Annual Report
National Center for Theoretical Sciences
December 2009 Annual Report December 2009 Annual Report
National Center for Theoretical Sciences
National Center for Theoretical Sciences
No. 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013 Mathematics Division Physics Division Tel: 886-3-5728263/5745253~5 Tel: 886-3-5734969 Fax: 886-3-5728161 Fax: 886-3-5735086 e-mail: [email protected] e-mail: [email protected] http://www.math.cts.nthu.edu.twl http://phys.cts.nthu.edu.tw December 2009 I. Words from the Director ----- 1
II. Mathematics Division ------3 Report of the Division Head ------4 Executive Committee Members ------6 Academic Committee Members ------7 Highlights of the Focus Programs ------8 Highlights of the Regional Programs ------56 Activities of Onsite Scientists ------77 Preprints ------90 Appendix ------100 I. Visiting Mathematicians ------100 II. Conference, Workshop, School & Special Lecture ------120
III. Physics Division ------129
Report of the Division Head ------130 Highlights of Programs ------134 Focus Group & Working Group Complex Systems and Soft Matter ------134 Condensed Matter Physics ------142 Particles and Fields ------153 Interdisciplinary Fields ------171 Topic Program ------182 Initiative ------186 Research Activities of Individuals ------196 Introducing New Members ------225
Annual Report Publisher: Editors: National Center for Theoretical Sciences Wen-Ching Winnie L Mandy Chen(Mathematics Division) December 2009 Sherry Pang(Physics Division) Words from the Director
any changes took research in theoretical sciences in p l a c e t h i s y e a r. Taiwan have improved remarkably, Fiscally, it is the beginning international cooperation and of the third phase of NCTS, collaborations were established, a six year project, funded by and many young scientists were the National Science trained and some are shining stars Council. The overall today. We salute him for his organization of the center outstanding achievements and and the programs within each division remain the thank him for his enduring same as before, except for contributions to the NCTS. the addition to the main Beginning September 1, the PI project in mathematics of a of the Subproject I in Taipei is r e g i o n a l p r o g r a m i n Professor Wei-Shu Hou from the theoretical statistics this Physics Department of National July. The new program is off Taiwan University (NTU), with to a good start, and the continuing programs are progressing and Professor Chuin-Chuan Chen from the improving steadily with several stellar Mathematics Department of NTU serving as the achievements in mathematics and theoretical co-PI in mathematics. For the Subproject II in physics. We welcome National Central University Tainan, the lead PI is Professor Yung-Guei Fu (NCU), which joined National Tsing Hua from the Physics Department of National Cheng University (NTHU) and National Chiao Tung Kung University (NCKU); his colleague University (NCTU) as a hosting institution of the Professor Yan-Tien Lu is the co-PI in physics. main project headquartered in NTHU. The co-PI in mathematics was Professor King-Fai There have been leadership changes in all Lai from the Mathematics Department of NCKU locations. Professor Jing Yu completed his term as from Feb. 1 to July 31; after Professor Lai moved the Director of NCTS on June 1 and the Head of to National Sun Yet-Sen University (NSYSU) this the Mathematics Division on May 14; his summer, his post was resumed by his former successor, Professor Wen-Ching Winnie Li, is colleague Professor Soon-Yi Wu as of August 1. from the Pennsylvania State University. Professor The Head of the Physics Division has been Yu has played a pivotal role at NCTS since its Professor Chung-Yu Mou from the Physics inauguration, serving as an acting director twice Department of NTHU since 2007. In 2010, and the director since 2006 on top of being the Professor Ling-Fong Li of Carnegie Mellon head of the mathematics division from 1997 to University will succeed him. We express our 2009 except for a four-year interruption. Under hearty thanks to the former PI's and co-PI's for his leadership, NCTS expanded steadily with their seless devotion to the development of the more research programs, more space and more center and welcome the new comers to work sponsoring institutions, the quantity and quality of jointly for the future well-being of the center.
1 ‹‹- Words from the Director The climax of the numerous lectures/courses at To further international cooperation, the NCTS this year is the one week lecture series in Subproject II in Tainan signed an agreement with July given by Professor Jean-Pierre Serre of Hong Kong University of Science and Technology Collège de France. His 4 lectures on "Variation in April of 2009. This is a welcome addition to the with p of the number of solutions modulo p of a existing formal cooperation agreements with system of polynomial equations" left a long- IHES, lasting impressive memory to a huge crowd KIAS, APCTP, and KEK. We wish them many coming from all over the country and abroad. years of fruitful collaborations ahead. Another very important event was the one week visit in October to all locations of NCTS by four Looking forward, we anticipate a new year of French delegates, two mathematicians and two vigorous, high quality activities aimed to elevate theoretical physicists, whose primary purpose was research quality, nurture young scientists, promote to seek further cooperation between Taiwan and international cooperation and collaborations, and France. The highlight of their visit was the develop new international and interdisciplinary bilateral cross-disciplinary "Taiwan-France programs. workshop on theoretical sciences" held at the headquarter of NCTS. This was the first joint scientific conference between the two divisions. Their initiative has led to planned cooperative Wen-Ching Winnie Li (李文卿) activities to be carried out next year. November 2009
Words from the Director -›› 2 Mathematics Division Report of the Division Head
his year marks the beginning of the third from NCU, seven from NCTU, five from NTHU, phase of NCTS, a six year project, funded one from NSYSU, and one from NCTS. Their by the National Science Council. Since its specialties are diverse: two in algebraic geometry, inauguration, the headquarter of NCTS has been three in analysis, five in dynamical systems, one housed in the National Tsing Hua University in geometry and mathematical physics, four in (NTHU). Starting this year, National Central number theory, one in partial differential University joined NTHU and National Chiao equations, one in probability, one in topology, and Tung University (NCTU) as one of the hosting one in scientific computation. institutions of the main project. The new regional program on theoretical statistics added to the main The new recipient of the Young Theorists project this July is off to a good start. Award of NCTS this year is Professor Nan-Kuo Professor Jing Yu completed his term as the Ho of NTHU. Professor Ho received her Ph.D. Head of the Mathematics Division on May 14, from University of Toronto. Her research area is 2009. His successor, Professor Wen-Ching Winnie symplectic geometry and mathematical physics. Li, is from the Penn State University. We are The continuing recipients are Professor Kuo- indebted to Professor Yu for his devotion and Chang Chen (NTHU) in dynamical systems, invaluable services to NCTS for so many years. Guan-Yu Chen (NCTU) in probability theory, We thank him for his leadership and enduring Cheng-Hsiung Hsu (NCU) in dynamical systems, contributions. Ming-Yee Lee (NCTU) in dynamical systems, and Jyh-Haur Teh (NTHU) in algebraic geometry and There are also leadership changes in the two topology. These recipients were selected from all Subprojects. The co-PI in mathematics of the applicants by the Executive Committee based on Subproject I in Taipei is Professor Chuin-Chuan the evaluations by international experts. Chen from the Mathematics Department of National Taiwan University (NTU). For the On the research front, this is a fruitful and Subproject II in Tainan, the co-PI in mathematics productive year. Compared to previous years, the was Professor King-Fai Lai from the Mathematics number of publications is increasing steadily, and Department of NCKU from Feb. 1 to July 31; the overall qualityis improving. There are after Professor Lai moved to National Sun Yet- outstanding results published in leading Sen University (NSYSU) this summer, his post international journals. We mention a few was resumed by his former colleague Professor highlights below. Soon-Yi Wu as of August 1. We deeply appreciate (a) In the area of arithmetic over function fields, the efforts made by the former co-PI's, and look great progresses have been made in recent forward to working together with the new comers years. In particular, in transcendence theory of for the well-being of the center. positive characteristic, all algebraic relations among special zeta values and gamma values In this year nineteen mathematicians either are determined. In fact, the motivic have completed or are currently holding the transcendence program in positive positions of center scientists: one from NTU, four characteristic is now fully realized.
Report of the Division Head -›› 4 (b) The zeta function identities for 2-dimensional exception. Professor Jing Yu organized visiting complexes were obtained. This breakthrough, groups to take young number theorists to visit made under the roof of NCTS, is the first since Leiden University in Netherlands, ETH in the 1-dimensional result was proved 40 years Switzerland, Waseda University in Japan, Tsing ago. Hua University in Beijing, and Nankai Institute of (c) In the area of N-body problem and asteroid Mathematics in Tienjing. In all institutions, the motions, a new milestone was established. group members gave talks. Professor Wen-Ching After successfully proving the existence of W. Li invited young mathematicians, including retrograde orbits for the three-body problem, Ph.D. students, to speak in the conference and explicit calculations for the restricted three- workshop she co-organized in Seoul and Pohang, and four-body problems, and the case of Korea. The progress of our young generations is elliptical asteroid were given. remarkable. Several graduate students have started (d) A big advance was made in the study of publishing their first papers. More and more mixing times in the theory of Markov chains. young researchers are active in international 2 The theory on the existence of L -cutoffs was arena. Several publish in top journals and become 2 established and the formula of L -mixing time major players in their respective field. This bodes was obtained and explicitly computed for well for the future of mathematics in Taiwan. practical examples. In the area of international cooperation, during (e) As a continuation of recent successes, several the year many bilateral conferences and breakthroughs in birational geometry, quantum cohomology and higher genus Gromov-Witten workshops were held, both in Taiwan and abroad, invariants were made this year. in which domestic speakers were showcased. Two of them, "Valuation distribution theory and The climax of the numerous lectures/courses at complex geometry" and "Taiwan-Norway joint NCTS this year is the one week lecture series in workshop on geometric analysis and mathematical July given by Professor Jean-Pierre Serre of physics" were also supported by NCTS and Collège de France. His 4 lectures on "Variation foreign sources. We encourage this kind of with p of the number of solutions modulo p of a international cooperation where foreign system of polynomial equations" left a long- participation is on a more equal footing. lasting impressive memory to a huge crowd. An intensive 25 hour course on the background In conclusion, we are proud of the materials was offered prior to Serre's arrival so achievements in 2009. With our joint efforts, 2010 that students could benefit most from his lectures. will be splendid as well. The notes of these lectures, initially taken by students, will be posted online. NCTS has a long tradition to strongly support Wen-Ching Winnie Li (李文卿) and nurture young mathematicians. This year is no November 2009
5 ‹‹- Report of the Division Head Executive Committee Members
Committees Affiliation
Chiun-Chuan Chen National Taiwan University
Meng-Kiat Chuah National Tsing Hua University
Wen-Ching Winnie Li National Center for Theoretical Sciences
Chin-Cheng Lin National Central University
Wen-Wei Lin National Chiao Tung University
Chin-Lung Wang National Taiwan University
Soon-Yi Wu National Cheng Kung University
Executive Committee Members -›› 6 Academic Committee Members
Committees Affiliation
Gerard J. Chang National Taiwan University
Shun-Cheng Chang National Taiwan University
Jung-Kai Chen National Taiwan University
Kuo-Chang Chen National Tsing-Hua University
Shun-Jen Cheng Academia Sinica
Liang-Chung Hsia National Central University
Sze-Bi Hsu National Tsing-Hua University
King-Fai Lai National Sun Yat-sen University
Wen-Wei Lin National Chiao Tung University
Tai-Chia Lin National Taiwan University
Yuah-Chung Sheu National Chiao Tung University
Chih-Wen Shih National Chiao Tung University
Dong-Ho Tsai National Tsing Hua University
Julie Tzu-Yueh Wang Academia Sinica
7 ‹‹- Academic Committee Members Highlights of the Focus Programs
D.1 Algebraic Geometry
Coordinators: Jungkai Chen (National Taiwan University) and Chin-Lung Wang (National Taiwan University)
he group of algebraic geometry obtained algebraic geometry under the framework of various important results in Gromov- International Conference of Mathematics Witten theory and higher dimensional minimal supported by NCTS and TIMS. The session was model program in recent years. Our program in organized by Chin-Lung Wang and Jung-kai the year of 2009 is circling around these two Chen. Invited speakers are chosen among world major topics. leading algebraic geometers with long-term We have weekly seminar and student seminar relationship with local people. The list of invited supported by NCTS that our local people and speakers includes: O. Fujino (Kyoto), M. Paun visitors contributes and denefits from them. We (Nancy, France), J. Wlodarczyk (Purdue Univ.), Y. also have a conference on algebraic geometry in Hu (Univ. Arizona), M. Liu (Columbia Univ.), J. July of 2009. C. Chen (NTHU/NCTS). Our ongoning student training program began to harvest not because some of our students 2-2 Seminars graduated and is going to graduate, but also they The regular joint seminar with TIMS was received certain recognition from many aspects. organized by Jungkai Chen and Chin-Lung Wang. One of the main focus of the seminar was on 1-1 Local Algebraic Geometry Group recent breakthrough in higher dimensional Jiun-Cheng Chen (NTHU), Jungkai Chen minimal model program by Birkar, Cascini, (NTU), Nan-Kuo Ho (NTHU), Hui-Wen Lin Hacon and McKernan. The other main focus was (NTU), Chin-Lung Wang (NTU), Eugene Xia on the Gromov-Witten theory around the joint (NCKU) , Jeng-Daw Yu (NTU). project of Yuan-Pin Lee, Hui-Wen Lin and Chin- Lung Wang. 1-2 Visitors There is also a regular student seminar Y.P. Lee (Utah), F. Campana (Nancy), V. organized by Jungkai Chen. The participants Maillot (Paris VI), Chen-Yu Chi , (Harvard) , S. consists of NCTS research assistants and students Hosono (Tokyo), O. Fujino (Kyoto), M. Paun from NTU, NCU. The main topics are on moduli (Nancy, France), J. Wlodarczyk (Purdue Univ.), Y. spaces and Hodge theory. Hu (Univ. Arizona), M. Liu (Columbia Univ.) 2-3 Summer Course 2-1. Conference In the summer of 2009, we held a summer In the July of 2009, we held an session in course: Elliptic curves-algebraic, arithmetic and
Highlights of the Focus Programs -›› 8 analytic aspects. This is a course organized by which the factorization is realized by the Jungkai Chen (NTU) with instructors includes canonical Albanese map. They proved that the Jungkai Chen (NTU), Chia-Fu Yu (Acedemia fiber of Albanese map has Kodaira dimension Sinica) and Yi-Fan Yang (NCTU/NCTS). These bounded by irregularity. They also show that 1 six weeks program provide a global view of the the relative Iitaka fibration is roduct of P theory of elliptic curves from three different bundle over an abelain variety, which is very close to being the product of well-known one aspects. dimensional situation. 3. Accomplishments (5). JiunCheng Chen and H.H. Tseng use the techniques developed in the Cone theorem (1) The long project of Chin-Lung Wang jointly paper to characterize projective space with with Yuan-Pin Lee (U. Utah) and Hui-Wen Lin mild singularities. The main breakthrough is (NTU) is continued and significant progress is to show that we can find rational curves made. through any point (with low anti-canonical The analytic continuation of quantum degree) when the pseudo-index is large. This cohomology under a general ordinary flop over property help us to show that this kind of a smooth base had received fundamental spaces have to be projective spaces. We also progress during the summer visit of Lee to prove a stronger result in dimension 3 using NCTS, Hsinchu in 2008. Investigation on the MMP. By using a double cover method to higher genus GW invariants was further avoid the assumption on isolatedness in the previous paper, the result can be further pursued through an attempt to understand and generalized. extend the fundamental works by BCOV (Bershdsky-Cecotti-Oguri-Vafa). 4. Publications (year 2008, 2009 and (2) Investigation of MMP from the analytic side preprints) was started in early 2009 following a course, delivered by Wang at NTU in the fall of 2008, [1] B. Fu and C.L. Wang, Motivic and quantum on Siu’s theory in complex geometry with invariance under stratified Mukai flops, J. focus on the general case of invariance of Differential Geometry 80 (2008), no.2, 261- pluri-genera. With his student Sz-sheng Wang, 280 C.-L. Wang wrote a paper on extension of [2] Y. Iwao, Y.P. Lee, H.W. Lin and C.L. Wang, pluri-canonical forms from the viewpoint of Invariance of Gromov-Witten theory under developing a multiple version of the Ohsawa- simple flops, preprint 2008, 29 pages Takegoshi extension theorem [3] F. Campana, J. A. Chen, T. Peternell, On (3) Jungkai Chen and Mang Chen investigate strictly nef divisors, Math. Ann., 342, (2008), some further results on the theory of baskets in 565-585. dimension three. They find various application [4] J. A. Chen, M. Chen, An optimal boundedness to finiteness and effective program in on weak $\bQ$-Fano threefolds, Adv. Math., birational geometry. Notable results includes 219, (2008), 2086-2104. effective generation of pluricanonical map for [5] J.A. Chen, M. Chen, The canonical volume of threefolds of general type, sharp lower bound threefolds of general type with X<1, J. of anticanonical volume for weak Q-Fano London Math. Soc., 78, (2008), 693-706. threefolds, finiteness of weighted complete [6] J.C. Chen and H. H. Tseng, A note on derived intersections in. McKay correspondence, Mathematical (4) Jungkai Chen and Christopher Hacon made a Research Letters, Volume 15 (2008), Issue 3, progress on Ueno’s conjecture K. The 435-445 conjecture predicts that varieties of Kodaira [7] J. C. Chen and H. H. Tseng, Cone Theorem dimension zero consist of products of Calabi- via Deligne-Mumford stacks, Mathematische Yau varieties and abelain varieties after Annalen, Volume 345 (2009), no. 3, 525-545 suitable etale covering and birational maps, in [8] J. A. Chen, C. D. Hacon, On the geography of
9 ‹‹- Highlights of the Focus Programs threefolds of general type, J. Alg., 321, Invariance of quantum rings under ordinary (2009), 2500-2507. flops, preprint 2009. [9] J. A. Chen, C. D. Hacon, On Ueno’s [14] C.-L. Wang and S.-S. Wang, Extensions of Conjecture K, Math. Ann., 345, (2009), 287- multiply twisted pluri-canonical forms, 296 preprint 2009. [10] Y. Iwao, Y.-P. Lee, H.-W. Lin and C.-L. [15] J. J. Chen, J. A. Chen, M. Chen, On weighted Wang, Invariance of Gromov-Witten theory complete intersections. J. Alg. Geom, to under simple flops, 29 pages, submitted. appear [11] C.-L. Wang, Quantum invariance under flop [16] J. A. Chen, M. Chen, Explicit birational transitions, in “Proceeding of Geometric geometry of threefolds of general type, I, Analysis: Present and Future, a conference in Ann. Sci. École Norm. Sup to appear honor of Professor Shing-Tung Yau’s 60th [17] D. Arcara and Y.P. Lee, Tautological birthday (Harvard University, Cambridge equations in genus 2 via invariance 2008)”, International Press 2009. conjectures, math.AG/0502488 [12] H.-W. Lin, Quantum invariance under P1 [18] D. Arcara and Y.P. Lee, Tautological flops of type (k + 2, k), in “Proceeding of equations in \Mbar_{3,1} via invariance 2008 East-Asia Conference in Algebraic conjectures, math.AG/0503184, to appear in Geometry” at Korea Institute of Advanced Canadian J. Math Study [19] J. C. Chen, On Fano varieties with large [13] Y.-P. Lee, H.-W. Lin and C.-L. Wang, pseudo-index, to appear in ASPM.
D. 2 Discrete Mathematics
Coordinators: Gerard Jennhwa Chang (National Taiwan University) and Xuding Zhu (National Sun Yat Sen University)
iscrete mathematics is an active research reading or the results they just get or the area in Taiwan. In the program of discrete difficulties they meet. We make the talks as mathematics supported by NCTS, we organize informal as possible, and allow any interruptions various kinds of activities to broaden the spectrum and discussions during the talks. The topics of research in Taiwan, to promote international discussed include: competition numbers, equitable collaborations, and to provide training and colorings, ranks and minimal ranks of graphs, opportunities for young scholars and students. The additive combinatorics, Roman domination, etc. activities we have organized and related results are as follows. The seminar in Kaohsiung is organized by Xuding Zhu. There is a seminar talk every D.2.1 Regular weekly seminar Thursday. Some of the talks are given by students The seminar in Taipei is organized by Gerard and some given by visitors and faculty members. Jennhwa Chang. The seminar is on Tuesday In these seminars, we may focus on one problem afternoon fro three hours. Each afternoon, two in a series of talks, to introduce an area of research faculty or visitors or students talk about there in detail. The topics covered last year include: list research, which may be the papers they are coloring of graphs, total weight choosability of
Highlights of the Focus Programs -›› 10 graphs, non-repetitive coloring of graphs, graph is the Distinguished Lecture Series. Fifteen homomorphisms, graph labelings, etc. lectures are scheduled in various topics in mathematics. Among them, Ronald L. Graham D.2.2 Workshops and Conferences talked on “The combinatorics of solving linear In January, we organized the 2009 Workshop equations”. In the second week, we have the on Graph Theory, National Sun Yet-sen International Conference of Mathematics, which University, January 10-14, 2009. It attracted about includes 9 sub-sessions. In the part of Discrete 120 participants. This conference has four plenary Mathematics, we have three speakers: Fun Chung. speakers: Pavol Hell (Simon Fraser University, Graham (UC, San Diego), Ko-Wei Lih (Academia Canada), Douglas B. West (University of Illinois Sinica) and Xuding Zhu (National Sun Yet-sen Urbana-Champaign, USA), Hal A. Kierstead University) (Arizona State University, USA) and Claude In November, we have the India-Taiwan Tardif (Royal Military College, Canada), and 18 Conference on Discrete Mathematics, National invited speakers. Participants come from Czech Taiwan University, November 9-12, 2009. This is Republic, Poland, France, Korea, United States, the first joint conference in Discrete Mathematics Slovenia, India, Canada, Japan and Taiwan. Many between India and Taiwan. The aim of this participants said they benefit from the conference. conference is to provide a platform for researchers Some students got inspiration from talks in the in discrete mathematics in India and Taiwan to conference, got in contact with scholars and speed share results, problems and ideas. To provide an up their research. opportunity for mathematicians from both sides to Besides this large conference, we also have better understanding of each other’s organized two mini-workshops in the south, research, and hopefully to initiate collaborations specializing in one topic each time. One is on among them. The speakers are all invited, 15 from graph homomorphisms, and the other on Thue India and 15 from Taiwan each give a 40-minute coloring of graphs. Each of the mini-workshops presentation. A 144-page extended abstract attracts about 15 participants. Because we volume is prepared. CV’s are collected from all concentrate on a single topic, participants can get speakers so that we can circulate them between more detailed information on the topic, on current the speakers for them to understand each others status of the research and on open problems. Some more. This conference was fist proposed during research works initiated in these mini-workshops the International Conference on Discrete are still going on. Mathematics, University of Mysore, India, June 6-10, 2008. Xuding Zhu, Ko-Wei Lih and Gerard We also organized two one-day conferences in Chang were invited to give talks at that the south: Xi-Wan Combinatorial Workshop conference. We had a chance to discuss with R. Series 2009 (2009.5.1 and 2009.5.8). This series Balakrishnan for the cooperation between India of conferences is to provide a platform for young and Taiwan. A first-contact conference was researchers to lecture on their research, exchange proposed that time. This had been finalized during ideas, problems, and to promote collaborations the January workshop mentioned above. After this among themselves and others. Each of the two four-day conference, four teams are form for one-day conferences has five or six speakers. further cooperation: Some of the young Ph.D. graduates found jobs at colleges where teaching load is higher and less • Graph Coloring (Bharathidasan University, stress is put on research. The platform provides India, National Sun Yat-sen University, Taiwan some stimulation for them to continue their and National Taiwan University, Taiwan); research career. • Domination in Graphs (Kalasalingam From June 29 to July 18, we have the activities University, India and National Taiwan University, Taiwan); of NTU Mathematics Month 2009. The first week
11 ‹‹- Highlights of the Focus Programs • Graph Classes (Cochin University of Science also a few joint papers are in preparation. and Technology, India and Tunghai University, Taiwan); D.2.4 Research results • Decomposition of Graphs (Annamalai In Taipei, we have finished some interesting University, India and Tunghai University, results on Roman domination, equitable coloring, Taiwan). and minimum ranks of graphs, etc. Many of them are new and exciting. Below are some of them D.2.3 Hosting aboard visitors that are in submitted papers. In this year, the following visitors are hosted using the supports from NCTS South and Taipei, [187] Roman domination on strongly chordal as well as support from Academy Sinica and graphs. National Sun Yat-sen University: Given integers b≧a > 0, an (a,b)-Roman Ronald Graham (University California, San dominating function of a graph G = (V, E) is a Diego, USA), Fan Chung Graham (University function f from V to{0, a, b} such that every California, San Diego, USA), Krishnaiyan vertex v with f(v) = 0 has a neighbor u with Thulasiraman (University of Oklahoma, USA), S. f(u) = b. An independent (a,b)-Roman dominating Arumugam (Kalasalingam University, India), A. function is an (a,b)-Roman dominating function f Muthusamy (Periyar University, India), T. such that {v: f(v) ≠ 0} is independent. For a Karthick (Indian Institute of Technology Madras, weight function w on V, the weight of f is w(f) the India), T. Tamizh Chelvam (Manonmaniam sum of w(v)f(v), where v runs over all vertices in Sundaranar University, India), Manoj Changat the graph G. The weighted (a,b)-Roman (University of Kerala), Partha Pratim Goswami domination numberγ^{(a,b)}_R (G,w) is the (University of Calcutta, India), Ramesh minimum weight of an (a,b)-Roman dominating Krishnamurti (Simon Fraser University, Canada), function of G. Similarly, we can define the Sandeep Sen (Indian Institute of Technology, Delhi, India), Subir Kumar Ghosh (Tata Institute weighted independent (a,b)-Roman domination of Fundamental Research, India), R. Balakrishnan number γ^{(a,b)}_{Ri} (G,w). We give linear-time (Bharathidasan University, India), A. Vijayakumar algorithms for findingγ^{(a,b)}_R (G,w) and (Cochin University of Science and Technology, γ^{(a,b)}_{Ri} (G,w) of a strongly chordal graph India), P. Paulraja (Annamalai University, India), G.. NP-completeness results are also obtained. R. Sampath Kumar (Annamalai University, India), S. Francis Raj (Bharathidasan University, India), [190] Roman domination on graphs. Andre Raspaud (Bordeaux University I, France), A Roman dominating function of a graph G is a Arnaud Pecher (Bordeaux University I, France), function f from V(G) to {0, 1, 2} such that Mickael Montassier (Bordeaux University I, whenever f(v) = 0, there exists a vertex u adjacent France), Pavol Hell (Simon Fraser University, to v such that f(u) = 2. The weight of f is w(f) is the Canada), Claude Tardif (Mount Royal College, sum of f(v), where v runs over all vertices in the Canada), Douglas West (University of Illinois at graph. The Roman domination number γ_R(G) of Urbana-Champaign, USA), Hal Kierstead G is the minimum weight of a Roman dominating (Arizona State University, USA), Yared Nigussie (East Tennessee State University, USA), Jaroslaw function of G. Chambers, Kinnersley, Prince and ≦ Grytczuk (Jagiellonian University, Poland), Jakub West conjectured that γ_R(G) (2n+2)/3 for any Przybylo (AGH University of Science and 2-connected graph G of n vertices. We give Technology, Poland), Jarik Nesetril (Charles counter-examples to the conjecture, and proves University, Czech). that γ_R(G) ≦ max{(2n+2)/3, 23n/34} for any During their visit, each of them have given 2-connected graph G of n vertices. We also some lectures on their research, and had characterize 2-connected graphs G for which γ_ discussions with local faculty members and R(G) = 23n/34 when 23n/34 > (2n+2)/3. students. Some collaborations are initiated, and
Highlights of the Focus Programs -›› 12 [193] Equitable colorings of Cartesian products optimal matrix if, for all fields F, the rank of A of graphs. over F is the minimum rank of the graph of A over A graph G is equitably k-colorable if there is a F. Recently, Dealba et al. [L. M. Dealba, J. Grout, mapping f from V(G) to{1, 2, …, k} such that L. Hogben, R. Mikkelson, K. Rasmussen, f(x)≠f(y) whenever xyεE(G) a n d Universally optimal matrices and field ||f^{-1}(i)| - |f^{-1}(j)|| ≦1 for 1≦ i, j≦k. The independence of the minimum rank of a graph, equitable chromatic number of a graph G, denoted Electron. J. of Linear Algebra, 18 (2009) 403-419] by χ_=(G), is the minimum k such that G is initiated the study of universally optimal matrices equitably k-colorable. The equitable chromatic and established field independence or dependence threshold of a graph G, denoted by χ_=^*(G), is of minimum rank for some families of graphs. We the minimum t such that G is equitably now give more interesting results on universally k-colorable for k≧t. The current paper studies optimal matrices and field independence or equitable chromatic numbers of Cartesian dependence of the minimum rank of a graph are products of graphs. In particular, we give exact presented, and some results of Dealba et al. are values or upper bounds of χ_=(G □ H) and improved. □ χ_=^*(G H) when G and H are paths, stars, In the south, the research group concerns cycles, complete or complete bipartite graphs. several aspects of graph theory. One important area is graph coloring and graph labeling. In this [198] Equitable colorings of Kronecker products area, we have obtained the following results: of graphs. (1) Thue choice number of paths is proved to be For a positive integer k, a graph G is equitably at most 4. Thue Theorem is a classical result k-colorable if there is a mapping f from V(G) to which is viewed as the starting point of Formal {1, 2, …, k} such that f(x)≠f(y) whenever xyεE(G) Language Theory or Automata Theory - these ≦ ≦ ≦ and ||f^{-1}(i)| - |f^{-1}(j)|| 1 for1 i < j k. are fundaments of Computer Science. Thue The equitable chromatic number of a graph G, theorem is easy to state and understand: there ⋯ denoted by χ_=(G), is the minimum k such that G is an infinite sequence s 1s 2s 3 in three is equitably k-colorable. The equitable chromatic symbols, say 0,1,2, (i.e., si ∈{0,1,2}) such that threshold of a graph G, denoted by χ_=^*(G), is any two adjacent blocks are distinct, i.e., for ⋯ ⋯ the minimum t such that G is equitably any i and n, sisi+1 sisi+n-1 ≠ si+nsi+n+1 si+2n-1. The k-colorable for k≧t. The current paper studies Thue choice number of paths asks the equitable chromatic numbers of Kronecker following question: What is the smallest products of graphs. In particular, we give exact integer k for which the following holds: If each Li is a set of k symbols (for distinct indices, the values or upper bounds on χ_=(G × H) and sets of symbols maybe distinct), then there is χ_=^*(G × H) when G and H are complete ⋯ an infinite sequence s1s2s3 such that any two graphs, bipartite graphs, paths or cycles. adjacent blocks are distinct and for each i,
si ∈ Li . It was known before our work that [205] Universally optimal matrices and field 3≤k≤16. Our result is that 3≤k≤4. This is a independence of the minimum rank of a joint work of X.Zhu with J.Grytczuk and graph. Przybylo. The two Polish mathematician For a simple graph G on n vertices, the visited NSYSU, under the support of NCTS. minimum rank of G over a field F, written as We initiated our collaboration on this subject mr^F(G), is defined to be the smallest possible during their visit, and finished the work later. rank among all n × n symmetric matrices over F (2) Adaptable coloring and adaptable list whose (i,j)th entry (for i≠j) is nonzero whenever coloring of graphs. We started the study of {i,j} is an edge in G and is zero otherwise. A adaptable coloring and adaptable list coloring symmetric integer matrix A such that every off- of graphs a few years ago, and we have diagonal entry is 0, 1, or -1 is called a universally continuing the study in the past year. In
13 ‹‹- Highlights of the Focus Programs particular, we have studied the adaptable So the question is more difficult, yet the result chromatic number of the product of graphs. It is stronger. The original proof uses is a collaboration between local reseachers and probabilistic method. The new proof uses a Prof. Pavol Hell. It is proved that the 4th simpler technique, and the proof is categorical power of a complete graph has its deterministic. This is a new area of research. chromatic number equals its adaptable (5) Circular coloring of graphs. Circular chromatic number, and the categorical square coloring of graphs has been one of the main of complete graphs on prime number of research interests of the group for a long time. vertices have their chromatic number equal The team is considered as the leading team in their adaptable chromatic number. We have this area. Recent years, some very good results been working on this topic for a few years. in this area are obtained by young researchers Besides Pavol Hell, we also collaborated with from Europe. Our group is still playing an quite a few visitors supported either by NCTS important role in the study of circular coloring or some other resources. Altogether we have of graphs. In the past few years, we have written 6 papers on this subject. studied list circular coloring of graphs, and (3) Total weight choosability of graphs. The successfully applied Combinatorial total weight choosability of graphs is a concept Nullstellensatz to the study of circular list we introduced and studied before. It is a coloring of graphs. This year, we have studied concept that builds a link between the well- circular chromatic index of graphs. Extended a studied choosability of graphs and edge solution of some European researchers on the weighting of graphs. We proposed a existence of subcubic graphs with given challenging conjecture, and verified some circular chromatic index to graphs of large cases of the conjecture. Last year, we made maximum degree. We are still pushing in the further progress on the subject. In particular, research, and a paper on this subject is under we characterized (1,2)-total-weight choosable preparation. trees. The paper is still under revision. We (6) Orientation of graphs. We study the initiated the study of this subject last year. The dependent arcs in the acyclic orientations of results obtained so far has attracted much graphs. D. B. West studied the number of attention. Professor Douglas West put one of dependent arcs in the acyclic orientations of our result in his textbook on combinatorics. complete bipartite graphs and show the set of Using the proof to demonstrate the application the numbers of dependent arcs among all of Combinatotial Nullstellensatz. Xuding Zhu acyclic orientations of any complete bipartite was invited to give a plenary talk on the graph is consecutive. He define that a graph is subject at EuroComb in Spetember 2009 (the fully orientable if the set of the numbers of largest European conference in the area of dependent arcs among all acyclic orientations discrete mathematics). of the graph is consecutive. And he asked (4) On line list coloring of graphs. It is proved whether there is a nonfully orientable graph or that a graph of chromatic number k and with n not. We find some classes of nonfully vertices has on-line choosability at most k ln orientable graphs and some classes of fully (n). This result improves the previous known orientable graphs. result in two aspects. Firstly, the previous known upper bound on the choosability of D.2.5 Publications such graphs is 948 k ln (n), which was proved by Alon. So the constant is reduced from 948 Subproject I to 1. Secondly, the list coloring we give here is [201] Y. Zhao and G. J. Chang, “Weighted on-line list coloring. Assume Vi is the set of competition numbers of some graphs,” Ars vertices for which color i is a permissible Combin. (accepted). ⋯ color. The sets V1,V2, , are given on-line. [189] G. J. Chang, J. Wu and X. Zhu, “Rainbow When Vi is given, one needs to decide which domination on trees,” Disc. Appl. Math. vertices to be colored by color i immediately. (accepted).
