs having different physical phenomena compared with repulsive BECs. Attractive BECs are only stable for a sufficiently small number of particles or very weak interactions, but mutual interactions can be reduced by the Fig.1 Coriolis force for rotating atoms. In a Caption: The Phase diagram of a rotating condensate in a / Ð harmonic trapping potential, instead of existing quadratic-plus-quartic potential in Ω 0 plane for =0.05. In extremely-weak interaction and highly-rotating vortices, the energetically favored state of speed regime, vortex state of large number of vortices is attractive rotating BECs is the center-of-mass generated to (CM) motion which absorbs all the angular lower the energy of the system. As the attractive momentum of rotation.3 On the hand, vortex interaction is enhanced to balance the centrifugal force and CM states are attainable via an and the anharmonic trapping force, the condensate anharmonic term in the trapping potential to energetically favors the center-of-mass motion. Before the collapse of the condensate, off-center vortex state can eliminate instability. exist in the grey region due to Landau-level mixing effect. Ground state properties of attractive rotating BECs have been studied (III) Generation of dc spin currents perturbatively under the LLL approximations.4 in narrow channel with Rashba To study systems with any arbitrary interaction and Dresselhaus spin-orbit strength and anharmonic trapping potential, an interactions emergent theory beyond the perturbative The success of dc front-gate control for the approach is needed. Together with professor measurement of Rashba coupling strength Szu-Cheng Cheng, in this work we calculated inspired proposals for spin current generation the energy functional of Gross-Pitaevskii by nonmagnetic means. These proposals equation by proposing variational wave include adiabatic quantum pumping in a functions of vortex and CM states within quantum dot with static SOI interfaced with a Landau-level mixing effects. We have proved time-dependent barrier and a spatially that ground-state energies, without Landau- separated Rashba SOI region, and an ac-biased level mixing, of vortex and CM states are Rashba-type two-dimensional (2D) disorder consistent with the many-body perturbation system or quantum channel.5 It is known that theory. We also found that, in fact, the lowest the translational invariance is broken in the energy of vortex or CM state should be the channel direction due to a spatially localized state including the effect of Landau-level time-dependent potential, thus allowing us to mixing. The effect of Landau-level mixing is explore coherent resonant inelastic scattering not negligible even under conditions of weak and time-modulated quasi-bound state interactions and small anharmonic trapping features. potentials. Vortex and CM states, whose ground-state energies are lowered, are Together with professor Chi-Shung Tang, stabilized by the effect of Landau-level we consider a narrow channel formed in a mixing. high-mobility electronic quantum well by applying negative bias on the front split gates. When a finger gate is deposited above the split gate separated by an insulating layer, a local time varying Rashba coupling parameter

163 ‹‹- Research Activities of Individuals (r,t)can be induced by ac-biasing the finger gate. We explored how the interplay among the static Rashba, the static Dresselhaus, and the dynamical Rashba SOI effects influences the efficiency of spin current generation in the absence of source-drain bias. The considered dynamical system for spin pumping is depicted in Fig. 2. The spin current generating features have been demonstrated and illustrated in detail. In Fig. 3, we demonstrate how the Dresselhaus spin-orbit coupling strength influences the dc spin current generated by the ac-biased front gate. Fig. 4 shows the spin-resolved transmission with dynamical Rashba coefficient. 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 Fig.3 pumped spin current in the high kinetic energy Caption: (a): Spin-resolved current transmission TRL(solid 6 red) and TRL(dashed blue) as a function of electron energy regime. Unlike the parametric quantum in units of driving frequency. (b): Generated dc spin current

pumping, in which two pumping potentials for the cases of 0= 0.0$ (dotted red), 0.02 (dashed with a phase difference is needed. Our green), and 0.04 (solid blue). L/L*=30, 0=0.13, 1=0.05, proposed spin current generating device is and \omega = 0.05∆ . achievable using a single ac-biased gate, and should be achievable within recent fabrication capability.

Fig.2 (sys.eps) Caption: Schematic illustration of the quantum wire with Rashba and Dresselhaus spin-orb interaction influenced by an ac-biased finger gate (with length L) across the wire.

Fig.4

Caption: (a): Spin-resolved current transmission TRL (solid

red) and TRL (dashed blue) as a function of electron energy in units of driving frequency. (b): Generated dc spin current for the cases of =0.03 (dotted red), 0.04 (dashed green),

and 0.05 (solid blue). L/L*=50, 0=0.13, 0=0.03, and \omega = 0.05∆ .

Research Activities of Individuals -›› 164 [5] L. Y. Wang, C. S. Tang, and C. S. Chu, Phys. Rev. B 73, 085304 (2006). References [6] C. S. Tang, W. H. Kuan, W. Xu, and Y. C. [1] S. Yi and L. You, Phys. Rev. A 61, 041604 Chang (accepted by JVST B 2008). (2000); ibid. 63, 053607 (2001). [2] Daw-Wei Wang, arxiv:cond-mat/ 07043868 (2007). [3] N. K. Wilkin, J. M. F. Gunn, and R. A. Smith, Phys. Rev. Lett. 80, 2265 (1998). B. Mottelson, Phys. Rev. Lett. 83, 2695 (1999). [4] G. M. Kavoulakis, A. D. Jackson, and G. Baym, Phys. Rev. A 70, 043603 (2004). A. Collin, E. Lundh and K.-A. Suominen, Phys. Rev. A 71, 023613 (2005).