Highlights of the Focus Programs -›› 14 [170] C.-C. Lin, G. J. Chang and G.-H. Chen, outerplanar graphs and trees, Discrete “The degree-preserving spanning tree Mathematics, 309 (2009), 3185-3196. problem in strongly chordal and directed [2] X. Zhu, Bipartite subgraphs of triangle-free path graphs,” Networks (accepted). subcubic graphs, Journal of Combinatorial [179] Y. Zhao and G. J. Chang (2009), “Note on Theory Series B, 99 (2009), 62-83. the m-step competition numbers of paths [3] M. Montassier, A. Raspaud and X. Zhu, An and cycles,” Disc Appl. Math. 157, 1953- upper bound on adaptable choosability of 1958. graphs, Eurpean Journal of Combinatorics, [177] B.-J. Li and G. J. Chang (2009), “The 30 (2009), 351-355. competition number of a graph with exactly [4] A. Guan abd X. Zhu, Adaptable choosability h holes, all of which are independent,” Disc. of planar graphs with sparse short cycles, Appl. Math. 157, 1337-1341. Discrete Mathematics, 309 (2009), 6044- [158] L.-H. Huang and G. J. Chang (2009), 6047. “L(h,k)-labelings of Hamming graphs,” [5] W. Lin, D. Liu and X. Zhu, Multi-colouring of Disc. Math. 309, 2197-2201. Mycielski graphs, Journal of Graph Theory, [153] G. J. Chang, C.-Y. Lin and L.-D. Tong to appear. (2009), “Independent arcs of acyclic [6] W. Lin and X. Zhu, Game circular colouring orientations of complete r-partite graphs,” of graphs, Discrete Mathematics, to appear. Disc. Math 309, 4280-4286. [7] P. Hell, Z. Pan, T.-L. Wong and X. Zhu, [149] G. J. Chang (2009), “A note on equitable Adaptabel colouring of graph products, colorings of forests,” Europ. J. Combin. 30, Discrete Mathematics, 309 (2009), 6153- 809-812. 6159. [141] G. J. Chang, C. Lu and S. Zhou (2009), [8] L. Esperet and X. Zhu, Game colouring of the “Distance-two labellings of Hamming square of graphs, Discrete Mathematics, to graphs,” Disc. Appl. Math. 157, 1896-1904. appear. [196] R.-Y. Wu, G.-H. Chen, J.-S. Fu and G. J. [9] L. Esperet, M. Montassier and X. Zhu, Chang (2008), “Finding cycles in Adaptable list colouring of planar Graphs, hierarchical hypercube networks,” Inform. J. Graph Theory, to appear. Process. Letters 109, 112-115. [10] Xuding Zhu, Bipartite density of triangle free [186] G. J. Chang, L.-H. Huang and H.-G. Yeh subcubic graphs, D i s c re t e A p p l i e d (2008), “On the rank of a cograph,” Linear Mathematics, to appear. Algebra Appl. 429, 601-605. [11] Tsai-Lien Wong and Xuding Zhu, [173] H. Lai, G. J. Chang and K.-W. Lih (2008), Distinguishing number of group actions, “On fully orientability of 2-degenerate Discrete Mathematics, 309(2009), 1760- graphs,” Inform. Process. Letters 105, 177- 1765. 181. [12] Xuding Zhu, Colouring graphs with bounded [171] G. J. Chang (2008), “The upper bound on generalized colouring number, Discrete k-tuple domination numbers of graphs,” Mathematics, 309 (2009), 5562-5568. Europ. J. Combin. 29, 1333-1336. [13] G. J. Chang, C.-Y. Lin, and L.-D. Tong, The [151] B.-J. Li and G. J. Chang, (2008), “Clique independent arcs of acyclic orientations of coverings and partitions of line graphs,” complete r-partite graphs, Discrete Disc. Math. 308, 2075-2079. Mathematics, 309 (2009), 4280-4286. [137] J. S.-t. Juan and G. J. Chang (2008), [14] L.-D. Tong, The (a,b)-forcing geodetic “Adaptive group testing for consecutive graphs, Discrete Mathematics, 309 (2009) positives,” Disc. Math. 308, 1124-1129. 1623-1628. Subproject II [15] L.-D. Tong, The forcing hull and forcing geodetic numbers of graphs, Discrete Applied [1] H. Chang and X. Zhu, Colouirng games on Mathematics 157 (2009) 1159-1163.
15 ‹‹- Highlights of the Focus Programs [16] J.-T. Hung, L.-D. Tong, and H.-T. Wang, The [24] P. Hell and X. Zhu, On the adaptable hull and geodetic numbers of orientations of chromatic number of graphs, European graphs, Discrete Mathematics, 309 (2009), Journal of Combinatorics, 29 (2008), 912- 2134-2139. 921. [17] L.-D. Tong, Geodetic sets and Steiner sets in [25] D. B. West and X. Zhu, Circular chromatic graphs, Discrete Mathematics, 309 (2009), index of product of graphs, Journal of Graph 4205-4207. Theory, 57 (2008), 7-18. [18] X. Zhu, Refined activation strategy for the [26] D. Yang and X. Zhu, Activation strategy for marking game, Journal of Combinatorial asymmetric marking games, European Theory Series B, 98 (2008),1-8. Journal of Combinatorics, 29 (2008), 1123- [19] J. Wu and X. Zhu, Lower bounds for the 1132. game colouring number of partial k-trees and [27] D. Liu and X. Zhu, Fractional chromatic planar graphs, Discrete Mathematics, 308 number of distance graphs generated by two (2008), 2637-2642. interval sets, E u ro p e a n J o u r n a l o f [20] W. Lin, D. Yang, C. Yang and X. Zhu, Combinatorics, 29 (2008), 1733-1743. Circular consecutive choosability of graphs, [28] X. Zhu, Game colouring Cartesian product of Taiwanese Journal of Mathematics, 12 graphs, Journal of Graph Theory, 59 (2008), (2008), 951-968. 261-278. [21] S. Norine and X. Zhu, Circular degree [29] J. Wu and X. Zhu, The 6-relaxed game choosability, Electronic Journal of chromatic number of outerplanar graphs, Combinatorics, 15 (2008), no. 1, Research Discrete Mathematics, 308 (2008), 5974- paper 100, 8pp. 5980. [22] S. Norine, T. Wong and X. Zhu, Circular [30] L.-D. Tong, P. L. Yen, and A. Farrugia, The choosability via combinatorial nullstellensatz, convexity spectra of graphs, Discrete Applied Journal of Graph Theory, 59 (2008), 190- Mathematics, 156 (2008), 1838-1845. 204. [31] L.-D. Tong and H.-T. Wang, Eccentric [23] A. V. Kostochka and X. Zhu, Adapted list spectrum of a graph, Taiwanese Journal of coloring of graphs and hypergraphs, SIAM Mathematics, 12 (2008), 969-977. Journal on Discrete Mathematics, 22 (2008), 398-408.
Highlights of the Focus Programs -›› 16 D.3 Dynamical System
Coordinators: Kuo-Chang Chen (National Tsing-Hua University), Cheng-Hsiung Hsu (National Central University), Chih-Wen Shih (National Chiao Tung University)
he primary investigators of this focus systems, and chaotic attractors. Regular seminars program are Kuo-Chang Chen (NTHU), have been held at a weekly base with talks given Jonq Juang (NCTU), Ming-Chia Li (NCTU), by visiting scholars, and local researchers. Song-Sun Lin (NCTU), Chih-Wen Shih (NCTU), Summer school in dynamical systems was Cheng-Hsiung Hsu (NCU) arranged with focus on specific topic. International conference or workshop is organized Coordinators: Kuo-Chang Chen, Cheng-Hsiung every year here in NCTS. Some mini courses are Hsu, Chih-Wen Shih arranged in the workshops. These activities The other investigators include Jung-Chao Ban broaden the spectrum of current research in (NDHU), Chang-Yuan Cheng (NPUE), Yi-Chuan Taiwan, promote the collaboration with Chen (Academia Sinica), Wen-Chiao Chen international scholars, and enhance the training of (CCUT), Shyan-Shiou Chen (NTNU), Bau-Sen graduate students. Both individual and group Du (Academia Sinica), Jin-Long Li ((NHCTC), researchers have delivered significant works in the Ken Palmer (NTU), Jun-Hsiung Hsia (NTU), past few years. We also have joint activities with Chen-Chang Peng (NCU), Shih-Feng Shieh the topical programs of mathematical biology and (NTNU), Li-Chin Yeh (NHCTC), Je-Chiang Tsai scientific computation on some applications and (NCCU), Ting-Hui Yang (Tamkang), Tzi-Sheng computational aspects of dynamical systems. The Yang (Tonghai), Suh-Yuh Yang (NCU) activities this year are listed below. Dynamical System is one of the major and classical research areas in mathematics and D.3.1 Dynamical System Seminar mathematical science. The discipline traces back The weekly seminar is primarily organized by to Newton, Poincare, and Birkhoff. Current Kuo-Chang Chen (National Tsing Hua University) interesting research topics in the field contain the and Chih-Wen Shih (National Chiao Tung ones of classical origin: celestial mechanics, University). About half of them are student Hamiltonian systems, the ones developed since seminars given by graduate students, among them the sixties: chaotic dynamics and ergodic theory, there were a series of talks on theory of and the ones that attract increasing attention: Hamiltonian systems, and a series of talks on random dynamical systems. In addition to the calculus of variations, synchronization for coupled theoretical side, the application of dynamical systems, chaotic behaviors for multi-dimensional system is closely linked to the nonlinear dynamics maps. The other seminars were mostly talked by in Physics, both historically and contemporarily. NCTS visitors. A listing of all the seminar talks The range of applications crosses from physics, are available at: http://www.math.cts.nthu.edu.tw/ biology, information science, engineering, to actnews/actnews.php?class=102 economy and finance. There are more than twenty active researchers in dynamical systems in D.3.2 Conference and Workshop Taiwan. Their research topics include n-body problem, homoclinic orbits, entropy, delayed NCTS 2009 Workshop on Dynamical equation, chaotic saddle, synchronization, multi- Systems, May 21-24, 2009 dimensional perturbation, heterodimensional Organizers: Kuo-Chang Chen:, Cheng-Hsiung cycles, noisy oscillators, anti-integrable systems, Hsu, Jonq Juang, Ming-Chia Li, geometric singular perturbation, monotone Chih-Wen Shih dynamics, traveling waves, lattice dynamical
17 ‹‹- Highlights of the Focus Programs The 2009 CTS Workshop on Dynamical Shih-Feng Shieh (NTNU, Taiwan) Systems will be held at the National Center for Title: Spatial Chaos for Soliton Solutions in a Theoretical Sciences on May 21-24, 2009. 2D Schrödinger Lattice The aim of this annual workshop is to bring Sergey Gonchenko (RIAMC, Russia) together active researchers with different Title: Homoclinic Bifurcations and Strange backgrounds to discuss recent and prospective Attractors advances in the areas related to dynamical systems. This year we have arranged lectures and Chun-Hsiung Hsia (NTU, Taiwan) talks related to Hamiltonian systems and celestial Title: The Effects of Stratification and Rotation mechanics, ergodic theory and its applications, on the Oceanic Convection Problem and chaotic attractors. The workshop include four Andrea Venturelli (University of Avignon, mini courses, several invited talks and contributed Avignon, France) talks. Title: Globally Minimizing Parabolic Solutions 1. Mini Courses in the Newtonian N-Body Problem Chenciner (Universite Paris VII and IMCCE, NCTS Dynamics Day- a workshop focusing France) on non-hyperbolic systems, November 6, 2009 Title: An introduction to weak KAM theory Organizers: Jonq Juang (NCTU), Ming-Chia Li Huyi Hu (Michigan State University, USA) (NCTU), Chih-Wen Shih (NCTU) Title: On decay of correlation Speakers: Kening Lu (Brigham Young University, USA) Lorenzo Diaz (Catholic University of Rio de Title: Dynamics and randomness for infinite Janeiro, Brazil) dimensional dynamical systems Title: Non-hyperbolicities (talk 1) Richard Moeckel (University of Minnesota, USA) Title: Robust homoclinic tangencies and Title: Topics in celestial mechanics heterodimensional cycles (talk 2) Teruhiko Soma (Tokyo Metropolitan University) 2. One-Hour Talks Title: Existence of generic cubic homoclinic Wen Huang (University of Science and tangencies for H´enon map Technology of China, China) Shin Kiriki (Kyoto University of Education) Title: Combinatorial Lemmas and Applications Title: An index changing bifurcation creating to Dynamics heterodimensional cycles Jung-Chao Ban (NDHU, Taiwan) Sergey Tikhomirov (NTU) Title: Thermodynamic Formalism and Title: Equivalence of the Lipschitz shadowing Multifractal Analysis for Products of and structural stability Non-negative Matrices under Countable Symbol Shift Katsutoshi Shinohara (University of Tokyo) Chengkui Zhong (Lanzhou University & Nanjing Title: On the index of homoclinic classes under University, China) the robust absence of dominated splittings Title: Exponential Attractors for Semigroups in Banach Spaces Ming Jiea Lyu (NCTU, Taiwan) Alain Albouy (IMCCE, France) Title: Topological dynamics for multidimensional perturbations of maps Title: Central Configurations -- Coorbital with snap-back repellers and with strong Satellites cone conditions Ken Palmer (NTU, Taiwan) Wen-Chiao Cheng (CCUT, Taiwan) Title: Lyapunov Exponents and Sensitive Title: Different types of variational principle Dependence for entropy and pressure
Highlights of the Focus Programs -›› 18 D.3.3 NCTS Summer Course on dynamical system with additive noises, Dynamical Systems Dynamical Systems-An International Journal 24, 139-155 (2009). Speakers: Sze-Bi Hsu(NTHU) ,Feng-Bin Wang (NTHU), Changyuan Cheng (NPUE) [7] Cheng-Hsiung Hsu, Suh-Yuh Yang, Ting-Hui Yang and Tzi-Sheng Yang, Existence of Dates: 7/6-8/14 ,Every Tuesday (7/7, 7/14, 7/21, periodic orbits for a system of delay 7/28, 8/4, 8/11) differential equations Nonlinear Analysis- 10:00am-12:00, 2:00pm-3:00pm Theory, Methods & Applications, (2009), accepted. Outlines: [8] Cheng-Hsiung Hsu, Suh-Yuh Yang, Ting-Hui (i) Theory of Monotone Dynamical Systems Yang and Tzi-Sheng, Yang, Stability and (ii) Applications to Nonlinear Systems of bifurcation of a two-neuron network with Ordinary Differential Equations, distributed time delays, Nonlinear Analysis- Cooperative Systems, Poincare-Bendixson Real World Applications, (2009), accepted. Theorem for Three Dimensional Competitive [9] John M. Hong, Cheng-Hsiung Hsu and Weishi Systems Liu, Sub-to-super transonic steady states and their linear stabilities for gas flows, submitted (iii) Applications to Diffusion-Reaction Systems to Archive for Rational Mechanics and Modeling Two Species Competition Analysis, (2009). (iv) Application to Delay Differential Equations [10] Cheng-Hsiung Hsu and Ting-Hui Yang, Traveling wave solutions of delayed lattice D.3.4 The accomplished and the differential system in Lotka-Volterra type, anticipations submitted to Discrete and Continuous [1] Kuo-Chang Chen, Variational constructions Dynamical Systems-B, (2009). for some satellite orbits in periodic [11] Cheng-Hsiung Hsu, Qin Jiang, Zhi-Xian Yu, gravitational force fields, Amer. J. Math., in Rong Yuan, Traveling waves for nonlinear press. cellular neural networks with distributed time [2] Kuo-Chang Chen and Y.-C.Lin, On action- delays, submitted to Journal of Differential minimizing retrograde and prograde orbits of Equations, (2009). the three-body problem, Comm. Math. Phys., [12] Cheng-Hsiung Hsu and Weishi Liu, Inviscid 291, 403-441 (2009). and viscous stationary waves of gas flow [3] John M. Hong, Cheng-Hsiung Hsu and Weishi through nozzles of varying area, Preprint, Liu, Inviscid and viscous stationary waves of (2009). gas flow through contracting-expanding [13] Cheng-Hsiung Hsu and Jian-Jhong Lin, nozzles, Journal of Differential Equations, Traveling wave solutions for discrete-time (2009), accepted. model of delayed cellular neural networks, [4] John M. Hong, Cheng-Hsiung Hsu and Weishi Preprint, (2009). Liu, Viscous standing asymptotic states of [14] Cheng-Hsiung Hsu, Tzi-Sheng Yang and Chi- isentropic compressible flows through a Ru Yang, Bifurcation analysis of a neural nozzle, Archive for Rational Mechanics and loop with distributed time delays, Preprint, Analysis, (2009), accepted. (2009). [5] Cheng-Hsiung Hsu, Ting-Hui Yang and Chi- [15] J. Juang and Y.H. Liang, Coordinate Ru Yang, Diversity of traveling waves in Transformation and Matrix Measure FitzHugh-Nagumo type equations, Journal of Approach for Synchronization of Complex Differential Equations 247, 1185-1205 (2009). Networks, Chaos, Vol. 19, 033131 (2009). [6] Jung-Chao Ban, Cheng-Hsiung Hsu, Yin- [16] C. Juang, C. L. Li, Y. H. Liang, and J. Juang, Heng Lin and Tzi-Sheng Yang, Pullback and Wavelet Transform Method for Coupled Map forward attractors for dissipative lattice Lattices, IEEE Trans. Circuits Syst. I, vol. 56, no. 4, April, 2009
19 ‹‹- Highlights of the Focus Programs [17] Chih-Wen Shih, Jui-Pin Tseng, [19] Kang-Ling Liao, Chih-Wen Shih, Snapback Synchronization, Oscillations and Repellers and Homoclinic Orbits for Multi- Multistability in a Coupled Neural Network dimensional Maps, submitted. with Delays, submitted. [18] Chih-Wen Shih, Jui-Pin Tseng, Collective dynamics for Delayed Neural Network with Nearest-neighbor Coupling, (with Jui-Pin Tseng), submitted.
D.4 Geometric Analysis and Differential Geometry
Coordinators: S.-C. Chang (National Taiwan University), J.-H. Cheng (National Taiwan University), Y.-I. Lee (National Taiwan University), C.-J. Sung (National Tsing-Hua University), D.-H. Tsai (National Tsing-Hua University)
he subject matter of Riemannian (ii) Mean curvature flow in higher co-dimension geometry has multiple faucets. NCTS has (at Taipei) held various programs and workshops in related (a) The soliton for Lagrangian mean curvature subject areas since the year 2004, focusing on flow ( by Yng-Ing Lee) various aspects of geometry and geometric analysis. The covered topics include Geometric (b) On the existence of Hamiltonian stationary Evolution Equations, Function and Map Theory, Lagrangian submanifolds in symplectic Geometric Structures. manifolds ( by Yng-Ing Lee) he subject matter of Riemannian geometry has (iii) The torsion flow and geometrization problem multiple faucets. NCTS has held various programs of contact 3-manifolds (at Taipei) and workshops in related subject areas since the (a) The CR Hamilton-Perelman's Entropy year 2004, focusing on various aspects of Formulae (by Shu-Cheng Chang and Jih- geometry and geometric analysis. The covered Hsin Cheng) topics include Geometric Evolution Equations, Function and Map Theory, Geometric Structures. (b) The Li-Yau-Hamilton Inequality for CR Yamabe Flow (by Shu-Cheng Chang) Main research focus of GADG group at NCTS • Function and Map Theory (i) Harmonic function Theory (at Hsinchu) • Geometric Evolution Equations (a) Eigenvalue estimate on minimal (i) The curvature flow of curves and submanifolds ( by Chiung-Jue Sung) hypersurfaces (at Hsinchu) (b) Harmonic forms on manifolds( by Chiung- (a) Expanding convex immersed closed plane Jue Sung) curves (by Dong-Ho Tsai) (c) Heat flow of Harmonic Maps ( by Chiung- (b) Evolving a convex closed curve to another Jue Sung) one via a length-preserving linear flow (by Dong-Ho Tsai). (ii) Function theory on pseudohermitian manifolds (at Taipei)
Highlights of the Focus Programs -›› 20 (a) The Weak Sub-Laplacian Comparison D.4.3 Workshops, Course and Seminars Theorem in Complete CR Manifolds ( by Shu-Cheng Chang) The Ninth Pacific Rim Geometry Conference, Dec. 10-14, 2008. (b) Complete pseudohermitian manifolds with positive spectrum ( by Shu-Cheng Chang) Organizers: Robert Bartnik (Monash University, Australia) (c) The CR splitting Theorem ( by Shu-Cheng Yng-Ing Lee (National Taiwan University) Chang). Chang-Shou Lin (National Taiwan University) • Geometric Structures Richard Schoen (Stanford University, USA) (i) Special Lagrangian and Hamiltonian Mao-Pei Tsui (University of Toledo, USA) stationary sub-manifolds (at Taipei) Mu-Tao Wang (Columbia University, USA) (a) On the existence of Hamiltonian stationary Invited Speakers: Lagrangian submanifolds in symplectic Kazuo Akutagawa (Tokyo University of manifolds ( by Yng-Ing Lee) Science, Japan), Robert Bartnik (Monash (ii) CR structures in Cauchy-Riemann geometry University, Australia), Jih-Hsin Cheng (Academic and topology of contact manifolds (at Taipei) Sinica, Taiwan), Jaigyoung Choe (Korea Institute for Advanced Study, Korea), Akito Futaki (Tokyo (a) The CR Bochner Identity and Stable Institute of Technology, Japan), Martin Guest Pseudoharmonic Maps on Pseudohermitian (Tokyo Metropolitan University, Japan), Mark Manifolds (by Shu-Cheng Chang). Haskins (Imperial College London, UK), Yng-Ing (b) Discovery of a Codazzi-like equation, Lee (National Taiwan University, Taiwan), fundamental theorem, and a Hopf-type Naichung Conan Leung (The Chinese University index theorem ( by Jih-Hsin Cheng). of Hong Kong, China), Zhiqin Lu (UC Irvine, USA), Richard Schoen (Stanford University, D.4.1 Researcher in local focus group USA), Chiung-Jue Sung (National Tsing Hua University, Taiwan), Luen Fai Tam (The Chinese PI: S.-C. Chang (NTU), J.-H. Cheng (Sinica), University of Hong Kong, China), Mu-Tao Wang River Chiang (NCKU), Y.-I. Lee (NTU), C.-J. (Columbia University, USA), Chin-Lung Wang Sung ( NTHU) and D.-H. Tsai (NTHU). (National Taiwan University, Taiwan), Takao AI: A. N. Wang (NTU), C.-J. Liu (NTU), J-.N. Yamaguchi (Tsukuba University, Japan), Xi-Ping Tsai (NTU), C.-C. Lin (NTNU), S.-C. Chu Zhu (Sun Yat-Sen University, China). (NCCU), S.Y. Hsu (NCCU), T.-H. Chang (NTHU), J.-T. Chen (NTNU), M.-L. Taiwan-Norway Joint Workshop on Yau(NCU), H.-L. Chiu (NCU), J.-F. Hwang Geometric Analysis and Mathematical (Sinica), D.-C. Wu (Sinica), S.-J. Kan Physics, Dec. 15-16, 2009 (Sinica), C.-C. Hsieh (Sinica), C-T. Wu (NPTEU), H.-G. Chan ( NPUE), Y.-J. Hung Organizers: (NCKU), E. Xia (NCKU), Roger Chen Chiung-Jue Sung (National Tsing-Hua Univ.) (NCKU), K.-H. Lam (NCKU), N.-K. Ho Alexander Vasilev (University of Bergen, Norway) (NTHU), R. Chiang (NCKU). Irina Markina (University of Bergen, Norway) D.4.2 Visitors Der-Chen Chang (NCTS & Georgetown Univ.) Yongzhi Steve Xu (University of Louisville), Invited Speakers: Xiao Jie (Memorial University of Newfoundland), Huei-Dong Cao (Lehigh University, USA), Jiaping Wang (University of Minnesota), Der- Der-Chen Chang (Georgetown University, USA & Chen Chang (Georgetown University), Changqing NCTS, Taiwan), Kenro Furutani (Tokyo Hu (Soochow University ), Peng Lu (University University of Science, Japan), Chisato Iwasaki of Oregon), S.W. Wei ( University of Oklahoma), (University of Hyogo, Japan), Irina Markina J.-Z. Tie ( University of Georgia) (University of Bergen, Norway), Duy-Minn Nhieu
21 ‹‹- Highlights of the Focus Programs (National Central University, Taiwan), Dmitri (National Tsing-Hua Univ.), Chun Heng Ko Prokhorov (Saratov State University, Russi), (National Tsing-Hua Univ.) B.-Wolfgang Schulze (Universitat Potsdam, Germany), Chiung-Jue Sung (National Tsing-Hua D.4.4 Important Results, Breakthrough University, Taiwan), Tomio Umeda (University of Hyogo, Japan), Alexander Vasilev (University of • Geometric Evolution Equations: Bergen, Norway. (i) The CR Hamilton-Perelman's Entropy Formulae (Group including Shu-Cheng 2009 NCTS Mini Course on Geometric Chang, Jih-Hsin Cheng, Hung-Lin Chiu, Chin- Analysis, May 18~July 27, 2009 Tung Wu, etc ): The study of Hamilton's Ricci Instructor: flow has been dominated by the maximum Der-Chen Chang (NCTS & Georgetown Univ.) principle with an exception to Hamilton's entropy estimate which holds for closed Chiung-Jue Sung 宋瓊珠 (NTHU) surfaces with positive Gaussian curvature. We are going to cover the following topics. Then it is very interesting to find monotonicity 1. Sub-Riemannian geometry: The Hamilton- formulas for integrals of local geometric Jacobi theory; The Hamilton formalism; The quantities. An exciting recent example is the Lagrangian formalism. Perelman's entropy formulas. The entropy formulas for the coupled torsion flow are 2. Sub-elliptic partial differential equations: derived which served as the CR analogoue of Constructions of heat kernels; Fundamental the Ricci flow. Moreover, we classify all solutions and possible sharp estimates. torsion flow solitons. 3. Related topics on geometric analysis: Kahler (ii) The soliton for Lagrangian mean curvature manifolds;Minimal surfaces; Isoperimetric flow (Group including Yng-Ing Lee, Mu-Tao inequality; Number of ends and local Wang, Mao-Pei Tsui, etc): We construct many symmetric spaces. self-similar and translating solitons for Seminars Lagrangian mean curvature flow, including Speakers include: Jiaping Wang (University of self-expanders and translating solitons with Minnesata), Chiung-Ju Liu (National Taiwan arbitrarily small Lagrangian angle. Our University), Bang-He Li (Graduate University of translating solitons play the same role as cigar Chinese Academy of Sciences), Xiao Jie solitons in Ricci flow, and are important in (Memorial University, Canada), Jui-Tang Chen studying the regularity of Lagrangian mean (National Taiwan Normal University) curvature flow. Student Seminars (iii) Self-similar solutions and translating Topics include: Solvability of the Dirichlet solutions for Lagrangian mean curvature Problem for Manifolds with Negative Currature, flow (Group including Yng-Ing Lee, Mu-Tao Conformal Normal Coordinates and Asymptotic Wang, Ma-Pei Tsui, etc): We construct many Expansion of green's Function, Gradient Estimate self-similar and translating solitons for of Heat Kernel, Basic Properties of Eigenvalues, Lagrangian mean curvature flow, including Comparison Theorem, Splitting Theorem, Mean self-expanders and translating solitons with Value Inequality, Complete Manifolds of arbitrarily small Lagrangian angle. Our Nonnegative Ricci Curvature, Mean Curvature translating solitons play the same role as Flow, Gaps Between Eigenvalues on Minimal cigar solitons in Ricci flow, and are important Submanifolds in S^n, Some results on stable in studying the regularity of Lagrangian harmonic maps, Curvature and Betti Numbers. mean curvature flow. Speakers include: Ting-Hui Chang (National (iv) (a) Expanding convex immersed closed plane Tsing-Hua Univ.), Jung-You Guo (National Tsing- curves (by Dong-Ho Tsai) : We study the Hua Univ.), Liang-Chu Chang, Kuan-Ho Lai evolution (expansion along its outward (National Tsing-Hua Univ.), Ting Jung Kuo normal direction) driven by curvature of a
Highlights of the Focus Programs -›› 22 given convex immersed closed plane curve. the geometric information of manifold. We We show that it will converge to a self- also extend the result to algebraic varieties. similar solution eventually. This self-similar solution may or may not contain singularities. • Geometric Structures: In case it does, we also have estimate on the (i) The CR Bochner Identity and Stable curvature blow-up rate. (b) Evolving a Pseudoharmonic Maps on Pseudohermitian convex closed curve to another one via a Manifolds (Group including Shu-Cheng length-preserving linear flow : Motivated by Chang, Ting-Hui Chang, etc): We first derive a curvature difference flow introduced by the CR Bochner identity for energy density of Professor S.-T. Yau, we use a simple a pseudoharmonic map which is involving an curvature flow to evolve a convex closed extra third order CR-pluriharmonic operator curve γ1 to another stationary one γ2 (under and does not appear in case of Riemannian the assumption that both curves have the Bochner identity. Secondly, we derive the same length). We show that, under the second variational formula for evolution, the length of γ1,t is preserved pseudoharmonic maps and the CR during the flow and if the curvature of γ1,t Weitzenböck formula for one-forms. Finally (γ 1,0 = γ 1) is bounded above during the we are able to obtain a vanishing theorem and evolution, then γ1 can be evolved to γ2 (up to solve a conjecture that any stable horizontal a translation) eventually. Moreover, the pseudoharmonic map from the average position vector of the evolving curve pseudohermitian sphere into any Riemannian γ1,t is independent of time. manifold must be a constant map. This is served as an CR analogue for the stable • Function and Map Theory: harmonic map. (i) (a) The Weak Sub-Laplacian Comparison (ii) Discovery of a Codazzi-like equation, Theorem in Complete CR Manifolds (Group fundamental theorem, and a Hopf-type index including Shu-Cheng Chang, Jianguo Cao, theorem (Group including Jih-Hsin Cheng, Jingzhi Tie, Chin-Tung Wu, etc): We first prove Jenn-Fang Hwang, Andrea Malchiodi, and the weak sub-Laplacian comparison theorem Paul Yang, etc): We discovered a Codazzi-like and obtain CR volume growth estimates. Then equation for p-area element and used it to it is shown that the natural CR analogue of analyze the local structure of the singular set Liouville-type theorem holds for the positive for $C^{1}$ smooth surfaces in the pseudoharmonic function in a complete Heisenberg group. We justified this Codazzi- pseudohermitian 3-manifold with vanishing like equation by proving a fundamental torsion and nonnegative Tanaka-Webster scalar theorem for local surfaces of constant p-mean curvature. Moreover, we obtain the global curvature in the Heisenberg group. The subgradient estimate as well. As a by-product, information about characteristic curves and the we recapture Koranyi and Stanton's result for singular set allowed us to prove a Hopf-type Liouville-type theorem where their method is index theorem for domains with boundary. only worked in Heisenberg groups. (b) (Jih-Hsin Cheng) Complete pseudohermitian manifolds with positive spectrum and the CR splitting theorem (iii) On the existence of Hamiltonian stationary (Group including Shu-Cheng Chnag, S.-W. Lagrangian submanifolds in symplectic Wei, Hung-Lin Chiu, J.-T. Chen, Z. Tie and manifolds (by Yng-Ing Lee): Hamiltonian T.-J. Kuo, etc). stationary Lagrangian submanifolds are critical points of the area functional among (ii) Eigenvalue estimate on minimal submanifolds Hamiltonian deformations. We show (by Chiung-Jue Sung): We give a sharp abundant existence of such examples in any estimate on a minimal submanifolds in compact symplectic manifolds with a nonnegatively curved manifolds. The estimate compatible metric, which is sharply different is universal in the sense that the upper bound from the cases for Lagrangian and minimal for the k-th eigenvalue only depends on k and submanifolds.
23 ‹‹- Highlights of the Focus Programs D.4.5 Accomplishments [8] Y.-I. Lee and M.-T. Wang , Hamiltonian stationary cones and self-similar solutions in [1] Y.-I. Lee and M.-T. Wang, A Note on the higher dimension, to appear in Transactions of Stability and Uniqueness for Solutions to the the American Mathematical Society. Minimal Surface System, Math. Res. Lett. vol. 15, no. 1 (2008), p197-206. [9] Y.-I. Lee and M.-T. Wang, Hamiltonian Stationary Shrinkers and Expanders for [2] Yu-Chu Lin and D.-H. Tsai, On a simple Lagrangian Mean Curvature flow, to appear in maximum principle technique applied to Journal of Differential Geometry. equations on the circle, Journal of Diferential Equations, 245 (2008), 377-391. [10] J.T. Chen and C.J. Sung, Harmonic Forms of Complete Manifolds with Weighted Poincaré [3] Shu-Cheng Chang and Hung-Lin Chiu, Inequality, Pacif. Jour. Math. 242 No 2 Nonnegativity of CR Paneitz operator and its (2009), 201-214. Application to the CR Obata's Theorem in a Pseudohermitian (2n+1)-Manifold, Journal of [11] Yu-Chu Lin and D.-H. Tsai, Evolving a Geometric Analysis, Vol. 19 (2009), 261-287. convex closed curve to another one via a length-preserving linear flow, Journal of [4] Shu-Cheng Chang and Hung-Lin Chiu, On the Differential Equations, 247, 2620.2636, 2009. CR Analogue of Obata's Theorem in a Pseudohermitian 3-Manifold, Math. Ann. Vol. [12] Tai-Chia Lin, C.-C. Poon and D.-H. Tsai, 345, No. 1 (2009), 33-51. Expanding convex immersed closed plane curves, Calculus of Variations & PDEs, 34, [5] Shu-Cheng Chang and Hung-Lin Chiu, The 153.178, 2009. Li-Yau-Hamilton inequality for Yamabe flow on a closed CR 3-manifold, Transactions of [13] L.-C. Chang, C.-L. Guo and C.-J. Sung, AMS (to appear). p -Harmonic 1-Forms on Complete Manifolds, to appear Archiv der Mathematik. [6] Shu-Cheng Chang, Jingzhu Tie and C.-T. Wu, Subgradient Estimate and Liouville-type [14] Yu-Chu Lin and D.-H. Tsai, Using Theorems for the CR Heat Equation on Aleksandrov Re.ection to Estimate the Heisenberg groups Hn, Asian J. Math. Location of the Center of Expansion, to (revised). appear in Proceedings of the American Mathematical Society. [7] Jih-Hsin Cheng, Jenn-Fang Hwang and Paul Yang, Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group, Math. Annalen, 344 (2009) 1-35.
Highlights of the Focus Programs -›› 24 D.5 Mathematical Biology
Coordinators: Sze-Bi Hsu (National Tsing-Hua University) and Chih Wen Shih (Natinal Chiao-Tung University)
he purpose of the topical program in Speaker: James Grover (Department of Biology, Mathematical Biology is to promote the University of Texas at Arlington) interdisciplinary interaction between Dec. 15, 2008-Jan.14, 2009. mathematicians, biologists, physicists, statisticians and computer scientists on the new problems (1) Basic chemostat theory and some of its arising from biology. In the past one year, we held extensions a biweekly seminars in theoretical ecology, A (2) Chemostat theory with several nutrients seminar in Reaction-Diffusion System with advections, an intensive course in Monotone (3) Application of chemostat theory to harmful Dynamical Systems for the graduate students, an algae: golden algae in Texas reservoirs. intensive course in applications of Partial Differential Equations to Spatial Ecology, an III. Seminar on Reaction-Diffusion intensive course in chemostat theory with Equations with Advections applications to Lake Ecology. We state as follows: Organizers: Sze-Bi Hsu (NTHU) Chih-Wen Shih (NCTU) D.5.1 Course and Seminars Jann Long Chern (NCU) I. Biweekly seminar in Theoretical Ecology Spaeker: Professor Luo Yuan (Ohio State University) Organizers: Sze-Bi Hsu (NTHU) Yu-Yun Chen (NCTS) Jan.7-Jan. 21, 2009 September 15-Decmber 15 (1) The evolution of dispersal In this seminar we study the book “Pelagic (2) Evolution of conditional dispersal: adaptive Nutrient Cycle” by Tom Anderson. We study the dynamic approach following subjects: (3) raking prey or tracking prey’s resource? (1) Phosphorus cycling and phosphorus household in lakes IV. Student seminar on the Reaction- Diffusion Equations with advections (2) Algae and nutrient: uptake and utilization of limiting nutrients in phytoplankton species Organizers: Sze-Bi Hsu (NTHU) Jann Long Chern (NCU) (3) Herbivores and algae: Food utilization, growth and reproduction in generalist filter Speakers: Feng-Bin Wang (NTHU) feeders Ting-Hao Hsu (Academia Sinica) Guo-Zi Hong (NTHU) (4) Nutrients, algae and herbivores-paradox of enrichment revisited March 15-April 30, 2009 (5) Approaching planktonic food webs: In this seminar the students presented the Competition, coexistence and chaos. works of Luo Yuan and Junping Shih on the reaction-diffusion equations. II. Chemostat Theory with applications to Lake Ecology V. Heterogeneous Partial Differential Equations Arising from Spatial Ecology Organizer: Sze-Bi Hsu (NTHU) Organizers: Sze-Bi Hsu (NTHU)
25 ‹‹- Highlights of the Focus Programs Shih-Hua Wang (NTHU) (2) Xiaoqiang Zhao ( Memorial University of J.C. Tsai (NCCU) Newfounder, Canada) , 5/27/2009 Speaker: Julian Lopez-Gomez (Complutense (i) Threshold Dynamics for Compartmental University of Madrid, Spain) Epidemic Models in Periodic Environment. July 15-Aug.14, 2009 (ii) Monotone Wave fronts in Reaction- Diffusion Systems In this series of talks, Professor Lopez-Gomez introduced us his work on Metasolution in Elliptic (3) Marcela Molina (University Carlos III,de PDE. Madrid Spain), 7/23/2009 (1) Introduction, Preliminary: maximal principle, Competition and Cooperation upper and lower solutions (2) The classical logistic equations D.5.2 Important Results, Breakthrough (i) S.B.Hsu and his master students Ting Hao Hsu (3) Uniform a priori bounds solve a conjecture in the competition model (4) Classical and large solution with internal storage in chemostat. Waltman and Hal Smith applied monotone dynamical (5) Dynamics and Metasolutions systems to determine the asymptotic behavior VI. A short course in Monotone Dynamical od solutions for two species. We use limit sup Systems and limit inf arguments to extend the competitive principle to n species case. The Organizers: Sze-Bi Hsu (NTHU) paper is published in SIAM Journal of Applied Feng-Bin Wang (NTHU) Mathematics. It is a breakthrough. Chang-Yuan Cheng (NPUE) (ii) S. B. Hsu and his Ph.D student Feng-Bin July 6-Aug.15, 2009 Wang present two different kinds PDE models This short course is to introduce the graduate for the competition of two phytoplankton students and advanced undergraduate students the species competing for one nutrient in the theory of Monotone Dynamical Systems with unstirred chemostat. The papers are accepted applications to Nonlinear ODE and Reaction- in JDE and DCDS Series A. We also publish a Diffusion Equations and Functional retarded paper in Math. Bioscience (to appear in 2010) differential equations. The text book is Monotone about the coexistence of phytoplankton Dynamical Systems by Hal Smith. species in the hydraulic storage zone. (1) Monotone Dynamical Systems (iii) It is commonly observed that in ocean the phytoplankton species concentrates at a thin (2) Stability and Convergence layer. In our two papers in SIAM J. Math. (3) Competitive and cooperative differential Analysis 2008, S.B.Hsu and Professor Du equations confirmed this phenomena and we get better results than the biologists predicted. (4) Irreducible cooperative systems (5) Cooperative systems of delay differential D.5.3 Works related to NCTS equations A. Refereed Papers (6) Quasi-monotone system of parabolic equations [1] S.B.Hsu and Lih-Ing Wu, Heteroclinic Cycles in Chemostat Models and the Winnerless VII. Several Invited Talks Competition Principle, J. Math. Analysis and Applications, To appear. (1) Chi-Kun Lin (NCTU), 4/16/2009 [2] J. Grover,S.B.Hsu and F.B.Wang, Competition Traveling wave fronts for time-delayed and Coexistence in Flowing Habitats with reaction-diffusion equation with local and Hydraulic Storage Zone, Mathematical nonlocal nonlinearity Bioscience, To appear.
Highlights of the Focus Programs -›› 26 [3] S.B.Hsu and Junping Shi, Relaxation [11] Yihong Du and S.B.Hsu, Concentration Oscillation Profile of Limit Cycle in Predator- Phenomena in a Nonlocal Quasilinear Prey namical Systems, Discrete and Problem Modelling Phytoplankton Continuous Dynamical Systems, Series B, II:Limiting Profile, SIAM J. Math. Analysis Vol. 11, No.4 (2009) pp.893-911. Vol.40, (2008) pp.1441-1470. [4] S.B.Hsu ,C.A.Klausmeier and Chiu-Ju Lin, [12] Ying-Hen Hsieh and S.B.Hsu, On the Role of Analysis of a Model of Two Parallel Food Asymptomatic Infection in Transmission Chains, Continuous Dynamical Systems, Dynamics of Infectious Diseases, Bulletin of Series B, Vol. 9, No.2 (2009) pp.337-359. Math. biology 70 (2008), pp134-155. [5] Bernold Fiedler and S.B.Hsu, Non-periodicity [13] C.W. Shih and J.P.Tseng, Global Consensus of Chemostat: a Multi-dimensional Negative for Discrete Time Competitive Systems, Bendixson Dulac Criterion, J. Math. Biology, Chaos,Solitons and Fratals 41,302-310 Vol.59, No.2 (2009) pp.233. (2009). [6] S.B.Hsu and F.B.Wang, Mathematical [14] C.W.Shih and J.P. Tseng, Convergent Analysis of Two Microbial Species Dynamics for Maulti-stable Delayed Neutral Competing for Two Complementary Netyworks, Nonlinaerity, 21, 2361-2389 Resources with Internal Storages and (2008). Different Removal rates, Bulletin of the [15] J.C.Tsai Global exponential stability of Institute of Mathematics Academia Sinica, traveling waves in monotone bistable Vol.3 ,No.4 (2008) pp.487-508. systems, Discrete and Continuous Dynamical [7] S.B.Hsu, Tzy-Wei Hwang and Kuang Yang, Systems, Series A, (2008), 601-623. Global Dynamics of a Predator-Prey Model with Hassell-Varley Type Functional B. Preprints Response, Discrete and Continuous [1] J.C.Tsai, Rotating Spiral Waves to lambda- Dynamical Systems, Series B, Vol.10, No.4 omega System on circlar domains. (2008) pp.857-871. [2] C.W.Shih and Jui-Pin Tseng, Synchronization, [8] S.B.Hsu and Xiaoqiang Zhao, Spreading Oscillations and Multi-stability in a Neural Speeds and Travelling Waves for Non- Network Coupled with Delays. Monotone Integro-difference Equations, [3] S.B.Hsu,Jifa Jiang and F.B.Wang,On a System SIAM J. Math. Analysis, Vol.40, No.2 (2008) of Reaction Diffusion Equations Arising from pp.776-789. Competition in Unstirred Chemostat with [9] S.B.Hsu and Ting-Hao Hsu, Competitive internal Storage. Exclusion of Microbial Species for a single [4] Yihong Du and S.B.Hsu, On a Nonlocal Nutrient with Internal Storage, SIAM J. Reaction-Diffusion Problem Arising from the Applied Math. Vol.68, No.6 (2008) pp.1600- modeling of Phytoplankton growth. 1617. [5] S.B.Hsu and F.B. Wang, On the Mathematical [10] Yihong Du and S.B.Hsu, Concentration Model Arising from Competition of Phenomena in a Nonlocal Quasilinear Phytoplankton with Internal Storage: Steady Problem Modelling Phytoplankton State Analysis. I:Existence, SIAM J. Math. Analysis Vol.40, [6] Yu-Yun Chen and S.B.Hsu, Infrequent (2008) PP.1419-1440. Synchronized Reproduction Promotes Species Coexistence.
27 ‹‹- Highlights of the Focus Programs D.6 Number Theory and Arithmetic Geometry
Coordinators: Jing Yu (NTHU & NCTS), J. Tze-Yue Wang (Academia Sinica), Chia-Fu Yu (Academia Sinica)
umber Theory at NCTS is understood in a (U. Houston), J. Tilouine (U. Paris Nord). E.-U. broad sense, including traditional Gekeler (Saarlandes), Kan-Wen Lan ( Princeton ), algebraic number theory, arithmetic geometry and Charles Li (U. Hong Kong), Z. Liu (East China automorphic representations. Diophantine Normal U.), Marco Garuti (Padova), David Harari geometry and arithmetic of algebraic function (Paris-Sud), H.-H. Chan (Singapore), E. fields are also among the main interests. As Viehmann (Bonn), and Ching-Li Chai Winnie Wen-Chin Li joins NCTS this year, the (Pennsylvania), D. Thakur(U. Arizona), M. scope of our number theory group is enlarging, Papanikolas (Texas A & M)., P. Vojta (UC . and more international connections will certainly Berke;ey), L. Long (Iowa State U.). Among them be established. C.-L. Chai, M. Ru, J. Tilouine, K.-W. Lan, L. Long, and M. Papanikolas are frequent visitors. Main Research Focus of the working group Geometry of arithmetic moduli D.6.3 Seminars and Courses Diophantine geometry NCTS Number Theory Seminar Modular forms This is regular weekly number theory seminar Automorphic Representations and zeta functions during the academic year. It includes talks given Coding theory by visitors to Taiwan from abroad and reports on Transcendence theory in positive characteristic research results obtained by number theory group at NCTS. D.6.1 Local participating members There is also Seminar on Arithmetic Geometry W. W.-C. Li (Director of NCTS), J. Yu (NCTS and Representation Theory at NCTS Taipei, and and NTU), C.-Y. Chang (Post doc), Y.-M. J.Chen Seminar on Number Theory at Academia Sinica in (NCU), W.-C. Chi (NTNU), L.-C. Hsia (NCU), Taipei. Ming-Lun Hsieh (NTU), A. Li (Fu Jen U.), S.-Y. Pan (NTHU), A. Schweizer (NCTS), Ki-Seng Tan Course on Abelian Varieties and Diophantine (NTU), C.-J. Wang (Post Doc), I. Longhi (post Approximations doctor), J. T.-Y. Wang (Academia Sinica), W.-C. This Spring 2009 course is given by L.-C. Hsia Yao (TMUE), Y. Yang (NCTU), C.-F. Yu and J. T.-Y. Wang. Contents : Heights, Mordell- (Academia Sinica), J.-D. Yu (NTU), Y.-J.Yu (N. Weil theorem for Abelian varieties, Falting’s Cheng-Chi U.). Presently there are also 15 Ph.D. theorem on Mordell conjecture. students and research assistants in this group, from NTHU, NTU, NCU, and NCTU. Also Course on Arithmetic Geometry: Etale research assistants at NCTS, Academia Sinica, cohomology local monodromy and 8 Ph. D. students from the U.S. and France . This is given by C.-F. Yu in Taipei. It started D.6.2 Visitors from contents of Chapater 1 of Milne’s book and Chapter 1 of Kieh-Freitag. Proofs of the base The most distinguished visitor is Jean-Pierre change theorem for proper morphisms and smooth Serre from College de France, in July. Serre is base change theorem are covered. The Picard- Fields medalist (1954), and won both the Abel Lefschetz formula is a focus. Topics include: prize (2003) and the Wolf Prize (2000). Lefschetz pencils, classification and deformations The short term visitors this year are : Min Ru of ordinary double points, local formulation of the
Highlights of the Focus Programs -›› 28 Picard-Lefschetz formula, vanishing and nearby Winter School on Number Theory at Aspire cycles. Also covered is the analytic theory of the Park, Feb. 1-Feb. 5, 2009. Picard-Lefschetz formula Subject: Diophantine Works of Corvaja and Zannier, Drinfeld Modular Curves NCTS Student's Seminar on Algebra and Shimura Curves, and Student's Project. Number Theory Speakers: Jing Yu (NCTS & NTHU), L.-C. Hsia This seminar during academic year aims at (NCU), J. T.-Y. Wang (Academia Ph.D. students, with students from NTHU, NTU, Sinica), A. Schweizer (NCTS), Y.-J.Yu NCU and NCTU join. Topics discussed including (N. Cheng-Chi U.). transcendence problems, Diophantine problems, elliptic curves, and algebraic number theory, etc. D.6.5 Summer Program for Students Preparation seminar for Serre’s Lectures In summer 2009 there is a 6-week summer program for undergraduates organized by C.-F. Organized by L.-C. Hsia , W.-C. Li, and Y. Yu, J. Chen and Y. Yang on “Elliptic Curves: Yang. More than 30 hours of intensive lectures on Analytic, Algebraic and Arithmetic”. It covered various advanced topics in June, 2009, to prepare such topics as differentials forms, basic Riemann students to benefit from and take notes of Serre's surfaces, lattices, tori and elliptic curves, lectures. Weirstrass parametrization, Riemann-Roch theorem, torsion points, rational points, the D.6.4 Advanced Schools and Workshops Mordell-Weil theorem etc. Lecture Series by Jean-Pierre Serre D.6.6 Important Results, Breakthrough The topic of this series is: variations with p of the number of solutions of a system of polynomial There are many progresses. Here we mention equations modulo p. Eight hours of lectures in the only the following directions: second week of July. This series is devoted to one On trascendence theory of positive of the most important current researches in characteristic, C.-Y. Chang and M. Papanikolas number theory and arithmetic geometry, and succeeded in proving the period conjecture for attracted biggest audience. In the final lecture, arbitrary rank Drinfeld modules. They are also open problems are discussed and precise able to deal with the algebraic independence conjectures are formulated. This visit by Serre will problem for Drinfeld logarithms, and quasi- certainly have great impact for the future logarithms for an arbitrary rank Drinfeld module. development of mathematics in Taiwan. The Motivic transcendence method together with lecture notes will be posted on the NCTS website. knowledge about Galois representations is the key. The complete work is now being written up. The Conference on Value Distribution Theory paper on the case of rank two has been accepted and Complex Geometry by Amer. J. Math. The rank one case (Papanikolas Organized by M. Ru, P. Vojta, J. T.-Y. Wang, written while visiting NCTS) was published in and J. Yu. This is cosponsored by NCTS, Institute Inventiones Math 2008. of Math. Of the Academia Sinica, and NSF of US. On arithmetic beometry of the moduli spaces, Foreign invited speakers include academician series works done by C.-F. Yu, a refined study of Y.-T. Siu (Harvard), P. Wong (Notre Dame), N. Siegel moduli, as well as Hilbert Blumenthal Sibony (Paris-sud), G. Patrizio (U. degi Studi di moduli. The latter has been accepted by Crell. Firenze), X. Liu(Notre Dame), Stephen S.-T. Yau Consequences of this development has bearings (U. Illinois, Chicago), A. Levin (Scuola Normale on Deligne-Lustig varieties, various mass Superiore), X. Zhou (Chinese Academy of formulas, and Shimura varieties of PEL type. Sciences). There are 20 participants from 7 Among them are joint works with U. Gortz, and countries. The week before the conference, there J.-D. Yu. is an instructional short course given by Min Ru to Works of Y. Yang with Zudilin, on modularity prepare local graduate students for this meeting.
29 ‹‹- Highlights of the Focus Programs of Picard-Fuchs equations, continuation of [6] L.-C. Hsia and J. Silverman, On a dynamic previous joint work with Yui published by Crell. Brauer-Manin obstruction, Journal de Theorie Also works of Yang with J.-D. Yu on cuspidal des Nombers de Bordeaux, Tome 21, no divisor class groups of modular curves, to appear 1(2009), p235-250. in J. London Math. Soc, and Yang-Fukurara on [7] M.-L.Hsieh, Eisenstein congruence on unitary explicit formulas for Hecke operastors, to appear groups and Iwasawa main conjectures for CM in Proc. Cambridge Phil. Soc. fields. NCTS/TPE Preprint 2009-013. On zeta functions of complexes, developed by [8] M.-L. Hsieh, Ordinary p-adic Eisenstein W. W.-C. Li, M.-H. Kang. Their joint paper with series and p-adic L-functions for unitary C.-J. Wang, is accepted b Israel J. Math. These Groups. NCTS/TPE Preprint 2009-014. totally new zeta functions are associated with [9] M.-L. Hsieh, The algebraic functional complexes of dimension 3. The combinatorics equation of Selmer groups for CM fields. involved are much more complicated. On the NCTS/TPE Technical Report 2009-015. other hand one can also give representation [10] M.-H. Kang and W.-C. Li, Zeta functions of theoretic approach to these zeta functions. W. complexes arising from PGL(3), preprint W.-C. Li is also a leading expert in the field of 2009. modular forms on non-congruence subgroups. [11] M.-H. Kang, W.-C. Li and C.-J. Wang, The T.-Y. Wang collaborating with Min Ru on new zeta functions of complexes from PGL(3): a approach of the Schmidt subspace theorem for representation theoretic approach, to appear subvarieties, using Chow forms. This is a central in Israel J. Math. issue of Diophantine geometry, with many [12] W.-C. Li, Modular curves and coding theory : unexpected developments and applications in the a survey, Proceedings of the Ninth last decade. International Conference on Finite Fields and L.-C. Hsia is collaborating with J. Silverman Applications, Dublin, Contemporary Math., on arithmetic dynamics. This is a hot recent to appear. direction in Diophantine geometry which leads to [13] A.W. Mason and A. Schweizer, Nonrational reformulations and variations of many important genus zero function fields and the Bruhat-Tits questions. tree, Communications in Algebra, 37 vol. 12 (2009), 4241-4258. D.6.7 Accomplishments [14] A. Schweizer, Value-sharing of meromorphic [1] C.-Y. Chang, A note on a refined version of functions on a Riemann surface, to appear in Anderson-Brownawell-Papanikolas criterion, JMAA. Journal of Number Theory, 129 (2009), 729- [15] A.W. Mason and A. Schweizer, The cusp 738. amplitudes and quasi-level of a congruence [2] C.-Y. Chang and M. Papanikolas, Algebraic subgroup of SL2 over any Dedekind domain, relations among periods and logarithms of preprint 2009. rank 2 Drinfeld modules to appear in Amer. J. [16] T.-Y. Wang and Chien-Wei Lin, Math. 2009. Generalizations of rigid analytic Picard [3] Chieh-Yu Chang, M. Papanikolas and J. Yu, theorems, to appear in Proceedings of A.M.S. Geometric gamma values and zeta values in [17] T.-Y. Wang Min Ru, An effective Schmidt's positive characteristic, to appear in Int. Math. subspace theorem for projective varieties Res. Notice, 2009, doi: 10.1093/imrn/rnp176. over function fields, preprint 2009. [4] Chieh-Yu Chang, M. Papanikolas, D. Thakue, [18] W.-C. Yao and J. Yu, On primitive roots for and J. Yu, Algebraic independence of rank one Drinfeld modules, to appear in arithmetic gamma values and Carlitz zeta Journal of Number Theory, 2009. values, to appear in Adv. Math, 2009, doi: [19] T.-F. Tu and Y. Yang, Defining equations forv 10.1016/z.airn.2009.09.013 X0(2^{2n}), Osaka J. Math 46 (2009), 105- [5] C.-Y. Chang, Transcendence and special 113. values of quasi-modular forms, preprint 2009.