165 ‹‹- Research Activities of Individuals Reseach Activities on Lattice Gauge Theory in Physics of the Large Hadron Collider

C.-J. David Lin (Institute of Physics, National Chiao-Tung University; email: [email protected]) Center Scientist, 2007/2/1~2009/1/31

ntroduction structure that is absent in the Standard Model. From August 2007 to August 2008, This structure cannot be probed by existing I started projects in physics related to the experiments performed with the B mesons Large Hadron Collider using large-scale which do not carry spin. With William numerical simulations in Lattice Gauge Detmold and Matthew Wingate, I have set up a Theory. This is reflected in two main research programme to pin down the relevant matrix avenues that I am pursuing. First, I am elements in the above decay channel as our studying the scenario of electroweak symmetry final goal. breaking via a strongly coupled gauge theory In our programme, we use the dynamical at TeV scale. Second, I am performing gauge configurations generated and kindly lent calculations for decay amplitude of baryons to us by the RBC Collaboration. The lattice containing a b quark, which is the main subject size is 24-cube times 64, with lattice spacing of the LHC-b experimental project. around 0.1 fm. The 2+1 flavours of dynamical quarks in these RBC configurations are Hardware domain wall fermions. We also use the same The start-up equipment fund for my fermions for our valence light quarks. For the position was granted in the summer of 2007, heavy quark, we use the static approximation from the National Science Council and Faculty where the heavy-quark mass is infinite. The of Sience, National Chiao-Tung University. most time-consuming step in this programme From August 2007 to December 2007, I played is to generate light-quark propagators. We the main role in the purchase of a PC cluster have finished two thirds of this task for our using this start-up fund. The cluster was initial investigation after running the program delivered between January and April 2008. on my PC cluster and other computing Now it contains twenty-six computing nodes. resources in the USA for five months. Each node has two quad-code CPUs and In lattice numerical simulations involving sixteen gigabites of memory (with error static heavy quarks, it is often important to checking). Twenty-two of these nodes are study the choice of the quark-level connected via a Double-Data-Rate (up to 20 interpolating operators for mesons and gigabits per second) infiniband switch. The baryons. This is because the statistical noise other four are on a gigabit network. In from the Monte-Carlo simulation can become addition to the computing nodes, we have a significant in this setting. To this end, we have six-terabite disc array for storage. investigated the two-point functions of these hadrons. In Fig. 1, two choices of parameters Physics of the b-baryon in the baryon interpolating operator are A b-baryon is composed of three valence presented. Here we are plotting the logarithm quarks, namely, a b-quark and two light of the ratio of the correlators at the nearest two quarks. The rare decay channels in which a euclidean lattice time slices as a function of non-stranged b-baryon decays into a stranged time. A plateau in such a plot signals a baryon baryon plus a photon or a lepton pair are state in the simulation, and the value of this sensitive to new physics effects involving the plateau is the baryon mass. From Fig. 1, it is mixing of quarks via right-handed coupling clear that the parameters in the left panel are

Research Activities of Individuals -›› 166 much better than those in the right panel.

Once the spectrum is calculatd, we will proceed to the calculations of various relevant matrix elements. Walking Technicolour Walking technicolour is one of the candidates that generate the electroweak symmetry breaking at TeV scale without the need for the Higgs particles. It is a strongly- coupled gauge theory, hence lattice gauge Fig. 1 theory can play an important role in this As the first step towards the calculation of research avenue. In the walking-technicolour rare decay matrix elements of b-baryons, we scenario, the coupling constant in the gauge have studied the spectrum of these baryons. In theory increases over a range of scale when the particular, we are investigating the light-quark energy is decreased, then it becomes "frozen". mass dependence of the spectrum. There have At the very low energy regime, it starts been very few lattice calculations for the b- increasing again, such that conformal baryon spectrum, and the parameters (quark symmetry and chiral symmetry are broken mass, lattice volume, etc.) in our work are the dynamically. The system then develops an closest to the physical values. Fig. 2 presents energy gap which generates the spectrum. the light-quark mass dependence of the mass The reason why such a scenario is required difference between the Lambda-b baryon and is due to the need to dynamically suppress the the B meson. One can see some hint that there flavour-changing neutral currents (FCNC) in may be some non-linear dependence here, as physics beyond the Standard Model. A predicted by Chiral Perturbation Theory. This walking theory is likely to produce large was never observed before in heavy baryon anomalous dimensions for the operators that systems, and we are currently generating more generate the Standard Model fermion masses. data to perform a detailed study. It will be This can then lift the scale at which flavour published in the near future in Ref. [1]. emerges, hence suppress the FCNC. It is not easy even just to find a theory which has the "walking" feature and dynamical symmetry breaking at low energy. Exploratory result using the step-scaling method was reported by Appelquist and collaborators recently [2]. These authors calculated the coupling constant in the so-called Schroedinger functional scheme for QCD-like theories with large numbers of flavours. They discovered that the coupling constant would stop running for a

167 ‹‹- Research Activities of Individuals range of scale in some of these theories. At the moment, we are preparing the However, this statement has to be checked in dynamical fermion simulations. In the future, other schemes. we will also try to compute the running of the condensate in these theories. This is the most At the moment, I have formed a crucial point in hunting for a walking collaboration with physicists in Professor technicolour theory. Tetsuya Onogi's group at the Yukawa Institute at the University of Kyoto. We are studying the scale dependence of the coupling constant in these theories in the Creutz-ratio scheme. We fix the scheme by keeping constant the Reference ratio between the Wilson-loop size and the [1] W. Detmold, C.-J.D. Lin and M. Wingate, lattice size, as indicated in Fig. 3. This "Lattice calculation of b-baryon spectrum specifies the scheme. We then perform with domain-wall light quarks", in calculations at various lattice sizes and preparation. extrapolate to the continuum limit at each step. [2] T. Appelquist, G. Fleming and E. Neil, The lattice size is the renormalisation scale in "Lattice study of the conformal window in this procedure. Since this is a new scheme, QCD-like theories", Phys. Rev. Lett. we have performed exploratory numerical 100:171607, 2008. study of the coupling constant in the quenched prroximation for QCD. Our numerical data fit [3] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, the two-loop running formula well at high C.-J.D. Lin, H. Matsufuru, H. Ohki, T. energy [3,4], as shown in Fig. 4 Onogi and T. Yamazaki, arXiv:0808.2875 (Proceedings for Lattice 2008, to be published in Proceedings of Science). [4] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi and T. Yamazaki, "A new method of calculating the running coupling constant", in preparation.

Fig. 3

Fig. 4

Research Activities of Individuals -›› 168 Research Activities on Spintronics

Hsiu-Hau Lin (Department of Physics, National Tsing Hua University; email: [email protected]) Center Scientist, 2006/2/1~2010/1/31

n the past year (2007-2008), I have On the low-dimensional correlated system continued my research on spintronics side, we tried to address various physical (S) and also low dimensional correlated properties in low dimensional systems systems (L), leading to the publications listed including the charge-density wave formation below. Let me briefly summarize our research [L3], conductance anomaly in carbon results here and leave detail explanations for nanotubes [L4] and flat-band freeomagnetism key findings in later paragraphs. in armchair graphene nanoribbon [L5]. One of the most striking feature we tried to investigate On the spintronics part, we applied the is symmetry restoration under renormalization developed self-consistent Green's function group transformation. We devise an elegant approach to nanoscale junctions and find the transformation to map the metallic zigzag carrier-mediated exchange coupling strongly carbon nanotube to a non-conventional two-leg depends on the topology of the Fermi surface ladder (without inter-leg hopping) and found topology [S2,S4]. We also collaborate with an approximate SO(6) symmetry in the neutral experimentalists to see whether the theoretical sector [L2]. Pursuing the same direction, we predictions can be verified. In p-type Si film combine the techniques of the perturbative implanted with B and Mn ions, the theoretical renormalization group and the non- predictions are in qualitative agreement with perturbative bosonization to obtain global the experimental data [S3]. Furthermore, in a phase diagram for zigzag carbon nanotube recent collaboration, we were able to achieve [L1]. As the interaction strength decreases into quantitative explanation of the magnetization the weak-coupling regime, symmetry curve in amorphous Si film doped with Cr restoration emerges giving rise to various non- [S1]. It is rather remarkable that the trivial binding mechanism and also excitation quantitative agreement between the theory and degeneracy, which may help us to understand the experiment can be achieved by only one how non-conventional pairing arises in fitting parameter! strongly correlated systems in low dimensions. [S1] Jia-Hsien Yao, Hsiu-Hau Lin and Tsung- [L1] J. E. Bunder and Hsiu-Hau Lin. Phase Shune Chin, Room temperature diagram of the metallic zigzag carbon ferromagnetism in Cr-doped nanotube. Phys. Rev. B 78, 035401 hydrogenated amorphous Si films. Appl. (2008). Phys. Lett. 92, 242501(2008). [L2] J. E. Bunder and Hsiu-Hau Lin. [S2] Wen-Min Hunag, Hsin-Hua Lai, Cheng- Dynamical Symmetry Enlargement in Hung Chang and Hsiu-Hau Lin. Carrier- Metallic Carbon Nanotubes. Phys. Rev. mediated exchange coupling and Fermi B 75, 075418 (2007). surface topology (invited article). Int. J. Mod. Phys. B 22, 88 (2008). [L3] Chao-Hung Du, Chung-Yu Lo, Hsiu-Hau Lin, Shih-Lin Chang, Nonlinearity and [S3] Hung-Ta Lin, W.-J. Huang, S.-H. Wang, dynamic phase transition of charge- Hsiu-Hau Lin and Tsung-Shune Chin. p- density-wave lattice. J. Appl. Phys. 101, Si(100) by sequential ion-implantation of 104915 (2007). B and Mn. J. Phys.: Condens. Matter 20, 095004 (2008). [L4] Po-Yao Chang, Wen-Min Huang and Hsiu-Hau Lin. Impurity induced [S4] Wen-Min Huang, Cheng-Hung Chang conductance anomaly in zigzag carbon and Hsiu-Hau Lin. Non-collinear nanotube. accepted for publication in J. magnetic junction mediated by Rashba Phys.: Conf. Series (2008). interaction. J. Mag. Mag. Mat. 310, e759 (2007).

169 ‹‹- Research Activities of Individuals [L5] Yen-Chen Lee and Hsiu-Hau Lin. Flat- band ferromagnetism in armchair graphene nanoribbon. accepted for publication in J. Phys.: Conf. Series (2008). Diluted Magnetic Semiconductors Carrier-mediated ferromagnetism, found in diluted magnetic semiconductors (DMS) such as III-V semiconductors doped with transition metals, opens up the possibility of electric manipulations of magnetic and optical properties because of the exchange coupling On the other hand, the situation simplifies between the localized moments of the quite a bit if the carriers are localized. transition metal and the itinerant spins in the Applying the percolation of magnetic polarons, semiconducting bands. In recent years, one can calculate the magnetization curve experimental progress has stimulated intense versus temperature. The only fitting parameter theoretical investigations of DMS those mainly is the ratio between the size of the magnetic focus on estimates of the critical temperature. polaron and the mean distance between the Although some experimental data is available magnetic dopants. We tried to compare the little theoretical attention has been paid to spin theoretical predictions and the experimental dynamics, which is crucially important in measurements in amorphous diluted magnetic understanding the spin coherence. semiconductors. In hydrogenated amorphous Si flim doped with Cr, the measured magnetization curve agrees with the theoretical prediction Ð with just one fitting parameter for the whole temperature range. Symmetry Restoration in Carbon Nanotubes Carbon nanotubes are fascinating materials with remarkable mechanical and physical properties. Due to their low dimensionality, It is important to emphasize that the carrier- correlations and quantum fluctuations arising mediated ferromagnetism can be roughly from electron-electron interactions cannot be divided into two categories depending on the ignored. It was beautifully demonstrated carriers are itinerant or localized. For itinerant theoretically and later verified in experiments carriers, the mediated exchange coupling that the unscreened Coulomb interactions drive sensitively depends on the band structure and the armchair nanotube into a Tomanaga- also the thermal fluctuations. Although the Luttinger liquid phase with exotic spin-charge band structure can be computed by the first- separation. On the other hand, if the Coulomb principles methods, however, the supercell interactions are screened so that only short- approach works poorly for predicting the ranged interactions remain, various correct magnetic behaviors. On the other hand, instabilities set in and the ground state phase the model approach can address more subtle diagram is rather rich. issues like spin-wave fluctuations. But, it is As a carbon nanotube has only a few rather difficult to integrate these theoretical conducting channels, it is not obvious how the methods with realistic band structures (often long-ranged Coulomb interactions can be very complicated). Therefore, quantitative screened. One proposal for the reduction of agreement between theories and experiments long-ranged Coulomb interactions is a thick remain a tough quest. arrangement of nanotubes in either array or rope form. Alternatively, one can make use of improving nanoscale technology and place a