Highlights of the Focus Programs -›› 30 [20] Y. Yang and S. Fukurara, Period polynomials [35] Y.-J. Yu, Ramakrishna-Khare Systems and and explicit formulas for Hecke operators on Modularity Lifting Theorems in Higher Gamma_0(2), Math. Proc. Cambridge Weights. NCTS/TPE Preprint 2009-016. Philosophical Society.146 (2009), 221-250. [36] Y.-J. Yu, Special fibers of Shimura curves and [21] Y. Yang and S. Fukurara, Twisted Hecke Steinberg representations. L-values and period polynomials, to appear in [37] Y.-M. J. Chen, Averaging class numbers in Journal of Number Theory. characteristic 2, Journal of Number Theory, [22] Y. Yang and A. Kontogeorgis, 128(2008), 2138-2158. Automorphidsm groups of hyperelliptic [38] Y.-M. J. Chen, Y. Yang and N. Yui, curves, to appear in LMS J. Comp. Math. Monodromy of Picard-Fuchs differential [23] Y. Yang, On congruence of the partition equations for Calabi-Yau threefolds, J. reine function, preprint 2009. angew. Math.616 (2008), 167-203. [24] Y. Yang, Modular Units and cuspidal divisor [39] Y.-M. J. Chen and J. Yu, On class number class groups of X1(N), J. Algebra 322 (2009), relations in characteristic two, Math. Zeit. 514-553. 259 (2008), no.1, 197-216. [25] Y. Yang and J.-D. Yu, Structure of the [40] L.-C. Hsia, On the reduction of a non-torsion n cuspidal rational torsion subgroup of J1(p ), point of a Drinfeld module, Journal of To appear in J. London Math. Soc. Number Theory 128 (2008), 1458-1484. [26] U. Görtz and C.-F.Yu, Supersingular [41] U. Görtz and C.-F. Yu, On the supersingular Kottwitz-Rapoport strata and Deligne- locus in Siegel modular varieties with Lusztig varieties, to appear in J. Inst. Math. Iwahori level structure. arXiv:0807.1229, 27 Jussieu, 2009. pages. (NCTS/TPE Technical Report 2008- [27] C.-F. Yu, Simple mass formulas on Shimura 013). varieties of PEL-type, to appear in Forum [42] A. O. L. Atkin, W.-C. Li and L. Long, On Math. 2009. Atkin and Swinnerton-Dyer congruence [28] C.-F. Yu, Irreducibilities of the Hilbert- relations (2), Math. Annalen 340 (2008), No Blumenthal moduli spaces with parahoric 2, 335-358. level structure, to appear in J. reine angew. [43] W.-C. Li and Y. Meemark, Hecke operators Math. 2009. on Drinfeld cusp forms, J. Number Theory [29] C.-F. Yu and J.-D. Yu, Mass formula for 128 (2008), 1941-1965. supersingular abelian surfaces, J. Algebra [44] M. Schütt and A. Schweizer, On the 322 (2009) 3733-3743. uniqueness of elliptic K3 surfaces with [30] C.-F. Yu, On finiteness of endomorphism maximal singular fibre, preprint 2008. rings of abelian varieties, to appear in Math. [45] M. Schütt and A. Schweizer, On Davenport- Res. Letters. Stothers inequalities and elliptic surfaces in [31] C.-F. Yu, Geometry of the Siegel modular positive characteristic, Quarterly J.Math. threefold with paramodular level structure. (Oxford) 59 (2008), 499-522. arXiv:0907.5263, 10 pp. (NCTS/TPE [46] T.-Y. Wang, Ta Thi Haoi An and William Technical Report 2009-012). Cherry, Algebraic degeneracy of non- [32] J.-D.Yu, Variation of the unit root along the Archimedean analytic maps, Indagationes Dwork family of Calabi-Yau varieties, Math. Mathematicae, 19 (2008), no. 3, 481-492. Ann. 343 (2009), 53-78. [47] Y. Yang, H.-H. Chan, Y. Tanigawa and W. [33] J.-D. Yu, Local structure of the moduli space Zudilin, New analogues of Clausen’s of K3 surfaces in positive characteristic, to identities arising from the theory of modular appear in Internat. Math. Res. Notices. forms, preprint 2008. [34] J.-D. Yu, Notes on Calabi-Yau ordinary [48] Y. Yang and W. Zudilin, On Sp4 modularity differential equations, Preprint. of Picard-Fuchs differential equations for Calabi-Yau threefolds, preprint 2008.
31 ‹‹- Highlights of the Focus Programs [49] C.-F. Yu, Irreducibility and p-adic The same group of people will also visit monodromies on the Siegel moduli spaces, Postech University Dec. 19-20, 2009 to attend a Adv. Math. 218 (2008) 1253-1285. number theory conference jointly organized by [50] C.-F. Yu, An exact geometric mass formula, Choie W.-C. Li. This is the first joint conference Int. Math. Res. Notice. 2008, Article ID between the Pohang Mathematics Institute and rnn113, 11 pages. NCTS. We expect to have more joint activities in the years to come. [51] J.-D. Yu and N. Yui, K3 surfaces of finite height over finite fields, J. Math. Kyoto Univ. Japan. March 2009, J. Yu, Y. Yang, C.-Y. 48 (2008), 499-519. Chang and F.-T. Tu were invite to conference on number theory and related topics at Waseda D.6.8 Exchange programs and University. Then Tu studied at Waseda in summer international cooperations with Hashimoto. Also in December 2009, K. Besides individual visits by members of our Hashimoto, A. Umegaki, and their Ph. D. students focus group to centers and universities in Canada, from Waseda visited NCTS, and a joint workshop China, France, Germany, Japan, Korea, U.S.A., on arithmetic of curves were held. highlights of 2009 international cooperations Switzerland. From February 16-20, NCTS include : group consisting of J. Yu, S.-Y. Pan, Y.Yang, J.-D. Canada. September 2009, J. Yu, C.-Y. Chang, Yu, and C.-Y. Chang, visited ETH, Zurich, and L.-C. Hsia, and 2 studentswere invited to BIRS, hosted by G. Wuestholz. A two day joint the Banff center, international workshop on workshop organized by J. Yu and G. Wustholz at t-motives, Hodge theory, and transcendence. This ETH, with four talks by the Taiwan side and three topic is one major field of our research group in talks by the Swiss side. This visit was supported Taiwan, and great progress were made in recent by NCTS, together with a National Chair Grant years at NCTS by the local groupas well as from the Ministry of Education. foreign collaborators visiting NCTS. The Netherlands. From February 9-13, NCTS China. On Aug, 18-21, the second East Asian group consisting of J. Yu, S.-Y. Pan, Y.Yang, J.-D. Number Theory Conference was taken place at Yu, and C.-Y. Chang, visited Leiden University, Beijing, Tsing Hua University, with number with H. Lenstra as host. J. Yu gave a colloquium theorists from Japan, China, Korea, and Taiwan lecture there, and the other four were invited joining. J. Yu is among the organizers, with L.-C. speakers to a special session on Feb.13, of the all Hsia, Y. Yang, M.-L. Hsieh, J.-D. Yu, C.-Y. Chang Dutch intercity number theory seminar held at as invited speakers from Taiwan. On Aug. 25-28, Leiden. This visit was supported by NCTS, this group continued visiting the Chern Institute in together with a National Chair Grant from the Tianjin, as invited speakers to another number Ministry of Education. theory conference held there. USA. Two Ph.D. students attended the Arizona Korea. A special session on "Modular forms winter school in march 2009, with local support and related topics" in KMS-AMS meeting in provided by AWS. Seoul, Korea, Dec. 16-17. is organized by W.-C. Li and J. Choie. Invited speakers from Taiwan include .C.-F. Yu, Y.Yang, M.-L. Hsieh, and F.-T. Wei.
Highlights of the Focus Programs -›› 32 D.7 Partial Differential Equations
Coordinators: Chiun-Chuan Chen (National Taiwan University), Tai-Chia Lin, Jenn-Nan Wang (National Taiwan University), Jong-Shenq Guo (National Taiwan Normal University)
D.7.1 Research Goals and Contents II. Inverse problems I. Parabolic equations We continue our research on the developing reliable reconstruction algorithm for determining the embedded object inside a domain. The background equation could be any elliptic equations or systems. The medium may be also here are two major research directions. inhomogeneous. A recent finished work is to study One is the study of singularities for this problem for the Helmholtz equation in two solutions of parabolic problems. The other is the dimensions. Since the quadratic form for the study of front propagation in continuous and/or Helmholtz equation is not positive, the usual discrete version of parabolic problem (or technique for the elliptic systems is no longer dynamical systems). effective. To overcome the difficulty, we have to In the first topic, there are questions on blow- analyze the forward problem, possible with up or dead-core for parabolic problems, such as discontinuous medium, in greater detail. This was the time asymptotic rate of the singularity and the in fact our goal we set for this year. We are locations of singularity. fortunately able to make a big progress and finish this project. It is know classically that the self-similar singular rates are found in many cases. Recently, We also planned to investigate the quantitative the non-self-similar rate is found in many uniqueness estimates for the shallow shell examples. One of them is so-called type II equations. This system is a combination of the singularity. elasticity equation and the plate equation. It turns out the system does not have a uniform order, the About the locations of singularity, we take a order for the elasticity part is two, while the order classical example with spatially dependent for the plate equation is four. For this situation, the potential. We are interested in determining Carleman method seems the most effective whether a zero of the potential can be a blow-up technique to derive the quantitative uniqueness point, if the solution blows up in finite time. This estimates. Our goal is not just to derive those is an on-going project. We have some interesting estimates, we have our mind in the application to results. inverse problems. We planned to study the size In the second topic, we are interested in the estimate problem for the shallow shell equation existence of entire solutions defined for all time with an inclusion. Currently, we are working on from negative infinity to plus infinity in reaction- the forward problem and the quantitative diffusion equations. In particular, the combination estimates. We expect to finish this project of two fronts coming from two far sides of real sometimes next year. line gives the so-called 2-front entire solution. In the PDE subprogram of the last year’s For discrete lattice dynamical systems, we project, we planned to extend the reconstruction have been studying the existence of traveling algorithm of identifying the embedded object by fronts for different settings, including boundary measurements to other situation homogeneous and heterogeneous media. These including the anisotropic medium. When the models arise in, for example, the study of dimension is two and the underlying equation is competition of two species when the habitat is the conductivity equation, we have successfully divided into discrete regions. developed a reconstruction algorithm for this case.
33 ‹‹- Highlights of the Focus Programs The key idea is to use the isothermal coordinates. We focus on a Liouville type equation with Unfortunately, this type of coordinates is only singular source terms, which is related to the available in two dimensions. In two dimensions, limiting case of the Chern-Simons model we could use any harmonic function as the phase proposed by Hong, Kim and Pac. It was shown by function of the complex geometrical optics Prajapat and Tarantello that the ground states of solutions. Therefore, we can take advantage of this equation, unlike those with a smooth source this property and design reliable and efficient term, can be non-radially symmetric. This means algorithm. In three dimensions or higher, the that the blowing-up behavior can be more situation is dramatically different. For higher complicated in this case. Therefore it becomes a dimensions, it seems that the special solutions new task in calculating the Leray-Schauder degree introduced by Kenig-Sjostrand-Uhlmann is so-far of the equation and obtaining a simple criterion the most effective ones. We hope to investigate the for the existence of solutions. We obtain a better problem in higher dimensions in much more detail formula for the Leray-Schauder degree and plan to next year. write down all the details of the proof in this year. Also we will find applications of this degree We also planned to study how the stability of formula in the existence problem of Liouville type the inverse problem depends on the wave number systems. in the equation. The motivation behind this study is the numerical observation of the increasing IV. Fluid dynamics stability phenomenon as the wave increases. Some situations been investigated by V. Isakov, yet, The incompressible Navier-Stokes equations there are more questions than answers. are one of the most fundamental systems in Unfortunately, we are unable to make progress on describing the behavior of fluid. The problem if a the problem this year. Besides of being dragged by solution with smooth initial value can form other problems, this problem itself is more singularities remains as one of the most difficult difficult than we expected. To analyze the problems unsolved in related fields. Axisymmetric dependence of the constants appeared in the case of these equations is important as a stability on the wave number is a quite mathematical problem and as a model of natural challenging task. The treatment of full nonlinear phenomena (e.g. typhoon). We focus on this case problem is out of reach at this point. Nevertheless, in this program and plan to study the blow-up the linearized problem will serve as a good behavior of the solutions and the Holder regularity starting point for the full nonlinear problem. We of related parabolic equations. are working on this question right now. V. Nonlinear Schrödinger equations and In deriving the quantitative uniqueness Bose-Einstein condensate estimates of some elliptic types of PDEs, we plan to give some interesting applications. The In the subprogram for systems of nonlinear application we have in mind is the inverse Schrödinger equations (NLS), the content may problem. More precisely, we planned to apply the cover the following problems: quantitative uniqueness estimates to the inverse (I.) Skyrmions in Gross-Pitaevskii functionals obstacle problem. The system we wanted to study is the shallow shell equation. This project is a bit (II.) Stationary wave patterns generated by an behind the schedule due to the difficulty in the impurity moving with supersonic velocity forward problem. Here the forward problem is the through a Bose-Einstein condensate (BEC). Neumann boundary value problem for the shallow (I.) Skyrmions shell equation. This problem was not fully studied Three-dimensional (3D) skyrmions in Gross- before. To treat the inverse problem, we need to Pitaevskii functionals with two-component wave have a very good understanding of the forward functions which have become a well-known problem. So currently we are working on the model to describe a binary mixture of Bose- forward problem. Einstein condensates called a double condensate. III. Liouville type equation In Bose-Einstein condensates (BECs), skyrmions can be characterized by pairs of linking vortex
Highlights of the Focus Programs -›› 34 rings coming from two-component wave we only consider the domain as a 3D unit sphere functions. Vortex rings formed in nature with which is topologically equivalent to the entire 3D various scales and composed of vortices whose space. However, when the domain is the entire 3D core is an one-dimensional close loop in three space, the problem is still open. The main space dimensions have fascinated scientists and difficulty is how to deal with the effect of mathematicians for a long time. They can also be boundary conditions at infinity. We hope to have observed in the trapped Bose-Einstein condensate further study in the next year. represented by one-component wave functions. In For the problem II, asymptotic formulae for a a double condensate described by two-component stationary far-field density distribution are wave functions, the skyrmion may be formed with obtained. Here we limit ourselves to the case of a a pair of linking vortex rings. The skyrmion can uniform condensate, which implies that the be depicted as a quantized vortex ring in one characteristic size of the structure is much less component close to the core of which is confined than the size of the condensate confined in a trap. the second component carrying quantized Besides that, we assume that the size of the circulation around the ring. In this subprogram, obstacle does not exceed the healing length and, we want to construct skyrmions and learn the hence, one can neglect the nonlinear structures configurations of skyrmions in BECs by studying generated inside the Mach cone. Comparison with critical points of Gross-Pitaevskii functionals with the three-dimensional numerical simulations two-component wave functions. demonstrates that these formulae are accurate (II.) Stationary wave patterns generated by an enough already at the distances from the obstacle impurity moving with supersonic velocity equal to a few wavelengths. On the other hand, through a BEC one may suppose that if the size of the obstacle exceeds the healing length, then in the 3D case In BECs, the detailed wave pattern generated formation of “conical solitons” would take place by a moving impurity is of considerable interest. above some critical velocity. This may cause the This problem became very topical in two- difficulty of the problem. dimensional (2D) case in connection with the results of the experiment in which the waves were generated by the flow of a condensate expanding Local focus group: through an obstacle created by a laser beam. Jong-Shenq Guo (NTNU), I-Liang Chern However, until now, there is not any result for a (NTU), Chang-Shou Lin (NTU), Chiun-Chuan three-dimensional (3D) flow, although it is of Chen (NTU), Chun-Hsiung Hsia (NTU), Tai-Chia considerable interest for the understanding of the Lin (NTU), Jenn-Nan Wang (NTU), Jyh-Hao wave processes in BECs. In this subprogram, we Lee(AS), Chun-Chi Lin (NTNU), Jenn-Long consider both analytically and numerically the 3D Chern (NCU), Je-Chiang Tsai (CCU), Dong-Ho wave pattern created by a small impurity moving Tsai (NTHU), Chao-Nien Chen (NCUE), Ching- with supersonic velocity through a bulk Bose- Lung Lin (NCKU) Einstein condensate. We propose to investigate the formation of stationary 3D wave patterns Short Term Visitors: generated by a small point-like impurity moving Arnd Scheel (Univ. of Minnesota), Vladimir through a BEC with supersonic velocity. Zykov (Technische Univ.), Francois Hamel (Univ. Analytically, we plan to derive asymptotic of Aix-Marseille III), Rhodri Nelson (University formulae for a stationary far-field density College London), Hiroshi Matano (Univ. of distribution. We also want to do numerical Tokyo), Yukihiro Seki (Univ. of Tokyo), Hirokazu simulations in order to support these asymptotic Ninomiya (Meiji Univ.), Chiu Yeung Chan (Univ. formulae. of Louisiana at Lafayette), Bei Hu (Univ. of Notre For the problem I, we successfully use Dame), Jerry Lloyd Bona (Univ. of Illinois at localized energy method to give a rigorous proof Chicago), Haïm Brezis (Rutgers Univ.), Fanghua. for the existence and the configurations of Lin (New York Univ.), Goong Chen (Texas A&M skyrmions in Gross-Pitaevskii functionals. Here Univ.), Mei-Chi Shaw (Univ. of Notre Dame), Horng-Tzer Yau (Harvard Univ.), Shih-Hsien Yu
35 ‹‹- Highlights of the Focus Programs (National Univ. of Singapore), Yuan Yu (Univ. of 5. Scattering for large data, repulsive case. Washington), YanYan Li (Rutgers Univ.), Eiji 6. Orbital stability of solitary waves. Yanagida (Tohoku Univ.), Tai-Peng Tsai (Univ. of 7. Asymptotic stability of small solitary waves. British Columbia), Kazumi Tanuma (Gunma University), Hideyuki Miura (Univ. of Tokyo), III. Localized patterns in partial differential Shin-Ichiro Ei (Kyushu Univ.), Masayasu equations, March 4 - June 17, 2009 Mimura (Meiji Univ.), Yoshihisa Morita (Ryukoku Speaker: Theodore Kolokolnikov (Dalhousie Univ.) Yasumasa Nishiura (Hokkaido Univ.) University) Xiaofeng Ren (George Washington Univ.), lzumi Many systems in nature lead to formation of Takagi (Tohoku Univ.), Shoji Yotsutani (Ryukoku patterns. Some examples include animal skin Univ.), Theodore Kolokolnikov (Dalhousie patterns, vegetation patches in semi arid University) landscapes, spiral waves in chemical reactions, Courses metal corrosion, hot spots in mircowave heating, and cell aggregation in chemotaxis. Often, these I. Minicourse on Stroh formalism and systems can be modelled using PDE's. In this Rayleigh waves, May 18-22, 2009 course we study various techniques that are used to construct these patterns and to study their Speaker: Kazumi Tanuma (Gunma University) stability. The emphasis will be on asymptotic The Stroh formalism is a powerful and elegant methods. Topics will be chosen from current mathematical method developed for the analysis research. These include: of the equations of anisotropic elasticity. The purpose of this short course is to introduce the • Turing instability; patch models in ecology essence of this formalism and demonstrate its • Localized patterns and matched asymptotics effectiveness in both static and dynamic elasticity. • Exponential ill-conditioning and metastability Professor Tanuma is the author of the book “Stroh • Hot spots in a microwave heating model Formalism and Rayleigh Waves” published by • Interface solutions, stability and self-replication Springer. This book is also an expository article appeared in Journal of Elasticity. IV. ODE theory and its application, July 20-August 28, 2009 II. Scattering and Soliton Dynamics, October, 2008 – January, 2009 Speakers: Jong-Shenq Guo (NTNU), Sheng- Chen Fu (NCCU), Je-Chiang Tsai Speaker: Tai-Peng Tsai (UBC) (CCU) and Chin-Chin Wu (NCTU) The subject of this lecture series is the long Content: time dynamics of dispersive waves. Our primary 1. Existence and uniqueness of solution for initial model is nonlinear Schr¨odinger equations. At value problem. times I will also discuss generalized KdV, wave, Klein-Gordon, and other dispersive equations. Our 2. Continuation of local solution. goal is not to survey all available results, rather, 3. Theory of continuous dependence. our goal is introduce (and attract) graduate 4. Shooting method. students to this fast growing area of partial 5. Boundary value problems. differential equations. Prerequisites for this course 6. Some special solutions to PDE problems. is familiarity with Sobolev spaces. Outline: Conferences and Workshops 1. Linear Schrӧdinger equations. I. Workshop on Theory and Applications of 2. Local wellposedness. Mathematical Analysis, 3. Global wellposedness, finite time singularity, October 21~22, 2009 and solitary waves. Invited Speakers: 4. Scattering for small data.
Highlights of the Focus Programs -›› 36 Min Wu (SCUT-Math, Prof & CS Dean), Jyh- Ming Hui (Academia Sinica,Taiwan) Hitoshi Ishii Hao Lee (AS-Math, Prof), Shenglin Zhou (SCUT- (Waseda University, Japan) Katsuyuki Ishii (Kobe Math, Prof), Jein-Shan Chen (NTNU-Math, A/ University, Japan) Toshio Ishimoto (Kyushu Prof), Bing Li (Post-doc Fellow), Quandi Wang University, Japan) Naoyuki Ishimura (SCUT-Math, Prof &Vice-dean), Gerard Jennhwa (Hitotsubashi University, Japan) Chiu-Yen Kao Chang (NTU-Math, Prof & Dept Chair), (The Ohio State University, USA) Shigeaki Koike Zhengrong Liu (SCUT-Math, Prof & Dept Chair), (Saitama University, Japan) Chun-kong Law Kin-Ming Hui (AS-Math, Prof), Ngai-Ching (National Sun Yat-Sen University, Taiwan) Wong (NSYSU-Applied Math, Prof), Yongsheng Ki-Ahm Lee (Seoul National University, Seoul, Li (SCUT-Math, Prof ), Narn-Rueih Shieh (NTU- Korea) Chi-Tien Lin (Providence University, Math, Prof) Taiwan) Chu-Pin Lo (Providence University, Taiwan) Hsiang Ning Luk (Taichung Veterans II. NTU Mathematics Month General Hospital, Taiwan; Providence University, Nonlinear Partial Differential Equations, July Taiwan) Philip K. Maini (Oxford University, UK) 6 - July 11 Masayasu Mimura (Meiji University, Japan) Yoshihisa Morita (Ryukoku University, Japan) Invited speakers: JanPou Nee (Chienkuo Technology University, G. Chen (Texas A&M University), Y. Y. Taiwan) Yasumasa Nishiura (Hokkaido Li (Rutgers University) Q. Nie (UC, Irvine), T. P. University, Japan) Xiaofeng Ren (The George Tsai ( University of British Columbia),E. Washington University, USA) Kunimochi Yanagida (Tohoku University), S. H. Yu (National Sakamoto (Hiroshima University, Japan) Takis University of Singapore), Y. Yuan (University of Souganidis (University of Chicago, USA) lzumi Washington) Takagi (Tohoku University, Japan) Dong Ho Tsai (National Tsing-Hua University, Taiwan) Yen His III International Conference on Reaction- Richard Tsai (University of Texas at Austin, USA) Diffusion Systems and Viscosity Solutions, Jack Xin (University of California at Irvine, USA) July 13-18, 2009, Providence University in Eiji Yanagida (Tohoku University, Japan) Li-Ming Taiwan Yeh (National Chiao Tung University, Taiwan) Shoji Yotsutani (Ryukoku University, Japan) Sponsored by National Center for Theoretical Sheng-Nan Wu (National Cheng Kung University Sciences, Mathematics Division Medical College, Taiwan) Tsu-Juey Wu (Taichung Organizers: Veterans General Hospital, Taiwan) Wei-Yueh Mark Lin (PU), Kuo-Ching Huang (PU), Chia-Hsing Nien (PU) D.7.2 Important Results, Breakthrough Invited speakers: I. Parabolic equations Chien-Hung Chang (Providence 1. The first breakthrough is the paper “Fast rate of University,Taiwan) Mao-Sheng Chang (Fu Jen formation of dead-core for the heat equation Catholic University, Taiwan) Chao-Nien Chen with strong absorption and applications to fast (National Changhua University of Education, blow-up” with Ph. Souplet published in Math. Taiwan) Chiun-Chuan Chen (National Taiwan Ann. (2006). The recent found example for type University, Taiwan) Jann-Long Chern (National II by Herreo and Velazquez is for very high Central University, Taiwan) Yihong Du spatial dimension. In this paper, we provide a (University of New England, Armidale, Australia ) very simple example in one space dimension. Shin-Ichiro Ei (Kyushu University, Japan) 2. The second breakthrough is the paper [9]. In Yoshikazu Giga (University of Tokyo, Japan) this paper with B. Hu, we study the blow-up Jong-Shenq Guo (National Taiwan Normal rate of the heat equation with a nonlinear University, Taiwan) Danielle Hilhorst (Universite gradient source term. This problem has been Paris-Sud XI ,France) Chien-Sen Huang (National open for many years. It was raised as one of Sun Yat-Sen University, Taiwan) Sze-Bi Hsu important open questions in the 2nd Euro- (National Tsing-Hua University, Taiwan) Kin-
37 ‹‹- Highlights of the Focus Programs Japanese Blow-up conference in Spain in 2006. II. Inverse problems Surprisingly, we find that the gradient blow-up 1. Sei Nagayasu, Gunther Uhlmann, and J.-N. rate is never self-similar. Moreover, the exact Wang, Depth dependent stability estimate in blow-up rate is found in the one space electrical impedance tomography, Inverse dimensional case when the solution is Problems, Vol 25 (2009), 075001. monotonically increasing in time. In this paper, we investigated how the stability 3. For entire solutions in reaction-diffusion depends on the depth of the obstacle. It has been equations, a very complete study of 1-d observed numerically that when the obstacle is problem can be found in [22], [21], [20]. This hidden deeper inside the domain, the includes KPP type nonlinearity and Allen-Cahn reconstruction error is large. This is no surprising type bistable nonlinearity. In particular, in the since the stability of the Cauchy problem for the balanced bistable case, the construction of elliptic equation has the same phenomenon. The 2-front entire solution is quite delicate and mian contribution of this work is that we gave a nontrivial. For the higher dimensional problem, precise quantitative description of this in [17], we have constructed traveling front phenomenon for a model problem having the with paraboloid type interface for the balanced inclusion as the unknown target. This study will case. This work is truly international team give us a deeper understanding on the ill- work. posedness of the inverse problem. 4. For the discrete lattice dynamical systems in the 2. Gunther Uhlmann, J.-N. Wang, and Chin-Tien homogeneous media, the bistable case has been Wu, Reconstruction of inclusions in an elastic studied almost completely. But, not too much body, J. Math. Pures Appl., Vol 91 (2009), 569- works are on the monostable nonlinearity. In a 582. series of joint works with X. Chen, we prove the existence, uniqueness and stability for the 3. Sei Nagayasu, Gunther Uhlmann, and J.-N. traveling fronts of lattice dynamical systems. Wang, Reconstruction of penetrable obstacles The important breakthrough is that in [18] we in acoustics, preprint. are able to treat the monostable case with In these works, we studied the reconstruction double degeneracy at two equilibria. Many new of embedded objects from boundary data using ideas were introduced in this paper. complex geometrical optics solutions (CGOS). 5. For the discrete lattice dynamical systems in the Unlike the classical CGOS with linear phases, we heterogeneous media, the first breakthrough is used CGOS solutions with quadratic phases which the joint work with F. Hamel [19]. In this paper, enable us to reconstruct more information of the we study the monostable nonlinearity with embedded object. CGOS with quadratic phases spatial periodic structure. Hence the habitat is are especially useful in treating inverse problems divided into discrete region and the in unbounded domains such as a slab. In two environment is periodic. We are able to derive dimensions, we have more freedom in choosing the existence of pulsating traveling front. Then, phases of the CGOS. The extra flexibility provides with C.-C. Wu in [1], we prove the uniqueness us a powerful tool in reconstructing the and stability of these traveling fronts. information of the object. In 3., we extended the method to the Helmholtz equation and considered 6. Another important breakthrough is the study of the penetrable obstacle case. The difficulty lies in traveling waves in discrete periodic media for the fact that the system is no longer positive and bistable dynamics [15]. This work is highly we need to estimate the energy gap more carefully. nontrivial. In this work, by adapting the idea commonly used in monostable case, we convert 4. Ching-Lung Lin, Gen Nakamura, and J.-N. the lattice dynamical system into an integral Wang, Optimal three-ball inequalities and equation. We introduce a general framework for quantitative uniqueness for the Lame system the study of traveling waves in discrete periodic with Lipschitz coefficients, arXiv:0901.4638. media. We give a complete study for the 5. Ching-Lung Lin and J.-N. Wang, Doubling existence, uniqueness and stability of the inequalities for the Lame system, preprint. traveling fronts.
Highlights of the Focus Programs -›› 38 6. Ching-Lung Lin and J.-N. Wang, Optimal three- The whole details of the proof of the above ball inequalities and quantitative uniqueness results will be written into two long papers. We for the Stokes system, arXiv:0812.3730. believe that our work will be one of the most important breakthroughs in this field. 7. Ching-Lung Lin, Sei Nagayasu, and J.-N. Wang, Quantitative uniqueness for the power of IV. Fluid dynamics Laplacian with singular coefficients,arXiv:0803.1012. The problem if a solution of the incompressible Navier-Stokes equations with smooth initial value 8. Ching-Lung Lin, Gen Nakamura, and J.-N. can form singularities remains as one of the most Wang, Quantitative uniqueness for second order important problems unsolved in related fields. In elliptic operators with strongly singular recent two years, we considered axisymmetric coefficients,arXiv:0802.1983. solutions with non-trivial swirl. We showed that if Motivated by the application to inverse the solution is bounded by the natural scaling problems and other topics, we got interested in the invariant bound “minus one scaling”, then the quantitative estimates of the unique continuation solution cannot blow up. This means that the for some elliptic equations or systems. Here the axisymmetric solutions cannot have a type I quantitative estimates include three-ball singularity. See reference [4] and [12]. inequalities (optimal or not) and doubling inequalities. We considered various equations with V. Nonlinear Schrödinger equations and systems with strongly singular coefficients. Our Bose-Einstein condensate main tool is the Carleman-type estimate. In a., we 1. Fanghua Lin, Tai-Chia Lin and Juncheng Wei, gave a quantitative estimate (optimal three-ball Skyrmions in Gross-Pitaevskii functionals, ( inequalities) for the isotropic elasticity system Dedicated to Professor Wu Wenjun on the with Lipschitz coefficients in any dimension. The occasion of his 90th birthday) Acta optimal three-ball inequalities immediately imply Mathematica Scientia 2009, 29B(3):751–776 the strong unique continuation property for the isotropic elasticity with Lipschitz coefficients in In Bose-Einstein condensates (BECs), any dimension, which is an interesting open skyrmions can be characterized by pairs of linking problem. It should be noted that the Lipschitz vortex rings coming from two-component wave regularity on the leading coefficients of the second functions. Here we construct skyrmions by order elliptic equation in dimension higher or studying critical points of Gross-Pitaevskii equal three is the least assumption for which the functionals with two-component wave functions. unique continuation holds. Using localized energy method, we rigorously prove the existence, and describe the III. Liouville type equation configurations of skyrmions in such BECs. In this year, we have completed the following 2. T.-L. Horng, S.-C. Gou, T.-C. Lin, G. A. El, A. study. P. Itin, and A. M. Kamchatnov, Stationary wave patterns generated by an impurity moving with (a) Obtain sharp estimates of the blow-up supersonic velocity through a Bose-Einstein behavior including the growth rate of the sup condensate, Phys. Rev. A 79, 053619 (2009). norm and the difference between the blow-up profiles and the ground states. The errors are Formation of stationary three-dimensional controlled within exponentially small orders. (3D) wave patterns generated by a small point-like impurity moving through a Bose-Einstein (b) Classify the eigenvalues and eigenfunctions of condensate with supersonic velocity is studied. the linearized equations around a bubble when Asymptotic formulae for a stationary far-field the vortex strengths are not integers. density distribution are obtained. Comparison (c) Some forms of formulas for the Leray- with the three-dimensional numerical simulations Schauder degree are defived. Especially one demonstrates that these formulae are accurate can use a generating function to write down enough already at the distances from the obstacle the formula explicitly. equal to a few wavelengths.