Research Activities of Individuals -›› 170 carbon nanotube close to a conducting plate. effective two-leg lattice model with the one- The induced image charges in the conducting loop renormalization group (RG) and the non- plate will render the Coulomb interactions perturbative bosonization techniques. Due to short-ranged. the spreading of the wave function, the effective interaction strength is reduced by a While most theoretical investigations factor of 1/N, where N is the number of unit concentrate on the armchair nanotube because cells around the circumference. This reduction of its simplicity, it is often assumed that the in the effective interaction strength is crucially low-energy physics should be the same for important as it allows the weak-coupling RG metallic zigzag carbon nanotubes, since for analysis to be valid. both honeycomb lattices the low-energy physics originates from the Dirac cones in the band structure. We looked into this issue carefully and found that the effective lattice model of the zigzag nanotube differs from that of the armchair. Ignoring the interactions momentarily, by integrating out the gapped modes, the metallic zigzag nanotube is described by an effective two-chain system. Note that the interchain hopping is absent in this effective lattice model. As a consequence, the Fermi velocities remain degenerate when the nanotube is doped away from half filling. It is important to emphasize that the Fermi The one-loop RG flows determine the velocities in the armchair nanotube are equal instabilities which may then be analyzed by to each other only at half filling and become non-perturbative bosonization (and different at finite doping. As we will explain refermionization) in order to identify gaps in later, the degeneracy of the Fermi velocities in different charge and spin sectors. From this, the zigzag carbon nanotube is crucially not only can the phase diagram be determined, important for symmetry restoration at finite but our numerical results also reveal symmetry doping. restoration of low-energy excitations above the In addition to the subtle velocity ground state. For a truly weak interaction degeneracy at finite doping, the differences strength U/t<0.5, symmetry restoration occurs between the zigzag and armchair nanotubes' and the system is described by the Gross- effective lattice models become obvious when Neveu model with an enlarged SO(6) one tries to write the effective interactions. It symmetry. The exact solution gives eight-fold turns out that, after integrating out the gapped kink/antikink excitations in the low-energy modes, the effective interactions for the zigzag limit. This differs from the usual behavior of are far more complicated than those for the two decoupled single chains which exhibit armchair. spin-charge separation but only have four-fold degenerate spinons. It is also not the same as the fully gapped two-chain systems, where spinons and holons are glued together by long- range gauge interactions, originating from various gaps in the charge and spin sectors. We also numerically compute the anomalous scaling of the gap/coupling ratios associated with the enlarged SO(6) symmetry. For bare couplings with approximate SO(6) symmetry, previous analytic calculations based on perturbation theory predict a universal exponent of 1/2 for the scaling functions of the gap/coupling ratios. Surprisingly, not only do we verify the predicted exponent numerically, We reanalyze the correlation effects in the we also find that the exponent is robust even

171 ‹‹- Research Activities of Individuals for large deviations in the bare couplings! armchair edges give rise to both itinerant Finally, for realistic material parameters U/t ~ Bloch and localized Wannier orbitals. As will O(1), the charge sector decouples and ruins the be explained later, these localized orbitals are SO(6) symmetry but there remains an enlarged direct consequences of quantum interferences SO(4) symmetry in the spin sector, indicating in armchair GNR and form flat bands with an unexpected degeneracy between the usual zero velocity. The carrier-mediated three-fold magnons and an additional neutral ferromagnetism can thus be understood in two particle-hole excitation. steps: Electronic correlations in the flat band generate intrinsic magnetic moments first, then Magnetism in Armchair Graphene the itinerant Bloch electrons mediate Nanoribbon ferromagnetic exchange coupling among them. One of graphene's superior properties is its As a result, the magnetic properties of pronounced ambipolar electric field effect. By armchair GNR sensitively depend on the applying gate voltages, the charge carriers can doping and thus can be manipulated by the be tuned between electrons and holes with external electric fields. concentration up to 1013 cm-2. Making use of Besides its potential applications to the sensitivity to the electric field, Son, Cohen spintronics at nanoscale, the ferromagnetic and Louie demonstrated zigzag graphene ground state in the armchair GNR also reveals nanoribbons (GNR) can become half metallic a new type of flat-band ferromagnetism, and their magnetic properties can be controlled different from those proposed by Mielke and by the external electric field. Their results not Tasaki. The key to Mielke-Tasaki only show that the electronic spin degrees of ferromagnetism is the finite overlap of freedom can be manipulated by the electric adjacent Wannier orbitals in the flat band. fields, but also bring up the possibility to Once the so-called local connectivity condition explore spintronics at the nanometer scale is achieved, the finite overlaps generate based on graphene. exchange coupling among these orbitals, Since open boundaries of GNR play a leading to flat-band ferromagnetism. However, crucial role at nanoscale, we expect the the Wannier orbital in armchair GNR has zero interplay between Coulomb interaction and the overlap with its adjacent neighbors. The flat edge morphology will lead to rich physics. It is band alone only accounts for the existence of then interesting to study GNR with armchair the magnetic moments and the ferromagnetic edges. Note that the edges are hydrogenated so order sets in only when itinerant carriers are that the dangling sigma bonds are saturated present. and only the pi bands remain active in low energy. By combining analytic weak-coupling analysis, numerical density matrix renormalization-group (DMRG) method, and the first-principles calculations, we show that armchair GNR exhibits novel carrier-mediated ferromagnetism upon appropriate doping.

Even though only pi bands are active in low-energy, in appropriate doping regimes, the

Research Activities of Individuals -›› 172 Research Activities on Relativistic Quantum Information

Shih-Yuin Lin (email: [email protected]) Assistant Research Scholar, 2006/8/1~2008/12/31