39 ‹‹- Highlights of the Focus Programs 3. Tai-Chia Lin, Chi-Cheung Poon, and Dong-Ho [6] Horng, T.-L.; Gou, S.-C.; Lin,T.-C.; El, G. A.; Tsai, Expanding convex immersed closed plane Itin, A. P.; Kamchatnov, A. M., Stationary curves, Calc. Var. (2009) 34:153–178. wave patterns generated by an impurity moving with supersonic velocity through a We study the evolution driven by curvature of Bose-Einstein condensate, Phys. Rev. A 79, a given convex immersed closed plane curve. We 053619 (2009). show that it will converge to a self-similar solution eventually. This self-similar solution may [7] Lin, Tai-Chia; Poon, Chi-Cheung; Tsai, Dong- or may not contain singularities. In case it does, Ho, Expanding convex immersed closed plane we also have estimate on the curvature blow-up curves, Calc. Var. and PDE (2009) 34:153- rate. 178. [8] Jong-Shenq; Wu, Chin-Chin, Uniqueness and 4. Xianjin Chen Tai-Chia Lin and Juncheng Wei, Blowup and solitary wave solutions with ring stability of traveling waves for periodic Journal profiles of two-component nonlinear monostable lattice dynamical system, of Differential Equations Schrodinger systems, preprint. 246 (2009), 3818- 3833. 5. Tai-Chia Lin, Juncheng Wei and Wei Yao, [9] Guo, Jong-Shenq and Hu, Bei, Blowup rate Orbital stability of bound states of nonlinear estimates for the heat equation with a Schrodinger equations with linear and nonlinear gradient source term, Discrete and nonlinear optical lattices, preprint. Continuous Dynamical Systems 20 (2008), 927-937. 6. Bob Eisenberg, Yunkyong Hyon, Tai-Chia Lin, [10] Takuwa, H.; Uhlmann, G.; Wang, J.-N., and Chun Liu, Energetic variational analysis Complex geometrical optics solutions for of ions in water and channels, preprint. anisotropic equations and applications. J. D.7.3 Publications Inverse Ill-Posed Probl. 16 (2008), no. 8, 791-804. [1] Guo, Jong-Shenq, Sasayama, Satoshi, and [11] Uhlmann, Gunther; Wang, Jenn-Nan, Wang, Chi-Jen, Blowup rate estimate for a Reconstructing discontinuities using complex system of semilinear parabolic equations, geometrical optics solutions. SIAM J. Appl. Communications on Pure and Applied Math. 68 (2008), no. 4, 1026-1044. Analysis 8 (2009), 711-718. [12] Chen, Chiun-Chuan; Strain, Robert M.; Tsai, [2] Uhlmann, Gunther; Wang, Jenn-Nan; Wu, Tai-Peng; Yau, Horng-Tzer; Lower bound on Chin-Tien, Reconstruction of inclusions in an the blow-up rate of the axisymmetric Navier- elastic body. J. Math. Pures Appl. (9) 91 Stokes equations. Int. Math. Res. Not. IMRN (2009), no. 6, 569-582. 2008, no. 9, Art. ID rnn016, 31 pp. [3] Nagayasu, Sei; Uhlmann, Gunther; Wang, [13] Lee, Chiun-Chang; Lin,Tai-Chia; Jenn-Nan, A depth-dependent stability Incompressible and compressible limits of estimate in electrical impedance tomography. two -component Gross-Pitaevskii equations Inverse Problems 25 (2009), no. 7, 075001, 14 with rotating fields and trap potentials, J. pp. Math. Phys., 49, 043517 (1-28) (2008) [4] Chen, Chiun-Chuan; Strain, Robert M.; Tsai, [14] Lin, Tai-Chia; Wei, Juncheng, Orbital Tai-Peng; Yau, Horng-Tzer, Lower bounds on stability of bound states of semi-classical the blow-up rate of the axisymmetric Navier- nonlinear Schrödinger equations with critical Stokes equations. II. Comm. Partial nonlinearity, SIAM J. Math. Analysis, Vol 40, Differential Equations 34 (2009), no. 1-3, No. 1, (2008) pp. 365-381 203-232. [15] Chen, Xinfu; Guo, Jong-Shenq; Wu, Chin- [5] Lin, Fanghua;Lin, Tai-Chia; Wei, Juncheng, Chin, Traveling waves in discrete periodic Skyrmions in Gross-Pitaevskii functionals, media for bistable dynamics, Archive for (Dedicated to Professor Wu Wenjun on the Rational Mechanics and Analysis 189 (2008), occasion of his 90th birthday) Acta 189-236. Mathematica Scientia (2009), 29B(3):751-776
Highlights of the Focus Programs -›› 40 [16] Chen, Xinfu; Fila, Marek; Guo, Jong-Shenq, [20] Chen, Xinfu; Guo, Jong-Shenq; Ninomiya, Boundedness of global solutions of a Hirokazu Entire solutions of reaction supercritical parabolic equation, Nonlinear -diffusion equations with balanced bistable Analysis, TMA 68 (2008), 621-628. nonlinearities, Proceedings of the Royal [17] Chen, Xinfu; Guo, Jong-Shenq, Francois Society of Edinburgh 136A (2006), 1207- Hamel, Hirokazu Ninomiya, and Jean-Michel 1237. Roquejoffre, Traveling waves with [21] Chen, Xinfu; Guo, Jong-Shenq, Existence paraboloid like interfaces for balanced and uniqueness of entire solutions for a bistable dynamics, Annales de l'Institut Henri reaction - diffusion equation, Journal of Poincare-Analyse Non Lineaire 24 (2007), Differential Equations 212 (2005), 62-84. 369-393. [22] Guo, Jong-Shenq; and Morita, Yoshihisa, [18] Chen, Xinfu; Fu, Sheng-Chen; Guo, Jong- Entire solutions of reaction-diffusion Shenq, Uniqueness and asymptotics of equations and an application to discrete traveling waves of monostable dynamics on diffusive equations, Discrete and Continuous lattices, SIAM Journal on Mathematical Dynamical Systems 12 (2005), 193-212. Analysis 38 (2006), 233-258. [19] Guo, Jong-Shenq; Hamel, Francois, Front propagation for discrete periodic monostable equations, Mathematische Annalen 335 (2006), 489-525.
41 ‹‹- Highlights of the Focus Programs D.8 Probability & Related Topics
Coordinators: Yuan-Chung Sheu (National Chiao Tung University) and Narn-Rueih Shieh (National Taiwan University)
D.8.1 Research Goals and Contents Diverse techniques have been introduced to study the total variation mixing of Markov processes since 1980s. Coupling and strong uniform time are discussed by Aldous, Diaconis, robability and statistics provide the Fill and many others. Jerrum and Sinclair use important tools to study the stochastic conductance to bound the spectral gap and the phenomena that come up in many areas of mixing time. Applications of representation theory application- physics, biology, computer science, are introduced by Diaconis and Shahshahani. and even a bit in economics and sociology. The Diaconis and Saloff-Coste used comparison main purpose of this focus program is to bring techniques in bounding the spectral gap and together local researchers and international eigenvalues. scholars to stimulate active studies in these During the past few years, Professor Guan-Yu exciting areas. In addition to the following main Chen (NCTU) and Professor Laurent Saloff-Coste research themes, the probability focus program of of Cornell University have successfully used the NCTS at Taipei-NTU is on Interplay of Analysis above developed techniques to determine the and Probability. mixing time of interesting models, such as randomized riffle shuffles. (A) Bioinformatics and system biology Our goal in 2008-2009 is twofold. One side is Graphical models bring together graph theory to make up the theory on the existence of and probability theory in a powerful formalism for 2 2 L -cutoffs and on the formula of L -mixing times large-scale multivariate modeling. While using the spectral information. The other side is to maintaining control over the computational cost implement the theoretical results on a couple of associated with these models, graphical models interesting and practical examples. Both of them have become a focus of research in many applied have been done and are composed in a recent joint fields, including bioinformatics, information paper of Guan-Yu Chen and Laurent Saloff-Coste theory, signal and image processing. The (70 pages, Journal of Functional Analysis, to mathematical structure of network/pathway appear). analysis (which is one of the most challenging problems in the era of functional genomics) is (C) Lévy processes and computational related to graphic models and their probabilistic finance properties. The theoretic properties for reconstruction of regulatory networks have been To take account of different stylized features of explored by the perspectives of probability and the markets and to improve the performance of the statistics. Between 2004 and 2007, we had Black-Scholes-Merton model, in recent years, focused on the studies of graphical models. We there has been a growing interest in the use of also investigated the regulatory networks of yeast Lévy processes and discontinuous as a model for eukaryotic cells. These researches semimartingales to model market behaviour. are conducted with the collaborations with Dr. However, unlike the diffusion case in which many Wen-Hsiung Li at the University of Chicago, Dr. functional are available in closed form, this is no Lei Li at the University of South California, Dr. longer the case for processes with jumps, Huai-Kuang Tsai and others at Acdemia Sinica. especially in the first-passage model. This is where the difficult in the pricing of securities (B) Markov chains and mixing times under a Lévy process arises. We study the expected discounted penalty for jump-diffusion
Highlights of the Focus Programs -›› 42 model. Our results provide explicit solutions to a have also trained students to learn and participate large amount of existing pricing problems in these different rese. Speakers in this series of finance. Also, by using our closed form solution seminars are: Dr. PC Lyu 呂平江 (Institute of as criterion, many structural form models in credit Bioinformatics and Structural Biology, NTHU), risk can be reconsidered and modified to see Dr. BS Chen 陳博現 (EE, NTHU), Dr. JM Yang whether more phenomenon in empirical studies 楊進木 (Institute of Bioinformatics, NCTU), Dr. can be captured by jump diffusion model. GH Huang 黃冠華 (Institute of Statistics, NCTU), D r. J K H w a n g 黃 鎮 剛 ( I n s t i t u t e o f On the other hand, motivated from credit risk 許文郁 modeling in finance, we investigate the Bioinformatics, NCTU), Dr. WY Shu (Institute of Statistics, NTHU), Dr. WY Chow 周 asymptotic behavior for the probability and its 姽嫄 variance (first and second moment) of rare events (Institute of Molecular and Cellular Biology, NTHU), YH Tzeng 曾雲輝 (GRC, AS, 中研院基 in joint default. We use Monte Carlo simulation to 因體中心 estimate the joint default probability and improve ) its accuracy by developing a variance reduction (B) Series of Seminars on Special Topics method – importance sampling. By applications of large deviation theory, we have proved that the Yu-Ting Chen: Applications of Continuous State developed importance sampling algorithm in one- Branching Processes in Biology (I)-(III) dimension is asymptotic optimal or called efficient Guan-Yu Chen: The quantitative analysis of if some spatial scale, that controls the occurrence Markov chains (I)- (III) of rare events, is a small parameter. Shuenn-Jyi Sheu: Stochastic Control Approach in (D) Connections Probability and other Math Finance (I)-(IV) Analysis: Ming-Chi Chang and Ming-You Tsai: Stochastic We shall also take account of different Portfolio Theory, Fall Semester, 2009. probability and stochastic features in theory and Karl Peterson: 12 lectures on Ergodic Theory applications of PDEs and other math analysis topics such as fractals, wavelets, dynamical Wojbor A. Woyczynski: 6 lectures on Burgers systems, multi-scale and multi-fractal analysis, We Turbulence shall concern with stochastic PDEs, and PDEs Michael Cranston: 4 lectures on Parabolic with random initial data, and some physics Anderson Model models related to them.. Antoine Ayache: 6 lectures on Wavelets and The role of probability and stochastic analysis Fractional Processes in traditional math analysis and PDE theory hasbeen emphasized not only by persons in (C) Summer Mini-Course on Stochastic probability but also by persons and analysis and Processes (July 7, 2009 ~ August 25, differential equations. 2009) D.8.2 Seminars/Mini-courses This course is organized for students (undergraduates in particular) interested in (A) Seminar on Bioinformatics and System stochastic processes and their applications. Instead Biology (Dec.1, 2008~Jan. 5, 2009) of confinement to formal proofs, we will introduce students to the standard concepts and Each time we invite two researchers to present. methods of stochastic modeling and illustrate the One focuss on the analysis perspective and the rich diversity of applications of stochastic other emphasizes the biological perspective. Thus, processes in the science. we can understand the biological issues with possible analysis approaches through these (D) Student Seminar on Stochastic Processes seminars and discussions. Researchers in different (Fall Semester, 2009) areas can also get together to discuss possible collaborations for interdisciplinary studies. We This is a year-long student seminar on stochastic processes. The purpose of this seminar
43 ‹‹- Highlights of the Focus Programs is to provide students a unified and comprehensive graduate study at the National Chiao-Tung account of Additive processes, stationary University. processes, Markov processes, and martingales (C) Professor Narn-Rueih Shieh(NTU) visited which constitute the four most important classes South China University at Guangzhou(hosted of stochastic processes. by Min Wu) in December 2008 and Queensland University of Technologu D.8.3 Highlights of international University at Brisbane, Australia(hosted by Vo exchange programs Anh) in September 2009. He was also an (A) During June 15-19,2009, a conference entitled invited speaker for the First ISM-APRM “Analysis and Probability in Nice 2nd session” Conference at Seoul National University in was held in Nice, France. The organizing June 2009. committee includes Persi Diaconis, Gilles Lebeau, Laurent Michel and Laurent Miclo. D.8.4 Local focus group: This conference is small with 20 expository Bor-Sen Chen (NTHU), Guan-Yu Chen talks aimed at teaching the problems and (NCTU and NCTS), Chuan-Hsiang Han (NTHU), techniques of one side to the other and Wen-Ping Hsieh (NTHU), Guan-Hua Huang building up real opportunities for interacting (NCTU), Henry Horng-Shing Lu (NCTU), Wen- between probabilists and analysts. The topics Hsiung Li (University of Chicago and Academia of this conference focus on the theme of Sinica), Chung-Chin Lu (NTHU),Yuan-chung quantitative bounds on large time behavior Sheu (NCTU), Wun-YShu (NTHU), Jengnan (equivalently, rates of convergence for Tzeng (Academia Sinica), Yun-Huei Tzeng Markov chains) and include, on the (AcademiaSinica), Ching-Tang Wu (NCTU), probability side, the convergence of Markov Shuenn-Jyi Sheu (Institute of Mathematics, chains, cutoff phenomena, random walks on Academia Sinica), N.-R Shieh (NTU), C.C.Chang groups and compact Riemannian manifolds, (NTU), K.Palmer (NTU), J.-N.Wang (NTU) percolations, random graphs, data augmentation algorithms and, on the analysis D.8.5 Short/Long term visitors side, isoperimetry for product of measures, eigenvalues of graphs and geometry. Guan-Yu Zhen-Qing Chen (Department of Mathematics, Chen was invited to introduce his latest work University of Washington), Jean-Pierre Fouque (joint with Laurent Saloff-Coste) on the L2 (Statistics & Applied Probability Director, Center convergence of Markov processes to their for Research in Financial Mathematics and stationarity. Statistics University of California Santa Barbara), Naoyuki Ichihara (Hiroshima University, Japan), (B) Professor Delmas holds a position at the Ecole Zbigniew J. Jurek (University of Wrocław, Nationale des Ponts et Chausées in Paris. Poland), Takahiro Aoyama (Tokyo University of During his visit of Taiwan in December 2008, Science, Japan), Makoto Maejima (Keio he gave several talks in NCTS Hsinchu and University, Japan),Karl Peterson(North Carolina Academia Sinica on introducing Le Gall's University, USA), Wojbor A. Woyczynski (Case theory of random trees and some of his works Western University, USA), Michael Cranston, UC in population genetics. This year, Yu-Ting Irvine, USA), Hui-Hsuing Kuo (Louisiana State Chen was invited by Professor Jean-Franc\ University, USA), Rongfeng Sun c{o}is Delmas to visit the Ecole Nationale des (NationaalUniversity of Singapore, SIN), Min Wu Ponts et Chausées in Paris. Yu-Ting Chen (South China University of Technology, China), continues his academia study at the University Zhengrong Liu (South China University of of British Columbia in Canada this year. Here, Technology, China), Antoine Ayache (Univisity he and Wei-Kuo Chen(PhD student(2009), Lille 1, France), Bing Li (post-doc fellow, Univ UC,Urvine) would like to give special thanks Picardie, France and Chua-Zhong Univ of Tech, for the National Center of Theoretical China). Sciences in Hsinchu for many years' support of their academic pursuit, ever since their D.8.6 Important Results, Breakthrough
Highlights of the Focus Programs -›› 44 (A) The quantitative analysis of Markov chains find many interesting applications in the fell mostly on the study of specific models in theory of optimal stopping, in the theory of physics, statistics, bioinformation and many optimal control, in the theory of insurance ruin others. But, however, it is very hard to and risk, in the theory of credit risk, in the conquer the problem on the computation of theory of branching processes and in the the mixing time and on the existence of the theory of fragmentation. The expected cutoff phenomenon. Till now, only few discounted penalty was studied via integral practical chains are precisely understood and equation approach in Gerber and Shiu(1998) let alone theoretical results. As it is well- and fluctuation approach in Asmussen, Avram, known that both the cutoff and the mixing and Pistorius(2004). By an ODE approach, we time are closely related, we (Laurent Saloff- worked under the assumption that the process Coste and Guan-Yu Chen) address both follows a two-sided phase-type jump problems (the existence of L2-cutoffs and the diffusion. As hints for possible finance and computation of the L2-mixing time) at the insurance applications of our results, we same time using the spectral theory. This is determined the optimal endogenous default the first time that the cutoff phenomenon is level and obtained the equity, debt and firm determined theoretically. Such a method values in closed form formulas for Leland's should be regarded as solving the L2-mixing- model with jumps. Based on these results, we time problem using functional analysis even (Yu-Ting Chen, Yuan-Chung Sheu and Cheng- though it depends strongly on the prerequisite Few Lee(Rutgers University, USA)) published of complete spectral formation. For an tthis work in Finance and Stochastics, a illustration, we supply a series of classical distinguished international journal in examples to clarify the intuition on the mathematical finance.Very recently, we gave L2-convergence of Markov chains, which can semi-explicit solutions for the expected be very different from the total variation discounted penalty whenever the process is a convergence. This is the first time that the matrix-exponential Lévy processes. Our result L2-convergence is studied in a very precise depends on an identity for the joint Laplace way. This work has been invited by Persi transform of the first entry time and the Diaconis to present in the conference entitled undershoot (Alili and Kyprianou (2005)) and a “Analysis and Probability in Nice, 2nd session” semi-explicit solution of the negative Wiener- which is held in Nice, France during June Hopf factor obtained by Lewis and Mordecki 15-19, 2009. (2008). (B) H. H.-S, Lu has conducted collaborations in (D) The scaling limits of some PDE systems with the research field of bioinformatics and random initial conditions. We (G,-R. Liu and systems biology with the research groups of N.-R. Shieh) employ some stochastic Dr. Wen-Hsiung Li (University of Chicago decoupling method and multiple Wiener-Ito and Academia Sinica), Dr. Lei Li (USC), Dr. integrals to discuss the scaling limits of heat- Curt Scharfe (Stanford) and others. The type system and fractional PDE system with research results in recent five years have been given random initial data. One 24 pp paper published in top leading journals, including has been accepted by Stochastic Analysis and Proceedings of the National Academy of Applications and one 39 pp paper has been Sciences of the United States of America accepted by Stochastics and Dynamics. (PNAS), PLoS Computational Biology, Journal of Computational Biology, D.8.7 Accomplishments Bioinformatics, BMC Bioinformatics, [1] Guan-Yu Chen, Ken Palmer and Yuan-Chung Molecular Biology and Evolution, Journal of Sheu, The least cost super replication Biomedical Informatics, IEEE Transactions on portfolio in the Boyle-Vorst model with Imag transaction costs. International Journal of (C) The expected discounted penalty is not only of Theoretical and Applied Finance Vol. 11, No. interest in the theory of probability, but also 1 (2008), 55-85.
45 ‹‹- Highlights of the Focus Programs [2] Guan-Yu Chen and Laurent Saloff-Coste, The [13] Y.T.Chen, Cheng-Few Lee and Y.C.Sheu, An cutoff phenomenon for randomized riffle Integral-Equation Approach for Defaultable shuffle. Random Structures and Algorithms 32 Bond Prices with Application to Credit (2008), no. 3, 346-374. Spreads. Journal of Applied Probability, [3] Guan-Yu Chen, Wai-Wai Liu and Laurent 46(2009), 71-84. Saloff-Coste, The logarithmic Sobolev [14] P. Mörters and Narn-Rueih Shieh, The exact constant of some finite Markov chains. packing measure of Brownian double points. Annales de la Faculte des Sciences de Probability Theory and Related Fields 143, Toulouse Vol. XVII, No. 2 (2008), 239-290. 2009, pp 113-136. [4] Guan-Yu Chen and Laurent Saloff-Coste, The [15] Narn-Rueih Shieh and Y.M. Xiao, Hausdorff cutoff phenomenon for ergodic Markov and Packing dimension results for the images processes. Electronic Journal of Probability, of random fields. Bernoulli, under revision. 13 (2008), 26-78. [16] M. Matsui and Narn-Rueih Shieh, On the [5] D. Khoshnevisan, Narn-Rueih Shieh and Y.M. exponentials of fractional Ornstein- Xiao, Hausdorff dimension of the contours of Uhlenbeck Processes. Electronic Journal of symmetric additive Levy processes. Probability 14, 2009, Paper no. 23, 594-611. Probability Theory and Related Fields 140, [17] V. Anh and N.N. Leonenko and Narn-Rueih 2008, pp 129-167. Shieh , Multifractal products of stationary [6] P. Mörters and Narn-Rueih Shieh, Multifractal diffusions. Stochastic Analysis and Analysis of Branching Measure on a Galton- Applications 27, 2009, pp 475-499. Watson Tree. In Proceedings of ICCM 2004, [18] V. Anh and N.N. Leonenko and Narn-Rueih pp 655-662, ed. K.S. Lau, Z.P. Xin, and S.T. Shieh, Multifractal moment-scalings in Yau. AMS/IP Studies in Advanced Math 42, geometric birth and death processes. 2008. Bernoulli 15, 2009, pp 508-531. [7] V. Anh and N.N. Leonenko and Narn-Rueih [19] Scharfe, C., Lu, H. H.-S., Neuenburg, J. K., Shieh, Multifractality of products of Allen, E. A., Li, G.-C., Klopstock, T., Cowan, geometric Ornstein-Uhlenbeck type processes. T. M., Enns, G. M., and Davis, R. W., Advances in Applied Probability 40, 2008, pp Mapping Gene Associations in Human 1129-1156. . Mitochondria using Clinical Disease [8] Tzeng, J., Lu, H. H.-S., and Li, W.-H., Phenotypes. PLoS Computational Biology Multidimensional Scaling for Large Genomic 5(4): e1000374. 2009. Data Sets. BMC Bioinformatics, 9:179 (SCI), [20] G. Molina, C.H. Han and J.P. Fouque, 2008. MCMC Estimation of Multiscale Stochastic [9] Chen, T.-B., Lu, H. H.-S., Lee, Y.-S., and Lan, Volatility Models, to appear on Handbook of H.-J., Segmentation of cDNA Microarray Quantitative Finance and Risk Management, Images by Kernel Density Estimation. Edited by C.F. Lee and A.C. Lee, Springer, Journal of Biomedical Informatics, 41, 1021- 2009. 1027. 2008. [21] J. P. Fouque and C.H. Han, Asymmetric [10] Guan-Yu Chen and Laurent Saloff-Coste, The Variance Reduction for Pricing American L2-cutoff for reversible Markov processe.(70 Options. Modelling and Numerical Methods pages), Accepted by J. Funct. Anal. in Finance Volume 15: Special Volume [11] Y.T. Chen and Y.C.Sheu, A note on (Handbook of Numerical Analysis) Editors A. $r$-balayages of matrix-exponential Lévy Bensoussan, Q. Zhang, and Ph. Ciarlet, processes. Elect. Comm. Probab. 14(2009), Elsevier 2009. 165-175. [12] Y.T.Chen and Y.C.Sheu, A generalized renewal equation for two-sided jump- diffusion models. Stochastic Analysis and Applications, 27(2009), 897-910.
Highlights of the Focus Programs -›› 46 D.9 Representation and Geometric Group Theory
Coordinators: Shun-Jen Cheng (Academia Sinica), Meng-Kiat Chuah (National Tsing-Hua University), Ching Hung Lam (Academia Sinica)
his research group investigates the by the Taipei Workshop in Lie Theory held in representation theory of groups, Lie Academia Sinica, which was sponsored by algebra, Lie superalgebras and vertex operator Academia Sinica. algebras. Research topics include the use of group S.-J. Cheng gave a talk in a special session in theoretic methods in geometry and applying the the AMS Meeting in Raleigh in April 2009. He underlying algebraic structures to representation also visited the University of Virginia for two theory and mathematical physics, the weeks in April 2009. He further attended a investigations of the relationship between the summer school in July 2009 in the East China representation theories of classical Lie algebras Normal University in Shanghai, and gave a talk in and Lie superalgebras and the structure theory of the following international workshop in Lie vertex operator algebras and their relationship algebras and related topics. He further attended with certain sporadic simple groups. the International Workshop on Lie Algebras and Investigators: Related Topics in NIMS, Daejeon, Korea, in October 2009, where he gave a talk. During his Shun-Jen Cheng (Academia Sinica), Meng- visit in Korea, he plans visited the University of Kiat Chuah (NTHU), Nan-Kuo Ho (NTHU), Seoul. Also S.J. Cheng has participated in several Ching Hung Lam (Academia Sinica), Shu-Yen Lie theory activities in NCTS/Hsinchu. Pan (NTHU), Jyh-Haur Teh (NTHU). S.J. Cheng has organized bi-monthly informal Visitors: seminar in Lie theory from January to July 2009 in Academia Sinica, attended by faculty and Jing-Song Huang (Hong Kong Univ. Sci. students. Topics include Shapovalov determinant Tech.), Tetsuhiro Moriyama (Univ. Tokyo), Ke formula for generalized Verma modules over Lie Zhu (Chinese Univ. Hong Kong),Weiqiang Wang superalgebras, Yangians and finite (University of Virginia), Jae-Hoon Kwon W-superalgebras, and Deligne-Lusztig character (University of Seoul), Raphael Rouquier formula. Regular seminar should resume in early (University of Oxford), Shrawan Kumar 2010. (University of North Carolina - Chapel Hill), H. Yamauchi (Aichi), Robert Griess (Michigan), In 2009, M. K. Chuah organized a Summer Masaaki Harada (Yamagata), Akihiro Munemasa Activities in Lie Theory, consisting of three mini (Tohoku), N. Chgira (Kumamoto), H. Yamaki workshops of 6-7 hours of lectures on linear (Kumamoto), H. Suzuki (ICU), Hiroki Shimakura algebraic groups, framed vertex operator algebras, (Aichi ), Hiroshi Yamauchi (Achi), Alexander Lie superalgebras. A one-day Lie Theory Ivanov (Imperial College, London). Workshop wass held on April 23, 2009. M. K. Chuah visited Hokkaido University in January In the end of December 2008, S.J. Cheng, 2009, and attended a summer school in Structures together with W. Wang, organized the NCTS/AS in Lie Representation Theory held at Jacobs Winter School in representation theory held in University (Germany) in August 2009. M. K. NCTS/TPE. The main speakers are Raphael Chuah also participated in the Taipei Workshop in Rouquier and Sharwan Kumar. Each gave 10 Lie Theory (December 2008, Sinica) organized by hours of lectures. Attendants of the winter school S. J. Cheng, and attended Mini Workshop on include, among others, mathematicians from Finite Groups in NCTS South organized by C. H. Kyoto and Tokyo. The winter school was followed Lam.
47 ‹‹- Highlights of the Focus Programs N. K. Ho co-organized the East Asian properly formulated categories of Lie algebras and Symplectic Conference in Taipei, May 2009. This Lie superalgebras should be equivalent. This was an international conference, with about 20 conjectural equivalence has been referred to as visitors from Hong Kong, Japan and Korea. N. K. super duality conjecture. This conjecture has been Ho plans to attend the conference " Algebraic established recently in a quite general setting. Structures in the Theory of Holomorphic Curves'' Among its consequences, the classical Kazhdan- at MSRI in December 2009. Lusztig polynomials also compute the character for Lie superalgebras. In Nov 2008 and Mar 2009, C.H. Lam organized two mini-workshops. One was on M. K. Chuah applied the method of geometric algebraic combinatorics and the other one was on quantization on symplectic manifolds to construct finite group theory. The main topics were coding unitary representations, and studied the irreducible theory, modular functions, vertex operator representations which occur in them. The algebras, finite groups and their representations. combinatorial technique of Dynkin diagrams was There were 7 speakers from Japan. C.H. Lam was used to classify the semisimple symmetric spaces. an invited speaker for a symposium on algebraic N. K. Ho used surface group representations combinatorics at RIMS, Kyoto in Jan 2009 and a and Morse theory to study the topology and workshop on vertex operator algebras and geometry of the moduli space of flat connections automorphic forms at Edinburgh in Sep 2009. In over compact orientable or nonorientable surfaces. addition, he participated in the Taipei Workshop in The main techniques come from symplectic Lie Theory (Dec 2008, Academia Sinica) geometry and differential geometry. organized by S. J. Cheng, and gave 6-hours lectures on framed vertex operator algebras at C.H. Lam has been studying some mysterious HsinChu in the summer of 2009. relationship between affine Dynkin diagrams and certain sporadic groups. As a continuation of his S. Y. Pan visited the Netherlands and work on McKay’s E8 observation, he obtained a Switzerland in February 2009, and lectured on vertex operator theoretical explanation for linear algebraic groups in the NCTS Summer McKay’s E7 and E6 observation on the Activities 2009. Babymonster and the largest Fischer J. H. Teh organized two seminars in the spring 3-transposition group. In addition, he also semester 2009. Each of them was a weekly obtained some partial results related to McKay- student seminar, one on differential topology and Glauberman-Norton theory on certain centralizers the other on algebraic topology. There were of the Monster group. In 2009, C. H. Lam started altogether 6 strong undergraduate students who a program on classifying holomorphic framed participated. J. H. Teh organized another student vertex operator algebras of central charge 24. seminar in summer 2009, on algebraic geometry Recently, he and his collaborators have classified and sheaf theory. Eight summer interns the structure codes for holomorphic framed vertex participated actively. The beginning students have operator algebras of rank 24. They also discovered read basic algebra; the more advanced students several new vertex operator algebras which have have studied sheaf theory. J. H. Teh also attended not been constructed before. a conference in Edinburgh, "Geometry and S. Y. Pan studied pairs of reductive Lie groups, Physics'' in celebration of Atiyah's 80-th birthday, and used the method of theta correspondences in in April 2009. representation theory. Important Results, Breakthrough J. H. Teh developed homology and S.-J. Cheng has been studying the relationship cohomology theory to study the homotopy groups between certain parabolic categories of the BGG of algebraic cycles on real and complex varieties. category O of Lie algebras and Lie superalgebras. As a result he proved a more general form of Motivated by earlier calculations of Kostant-type Harnack-Thom theorem that relates Lawson cohomology groups of Lie algebras and Lie homology and morphic cohomology to superalgebras it was conjectured that certain Grothendieck standard conjecture, and proved an equivalent result on the dimension of algebraic
Highlights of the Focus Programs -›› 48 subspace of cohomology groups of two birational Research Notice (2009); doi: doi: 10.1093/ Calabi-Yau manifolds. imrn/rnp091. [11] C. Dong, C.H. Lam, Q. Wang and H. Accomplishments Yamada, The structure of parafermion vertex [1] S.J. Cheng, W. Wang and R. B. Zhang, Super operator algebras, Journal of Algebra (2009), Duality and Kazhdan-Lusztig Polynomials, in press. Transactions of the American Mathematical [12] N. K. Ho and C. C. M. Liu, Yang-Mills Society, 360 (2008), no. 11, 5883-5924. connections on nonorientable surfaces, [2] S.J. Cheng and J.-H. Kwon, Howe Duality Comm. Anal. Geom. 16 (2008), 617-679. and Kostant Homology Formula for infinite- [13] C.H. Lam and H. Yamauchi, On the structure dimensional Lie Superalgebras, International of framed vertex operator algebras and their Mathematics Research Notices, 2008 (2008), pointwise frame stabilizers, Communications no. rnn085, 1-52. in Mathematical Physics, Vol. 277, No. 1 [3] S. J. Cheng and W. Wang, Remarks on (2008), 237-285. DOI: 10.1007/s00220-007- modules of the ortho-symplectic Lie 0323-2. superalgebras, Bulletin of the Institute of [14] J. H. Teh, Harnack Thom theorem for higher Mathematics Academia Sinica, 3 (2008), no. cycle groups and Picard varieties, Trans. 3, 353-372. Amer. Math. Soc. 360 (2008), 3263-3285. [4] S.J. Cheng and N. Lam, Irreducible Character [15] J. H. Teh, Grothedieck standard conjectures, of General Linear Superalgebra and Super morphic cohomology and Hodge index Duality, preprint 2009. theorem, Math. Z. 260 (2008), 849-864. [5] S.J. Cheng, N. Lam and W. Wang, Super [16] J. H. Teh, Motivic integration and projective Duality and Irreducible Characters of Ortho- bundle theorem in morphic cohomology, symplectic Lie superalgebras, preprint 2009. Math. Proc. Cambridge Phil. Soc. 147 [6] M. K. Chuah, Regular principal models of (2009), 295-321. split semisimple Lie groups, J. Reine Angew. [17] J. H. Teh, A homology and cohomology Math. 623 (2008), 195-211. theory for real projective varieties, Indiana [7] M. K. Chuah and J. S. Huang, Double Vogan Univ. Math. J., to appear. diagrams and semisimple symmetric spaces, [18] S.J. Cheng, J.-H. Kwon and N. Lam: A BGG- Trans. Amer. Math. Soc., to appear. type resolution for tensor modules over [8] R.L. Griess Jr. and C. H. Lam, Rootless pairs general linear superalgebra, Letters in of EE8-lattices, Electronic Research Mathematical Physics, 84(2008), no. 1, Announcements in Mathematical Sciences, 75-87. Vol. 15, 2008, 52-61. [19] N. K. Ho and C. C. M. Liu, Yang-Mills [9] C. Dong, C.H. Lam and H. Yamada, connections on orientable and nonorientable W-algebras related to parafermion algebras, surfaces, Memoirs Amer. Math. Soc., to Journal of Algebra 332 (2009), 2236-2043. appear. [10] C.H. Lam and H. Shimakura, Frame [20] C. H. Lam and S. Sakuma, On a class of Stabilizers for framed vertex operator vertex operator algebras having a faithful algebras associated to lattices having S n+1-action, Taiwanese Journal of 4-frames, International Mathematics Mathematics, 12 (2008), 2465-2488.
49 ‹‹- Highlights of the Focus Programs D.10 Scientific Computation at NCTS
Coordinators: Ming-Chih Lai (National Chiao Tung University), Wen-Wei Lin (National Chiao Tung University), Wei-Cheng Wang (National Tsing-Hua University)
ue to the development of computer active collaborator with our group. Recently he technology and mathematical science, finished two joint works as follows. Scientific Computation (SC) has become an (1) "Convergence Analysis of the Doubling indispensable means for solving problems in both Algorithm for Several Nonlinear Matrix theoretical sciences and engineering disciplines. Equations in the Critical Case", Chun-Yueh Numerical simulation tools have increasingly Chiang, Eric King-Wah Chu, Chun-Hua become a vital component in the research as well Guo, Tsung-Ming Huang, Wen-Wei Lin and as application of modern technologies ranging Shu-Fang Xu. from environment, aerospace, materials, biology, to electrical engineering. Based on the support of (2) "Convergence Rates of Some Iterative NCTS, Scientific Computation has gradually Methods for Nonsymmetric Algebraic received proper attention among the mathematics Riccati Equations Arising in Transport community. In addition to promoting Theory", Chun-Hua Guo and Wen-Wei. interdisciplinary research activity with other Lin. sciences, the Scientific Computation program at NCTS also cooperates well with the PDE, 3. Professor JianXin Zhou (Texas A&M Mathematical Biology, and Dynamical Systems University), May. 11-May. 13, 2009 programs in Mathematics Division. Prof. Zhou attended conference “2009 NCTS We now report the activities of SC group in Interdisciplinary Conference on Applied Analysis this year. We have organized one international and Mathematics”. conference and three workshops. Meanwhile, we also have invited a number of distinguished 4. Professor Goong Chen (Texas A&M researchers to offer some short courses and to University), May. 11-May. 13, 2009 conduct cooperative research with our community. Prof. Chen attended conference “2009 NCTS Activities of this year can be summarized as Interdisciplinary Conference on Applied Analysis follows. and Mathematics”.
D.10.1 Visiting Scientists 5. Professor Zhaojun Bai (University of California, Davis), May. 11-May. 13, 2009 1. Professor Zhenyue Zhang (Zhejiang University), Jan. 4-Jan. 12, 2009 Prof. Bai attended conference “2009 NCTS Interdisciplinary Conference on Applied Analysis Prof. Zhang visited NCTS and gave one or and Mathematics”. In addition, he cooperated with more speeches on “Spectral Analysis of Wen-Wei Lin and Yung-Ta Li to finish a paper Alignment in Manifold Learning”. "Structure-preserving model reduction of large scale second-order systems via SQAR approach". 2. Professor Chun-Hua Guo (University of Regina), Mar. 1-Jun. 30, 2009 6. Professor Eric King-Wah Chu (Monash Prof. Guo visited NCTS four months this year University), Jul. 6 - Jul. 31, 2009 & Nov. and gave one or more speeches on “Newton's 15 - Dec. 31, 2009 Method and Halley's Method for the Principal pth Prof. Chu visited NCTS about two months this Root of a Matrix”. However, he is already an
Highlights of the Focus Programs -›› 50 year and continued doing further work with our (4) "A Null Free Jacobi-Davidson Iteration for group. In the mean time, he finished three joint Maxwell's Operator", Tsung-Ming Huang, works as follows. Yin-Liang Huang, Wen-Wei Lin and Wei- Cheng Wang. (1) "Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix 9. Professor Shih-Feng Shieh (NTNU) Equations in the Critical Case", Chun-Yueh Chiang, Eric King-Wah Chu, Chun-Hua Prof. Shieh visited NCTS this summer and Guo, Tsung-Ming Huang, Wen-Wei Lin and finished two works as follows. Shu-Fang Xu. (1) "A Minimal Energy Tracking Method for (2) "Perturbation Results Related to Non-radially Symmetric Solutions of Palindromic Eigenvalue Problems", Eric Coupled Nonlinear Schrödinger King-Wah Chu, Wen-Wei Lin and Chern- Equations", Yueh-Cheng Kuo, Wen-Wei Shuh Wang. Lin, Shih-Feng Shieh and Weichung Wang. (3) "The Palindromic Generalized Eigenvalue (2) "Horseshoes for coupled discrete nonlinear Problem A*x=λAx : Numerical Solution Schrodinger equations", Shih-Feng Shieh. and Applications", Tiexiang Li, Chun-Yueh Chiang, Eric King-Wah Chu and Wen-Wei 10. Professor Yuen-Cheng Kuo (NUK) Lin. Prof. Kuo visited NCTS this summer and focused on "palindromic eigenvalue problem" to 7. Professor Chern Shuh Wang (NCKU) develop a more effective transformation rather Prof. Wang introduced some his recent results than S+S-1- ransformation. In addition, he also on the structure-preserving algorithm and then he finished two joint works as follows. finished a joint work as follows. (1) "Solutions to a Quadratic Inverse (1) "Structured Backward Error for Eigenvalue Problem", Yun-Feng Cai, Yuen- Palindromic Polynomial Eigenvalue Cheng Kuo, Wen-Wei Lin and Shu-Fang Problems", Ren-Cang Li, Wen-Wei Lin and Xu. Chern-Shuh Wang. (2) "A Minimal Energy Tracking Method for Non-radially Symmetric Solutions of 8. Professor Tsung-Min Huang (NTNU) Coupled Nonlinear Schrödinger Prof. Huang visited NCTS this summer and Equations", Yueh-Cheng Kuo, Wen-Wei finished four joint papers as follows. Lin, Shih-Feng Shieh and Weichung Wang. (1) "Structured Doubling Algorithms for Weakly Stabilizing Hermitian Solutions of D.10.2 Regular Seminar Algebraic Riccati Equations", Tsung-Ming 1. Weekly seminar: Oct. 3-Dec. 26, 2008 & Huang and Wen-Wei Lin. Mar. 6-Oct. 31, 2009. (2) "Convergence Analysis of the Doubling Subjects: Algorithm for Several Nonlinear Matrix (1) Quadratic Eigenvalue Problems Equations in the Critical Case", Chun-Yueh (2) Jacobi-Davidson Type Methods Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-Wei Lin and (3) Maxwell Equation Shu-Fang Xu. (4) Continuation Methods (3) "Structure-Preserving Algorithms for (5) Model Reduction Palindromic Quadratic Eigenvalue (6) Arnoldi Method Problems Arising from Vibration of Fast (7) Inexact Krylov Method Trains", Tsung-Min Hwang, Wen-Wei Lin (8) Dynamical System and Jiang Qian. (9) Chaos-based Cryptography
51 ‹‹- Highlights of the Focus Programs (10) Immersed Interface Finite Element Taiwan), Henry Horng-Shing Lu (National Method Chiao Tung University, Taiwan), Hung-Chi (11) Atomistic and Multiscale Modeling of Kuo (National Taiwan University, Taiwan), Materials and Structure Jinn-Chuang Yang (National Chiao Tung University, Taiwan), Li-Ming Yeh (National (12) Image Reconstruction Chiao Tung University, Taiwan), Chu-Pin Lo 2. NCTS Seminar on Scientific (Providence University, Taiwan), Jin-Jia Hu Computation: Dec. 5-Dec. 26, 2008. (National Chiao Tung University, Taiwan), Cheng-Hung Chang (National Chiao Tung Subjects: University, Taiwan) (1) Introduction of Digital Chaotic Cipher (2) Chaotic Vibrations of the 1D Wave System Organizer: Ming-Chih Lai (NCTU, Taiwan) (3) Polynomial Eigenvalue Problem 2. 2009 NCTS One-DAY Workshop on (4) Riccati Equations Modeling and Computing in MRI, February 12, 2009 D.10.3 Schools and Short Courses Magnetic resonance imaging (MRI) in medical 1. Tutorial course I: Maxwell equation, Tsung- imaging applications is becoming important. In Ming Huang (National Taiwan Normal 2003, Paul C. Lauterbur and Sir Peter Mansfield University), Sep. 24-Oct. 1, 2009. were awarded the Nobel Prize in Medicine 2. Tutorial course II: Continuation methods, particularly for their discoveries concerning Yueh-Cheng Kuo (National University of magnetic resonance imaging. Mathematics plays a Kaohsiung), Oct. 8-29, 2009. very important role in MRI, for examples: the ill- posed differentiation and Integral equation apply D10.4 Conferences and Workshops in images of inversion, the statistics and matrix computations apply in filtering of the noise signals 1. 2009 NCTS Interdisciplinary Workshop and identification of image features, and the on Mathematical Modeling and Scientific others how to extract meaningful information Computing, January 19-20, 2009 from the signal data. There are many researching In recent years, interdisciplinary research is topics which are waiting mathematicians to give one of the key projects promoted by NCTS. As appropriate answers. Through this workshop we scientific problems are increasingly complex, hope to exchange research experiences and interdisciplinary cooperations are also promote the cooperation between computing increasingly important. In the past experience, mathematics and medical engineering. different disciplines often have the same Speakers: problems, but they has developed different Henry Horng-Shing Lu (National Chiao Tung solutions in their respective disciplines. The University, Taiwan), Fa-Hsuan Lin (National purpose of this workshop is to gather researchers Taiwan University, Taiwan), Yuh-Jye Lee from physics, chemistry, mechanical engineering, (National Taiwan University of Science and civil engineering, communication engineering and Technology, Taiwan), Chien-Yuan Lin applied mathematics for exchanging experiments (Academia Sinica, Taiwan) and theories, increasing understanding of different Organizer: Wen-Wei Lin (NCTU, Taiwan) discipline and providing more interdisciplinary collaboration opportunities. 3. 2009 NCTS One Day Workshop on Speakers: Interface Problems, February 19, 2009 Wen-Wei Lin (National Chiao Tung University, Interface problems occur in numerous natural Taiwan), Henryk Witek (National Chiao Tung phenomena and industrial applications, especially, University, Taiwan), Yiming Li (National for the fluid mechanics system. Very often, the Chiao Tung University, Taiwan), Peilong Chen mathematical models involving an interface are (National Central University, Taiwan), Ching- some PDEs with moving interface which Yao Chen (National Chiao Tung University, boundary conditions must be specified along the
Highlights of the Focus Programs -›› 52 interface. Since the interface position is unknown Texas-Pan American, USA), Shih-Hsun Hsu and must be solved as a part of solution, this poses (National Taiwan University, Taiwan), Tzy- challenging difficulties from numerical point of Wei Hwang (National Chung Cheng view. For the past decades, the research effort University, Taiwan), Ying-Hen Hsieh (National spent on this topic is overwhelming and is still Chung Hsing University, Taiwan), Yu Huang popular in applied mathematics community. (Zhongshan University, China), Jonq Juang (National Chiao Tung University, Taiwan), Speakers: Chu-Pin Lo (Providence University, Taiwan), I-Liang Chern (National Taiwan University, Ming-Chia Li (National Chiao Tung Taiwan), Eunok Jung (Konkuk University, University, Taiwan), Chih-Wen Shih (National Korea), Do Wan kim (Hanyang University, Chiao Tung University, Taiwan), Junping Shi Korea), Yongsam Kim (Chung-Ang University, (College of William and Mary, USA), Yun- Korea), Yu-Hau Tseng (National Chiao Tung Huei Tzeng (Academia Sinica, Taiwan), Shin- University, Taiwan) Hwa Wang (National Tsing Hua University, Organizer: Ming-Chih Lai (NCTU, Taiwan) Taiwan), Weichung Wang (National Taiwan University, Taiwan), Xiaoqiang Zhao 4. 2009 NCTS Interdisciplinary Conference (Memorial University of Newfoundland, on Applied Analysis and Mathematics, Canada), Jianxin Zhou (Texas A&M May 11-13, 2009 University, USA) This international conference is aimed at The Organizing Committee: promoting the interactions between analysis, Goong Chen (Texas A&M University, USA), applied mathematicians, and scientists from other Ming-Chih Lai (National Chiao Tung disciplines doing interdisciplinary research in University, Taiwan), Chang-Shou Lin mathematical analysis and applied mathematics, (National Taiwan University, Taiwan), Wen- including partial differential equations, dynamical Wei Lin (National Chiao Tung University, systems, inverse problems, fluid dynamics, Taiwan) mathematical biology, scientific computing, etc. We aim at including broad, diverse topics, and D.10.5 Important Results, Breakthrough bringing together researchers from different backgrounds to foster interdisciplinary research, SC group has 14 publications in 2009. Many of as well as encourage the participants to learn and them appear on first rated journals. We describe exchange ideas in a friendly atmosphere. the important research achievements such as the following:
Plenary Speakers: -1 Tai-Ping Liu (Academia Sinica, Taiwan), Tien- (1) Using the (S+S )-transform we develop a Yien Li (Michigan State University, USA), structure-preserving algorithm for solving the Masayasu Mimura (Meiji University, Japan), T-symplectic pencil resulting from the Paul Waltman (Emory University, USA) palindromic quadratic eigenvalue problem (QEP) raised in the study of the vibration in Invited Speakers: the structural analysis for fast trains. For large Zhaojun Bai (University of California, USA), sparse palindromic QEP, we also develop a Chiun-Chuan Chen (National Taiwan generalized T-Skew-Hamiltonian implicitly University, Taiwan), Chao-Nien Chen restarted shift-and-invert Arnoldi algorithm for (National Changhua University of Education, solving the resulting T-Skew-Hamiltonian Taiwan), Goong Chen (Texas A&M University, pencils. USA), Jann-Long Chern (National Central University, Taiwan), Kuo-Chang Chen (2) A mathematical theory on updating with no (National Tsing Hua University, Taiwan), spillover is understood in [97]. However, other Yi-Chiuan Chen (Academia Sinica, Taiwan), imperative issues such as maintaining positive Bau-Sen Du (Academia Sinica, Taiwan), definiteness in the coefficient matrices remain Yihong Du (University of New England, to be addressed. In this paper, we highlight Australia), Zhaosheng Feng (University of several theoretical aspects about updating that
53 ‹‹- Highlights of the Focus Programs preserves both no spillover and positive Vol. 10, Issue 2 (2009), 869-880. definiteness of the mass and stiffness matrices. [2] T. M. Hwang and W. W. Lin, Structured Some necessary and sufficient conditions for Doubling Algorithms for Weakly Stabilizing the solvability conditions are established. Hermitian Solutions of Algebraic Riccati (3) A lid-driven cavity flow with multiple Equations, Lin. Alg. Appl., Vol. 430 (2009), obstacles and different geometries are also 1452-1478. presented.An augmented method based on a [3] Y. F. Cai, Y. C. Kuo, W. W. Lin and S. F. Xu, Cartesian grid is proposed for the Solutions to a Quadratic Inverse Eigenvalue incompressible Navier–Stokes equations in Problem, Lin. Alg. Appl., Vol. 430 (2009), irregular domains. The irregular domain is 1590-1606. embedded into a rectangular one so that a fast [4] C. Y. Chiang, E. K. W. Chu, C. H. Guo, T. M. Poisson solver can be utilized in the projection Huang, W. W. Lin and S. F. Xu, Convergence method. Unlike several methods suggested in Analysis of the Doubling Algorithm for the literature that set the force strengths as Several Nonlinear Matrix Equations in the unknowns, which often results in an ill- Critical Case, SIAM Matrix Anal. Appl., Vol. conditioned linear system, we set the jump in 31, No. 2 (2009), 227-247. the normal derivative of the velocity as the [5] E. K. W. Chu, W. W. Lin and C. S. Wang, augmented variable. The new approach Perturbation Results Related to Palindromic improves the condition number of the system Eigenvalue Problems, ANZIAM J., 2009, to for the augmented variable significantly. Using appear. the immersed interface method, we are able to achieve second order accuracy for the velocity. [6] T. M. Hwang, W. W. Lin and J. Qian, Numerical results and comparisons to Structure-Preserving Algorithms for benchmark tests are given to validate the new Palindromic Quadratic Eigenvalue Problems method. A lid-driven cavity flow with multiple Arising from Vibration of Fast Trains, SIAM obstacles and different geometries are also Matrix Anal. Appl., Vol. 30, No. 4 (2009), presented. 1566-1592. [7] D. Chu, M. Chu and W. W. Lin, Quadratic We present a finite difference method to track a Model Updating with Symmetry, Positive network of curves whose motion is determined by Definiteness and No Spill-Over, SIAM Matrix mean curvature. To study the effect of Anal. Appl., Vol. 31, No. 2 (2009), 546-564. inhomogeneous surface tension on the evolution of the network of curves, we include surfactant [8] C. H. Guo and W. W. Lin, Convergence Rates which can diffuse along the curves. The governing of Some Iterative Methods for Nonsymmetric equations consist of one parabolic equation for the Algebraic Riccati Equations Arising in curve motion coupled with a convection-diffusion Transport Theory, Lin. Alg. Appl., 2009, to equation for the surfactant concentration along appear. each curve. Our numerical method is based on a [9] Y. C. Kuo, W. W. Lin, S. F. Shieh and W. direct discretization of the governing equations Wang, A Minimal Energy Tracking Method for which conserves the total surfactant mass in the Non-radially Symmetric Solutions of Coupled curve network. Numerical experiments are carried Nonlinear Schrödinger Equations, J. Comp. out to examine the effects of inhomogeneous Physics, Vol. 228, No. 21 (2009), 7941–7956. surface tension on the motion of the network, [10] K. Ito, M. C. Lai and Z. Li, A well- including the von Neumann law for cell growth in conditioned augmented system for solving two space dimensions. Navier-Stokes equations in irregular domains, Journal of Computational Physics, D.10.6 Publications Vol. 228 (2009), 2616-2628. [1] S. M. Chang, M. C. Li and W. W. Lin, [11] M. C. Lai, C. W. Hsu and H. Huang, A front- Asymptotic Synchronization of Modified tracking method for motion by mean Logistic Hyper-Chaotic Systems and its curvature with surfactant, Advances in Applications, Nonlin. Anal. Real World Appl., Applied Mathematics and Mechanics, Vol. 1, No. 2 (2009), 288-300.
Highlights of the Focus Programs -›› 54 [12] F. Y. Lin, S. Y. Tu, C. C. Huang and S. M. [15] E. K. W. Chu, T. M. Hwang, W. W. Lin and Chang, Nonlinear Dynamics of C. T. Wu, Vibration of Fast Trains, Semiconductor Lasers under Repetitive Palindromic Eigenvalue Problems and Optical Pulse Injection, IEEE Journal of Structure-Preserving Doubling Algorithms, J. Selected Topics in Quantum Electronics, Vol. Comp. Appl. Math., Vol. 219, No. 1 (2008), 15, No. 3 (2009), 604-611. 237-252. [13] S. F. Shieh, Horseshoes for coupled discrete [16] S. L. Chen, S. M. Chang, W. W. Lin and T. T. nonlinear Schrodinger equations, Journal of Hwang, Digital Secure-Communication Mathematical Physics, Vol. 50, No. 2 (2009), Using Robust Hyper-Chaotic Systems, Int. J. 022701. Bifur. and Chaos, Vol. 18, No. 11 (2008), [14] G. Uhlmann, J. N. Wang and C. T. Wu, 3325-3339. Reconstruction of inclusions in an elastic [17] Y. C. Kuo and S. F. Shieh, Phase separation body, J. Math. Pures Appl, Vol. 91, No. 6 of multi-component Bose-Einstein (2009), 569-582. condensates in optical lattices, Journal of Mathematical Analysis and Applications, Vol. 347, No. 2 (2008), 521-533.
55 ‹‹- Highlights of the Focus Programs Highlights of the Regional Programs
E.1 Regional Programs at Hsinchu E.1.1 Statistics Coordinators: C.-D. Fuh (National Central Univ. and Academia Sinica), S.-T. Tseng (National Tsing-Hua University), H. Wang (National Chiao-Tung University), N.-J. Hsu (National Tsing-Hua University)
his program began to operate in July this (B) Research areas and topics: year. The major work at the first year is to Profile monitoring and fault detection and form research groups. Currently, we have two classification (FDC) research groups, the industrial statistics research group and the financial mathematics and empirical Statistical and engineering process control (SPC, research group. The mission of both groups is to EPC) and R2R control promote frontier research of statistical methods Lifetime inference of highly-reliable products that can be efficiently applied to the real problems (such as nano-device reliability) encountered in finance and industry. Under this goal, the collaboration between academics and the Design and analysis of complex experiment people from the practical fields is very important (C) Monthly regular seminar for exchanging ideas. The following summaries the recent activities of both research groups. We run a one-day regular ISRG seminar inside NCTS monthly. Up to now, we have already Industrial Statistics Research Group invited four speakers to introduce contemporary (ISRG) research topics in industrial statistics (such as inference and modeling of nano-device reliability, Goal: to promote frontier research of statistical profile monitoring, fault detection and methods that can be efficiently applied to improve classification and etc.) Except for running regular the quality and productivity of high-tech industry seminar, we also have a 2-hour subgroup meeting in the nearby Science Research Park. time that allows all participants to exchange their (A) Active research members: research experience. We hope that it can promote useful, collaborated research works. PI: Tseng, S-T (National Tsing Hua Univ.) Cheng, S-W (National Tsing-Hua Univ.) (D) Workshop in summer/winter break Fan, T-H (National Central Univ.) In this July (July 10- August 7), Prof. Cheng, Huang, M-N-L (National Sun-Yat-Sen Univ.) C-S (UC Berkeley and a scientist of NCTS) gave Huwang, Longcheen (National Tsing-Hua Univ.) a series of lectures on design and analysis of experiments. He introduced a unified approach to Jeng, S-L (National Cheng-Kung Univ.) handle the design and analysis of experiments. Lin, T-C (Tamkang Univ.) This new approach allows us to use a generalized Shiau, J-J-H (National Chiao-Tung Univ.) linear model (GLM) to handle blocking, plots and Others (around 40 members from major treatments simultaneously. Currently, Prof. Cheng, universities in Taiwan) S-W and Dr. Peng, C-Y have some joint research works with him.