y research in 2008 is focused on the excited state to the steady state very close to dynamics of detectors or atoms in a the ground state of the free detector. Under the relativistic quantum field, with more emphasis most general conditions, however, the detector on the emerging theory of relativistic quantum never recovers its quantum coherence and the information and the applications to the black entanglement between the detector and the hole physics. field remains large at late times. [2] Based on a series of work on the detector- To the extent this model can be used as an field system done in collaboration with Prof. analog to the system of a black hole interacting Bei-Lok Hu at University of Maryland, we with a quantum field, our result seems to turned to look at the reduced density matrix of suggest in the prevalent non-Markovian the detector and discovered new features in the regime, assuming unitarity for the combined dynamical evolution of the detector's internal system, that black hole information is not lost degree of freedom [1]. Our exact results show but transferred to the quantum field degrees of clearly the differences from the ordinary result freedom. Our combined system will evolve where the quantum field's back-reaction is into a highly entangled state between a ignored in that the detector no longer behaves remnant of large area (in Bekenstein's black like a perfect thermometer. The interaction hole atom analog) without any information of between the detector and the field engenders its initial state, and the quantum field, now entanglement between them, and tracing out imbued with complex information content not- the field leads to a mixed state of the detector so-easily retrievable by a local observer. [2,3] even for a detector at rest in Minkowski In [4] we study the dynamics of quantum vacuum. We find that the transition probability entanglement between two Unruh-DeWitt in the ordinary description for the Unruh effect detectors, one stationary (Alice) and another from the initial ground state to excited states uniformly accelerating (Rob), with no direct derived from time-dependent perturbation interaction but coupled to a common quantum theory is existent in the exact solution only in field in (3+1)D Minkowski space. In our transient under special limiting conditions consideration, the Unruh effect, the retardation corresponding to the Markovian regime. of mutual influences, the observer-dependence Further, the detector at late times never sees an of the physical quantities and the fiducial time exact Boltzmann distribution over the energy of the system are naturally included. We find eigenstates of the free detector, and in the non- that for all cases studied the initial Markovian regime the Unruh temperature entanglement between the detectors disappears cannot be identified inside the detector. in a finite time (sudden death). After the For the detector initially in its excited state, moment of total disentanglement the we monitor the purity function in the detector correlations between the two detectors remain to study the evolution of quantum nonzero until late times. In our case (Gaussian entanglement between the detector and the states of a linear system) the reduced density field. We explicitly show that, only in the matrix and the separability of the Gaussian ultraweak coupling regime could some degree state at two events in spacetime are of recoherence in the detector appear at late independent of time-slicing scheme. We times, but never in full restoration. This believe that this is a general feature of corresponds to the relaxation process from the quantum entanglement in relativistic quantum

173 ‹‹- Research Activities of Individuals information theory. Nevertheless, the [2] S.-Y. Lin and B. L. Hu, Quantum entanglement dynamics and the entanglement, recoherence and disentanglement (proper) time are coordinate- information flow in an accelerated detector dependent, because in general two events - quantum field system: Implications for simultaneous in one coordinate are not black hole information issue, Class. simultaneous in another, while quantum Quantum Grav. 25, 154004 (2008) [arXiv: entanglement is a property of a quantum state 0710.0435]. of two events at the same time slice. Indeed, [3] B. L. Hu and S.-Y. Lin, Black Hole we found that the relation between the Information in a Detector-Field Analog, in disentanglement time and Rob's proper Proceedings of From Quantum to acceleration is observer-dependent. The larger Emergent Gravity: Theory and the acceleration is, the longer the Phenomenology, Trieste, Italy , June 11-15 disentanglement time in Alice's coordinate, but 2007 (PoS(QG-Ph)019) [arXiv: the shorter in Rob's coordinate. 0712.3643]. Currently we are looking at the case of two [4] S.-Y. Lin, C.-H. Chou and B. L. Hu , inertial detectors, both at rest in a relativistic Disentanglement of two harmonic quantum field. We expect that the quantum oscillators in relativistic motion, submitted entanglement between the two detectors will to Phys. Rev. D [arXiv:0803.3995]. have interesting dependence on their spatial separation. We are studying the dynamics of entanglement for this set-up, and trying to see whether there is residual entanglement at late times.

References [1] S.-Y. Lin and B. L. Hu, Backreaction and Unruh Effect: New Insights from Exact Solutions of Uniformly Accelerated Detectors, Phys. Rev. D 76, 064008 (2007) [gr-qc/0611062].

Research Activities of Individuals -›› 174 Research Activities Report on Complex Systems

Yu-Pin Luo (National Formosa University; email: [email protected]) Postdoctoral researcher, 2007/8/1~2008/7/31

uring my being a postdoctoral fellow two-dimensional regulatory network near a in NCTS, I have worked on two stable equilibrium explicitly. Two examples, topics. One is the Ising model on two- autoregulatory network and toggle switch, are dimensional lattices, and the other is the discussed. In general, the finite correlation- intrinsic fluctuations in gene regulatory time of noise reduces the fluctuations and networks. We have published one paper in enhances the correlation between the Phys. Rev. E [1] and finished another paper fluctuations of two molecular components. submitted to Phys. Rev. E [2]. Our main Recently, I also start to work on "system- research results are: coordination for the scale-free network." (I) Self-similarity in the classification As is known, many natural and social of finite-size scaling functions for systems display global organization and toroidal boundary conditions coordination without centralized control. Examples include conventions and norms and The conventional periodic boundary social learning in animals and humans as well conditions in two dimensions are extended to as fads and rumors. We are interested in the general boundary conditions, prescribed by origin of the global coordination. As an primitive vector pairs that may not coincide example of our study, we have considered the with the coordinate axes. This extension is scale-free networks based on the Barabasi- shown to be unambiguously specified by the Albert (BA) construction algorithm. By twisting scheme. Equivalent relations between modifying the preferential attachment step of different twist settings are constructed the BA construction algorithm [3], we specify explicitly. The classification of finite-size the power of degree distribution and the scaling functions is discussed based on the clustering coefficient. Our study shows that the equivalent relations. A self-similar pattern for efficiency of system coordination is influenced distinct classes of finite-size scaling functions by degree distribution and clustering is shown to appear on the plane that coefficient in scale-free network. Related parametrizes the toroidal geometry. results have been presented in a draft [4] to be submitted for publication in the near future. (II) Intrinsic Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise References: The study of intrinsic fluctuations in gene regulatory networks is extended to the case of [1] Tsong-Ming Liaw, Ming-Chang Huang, Gaussian colored noise. Firstly, the solution of Yu-Pin Luo, Simon C. Lin, Yen-Liang the corresponding Langevin equation with Chou, Youjin Deng "Self-Similarity in the colored noise is expressed in terms of Ito Classification of Finite-Size Scaling integral. Then, two important lemmas Functions for Toroidal Boundary concerning with the variance of an Ito integral Conditions", Phys. Rev. E 77, 010101(R) and the covariance of two Ito integrals are (2008). shown. Based on the lemmas, we give the [2] Ming-Chang Huang, Jinn-Wen Wu, Yu-Pin general formulae for the variances and Luo, and Karen G. Petrosyan , "Intrinsic covariance of molecular concentrations for a Fluctuations in Gene Regulatory Networks

175 ‹‹- Research Activities of Individuals as Gaussian Colored Noise". Submitted to Phys. Rev. E. [3] C.C.Leary et. al., "Tuning degree distributions: Departing from scale-free networks", Physica A 382, 731 (2007) . [4] Yu-Pin Luo, "System-wide coordination for tunable scale-free networks ", preprint.