Highlights of the Regional Programs -›› 56 Financial Mathematics and Empirical [6] D.-F. Cheng (NTU) Research Group (FMERS) Good Day Sunshine: Stock Returns and the Goal: to build a platform for integrating the ideas Weather (August 18, 2009) and methodologies among statistics, finance and [7] R.-H. Wang (NCU) information science, and further lead to new Rain or Shine: Where is the Weather Effect? research directions. (August 18, 2009) (A) Active research members: [8] S.-F. Luo (NTU) PI: C.-D. Fuh (NCU and Academia Sinica) Price Limit Performance: Evidence from the Charles Chang (Cornell University) Tokyo Stock Exchange (September 8, 2009) S.-K. Lin (National University of Kaohsiung) [9] J.-J. Horng Shiau (NCTU) R.-H. Wang (National Central Univ.) Title: Introduction for Profile Monitoring N.-J. Hsu (National Tsing-Hua Univ.) (September 25, 2009) Others (more than 10 graduate students) [10] S.-L. Jeng (NCKU) Reliability Models on Nanotechnology (B) Regular seminar (September 25, 2009) Regular seminars are run on Friday afternoon. [11] R.-H. Wang (NCU) The seminar contains two parts: a talk presented in English and some extended discussions after Risk, Return, and Equilibrium: Empirical Tests the talk. This mode of operation works very well (October 2, 2009) to exchange ideas among people in different [12] Kuo-Bin Li (National Yang-Ming University) disciplines (statistics, finance, econometrics, Applying Computational Sequence Analysis to information science). The participants learned MicroRNA-mediated Gene Regulation knowledge from other fields; students got well (October 23, 2009) trained during the activities and great research ideas were generated from the discussion. [13] J.-K. Tseng (NTU) Dealership Market: Market-Making with Seminar Activities Inventory (October 30, 2009) [1] Ching-Shui Cheng (Academia Sinica, UC [14] Spearker: David Shan Hill Wong (NTHU) Berkeley) Health Monitoring of Multi-On-Off-Stage Lectures on Multistratum Fractional Factorial Batch Processes in Semiconductor Designs (July 16, 23, 30 & Aug. 8, 2009) Manufacturing (October 30, 2009) [2] H.-J. Zhuang (NTU) [15] Jialin Liu (Fortune Institute of Technology) Common Factors in Default Risk Across Plant Information Management System and Countries and Industries (July 7, 2009) Data-Driven Process Monitoring (October 30, [3] L.-C. Cheng (NTU) 2009) [16] Professor Wei-Sheng Wu (NCKU) Herding and the Role of Foreign Institutions in Emerging Equity Markets (July 14, 2009) Systematic Identification of Yeast Cell Cycle Transcription Factors Using Multiple Data [4] C.-L. Kao (NTU) Sources (Nov 20, 2009) Differences of Opinion and the Cross Section [17] Speaker: Professor Shao-Wei Cheng (NTHU) of Stock Returns (July 28, 2009) Experimental design and analysis on a circle [5] J.-I. Cheng (NTU) (Nov 27, 2009) Valuation of Simplex Options by the Extended Black-Scholes Formula (August 4, 2009)
57 ‹‹- Highlights of the Regional Programs E.2 Regional Program at Taipei E.2.1 Multiscale Modeling, Analysis and Computation Coordinators: I-Liang Chern (National Taiwan University), Chien-Cheng Chang (National Taiwan University), Din Ping Tsai (National Taiwan University), Tony W. H. Sheu (National Taiwan University)
E.2.1.1 Background and Description Regular joint seminars and short courses have been organized. We also held several international workshops on scientific computing to bring international researches and local researchers he rapid growth of high performance together. computers has transformed the methodology of scientific investigation. E.2.1.2 Local focus group Computing is nowadays joined experiment and (1) Multiscale analysis and computation: theory as one of the fundamental tools of I-Liang Chern (NTU), Chien-Cheng Chang investigation. It is safe and cheap. Further, in (Academic Sinica and NTU), Yu-Chen Shu many cases, it can go beyond experiments or (Academic Sinica), Wei-Chung Wang (NTU) observation, as those in astrophysics or (2) Computational Fluid Dynamics: Tony W. H. meteorology, etc. The development of Sheu (NTU), K. M. Shyue (NTU), J. Y. Yang computational science needs integration of (NTU), D. L. Yang (NTU), M. J. Huang researchers from different disciplines: (NTU), J. H. Lee (NTU), C. C. Yen (Fu-Jen), mathematics, physics, chemistry, biology, S. F. Tsai (NTOC) geoscience, engineering, computer science, etc. The funding of NCTS provided opportunities to (3) Computational Nano-optics: Din Ping Tsai bring researchers from different disciplines (NTU), Pui-Tak Leung (NTU), Railing Chang together. In the year 2008/8-2009/7, we focus on (NTOU), Hai-Pang Chiang (NTOU), Pi-Gang three interdisciplinary topics: (1) multiscale Luan (NCU), I-Liang Chern (NTU), Guang-Yu analysis and computation, (2) computational Guo (NTU), Shen-Chung Chen (FEC), Yung- nano-optics, and (3) computational mechanics. Chiang Lan (NCKU), Chien-Cheng Chang Multiscale analysis and computation focuses on (NTU), Ruey-Lin Chern (NTU), Chien Liu interface problems, especially on computing Chang (NTU), Yuan Fong Chau (LIT), Tai surface plasmon polariton appeared in nano- Huei Wei (NCCU), Wei-Chih Liu (NTNU), optics. We also introduce multiscale Jia- Han Li (NTU), Sy-Hann Chen (NCYU), computational methods by organizing short Bing-Hung Chen (NDHU), He-Nan Lin courses. Computational fluid dynamics focuese on (NTHU), Ru-Shi Liu (NTU), Kuo-Pin Chiu CFD code implementation on PC-cluster, multi- (NTU), Yuan-Hsing Fu (NTU), Chih-Ming grid and multi-level, preconditioner designs for Wang (NDHU) flow solver. Application of CFD technique to computational medicine and industrial problems. E.2.1.3 Short Term Visitors (2008/8- Nano-optics focuses on investigating the topics of 2009/7) optical responses in nanometer scale and the Boniface Nkonga (Université Bordeaux 1, resultant intriguing phenomena such as surface France), Richard Y-H Tsai (Univ. of Taxes - plasmon resonances, plasmonic band gaps, and Austin), Chiu-Yen Kao (Ohio State Univ.), Ue-Li anomalous light propagation in meta-materials. Pen (CITA Canada), Olof Runborg (KTH, Through these programs, we integrate researchers Sweden), Goong Chen (TAMU, USA), Houman from mathematics, physics and engineering. Owhadi (California Institute of Technology,
Highlights of the Regional Programs -›› 58 USA), K. Zhang (University of Exeter, UK), Workshops Thomas Yizhao Hou (California Institute of (1) Workshop on Nanophotonics: Numerical Technology, USA) N. Zheludev (University of Computations and Simulations, Metal- Southampton, UK), D. Hewak (University of Dielectric Composite Superlenses, by M. Southampton, UK), R. Bakker (Purdue University, Thoreson (Photonics & Spectroscopy Lab., USA), M. Thoreson (Purdue University, USA), B. Purdue University, USA), Optical Wakeham (University of Southampton, UK), S. N. nanoantennae: Initial design and Zhu (Nanjing University, China), S. Maier characterization with an eye towards device (Imperial College London, UK), S. Yannick development, by R. Bakker (Photonics & (Imperial College London, UK), Z. Y. Li (Chinese Spectroscopy Lab., Purdue University, USA). Academy of Science, China), F. C. Zhang (The January 04 (Fri.), 2008 University of Hong Kong, China), S. I. Park (Park Systems Corp., Korea), V. Fedotov (University of (2) Workshop on Numerical Methods for Complex Southampton, UK), E. Plum (University of Fluid Flows and It’s Applications to Natural Southampton, UK), E. Arthurs (CEO of SPIE), A. Hazards, October 16, 2008, The invited Vitkin (University of Toronto, Canada), A. Q. Liu speakers in this workshop are Boniface (Nanyang Technological University, Singapore), Nkonga (Univ. of Bordeaux 1, France), Dartzi S. Y. Lin (Rensselaer Polytechnic Institute, USA), Pan (National Cheng Kung Univ.),Mario G. F. Jin (Tsinghua University, China), F. Yu (The Ricchiuto (INRIA, France) Pennsylvania State University, USA), Z. Samson (3) Workshop on high resolution image restoration (Optoelectronics Research Centre, UK), K. October 24(Friday), 2008, The invited Kitahara (International Christian University, speakers in this workshop are Raymond H. Japan), H. Chan (The Hong Kong Polytechic Chan (Chinese Univ. of Hong Kong), Thierry University, China), X. Zhang (The Hong Kong Blu (Chinese Univ. of Hong Kong) Polytechic University, China), C. H. Haur (National University of Singapore, Singapore), (4) NTU Mathematics Month June 29 - July 18, Pui Tak Leung (Univ. of Portland, USA). 2009, The invited speakers in this workshop are: I. Daubechies, B. Engquist, S. Altschuler, E.2.1.4 Seminars, short courses and S.-B. Hsu, C.-Y. Kao, S.-Y. R. Li, H. Owhadi, workshops U.-L. Pen, O. Runborg, Y.-H. Tsai, L.-F. Wu, K. Zhang. Regular seminars: there are 58 seminars in (5) International Workshop on Metamaterial 2008/8-2009/7 Plasmonics, October 10, 2008. The aim of this (1) Computation and Simulation Monthly short course is to introduce the fundamental Seminars on Nano-photonics. (whole year) theory and novel optical properties of metamaterials, plasmonic nanostructures for (2) Multi-scale analysis and computation on every application to nano- and micro-photonic Friday. We hold 17 meetings on scattering, devices. The invited speakers in this workshop band gap optimization, homogenization and are: Xiang Zhang, Jia Han Li, Takuo Tanaka, flow in micro-channel. (2009,2-2009-6) Prof. Pi Gang Luan, Prof. Wei Chih Liu, Yung (3) Computational optimization on every Chiang Lan, Ruey Lin Chern, Juen Kai Wang, Thursday. (2009,2-2009-6) Hai Pang Chiang, Pei Kuen Wei, Sheng Chung Chen, Din Ping Tsai, (4) Frontier Nano-photonic: 7 meegings. Two talks in each meeting. (6) Nanophotonics and Metamaterials 2009, April 28 - May 02, 2009. The 2009 East-West Short courses and schools Summit on Nanophotnics and Meta-Materials (1) NCTS(TPE)/TIMS Joint Summer Course on seminar will bring together the top Image Science, by I-L Chern, July. 20, 2009 - professionals in nanophotonics and meta- August. 28, 2009. There are about 20 students materials from Hong Kong, Japan, Korea, participating. More than 15 two-hour lectures. Singapore, the U. K., and Taiwan. The invited At the end, each student gave one hour report. speakers will brief on their novel research
59 ‹‹- Highlights of the Regional Programs results, while the most deliberated and vibrant Mass Density of a Periodic Array of Acoustic discussions are also anticipated. The invited Media by Homogenization Analysis. speakers are listed as follows: Allan [9] V. C. Huang, Tony W. H. Sheu (2009), Heat Boardman, Che Ting Chan, Cheng Hsuan transfer involved in acupuncture with burning Chen, Ruey Lin Chen, Shean Jen Chen, Hai moxibustion on the top of the handel of the Pang Chiang, Tow Chong Chong, Ming Wen acupuncture needle, Acupuncture and Electro- Chu, Richard DeLaRue, Shang Jr Gwo, Therapeutics Research (accepted, in press) Ortwin Hess, Kyoung Youm Kim, Yung (SCI) Chiang Lan, El Hang Lee, Ulf Leonhardt, Pui [10] Kuo, H.-C., C.-P. Chang, Y.-T Yang, H.-J. Tak Leung, Jia Han Li, Er Ping Li, Ai Qun Jiang, 2009, Western North Pacific typhoons Liu, Wei Chih Liu, Boris Luk' yanchuck, with concentric eyewalls, Mon. Wea. Rev., in Stefan Maier, Masayuki Naya, David Payne, press. SCI Richard Penty, John Ryan, Ze Xiang Shen, Hiroharu Tamaru, Takuo Tanaka, Din Ping [11] R.Fovell., K. L. Corbosiero and H.C. Kuo, Tsai, Juen Kai Wang, Yuh Lin Wang, Pei Kuen 2009, Cloud microphysics impact on Wei, Anatoly Zayats, Nikolay Zheludev, Lei hurricane track as revealed in idealized Zhou. experiments, J. Atmos. Sci., in press. SCI [12] Hsieh, C.T., Chang, C.C. & Chu, C.C. E.2.1.5 Select publications of the local (2009), Revisiting the aerodynamics of focus group insect flight using simple models, Journal of Fluid Mechanics 623, 121-148. (SCI) [1] I-Liang Chern, Hai-Liang Li, Long-time Behavior of the nonlinear Schrödinger- [13] Tsui, P.H., Yeh, C.K. & Chang, C.C. (2009), Langevin equation, preprint 2009. Microvascular flow estimation by microbubble-assisted Nakagami imaging, [2] Daomin Cao, I-Liang Chern, Jun-Cheng Wei, Ultrasound in Medicine and Biology 35, On Ground State of Spinor Bose-Einstein 653-671. (SCI) Condensates, preprint 2009. [14] Chen, C.F., Liu, J, Hromada, L., Tsao, C.W., [3] Yu-Chen Shu, Chien. C. Chang and I-Liang Chang, C.C. & DeVoe, D.L. (2009), High- Chern, Augmented Coupling Interface Method pressure needle interface for thermoplastic for Solving Plasmonic Eigenvalue Problems, microfluidics, Lab on a Chip 9, 50-55. (SCI) preprint 2009. [15] Liu, J., Chen, C.F., Tsao, C.W., Chang, C.C., [4] Yu-Chen Shu, Yi-Cheng Hsu, Chien. C. Chu, C.C. and DeVoe, D.L. (2009), Polymer Chang and I-Liang Chern, Complete Band Microchips Integrating Solid Phase Gaps Optimization for Geometric Parameters Extraction and High Performance Liquid of Phontonic Crystals, preprint 2009. Chromatography Using Reversed-Phase [5] Raymond H. Chan, I-Liang Chern, and Hai- Polymethacrylate Monoliths, Analytical Xia Liang, Forward-Backward Splitting, Chemistry 81, 2545-2554. (SCI) Bregman, Linearized Bregman, Iteration [16] Kung, C.F., Chiu, C.F., Chen, C.F., Chang, Methods and the Majorize-Minimize C.C. & Chu, C.C. (2009), Blood flow driven Algorithm, preprint 2009 by surface tension in a microchannel, [6] Raymond H. Chan, I-Liang Chern, Chi-Kin Microfluidics and Nanofluidics 6, 693-697. Tai and Wen-Yih Isaac Tseng, Reconstruction (SCI) of parallel MRI Images Using High [17] Chen, C.N., Lin, J.J., Lee, H.Y., Chen, Y.M., Resolution Image Reconstruction Techniques, Chang, K.J., Hsieh, F.J., Lai, H.S., Chang, 2009 C.C. & Lee, P.H. (2009),Association [7] Ying-Hong Liu and Chien C. Chang, Effective between color Doppler vascularity index, group velocity of the elastic waves in the angiogenesis-related molecules, and clinical periodic structure of elastic composites: a outcomes in gastric cancer, Journal of homogenization study, 2009. Surgical Oncology (SCI, accepted in press). [8] Ying-Hong Liu and Chien C. Chang, Effective
Highlights of the Regional Programs -›› 60 [18] Kuo, C.Y., Chern, R.L. & Chang, C.C. Commun. 149, 625 (2009). (2009), Sound scattering by a compact [31] K. P. Chiu, K. F. Lai, S. C. Yen, D. P. Tsai, circular pore, Journal of Sound and Opt. Rev. 16, 326 (2009). Vibration 319, pp. 622-645. (SCI) [32] H. Y. Xie, P. T. Leung, D. P. Tsai, J. Math. [19] Tsui, P.H., Yeh, C.K. & Chang, C.C. (2008), Phys. 50, 072901 (2009). Feasibility exploration of blood flow [33] K. P. Chiu, N. L. Wu, C. S. Wu, Y. H. Fu, C. estimation by contrast-assisted Nakagami H. Chu, H. Y. Chung, F. H. Chen, L. D. Lin, imaging, Ultrasonic Imaging 33, pp. 133- L. H. Huang, C. D. Shue, and D. P. Tsai, 150. (SCI) Proceedings of SPIE 7392, 73920B (2009). [20] Tsui, P.H., Yeh, C.K., Chang, C.C. & Liao, [34] Tony W. H. Sheu, C. F. Chen, L. W. Hsieh Y.Y. (2008), Classification of breast masses (2008), Development of a three-point sixth- by ultrasonic Nakagami imaging: a order compact Helmholtz scheme for feasibility study, Physics in Medicine and scattering wave propagation, Journal of Biology 53, pp. 6027-6044. (SCI) Computational Acoustics, Vol. 16(3), pp. [21] Tsui, P.H., Yeh, C.K., Chang, C.C. & Chen, 343-359 (SCI; Impact Factor: 0.508; Cited W.S. (2008), Performance evaluation of Half-life 6.8; Ranking: 57/74) ultrasound Nakagami image in tissue [35] Vincent C. L. Huang, Tony W. H. Sheu characterization, Ultrasonic Imaging 30, pp. (2008), On a dynamic view on the meridian 78-94. (SCI) transmission, Journal of Accord Integrative [22] Liu, Y.H., Chang, C.C. & Kuo, C.Y. (2008), Medicine, Vol. 4(2), pp. 97-107 Propagating modes of periodic solid layers [36] V. C. Huang, Tony W. H. Sheu (2008), Heat in an ideal or viscous fluid by transfer involved in a warm (moxa-heated) homogenization analysis, Physical Review B needle treatment, Acupuncture and Electro- 78, 054115. (SCI) Therapeutics Research, Vol. 33(3-4), pp. [23] Kuo, C.Y., Wang, C.Y. & Chang, C.C. 169-178 (SCI) (2008), Generation of directional electro- [37] Tony W. H. Sheu, C. H. Yu, P. H. Chiu osmotic flow by interactive oscillatory zeta (2009), Development of a dispersively potential, Electrophoresis 29, 1-5. (SCI) accurate conservative level set scheme for [24] Chang, C.C., Shu, Y.C. & Chern, I.L. (2008), capturing interface in two-phase flows, Solving guided wave modes for plasmonic Journal of Computational Physics, Vol. 228, crystals, Physical Review B 78, 035133. pp. 661-686 (SCI) (SCI) [38] V. C. Huang, Tony W. H. Sheu (2009), [25] Wang, C.Y., Liu, Y.H. & Chang, C.C. (2008), Tissue fluids in microchannel subjected to an Analytical solution of electro-osmotic flow externally applied electric potential, in a semi-circular micro-channel, Physics of International Journal of Numerical Methods Fluids 20, 063105. (SCI) for Heat and Fluid Flow, Vol. 19(1), pp. [26] Pan, T.W., Chang C.C. & Glowinski R. 64-77 (SCI) (2008), On the motion of a neutrally buoyant [39] P. H. Chiu, Tony W. H. Sheu (2009), On the ellipsoid in a three-dimensional Poiseuille development of a dispersion-relation- flow, Computer Methods in Applied preserving dual-compact upwind scheme for Mechanics and Engineering 197, pp. 2198- convection-diffusion equation, Journal of 2209. (SCI) Computational Physics, Vol. 228(10), pp. [27] K. P. Chiu, K. F. Kai, D. P. Tsai, Optics 3640-3655 (SCI) Express 16, 13885 (2008.) [40] Tony W. H. Sheu, S. H. Kuo (2009), [28] H. Y. Xie, P. T. Leung, D. P. Tsai, Phys. Rev. Numerical study of an electroosmotically A 78, 64101 (2008). driven microchannel flow with Joule heating [29] H. Y. Xie, P. T. Leung and D. P. Tsai, J. Phys. effect, Numerical Heat Transfer. Part B: A: Math. Theor. 42, 045402 (2009). Fundamentals, Vol. 55, issue 6, pp. 503-522 (SCI) [30] H. Y. Xie, P. T. Leung, D. P. Tsai, Solid State
61 ‹‹- Highlights of the Regional Programs [41] Tony W. H. Sheu, M. C. Hsu (2009), Finite for Numerical Methods in Fluids (in print) element simulation of incompressible (SCI) viscous flows in moving meshes, Numerical [44] J. H. Li, Y. W. Cheng, Y. C. Chue, C. H. Lin, Heat Transfer. Part B: Fundamentals, Vol. Tony W. H. Sheu (2009), Influence of 56, pp. 1-20 (SCI) propagating and evanescent waves on for [42] . H. Chiu, Long Lee, Tony W. H. Sheu foursing properties in zone plate structures, (2009), A dispersion-relation-preserving Optics Express (accepted) (SCI) algorithm for a nonlinear shallow-water [45] C. M. Ho, R. K. Lin, S. F. Tsai, P. C. Liang, wave equation, Journal of Computational Tony W. H. Sheu, P. H. Lee (2009), Physics, Vol. 228, pp. 8034-8052 (SCI) Simulation of portal hemodynamic changes [43] Tony W. H. Sheu, Y. W. Hung, M. H. Tsai, J. in a donor after right hepatectomy, Journal H. Li (2009), On the development of a triple- of Biomechanical Engineering (accepted) preserving Maxwell's equations solver in (SCI) non-staggered grids, International Journal
E.2 Regional Program at Taipei E.2.2 Statistics Coordinators: Ming-Yen Cheng (National Taiwan University)
E.2.1.1 Important Results, Breakthrough support by NTU TIMS by any means. Together with Liang Peng, we propose a new method for estimating the conditional variance in heteroscedasticity regression models. For heavy irst, please note that all the research tailed innovations, this method is in general more outcomes and publications given in this efficient than either of the local linear and local section did acknowledge NCTS for its support, likelihood estimators. Secondly, we apply a most of which was to sponsor visits of the variance reduction technique to improve the international research collaborators. In particular, inference for the conditional variance. The those 2009 publications did not receive any proposed methods are investigated through their financial support from the Taida Institute of asymptotic distributions and numerical Mathematical Science (TIMS) of National Taiwan performances. University (NTU), nor Ming-Yen Cheng involved in the NTU TIMS grant during 2008-2009. Ming- Multiparameter likelihood models (MLMs) Yen Cheng knew only in mid October that Hung with multiple covariates have a wide range of Chen, who is principal investigator for the applications; however, they encounter the “curse statistics sub-project of NTU TIMS grant, copied of dimensionality” problem when the dimension without her consent her 2009 research of the covariates is large. Ming-Yen Cheng, publications from her webpage to the NTU TIMS Wenyang Zhang, and Lu-Hung Chen develop a 2009 annual report as part of the statistics sub- generalized multiparameter likelihood model that project’s research outcome, which cannot be true copes with multiple covariates and adapts to at all since those research activities were not dynamic structural changes well. It includes some popular models, such as the partially linear and
Highlights of the Regional Programs -›› 62 varying-coefficient models, as special cases. They smoothing estimate of the hazard ratio is present a simple, effective two-step method to proposed. The proposed procedure and the one estimate both the parametric and the based on Cox proportional hazard modeling with nonparametric components when the model is Box-Cox transformation of the time to event are fixed. The proposed estimator of the parametric both evaluated by Monte–Carlo simulations and component has the root-n convergence rate, and applied to two clinical trial datasets. the estimator of the nonparametric component enjoys an adaptivity property. They suggest a E.2.2.2 Accomplishments data-driven procedure for selecting the [1] Cheng, M.-Y. and Raimondo, M. (2008). bandwidths, and propose an initial estimator in Kernel methods for optimal change-points profile likelihood estimation of the parametric part estimation in derivatives. Journal of to ensure stability of the approach in general Computational and Graphical Statistics, 17, settings. They further develop an automatic 56-75. procedure to identify constant parameters in the underlying model. They provide a simulation [2] Chen, L.-H., Cheng, M.-Y. and Peng, L. study and an application to infant mortality data of (2009). Conditional variance estimation in China to demonstrate the performance of our heteroscedastic regression models. Journal of proposed method. The phenomenon of crossing Statistical Planning and Inference, 139, 236- hazard rates is common in clinical trials with time 245. to event endpoints. [3] Cheng, M.-Y., Zhang, W. and Chen, L.-H. (2009). Statistical estimation in generalized Many methods have been proposed for testing multiparameter likelihood models. Journal of equality of hazard functions against a crossing the American Statistical Association, 104, hazards alternative. However, there have been 1179-1191. relatively few approaches available in the literature for point or interval estimation of the [4] Cheng, M.-Y., Qiu, P., Tan, X. and Tu, D. crossing time point. Ming-Yen Cheng, Peihua Qiu, (2009). Nonparametric con_dence intervals Xianman Tan, and Dongsheng Tu consider the for the crossing point of two hazard functions. problem of constructing confidence intervals for Lifetime Data Analysis, to appear. the first crossing time point of two hazard [5] Cheng, M.-Y., Paige, R.L., Sun, S. and Yan, functions. After reviewing a recent procedure K. (2008). Variance reduction for kernel based on Cox proportional hazard modeling with estimators in clustered/longitudinal data Box-Cox transformation of the time to event, a analysis. Submitted. nonparametric procedure using the kernel
63 ‹‹- Highlights of the Regional Programs E.3 Regional Programs at Tainan E.3.1 Algebra and its application Coordinators: Ching Hung Lam (National Cheng-Kung University) and Wen-Fong Ke (National Cheng-Kung University)
here are three main research directions in Yamaki (Kumamoto), Hiroshi Suzuki algebra and its applications. One is the (ICU), N. Chigira (Kumamoto) research leading by Ching Hung Lam and Ngau Organizer: C. H. Lam Lam on the representations of vertex operator algebras, Lie super-algebras and finite groups. Foreign visitors: H. Yamauchi (Aichi), Robert Another direction is on the model of p-adic Griess (Michigan), Masaaki representations of groups by Chu-Feng Nien. The Harada (Yamagata), Manabu third topic is on the study of combinatorial Oura (Kochi), Akihiro structures related to representation theory, jointly Munemasa (Tohoku), Tsuyoshi organized by Wen Fong Ke, Po Yi Huang and Miezaki (Kyushu), Hiroki Ching Hung Lam. Shimakura (Aichi ) I. Student Seminar on Algebra IV. Arithmetic Seminar A student seminar is run by Wen Fong Ke and We organized two parallel biweekly number Po Yi Huang at weekly basis at Tainan. This theory seminar. seminar primarily aims at graduate students. The (A) Joint National Taiwan University and National main subject is Lie algebra and representations of Cheng Kung University Arithmetic Seminar groups. was organized by K.S. Tan (NTU) and K. F. Workshops: Lai (NCKU) on Iwasawa Theory in characteristic p and was held once every 2 We also held two mini-workshops in weeks alternately in NCTS Taipei and in 2008/2009 NCTS Tainan. The following lectures/ II. Mini-workshop in algebraic multiple-lectures were given: combinatorics (Nov. 29, 2008) (1) Ignazio Longhi (NTU), Drinfeld modules and explicit class field theory over function Subjects: Coding theory, modular functions, fields, 1&2. vertex operator algebras (2) K. F. Lai (NCKU), Cohomological Speaker: Masaaki Harada (Yamagata University), backgrounds for Abelian Varieties over Manabu Oura (Kochi University), function fields, 1 & 2. Akihiro Munemasa (Tohoku University), Tsuyoshi Miezaki (Kyushu University), (3) K.S. Tan, Selmer Groups over function Hiroki Shimakura (Aichi University of fields, 1&2 Education) (4) Ignazio Longhi (NTU), L-functions and Organizer: C.H. Lam modular symbols for elliptic curves over function fields III. Mini-workshop on finite groups (B) Joint National Chung Ching University and (March 13, 2009) National Cheng Kung University Arithmetic Subjects: Finite groups and its representations Seminar was organized by M.K. Eie (CCU), Speaker: Koichiro Harada (Ohio-State), H. Po Yi Huang (NCKU) and K. F. Lai (NCKU) on Multiple Zeta Values and was held once
Highlights of the Regional Programs -›› 64 every 2 weeks in NCTS Tainan. The following [3] A historical introduction to classfield theory, lectures/multiple-lectures were given: by K. F. Lai (NCKU) (1) Minking Eie (CCU), Multiple Zeta Values [4] Lusternik-Schnirelmann category and systolic - Evaluations and relations- 1, 2,3 geometry of low dimensional manifolds by Jose-Carlos Gomez-Larranaga, Centro de (2) Wen-Chin Liaw (CCU), Multiple Zeta Investigacion en Mathematics, Mexico. Values 4 [5] The topology of Brownian Motion on a (3) Yao-Lin Ong (CJCU), Multiple Zeta Riemannian Manifold, Ricardo F. Vila Freyer, Values, 5 CIMAT, Mexico (4) Hung-Min Liao (National Taiwan Normal [6] Quantum Field Theory and the Jones University) Quadratic Twists of Elliptic Polinomial for measure preserving Flows on a Curves 3 dimensional manifold, Ricardo F. Vila Freyer, CIMAT, Mexico V. Algebra Seminar [7] Canonical basis of singularity Ringel-Hall An algebra seminar was organized by W-F. Ke algebras, G.-L. Zhang (SJTU, China) and K. F. Lai which meets as speakers arrived. [8] Backgrounds on Mutually Unbiased Bases The following talks were given: and its applications to quantum computation, given by K. F. Lai (NCKU) [1] Geometric realization of Lie algebras in terms [9] On the Edge-graceful trees conjecture, Sin- of derived categories of finite-dimensional Min Lee, San Jose State University algebras, 1,2,3 by Guanglian Zhang, Department of Mathematics, Shanghai [10] Explicit Construction Of Moduli Space Of Jiaotong University Bounded Complete Reinhardt Domains In C^N And Hilbert 14th Problems, Stephen S. [2] On some basic problems in the modren T. Yau (University of Illinois) Theory of Automorphic forms, Dihua Jiang, University of Minnesota
E.3 Regional Programs at Tainan E.3.2 Geometry Coordinators: Eugene Xia (National Cheng-Kung University) and River Chiang (National Cheng-Kung University)
he geometry research here at NCTS Ji Hong, Eugene Z. Xia, River Chiang, Nan-Kuo (South) ranges from symplectic geometry Ho (left Aug. for NTHU), Kwan Hang Lam (left to algebraic geometry to geometric analysis. Aug. for HK), Kung-Ho Chan (joined Aug.). Research topics include: moduli space of flat Foreign visitors from 2008/9 to 2009/10: T. bundles, moment maps in various geometries, Moriyama (Tokyo), T. Yoshida (Meiji), M. Akaho lagrnagian submanifolds, harmonic functions (Tokyo Metropolitan), V. Ginzburg (UC Santa theory, geometric flow, mapping class group, Cruz), K. Niederkruger (Ecole Normale kahler structure. Superieure de Lyon), O. van Koert (Hokkaido), K. Local researchers (NCKU): Roger Chen, Ying- Zhu (Chinese University of Hong Kong), H.