Research Activities of Individuals -›› 176 Research Activities on Quantum Information Processing

Kazutomu Shiokawa (Institute of Physics, Academia Sinica; email: [email protected]) Visiting Scientist, 2006/4/4~2008/3/31

uantum information science and approximation is not suitable for describing technology is one of the most active short time dynamics in a strong coupling fields of research in science[1]. It is also an regime. interdisciplinary field that overlaps with many Many works have been devoted to clarify different areas in theoretical and experimental the rigorous criteria for entanglement in sciences thus provides a good topic to be quantum information science. For continuous pursued at the institute like NCTS that has variables, the necessary and sufficient criteria interdisciplinary perspectives and resources. for entanglement can be given in terms of Implementing quantum information Peres-Horodecki criteria[2], negativity[3], and processing devices requires precise knowledge entanglement of formation[4]. Most of these of quantum open systems. The detailed study works are devoted to study the static properties of quantum open systems are often prevented of general pure and mixed states. In light of by a limitation of analytical or numerical information processing, it is also desirable to resources to probe systems with large degrees study the dynamical properties based on the of freedom. The first principle calculation of realistic models in an open system setting. open quantum systems yields reduced In this work, we study the precise dynamics that follows non-Markovian mechanism of open system entanglement evolution carrying the memory of dynamics based on a Brownian oscillator environment. Solving the equations of motion model[5][6][7], where both system and obtained by these method directly is generally environment consist of harmonic oscillators. difficult to deal with as they are given by Realization of quantum protocols based on integro-differential equations. continuous variables such as quantum Various approximation schemes have been teleportation[8] and quantum key used to simplify the exact evolution to study distribution[9] show that they also play the open system evolution. Most commonly used similar crucial role in quantum information approximation is Born approximation in which science. So far most of the studies of the system-bath interaction is treated continuous variables for open systems are perturbatively. However, naive Born based on the master equation under Born- approximation applied to quantum open Markov rotating wave approximation such as systems does not guarantee the positivity of Lindblad equations or the phenomenological the density matrix and is not suitable when model with high temperature Markovian bath. evaluating quantities sensitive to positivity Applications of these methods are limited to such as quantum entanglement. the high temperature regime or slow dynamics with Ohmic noise, while actual solid state In the commonly used Born-Markov implementation operates at low temperatures approximation, the bath correlation is ignored. manipulated with fast pulses and often suffers At sufficiently low temperature, however, the from 1/f noise. bath memory can persist for a long time and this approximation is expected to break down. Since our model is formally exactly Regardless of the temperature, the noise with solvable, it makes us possible to probe the long range correlation such as 1/f noise cannot precise dynamics of decoherence effects on be treated under this approximation. Further entanglement without conventional approximation such as rotating-wave approximations. Previous works for the study

177 ‹‹- Research Activities of Individuals of a two-level system revealed that non- Markovian dynamics that plays the major role References at low temperatures is highly nontrivial[10]. [1] M. A. Nielsen and I. L. Chuang, Quantum Below I showed the temporal evolutions of Computation and Quantum Information, two mode uncertainty —and entanglement ζ Cambridge University Press, Cambridge, measured by uncertainty after partial transpose 2000. operation λ—[11] of two modes damped oscillators with frequencies Ω and damping [2] A. Peres, Phys. Rev. Lett. 77, 1413 (1996); constant γ for different squeezing parameters r P. Horodecki, Phys. Lett. A 232, 333 . (1997); R. Simon, Phys. Rev. Lett. 63,2726 (2000). [3] G. Vidal and R. F. Werner, Phys. Rev. A65, 032314-1 (2002). [4] G. Giedke, M. M. Wolf, O. Kruger, R. F. Werner, and J. I. Cirac, Phys. Rev. Lett. 91, 107901-1 (2003). [5] A. O. Caldeira and A. J. Leggett, Physica A121, 587 (1983). [6] F. Haake and R. Reibold, Phys. Rev. A32, 2462 (1985). [7] H. Grabert, P.Schramn and G. L. Ingold, Phys. Rep. 168, 115 (1988). Figure 1: The temporal evolution of the uncertainty function ζ_ is plotted. The initial condition is a two [8] A. Furusawa, et. al, Science 282, 282 mode squeezed state with r = 0. Other (1998). parameters are γ = 0.01[GHz]. We take Ω = 1.0[GHz] for all the figures. [9] F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, Nature 421, 238 (2003). [10] K. Shiokawa and B. L. Hu, Quantum Information Processing, V. 6, 55 (2007). [11] K. Shiokawa, Jour. of Math. Chem. (2008); K. Shiokawa, submitted to Phys.Rev. A (2008).

Figure 2: The temporal evolution of the uncertainty function λ_ after partial transpose is plotted. The initial condition is a two mode squeezed state with r = 0.1 for the thick solid curve and a coherent state (r=0) for the thin solid curve. Other parameters are γ = 0.1[GHz], Ω = 1.0[GHz], T =0.

Research Activities of Individuals -›› 178 Research Activities on String

Yi Yang (Electrophysics Department, National Chiao Tung University; email: [email protected]) Assistant research scholar, 2007/8/1~2008/7/31

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

179 ‹‹- Research Activities of Individuals space dimension on a circle to break all University of British Columbia (UBC) in supersymmetries, and adding flavor D-branes, Vancouver, Canada. I would like to thank the boundary field theory is conjectured to NCTS to support me attending the dual to QCD. Of many AdS/QCD models, international activities. Sakai-Sugimoto model is the most promising one and has been studied extensively during the last several months. Some meson spectrum was calculated by AdS/QCD and the results have been compared to the experimental data References and to lattice QCD, a good agreement was [1] J.C. Lee, Y.Y., Power-law Behavior of obtained. In addition, spontaneously chiral High Energy String Scatterings in symmetry breaking has been constructed in the Compact Spaces, arXiv: 0709.4657. model and Goldstone boson is identified with [2] J.C. Lee, Y.Y., High-energy Massive pion, whose action is consistent with Skyrme String Scatterings from Orientifold Planes, model. The AdS/QCD at finite temperature has arXiv: 0712.4245. also been studied. Confinement- disconfinement, S/ SB phase transitions [3] J.C. Lee, T. Takimi and Y.Y., High-energy were studied; the results are consistent with the String Scatterings of Compactified Open ones obtained by lattice QCD. However, there String, arXiv: 0805.316. are still many questions remained in the model. [4] M. Huang, Q. Yan and Y.Y., Confront I have collaborated with the NCTS members in Holographic QCD with Regge phenomenology focus group and also with the Trajectories, arXiv: 0710.0988. faculty in Institute of High Energy Physics [5] M. Huang, Q. Yan, Y.Y., Toward a more (IHEP) in Beijing. We studied the AdS/QCD realistic holographic QCD model, arXiv: for different string backgrounds and the 0804.2731. corresponding QCD theories [4,5]. Hopefully we will refine our model to be more concrete and to make some predictions for the already running LHC. Moreover, during the last year, I have visited Kavli Institute of Theoretical Physics of China (KITPC) in Beijing. I joined their String Theory and Cosmology program. During the program, I gave a talk to present my research of ADS/QCD and had many useful discussion with the string people there. I also attend the Summer School "Particles,Fields and Strings" hold at the

Research Activities of Individuals -›› 180 Research Activities on Particle Physics Beyond the Standard Model

Tzu Chiang Yuan (Institute of Physics, Academia Sinca; email: [email protected]) Assistant research scholar, 2007/8/1~2008/7/31

y research activities during 2007 focus missing energy at hadron colliders; virtual mainly on physics beyond the effects of unparticle in Drell-Yan process and Standard Model, in particular in the new area muon anomalous magnetic moment. More of unparticle physics. The notion of unparticle details of these processes and the was invented in March 2007 by Georgi to generalization to spin 2 unparticle operator are describe an exact scale invariance hidden presented in the longer paper in Ref. [2]. sector stuck at an infrared fixed point located While I was visiting my old friend at a high scale. At low energy that can be Professor Chong Sheng Li at the beautiful probed by the Large Hadron Collider at campus of Peking University last fall, I came CERN, the unparticle sector manifest itself as up with the idea that one might be able to various interpolating fields of arbitrary scaling detect a vector unparticle from the rare process dimensions. These fields can couple to of Higgs decay into a single photon plus the Standard Model fields using the machinery of invisible unparticle. The thought was written effective field theories, as suggested by up in Ref. [3] where we showed that in certain Georgi. Because of the scale invariance and parameter space the branching ratio of this rare the non-integral value of the scaling process could be quite comparable to the dimension, the phase space of the unparticle discovery two photons mode for an has a continuous spectrum. This leads to intermediate mass Higgs. In Ref. [4], we peculiar signals of unparticle in the missing extended this idea to a similar process of Z energy and momentum distribution carries boson decay into a single photon plus an away by the unparticle, in contrast with other invisible unparticle. missing energy and momentum distribution carried away by the neutrinos or the lowest A TeV photon collider is one of the supersymmetric particle of the so-called possibilities for the International Linear minimal supersymmetric standard models. Collider (ILC). In Ref. [5], together with This feature is unique for real production of Kingman Cheung and his PhD student Chun- unparticle as was emphasized by Georgi s Fu Chang, we studied the virtual effects of first paper on unparticle. spin 0 and spin 2 unparticles using elastic photon photon scattering. We showed the In Ref. [1], together with Kingman Cheung effects of tree level unparticle exchange could and Wai-Yee Keung, we extended the notion of easily beat the standard model contributions the unparticle to off-shell propagation and that are in general suppressed by the one loop derive the propagators for the scalar and vector mechanism. unparticles using the symmetry of scale invariance. Georgi himself also did the same Physics beyond the standard model is fun thing in his second paper of unparticle. and last year has been a very productive year Incidentally, both our paper and Georgi s for the focus group. I plan to continue my second paper appeared the same day on the effort to make further contributions in this archive. In Ref. [1], besides deriving the direction in foreseeable future. More unparticle propagators, we also present 5 excitement is ahead of us when LHC is different possible signals of unparticle physics. expected to be on line later this year and real These includes Z boson decay and electron- data is unearthed. positron annihilation into single photon plus missing energy; monojet production plus

181 ‹‹- Research Activities of Individuals References: [1] Kingman Cheung, Wai-Yee Keung, and T. C. Yuan, Phys. Rev. Lett. 99:051803 (2007). [2] Kingman Cheung, Wai-Yee Keung, and T. C. Yuan, Phys. Rev. D76:055003 (2007). [3] Kingman Cheung, Chong Sheng Li, and T. C. Yuan, Phys. Rev. D77:097701 (2008). [4] Kingman Cheung, Thomas W. Kephart, Wai-Yee Keung, and T. C. Yuan, Phys. Lett. B662, 436 (2008). [5] Chun-Fu Chang, Kingman Cheung, and T. C. Yuan, Phys. Lett. B664, 291 (2008).

Research Activities of Individuals -›› 182 Introducing New Members

Dr. Chih-Hao Chen

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

started as a postdoctoral fellow in shown to give convincing results, they have November of 2007 after working as a been outgrown by the fast-developing postdoctoral fellow at National Central microarray technologies - in respect of University under the supervision of Professor resolution, essentially. With the resolution of Hoong-Chien Lee. today's microarrays, the demands for computation speed and computer memory are My research interests are in systems no longer realistic. The complexity of these biology. Specifically, I am developing a simple algorithms poses another problem as users mathematical principle for various need to tune the parameters either for using applications. This principle, dubbed pairwise different types of arrays or for investigating Gaussian peak merging (PGPM), is being different types of genomic aberrations. The applied to a segmentation algorithm for development of our algorithm is close to its processing microarray data. Somatic completion. The breakthrough lies in the alterations in cellular DNA underlie almost all simplicity of PGPM and the resultant human cancers. The prospect of targeted astounding computation speed. In terms of therapies and the development of high- accuracy and memory usage, our algorithm has resolution, genome-wide approaches are now been shown to lead the competition by wide spurring systematic efforts to characterize margins. Our algorithm has only two cancer genomes. Before microarray data can parameters which are relatively easier for the be analyzed, segmentation algorithms must be users to understand and tune for their own applied to smooth out the system or statistical purposes. For the future, we are planning to noise and to locate the breakpoints. Numerous apply PGPM to DNA-based biological algorithms have been developed for this taxonomy. purpose. Even though a few of them have been

183 ‹‹- Introducing New Members Dr. Hiroaki Kohyama

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

became a postdoctoral research fellow quark gluon plasma phase, where quarks in the physics division of NCTS after become free particle having enough energy to graduating from Osaka City University on escape from the confinement, and (III) color March, 2008. I have studied the theoretical super conducting phase, the state in which the aspects of finite temperature field theory under quarks near the Fermi surface become the supervision of Professor Akira Niegawa. correlated to form quark-quark (diquark) Cooper pairs. Nambu Jona-Lasinio model My current interest is in the phenomena of successfully describes above mentioned symmetry breaking. Especially, to investigate aspects of quark matters. I have confirmed that the properties of quark matters and the phase the similar phase structure is found in the case structure of QCD (Quantum Chromodynamics) of the lower dimensional Nambu Jona-Lasinio are hot issues now. Through my recent works, model (Gross-Neveu model). I believe it is I have focused on various states of quark interesting because the lower dimensional matters. I believe that the knowledge of quark model can be related to the real world in the states will lead us to deeper understanding of similar manner seen in the field of condensed the phenomena of symmetry breaking. matter physics. In my previous papers, I have studied the Thus I have studied the phenomena of competition between the quark-antiquark and symmetry breaking through investigating the diquark condensates in the 2+1 space time properties of quark matters. I am also dimensional Gross-Neveu model within the 2 interested in the following subjects: component and 4 component spinor representations. Gross-Neveu model is the -Higgs mechanism in Standard Model lower dimensional theory of the Nambu Jona- -strongly coupled gauge theory Lasinio model which is believed to be the low -LHC experiments and its phenomenology energy effective theory of QCD. We now believe that quark matters have mainly three I am sure that these subjects are extremely states: (I) hadron phase, where quarks are important to explain the phenomena of the confined into hadrons and never be free, (II) symmetry breaking.

Introducing New Members -›› 184 Dr. Jae Sik Lee

Assistant research scholar (Ph.D., Korea Advanced Institute of Science and Technology) email: [email protected], [email protected]

am starting as a new staff scientist in the LHC and the discovery will open a new era the Physics Division from the 1st July of Particle Physics, shedding lights on the 2008. The institutes and universities where I Grand Unified Theory and the composition of have accumulated my professional experiences the Universe. include: KAIST (Korea), KIAS (Korea), KEK My current research interests lie in (Japan), University of Manchester (UK), Seoul phenomenological aspects of SUSY, especially National University (Korea). Finally, I was a in the presence of CP violation. I have been visiting professor at National Central recognized as one of the leading University before I join NCTS. Now I am phenomenologists on the subject of Higgs- living in the Guest House II on campus with sector CP and Flavour violation in the my wife and sons. framework of the Minimal Supersymmetric Now we are entering the most important Standard Model (MSSM) and its manifestation stage of Particle Physics with the imminent at present and future high-energy colliders. In advent of the Large Hadron Collider (LHC) at parallel with the direct exploration at colliders, CERN. One of the main targets to be achieved precision experiments at low energies continue at the LHC is to hunt down the Higgs particle to place important constraints on the possible and unravel the mystery of the origin of mass. flavour and CP-violating structure of any TeV- Here a problem is that the very existence of the scale Physics. Prominent examples include Higgs boson introduces a severe difficulty in experiments on B and K mesons, and probes of Quantum Field Theory. The quantum electric dipole moments. Recently we are corrections to the Higgs-boson mass are working to develop a consistent and coherent naturally 15 orders of magnitude larger than framework for both low- and high-energy the Higgs-boson mass itself. This so-called experiments, including the state-of-the-art hierarchy problem can be solved by results. My research interests also go beyond introducing Supersymmetry (SUSY). New SUSY models and my expertise is broader additional SUSY particles protect the Higgs- than I can describe in this short self- boson mass from being destabilised against introduction. Many works need to be done and quantum corrections. Moreover, these new we welcome your active collaboration! SUSY particles would be brought to light at

185 ‹‹- Introducing New Members Dan Tomino

Assistant research scholar (Ph.D., Osaka University) email: [email protected], [email protected]

esearch interest: string theory, matrix those are obtained by a dimensional reduction model of Yang-Mills type large N gauge theory. My current research interest is space(time) picture Reformulation of superstring theory has which can emergent from matrix model and its been a long standing problem in recent years. dynamics. Recently, I discussed that the Well established formulation of string theory is Schrodinger equation of large N matrix a 1st quantized theory, namely a perturbative quantum mechanics can be regarded as a formulation around a specified spacetime, Wheeler-DeWitt equation which determine therefore this is not so powerful to study non- wave function of universe. I hope to develop perturbative aspects of the string theory. To this idea to investigate on quantum theory of overcome such a difficulty several matrix gravity by matrix models for string theory. model proposals for non-perturbative definition of string theory were proposed,

Dr. Chih-Wei Wang

Postdoctoral researcher (Ph.D., University of South California) email: [email protected]

am starting this spring 2008 as a new large entropy (horizon) and the other is the post doc in the physics division of famous information paradox. Therefore, my NCTS after finished my Ph.D. in University of particular research focus is on trying to South California under the supervision of my understand the black holes from advisor, Professor Nicholas Warner. superstring/supergravity point of view regarding these two puzzles. Recently, there Currently my interests are in the conflict are some progresses in that direction, namely between general relativity and quantum field fuzzball conjecture proposed by Mathur and theory. These two theories are the two pillars the concept of microstate geometries. If these of the modern theoretical physics. However, proposals are correct, they will solve the two there are some conflicts between them require puzzles and at the same time imply the a better understanding before we can formulate quantum gravity effect may have some impact quantum gravity. A particular good stage to see on the geometry at macroscopic scale. I these conflicts is a black hole. The existence of believe it is very important to verify these black holes in general relativity bring the proposals more and further, understand the following two puzzles: the first one is the macroscopic quantum gravity effects. conflict between black hole uniqueness and large number of microstates associated with it's

Introducing New Members -›› 186 A n u a l R e p o r t N a t i o n l C e r f

October 2008 Annual Report

o r October 2008 T h e o r

Annual Report National Center for Theoretical Sciences e t i c a l S n s

National Center for Theoretical Sciences

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