65 ‹‹- Highlights of the Regional Programs Chang (first visit: SISSA, second visit: Hong (1) Embedding property of J-holomorphic Kong University of Science and Technology). curves in Calabi-Yau manifolds for generic J (2) Floer trajectories of immersed nodes and Activities at NCTS (South): scale-dependent gluing In December 2008, we organized a Fujisan One-day Workshop in Geometry and Topology. 5. Seminars: (http://www.ncts.ncku.edu.tw/math/ (1) Mr. Chung-I Ho (University of Minnesota, workshop/081227/) USA), Luttinger surgery and Kodaira 1. Manabu Akaho (Tokyo Metropolitan dimension University, Japan), Immersed Lagrangian Floer (2) Prof. Nan-Kuo Ho (National Cheng Kung theory University, Taiwan), A symplectic structure 2. Tetsuhiro Moriyama (University of Tokyo, on the moduli space of flat connections Japan), On embeddings of 3-manifolds in over a Riemann surface 6-manifolds and the configuration space (3) Seminar on Banach Manifold and integrals for links and 3-manifolds Applications 3. Takahiko Yoshida (Meiji University, Japan), Ngai- Ching Wong (NSYSU), King Fai Lai Acyclic polarizations and localization of (NCTS, NCKU) organized an "open ended" Riemann-Roch numbers seminar without fixed themes except that we shall In spring 2009, in preparation for the East discuss Banach manifolds, Hilbert manifolds, Asian Symplectic Conference 2009 at Academia related structures and problems on such manifolds Sinica, we hosted several activities at NCTS and applications in particular to quantum physics (South). These include: and general relativity. 1. Lecture series: Prof. Viktor Ginzburg Between 27th February and 12th June we met (University of California, Santa Cruz, USA), almost every Friday between 2.00 to 3.30pm Periodic orbits of Hamiltonian systems (i) A during in the NCTS in NCKU. The following symplectic topological perspective (ii) The talks were given: Conley conjecture and resonance relations (1) K. F. Lai, Open Problems on Banach 2. Lecture series: Prof. Quo-Shin Chi Manifolds (Washington University, St. Louis, USA), (2) Chi-Cheung Poon,National Cheng Cheng Isoparametric hypersurfaces with four principal University , Dolbeault complex in infinite curvatures in spheres I and II dimensions 3. Miniworkshop on Contact Geometry (http:// (3) Ching You Liao (NSYSU) Smooth www.ncts.ncku.edu.tw/math/ Functions On Banach Manifolds workshop/090412/) (4) Chun Wen Tsai (NSYSU) Orthogonality Dr. Otto van Koert (Hokkaido University, Preserving Linear Maps of Continuous Japan), Convex surfaces in contact 3-manifolds Field of C*-algebras and minimal coverings (5) Nan Kuo Ho (NCKU), A symplectic Dr. Klaus Niederkruger (Ecole Normale structure on the moduli space of flat Superieure de Lyon, France), Resolution of connections over a Riemann surface symplectic orbifolds obtained from reduction (6) Chung-Wen Tsai (NSYSU), Open Prof. Shu-Cheng Chang (National Taiwan embeddings of certain Banach manifolds University), The Perelman-Type Entropy (7) Ady Mann, Dept. of Physics, Institute of Formulas on Pseudohermitian Manifolds Technology, Israel, Some open problems in 4. Lecture series: Dr. Ke Zhu (The Chinese MUB from the eyes of physicists University of Hong Kong, Hong Kong), In Fall 2009, we started an informal geometry
Highlights of the Regional Programs -›› 66 seminar aiming for geometers to understand each Morse stratification and Orientability in Yang- other’s research areas. Also, we joined with the Mills theory over nonorientable surfaces. R. math colloquium to arrange general geometry Chiang has a preprint on Convexity package for talks aiming for students and faculty members in momentum maps on contact manifolds. different disciplines. These include: 1. Prof. Martin Guest (Tokyo Metropolitan NCTS affiliated Publications 2008-2009: University), The mysterious Toda lattice [1] Chiang, R.; Xia, Eugene Z. Strong Lefschetz property under reduction. Israel J. Math. 174 2. Prof. King-Fai Lai (National Sun Yat-Sen (2009), 369-380 Univresity), A little conversation on the interplay between groups and functions [2] Xia, Eugene Z. Explicit connections with SU(2)-monodromy. Forum Math. 21 (2009), 3. Dr. Hironori Sakai (National Cheng Kung no. 5, 827-832 University), Quantum differential equation of [3] N.-K. Ho and C.-C. M. Liu, Yang-Mills weighted projective spaces connections on nonorientable surfaces, Commun. Anal. Geom. 16 (2008), no.3, 617- Member activities: 679. R. Chiang and N.-K. Ho organized the East Asian Symplectic Conference 2009 at Academia Other Publications 2008-2009: Sinica in May 2009. [1] N.-K. Ho and C.-C. M. Liu, Yang-Mills R. Chiang and N.-K. Ho participated in the connections on orientable and nonorientable IHES 50th anniversary conference on surfaces, to appear in Memoirs of the Mathematical Sciences at Tokyo and Keio American Mathematical Society. University in October 2008. E.Z. Xia participated [2] Goldman, William M.; Xia, Eugene Z. Rank in the Mathematical Society of Japan (MSJ) one Higgs bundles and representations of Seasonal Institute (SI) 2009 on Arrangements of fundamental groups of Riemann surfaces. Hyperplanes at Hokkaido University in August Mem. Amer. Math. Soc. 193 (2008), no. 904. 2009 and also Arithmetic Geometry and Moduli Future Plans: We will continue our research in Spaces in Algebraic Geometry in August in Hang- algebraic geometry, dynamical systems, th Zhou, China. R. Chiang participated in the 5 and symplectic and contact geometry. We plan to th 6 Takagi lectures in Tokyo in October 2008 and organize several joint seminars, workshops, short Hokkaido in June 2009 as well as the MSRI courses and lecture series with Taipei and Hsin connection for women workshop and introductory Chu. We hope these activities can promote workshop in symplectic and contact geometry and geometry in the math society in Taiwan and lead topology in August 2009. to future collaboration. R. Chiang gave a talk at OCAMI-TIMS Joint Visitors on the anticipated list for 2010: Huai- International Workshop on Differential Geometry Liang Chang (HKUST), Tara Holm (Cornell), and Geometric Analysis at Osaka City University Rebecca Goldin (George Mason), Urs in March 2009. Frauenfelder (Seoul), Otto van Koert (Seoul), Federica Pasquotto (Vrije), Takashi Sakai (Tokyo Research Results: Metropolitan), Mikiya Masuda (Osaka City), E.Z. Xia has preprints on Dehn twists and Reyer Sjamaar (Cornell), Eugene Lerman invariant classes, and Ergodicity of mapping class (Illinois), Hiroshi Iriyeh (Tokyo Denki), Mark group actions on SU(2)-charater varieties. N.-K. Hamilton (Tokyo), Jongil Park (Seoul). Ho has updated her preprints on Anti-perfect
67 ‹‹- Highlights of the Regional Programs E.3 Regional Programs at Tainan E.3.3 Applied Mathematics Coordinators: Soon-Yi Wu (National Cheng-Kung University) and Yung-Fu Fang (National Cheng-Kung University).
here are two main research directions for Computation. the focus group in Applied Mathematics. 1. Soon-Yi Wu organized “Mini-workshop for One is the Optimization and Numerical Optimization” on January 14, 2009. Speakers Conputation and the other one is Differential in this conference were Prof. Nicolas Equations. Hadjisavvas (University of the Aegean), Prof. Nguyen Dong Yen (Vietnamese Academy of Section A. Optimization and Numerical Science and Technology), Prof. Chong Li Computation (Zhejiang University), Prof. Nguyen Huy The research group on Optimization and Chieu (Vinh University), and Prof. Jian-Wen Numerical Computation are Soon-Yi Wu Peng (Chongqing Normal University). The title (NCKU), Jen-Chih Yao (NSYSU), Rey-Lin Sheu of their talks are as follows: (NCKU), Huang-Nan Huang (THU), Mei-Hsiu (1) “Maximal monotone bifunctions” by Prof. Chi (CCU), Shen-Yu Chen (Fortune IT), Jen-Yen Nicolas Hadjisavvas Lin (NCYU), and there are 4 Ph.D students in optimization and numerical computation and (2) “Relationships between the Robinson related topics presently. There is also 1 post doctor robust stability and the Aubin continuity at NCKU at the moment. property of implicit multifunctions” by Prof. Nguyen Dong Yen The visiting professors and their visiting dates during this year are: (3) “Qualifications for Infinite System of Convex Inequalities in Banach Spaces with 2008-09-15~09-28: Prof. Shunsuke Hayashi Applications” by Prof. Chong Li (Kyoto University) (4) “Limiting Subdifferentials of Indefinite 2008-11-10~11-13: Prof. King-Fai Lai (The Integrals” by Nguyen Huy Chieu University of Sydney) (5) “Common Solutions of an Iterative Scheme 2008-12-01~12-07: Prof. Marco Lopez (Alicante for Variational Inclusions, Equilibrium University) Problems and Fixed Point Problems” by 2008-12-26~12-30: Prof. Ka-Fai Yiu (The Hong Prof. Jian-Wen Peng Kong Polytechnic University) 2. Optimization Seminar was organized by Soon- 2009-01-06~01-10: Prof. King-Fai Lai (The Yi Wu (NCKU). The following talks were University of Sydney) given: 2009-09-06~09-29: Prof. Shunsuke Hayashi (1) On the Finite Convergence of an Explicit (Kyoto University) Exchange Method for Convex Semi- 2009-11-22~12-06: Prof. Marco A. Lopez Infinite Programming Problems with (Alicante University) Second-Order Cone Constraints, Shunsuke Hayashi, Kyoto University, September 22, 2009-12-20~01-20: Prof. Dong-Hui Li (Hunan 2008. University) (2) An infinite-dimensional mathematical Followings are the activities for the focus programming approach to separation in Lp group on Optimization and Numerical
Highlights of the Regional Programs -›› 68 (X, A,μ), by Marco Lopez, Alicante Lin, China Medical University, October 13, University, Spain, December 15, 2008. 2009. (3) A Unified Quadratic Semi-Infinite (8) Augmented Lagrange Dual Approach for Programming to Optimal Least SquareFIR Generalized Fractional Programming, by Filter Design, Shang-Linh Chen (National Prof. Jen-Yen Lin, NCYU, October 29, Cheng Kung University), December 4, 2009. 2008. (9) Effective Wideband Acoustic Sonar Signal (4) Speech enhancement via optimization Detection Based on Adaptive Neuro-Fuzzy techniques, Ka-Fai Yiu, Department of Processor and Optimal Wavelet Transform, Applied Mathematics, Hong Kong by Prof. Jason Tseng, Kun Shan University, Polytechnic University, December 29, November 3, 2009. 2008. (10) Convergence analysis for Newton’s (5) Jein-Shan Chen (National Taiwan Normal method on Lie groups, by Prof. Chong Li, University), Soc function, January 9. Zhejiang University, China., November 30, 2009. 3. Seminar in Computational and Optimization and Applications was organized by Soon-Yi (11) Separating sets in a normed space by Wu (NCKU). Totally, 7 talks are presented and using infinite-dimensional optimization, 8 talks scheduled to be presented. We list here by Prof. Marco Lopez, Alicante these talks in the following: University, Spain, November 30, 2009. (1) Large-scale linear programming and semi- (12) Numerical methods for inverse eigenvalue infinite programming, by Soon-Yi Wu, problems, by Prof. Chong Li, Zhejiang NCKU, September 15, 2009. University, China., December 1, 2009. (2) An explicit exchange algorithm for linear (13) Lipschitzian stability of infinite and semi- semi-infinite programming problems with infinite optimization problems, by Prof. second-order cone constraints, by Prof. Marco Lopez, Alicante University, Spain, Shunsuke Hayashi, Kyoto University, December 1, 2009. September 17, 2009. (14) Prof. Weichung Wang, National Taiwan (3) Solving convex semi-infinite programming University, December 22, 2009. problems with second-order cones, by Prof. (15) Prof. Hsien-Chung Wu, National Shunsuke Hayashi, Kyoto University, Kaohsiung Normal University, January 5, September 22, 2009. 2010. (4) Newton method for large-scale logistic (16) Prof. Yuh-Jye Lee, National Taiwan regression and linear support vector University of Science and Technology, machines, by Prof. Chih-Jen Lin, National January 12, 2010. Taiwan University, September 24, 2009. (17) Mr. Ting-Jang Shiu, NCKU. (5) On generalized Fischer-Burmeister NCP- function, by Prof. Jein-Shan Chen, National Section B. Differential Equations Taiwan Normal University, September 29, 2009. The work carried out in this year is within the realm of the original goals. (6) Fractional Programming with Applications, by Prof. Ruey-Lin Sheu, NCKU, October 1, We improve the unique continuation property 2009. of the solution for the elastic transversely isotropic dynamical systems. We generalize the asymptotic (7) Solvabilities of the Vector Variational exponential stability of traveling front solutions Inequalities Problems and the Vector for a general monotone reaction-diffusion bistable Complementary Problems for F -implicit system. We give a reduction formula for the Generalized Cases, by Prof. Yen-Cherng characteristic functions of the Sturm– Liouville
69 ‹‹- Highlights of the Regional Programs boundary value problems. We get better results of materials containing negative stiffness reconstruction and stability of the inverse nodal inclusions, April 7, 2009. problem. We give new proofs for bilinear (6) Yun-Che Wang (Dept. of Civil Engineering, estimates and null form estimates for waves. NCKU), Strong ellipticity conditions and The research group on Differential Equations thermodynamic stability of negative- are Yung-Fu Fang (NCKU), Ching-Lung Lin stiffness composites, April 14, 2009. (NCKU), Kuo-Ming Lee(NCKU), Jiann-Sheng (7) Feng-Tai Hwang (NSPO), 最佳化數學模 Jiang (Tung Fang IT), Tsung-fang Wu (NUK). 型及其解法, April 16, 2009. During the past year, we have invited several (8) Cynthia Liu (NSPO), 數學在影像處理的 excellent scholars in differential equations to visit 應用, April 16, 2009. our Center. They are 李 志 豪 (9) Yun-Che Wang (Dept. of Civil Engineering, J y h - H a o L e e ( ) ( I n s t i t u t e o f NCKU), Negative-stiffness composites Mathematics, Academia Sinica), under the framework of the Cosserats Chi-kun Lin (林琦焜) (Department of Applied mechanics, April 21, 2009. Math, N. Chiao Tung University), (10) Henry Horng-Shing Lu (Institute of Yun-Che Wang (王雲哲 教授) (Department of Statistics, NCTU), Reconstruction, Civil Engineering, NCKU), and Visualization and Analysis of Medical Images, May 14, 2009. Dehao Yu (余德浩) (Academy of Mathematics and Systems Science, Chinese Academy of (11) Chien-Chih Huang (Dept. of Mathematics, Sciences) NTHU), Chaos-based cryptography and STPCS stream cipher, May 21, 2009. They were actively engaged in discussions with our subgroup. Besides those formal talks (12) Jyh-Hao Lee (Institute of Mathematics, listed below, they also give some talks for our Academia Sinica), Solitions in DNLS and graduate students. Moreover, our activities are DNLS with Quantum Potential, June 15, listed as follows: 2009. 1. Applied mathematics seminar was organized (13) Chi-Kun Lin (Dept. of Applied by Yung-fu Fang (NCKU), Wen-Ching Lien Mathematics, NCTU), 熱的解析理論與 (NCKU), and Chern-Shun Wang (NCKU). The Fourier分析, June 15, 2009. following talks were given: (14) Dehao Yu (Academy of Mathematics and (1) Hsiu-Chuan Huang (NCKU), Strichartz Systems Science, Chinese Academy of estimates for the Schrodinger equations- Sciences), Artificial Boundary Method for Movitation, March 10, 2009. Exterior Problems of Partial Differential Equations, September, 22, 2009. (2) Hsiu-Chuan Huang (NCKU), Strichartz estimates for the Schrodinger equations- (15) Tsung-Fang Wu (Dept. of Applied Application, March 12, 2009. Mathematics, NUK), Multiple positive solutions of semilinear elliptic equations (3) Hsiu-Chuan Huang (NCKU), Strichartz involving sign-changing weight functions, estimates for the Schrodinger equations- October 29, 2009. Proof the non-endpoint cases, March 17, 2009. 2. Summer School on PDE at Tainan, organized by Prof. Yung-Fu Fang, entitled “Topical (4) Hung-Chi Kuo (Dept. of Atmospheric Program in Partial Differential Equations” was Sciences, NTU), Two dimentional held from July 14 to August 11, 2009. The Turbulence, Typhoon Dynamics and subjects in this summer school are Scientific computing, March 26, 2009. Homogenization Problem, Calderons (5) Yun-Che Wang (Dept. of Civil Engineering, uniqueness theorem and Scattering theory. The NCKU), Stability of discrete composite speakers and their talks are:
Highlights of the Regional Programs -›› 70 (1) 江鑑聲 Jiann-Sheng Jiang collaborative paper with Prof. Shunsuke Hayashi (entitled “An explicit exchange algorithm for 1. Homogenization and Two-Scale linear semi-infinite programming problems with Convergence for Partial Differential second-order cone constraints”). The algorithm Equations, July 14, 2009. ideas proposed in these two papers are quite 2. Homogenization and Memory Effects, July similar; however, they prove that there are very 16, 2009. good convergence rate on their different SIP (2) 林景隆 Ching-Lung Lin problems. Besides, the implement results for this algorithm we get is better than other exiting 1. Uniqueness for the first order elliptic algorithms for SIP. This is a breakthrough in the differential operators and its application (I), implement of infinite programming. (II), (III), respective on July 21, July 23 and July 28, 2009. Section B. Differential Equations 2. Calderons uniqueness theorem and its 1. Ching-Lung Lin (林景隆). We prove the application (I), July, 30, 2009. unique continuation property of the solution for 3. Quantitative uniqueness for second order the elastic transversely isotropic dynamical elliptic operators with strongly singular systems with smooth coefficients satisfying coefficients, August 11, 2009. some conditions and apply it to extending the Dirichlet to Neumann map. The proof is based 黃秀娟 (3) Hsiu-chuan Huang on the localized Fourier–Gauss transformation 1. Scattering theory, Strichartz estimates, LWP; and Carleman type estimate. GWP, Morawetz estimates & Scattering, (I), 2. J.-C. Tsai (蔡志強). We study the asymptotic (II), respective on August 4, and August 6, exponential stability of traveling front 2009. solutions for a general monotone reaction- 1. The seminars are run on weekly base and diffusion bistable system with some diffusion students are required to study some topics from coefficients being zero. The main tools to books or papers, and present to the group in the obtain our results are comparison principle, classroom. The seminars are in two themes. suitably constructed super-sub solutions, and One is lead by Yung-fu Fang in the direction of squeezing methods. No spectrum analysis of investigating the well-posedness problem of the linear operator associated with traveling wave type equations, including bilinear front solutions under study is needed. estimates for wave equations and Schrödinger Therefore, our results not only recover and/or equations and related scattering problems. The complement earlier stability results in the other direction is lead by Ching-Lung Lin literature, but also provide a simple method to toward the study of the uniqueness show the asymptotic exponential stability of continuation theorem, Carleman estimates, and traveling front solutions for a general its application in the inverse problem. monotone reaction-diffusion bistable system with positive diffusion. 2. "2009 International Workshop of Differential 羅春光 Equations and their Applications", 3. Chun-Kong Law ( ) . We g i v e a 2009/12/18~2009/12/21. reduction formula for the characteristic functions of the Sturm-Liouville boundary Research Results: value problems defined on a tree. We also discuss the multiplicity of the eigenvalues and Section A. Optimization and Numerical interlacing properties between two spectral sets Computation associated with different boundary conditions. The research results of this year are the 4. Chun-Kong Law (羅春光). We study the issues collaborative paper with Prof. Liping Zhang of reconstruction and stability issues of the (entitled “A New Exchange Method for Convex inverse nodal problem for the one-dimensional Semi-Infinite Programming”) and another p-Laplacian eigenvalue problem. A key step is
71 ‹‹- Highlights of the Regional Programs the application of a modified Prüfer [1] S. J. Li, C. R. Chen and S. Y. Wu, Conjugate substitution to derive a detailed asymptotic dual problems in constrained set-valued expansion for the eigenvalues and nodal optimization and applications, European lengths. Two associated Ambarzumyan Journal of Operational Research, Vol. 196, problems are also solved. 21-32. 5. Yung-Fu Fang (方永富). We give new proofs [2] N. J. Huang, J. Li and S. Y. Wu, Optimality of bilinear estimates and null form estimates Conditions for Vector Optimization Problems, for Waves. Modify the techniques for waves, Journal of Optimization Theory and we can prove a bilinear estimates for Application, Vol. 142, 323-342. Schrödinger waves. [3] L. P. Zhang and S. Y. Wu, An algorithm based on the generalized D-gap function for Publications: equilibrium problems, J o u r n a l o f Computational and Applied Mathematics, Vol. 2008 231, 403-411. [1] S. Y. Chen and S. Y. Wu, Algorithms for [4] L. P. Zhang and S. Y. Wu, Improved Infinite Quadratic Programming in Lp Spaces, Smoothing Newton Methods for $P_0$ Journal of Computational and Applied Nonlinear Complementarity Problems, Mathematics, Vol. 213, 408-422. Applied Mathematics and Computation, Vol. [2] S. C. Fang, David Y. Gao, R. L. Sheu and S. 215, 324-332. Y. Wu, Canonical Dual Approach to Solving [5] Chun-Kong Law and V. Pivovarchik, 0-1 Quadratic Programming Problems, Characteristic functions of quantum graphs, Journal of Industrial and Management Journal of Physics A: Mathematical and Optimization, Vol. 4, 125-142. Theoretical, Vol. 42(3), Article Number: [3] J. Ye and S. Y. Wu, First Order Optimality 035302. Conditions for Generalized Semi-Infinite [6] X. J. Tong, S. Y. Wu and R. J. Zhou (2009), Programming problems, J o u r n a l o f New Approach for the Nonlinear Optimization Theory and Applications, Vol. Programming with Transient Stability 137, 419-434. Constraints Arising from Power Systems, to [4] S. Y. Chen and S. Y. Wu, An Algorithm for appear in Computational Optimization and Semi-Infinite Transportation Problems, Applications. Journal of Computational and Applied [7] C. Ling, Q. Ni, L. Qi and S. Y. Wu, A New Mathematics, Vol. 217, 365-380. Smoothing Newton-Type Algorithm for Semi- [5] N. J. Huang, J. Li and S. Y. Wu, Gap Infinite Programming, to appear in Journal of Functions for a System of Generalized Vector Global Optimization. Quasi-Equilibrium Problems with Set-Valued [8] S. Hayashi and S. Y. Wu, An Explicit Mappings, Journal of Global Optimization, Algorithm for Linear Semi-Infinite Vol.41, 401-415. Programming Problem with Second-order [6] K. Kimura, Y. C. Liou, S. Y. Wu and J. C. Cone Constraint, to appear in SIAM Journal Yao, Well-Posedness for Parametric Vector on Optimization. Equilibrium Problems with Applications, [9] S. Ito, S. Y. Wu, T. J. Shiu and K. L. Teo Journal of Industrial and Management (2009), A Numerical Approach to Infinite- Optimization, Vol. 4, 313-327. Dimensional Linear Programming in L1 [7] Ching-Lung Lin, Gen Nakamura, and Mourad Spaces, to appear in Journal of Industrial and Sin, Unique continuation for the elastic Management Optimization. transversely isotropic dynamical systems and [10] L. P. Zhang and S. Y. W, A New Approach to its application, J. Differential Equations, Vol. Supply Chain Network Equilibrium Models, 245, 3008–3024. to appear in Acta Mathematica Scientia. 2009 [11] M. López, S. Y. Wu, C. Ling and L. Qi, An Infinite-Dimensional Mathematical
Highlights of the Regional Programs -›› 72 Programming Approach to Separation in Lp Preprint (X, A, μ) , to appear in Journal of Convex [1] L. P. Zhang, S. Y. Wu and M. A. Lopez Analysis. (2009), A New Exchange Method for Convex [12] Chun-Kong Law, W.C. Lian, and W.C. Wang, Semi-Infinite Programming, preprint. Inverse nodal problem and Ambarzumyan [2] Yung-Fu Fang, A New Proof for a Bilinear problem for the p-Laplacian, to appear in Estimates of Waves, preprint. Proceedings of the Royal Society of Edinburgh.
E.3 Regional Programs at Tainan E.3.4 Statistics Coordinators: Wu Tiee-Jian (National Cheng-Kung University)
Overview The focus group on industrial statistics has started its activities since 2009. The NCTS (South) has sponsored a 2009 Statistics & Machine Learning workshop in Apr., 2009 and 林共進 he statistics program started its operation invite professors including Dennis Lin ( ) 鄭惟 in mid-March, 2008. It is now only one of Penn. State University and Smiley Cheng ( 孝 year and five months old. Six academicians of ) of University of Manitoba to visit the center Academia Sinica have served as advisory and give lectures, among other scholarly activities members of our program and have made From September 1, 2008 until August, 2009, 周 significant contributions. They are Y.-S. Chow ( our program has already invited totally 11 short- 元燊院士 刁錦寰院士 ), George Tiao ( ), Jeff Wu term visiting scholars (among them, four: Y.-S. 吳建福院士 黎子良院士 ( ), T.-L. Lai ( ), K.-Y. Chow, George Tiao, T.-L. Lai & W.-H. Li are 梁賡義院士 蔡瑞胸院士 Liang ( ) and R. Tsay ( ). academicians of Academia Sinica and one: Zang- Our Academic Executive Committee, expanded Hee Cho is an academician of both the National from three members last year to five members this Academy of Science of USA and that of Korea); 吳鐵肩 year, currently includes T.-J. Wu ( ), M.-M held 20 seminar talks; sponsored the 2008 任眉眉 鄭順林 Zen ( ) and S.-L. Jeng ( ) of Bioinformatics workshop (about 120 participants), 黃 Department of Statistics, NCKU, W.-J. Huang ( 2009 Probability workshop (about 80 participants) 文璋 ) of Department of Applied Mathematics, and 2009 Symposium in Statistics and Probability 郭美惠 NUK and M.-H. Guo ( ) of Department of (about 200 participants); and co-sponsored the Applied Mathematics, NSYSU. This committee 2009 Statistics Conference of Southern Taiwan will be expanded as our program develops further (about 300 participants) and the 2009 Statistics & in the future. Machine-Learning Conference (about 250 The focus group this year is classified as (i) participants). Furthermore, we have already Probability and Statistical Methods and (ii) supported 2 young scholars to go abroad for Applied Statistics, while the latter includes research collaborations and/or international Biostatistics & Bioinformatics, Financial Statistics conferences. Between them, one is an associate & Time Series, and Industrial Statistic. professor (Ray-Bing Chen) from NUK and the
73 ‹‹- Highlights of the Regional Programs other is an assistant professor (May-Ru Chen) Coordinator: Tiee-Jian Wu from NSYSU. Finally, under the (partial) support The activities from September 1, 2008 to of our program, seven papers and one lecture note August, 2009 are as follows: in the form of reprints or preprints have been generated and acknowledged the support of NCTS 1. Seminar (South) (See Appendix: Publication). Prof. Chin-Tsang Chiang of Dept. of Math., Probability and Statistical Methods NTU gave a lecture entitled: ” Optimal Composite Markers for Time-Dependent ROC Curves with I. Probability Program Censored Survival Data” on September 25, 2008 Coordinator: Wen-Jang Huang at NCKU, W. K. Härdle of Humboldt-Universitat zu, Berlin a lecture: ” The Stochastic Fluctuation The main goal is to generate some common of the Quantile Regression Curve” on October 2 , research interest among members and to learn 2008 at NCKU, Ray-Bing Chen of NUK a lecture: some new topics. ”Independent Component Analysis via Copula The activities from September 1, 2008 to Techniques” on Oct. 16, 2008 at NCKU, Jing- August, 2009 are as follows: Shiang Haung of Academia Sinica a lecture: “ A new latent structure model for binary network 1. Seminar analysis” on Nov.6, 2008 at NCKU, Chin-Shang Li of UC, Davis a lecture: “Using P-splines to test Professor W. Chen (陳文憲) of U. Miami has for linearity in partially linear models” on Nov. given a seminar talk entitled: ”A note on the first 24, 2008 at NCKU, Q. Yu of Binghamton Univ., occurrence of strings” at NCKU on Oct. 9, 2008 , USA a lecture: “Relationship between the Cox, Weiwei Zhuang of Department of Statistics and Lehmann, Weibull and accelerated lifetime Finance, USTC a talk entitled:” Stochastic models” on Dec. 25, 2008 at NCKU, and J.B. Comparisons of Generalized Order Statistics” on Filho of Universidade Federal de Lavras-UFLA, Apr. 16, 2009 at NCKU, and A.K. Gupta a talk at Brazil a lecture: ” Bayesian analysis of interfering NUK in June, 2009. and toxicity effects in dilution assays” on Feb. 19, 2. Visitor 2009 at NSYSU There were two visitors Y.-S. Chow (周元燊院 2. Visitors 士 ) from June 10-12, 2009 and A. K. Gupta, Tze-Leung Lai of Stanford University visited distinguished university professor of Bowling our center from Jan. 8-10, 2009 (see below for his Green State University, from June 21 to July 5, activities). Prof. J.B. Filho of Universidade 2009. In addition to the activities described above, Federal de Lavras-UFLA, Brazil visited our center A.K. Gupta attended the 2009 Statistics from 2/15/2009 to 3/04/2009 and gave a lecture at Conference of Southern Taiwan (held from June NSYSU and discussed research ideas with Prof. 26-27, 2009 at NSYSU) and gave a lecture M-N. Lo of NSYSU. Professor P-Y. Chen (陳平 entitled: “Estimation and model identification 雲) of Syracuse University visited NCTS (South) based on maximum product of spacings for a from 6/22/2009 to 7/5/2009 and gave a talk multivariate skew normal family” in that entitled: “A Hybrid Selection and Testing conference. Procedure with Curtailment for Comparative 3. Workshop Clinical Trial.” He has also discussed a joint research work with Tiee-Jian Wu on “Order The ”2009 Probability Workshop” was held on selection for multivariate multiple regression and June 11, 2009 at NCKU. There were a series of time series data”. A manuscript on this subject will lectures: “On the theory of optimal stopping I and be completed soon. II”, given by Y.-S. Chow (周元燊院士). Totally, there were about 80 participants. 3. Short course and Symposium Tze-Leung Lai gave a 2 and 1/2 hours short II. Statistical Methods course on: “Self-Normalized Processes: Limit
Highlights of the Regional Programs -›› 74 Theory and Statistical Applications“ on Jan. 8, 3. Workshop 2009 at NCKU. There are about 100 participants. The ”2008 workshop in Bioinformatics” was Further, our center sponsored the 2009 held in Nov. 27. Prof. W-H Lee (李文雄院士) Symposium in Statistics and Probability on Jan. 9, gave two lectures entitled: ”Identification of 2009 at NUK (about 200 participants) and Prof. functional signals in DNA sequences“ and Tze-Leung Lai has given a speech in that “Prediction of new microRNAs in the human symposium too. genome”, respectively. There were about 120 participants. III. Biostatistics and Bioinformatics Coordinator: Tiee-Jian Wu IV. Financial Statistics and Time Series The activities from September 1, 2008 to Coordinator: Mei-Hui Guo August, 2009 are as follows: The activities from September 1, 2008 to August, 2009 are as follows: 1. Seminar Professor Wei-Chung Liu of Academia Sinica 1. Seminar gave a lecture entitled:” Parasitism in Ecological Prof. W. K. Härdle of Humboldt-Universitat Networks” on Oct. 23, 2008 at NCKU, Zang Hee zu, Berlin gave a lecture entitled: “Implied Market Cho, an academician of both the National Price of Weather Risk” on Oct. 1, 2008 at Academy of Science of USA and that of Korea a NSYSU, and George Tiao a lecture: “A lecture: ” Tomography” on Nov. 28, 2009 at Generalized Methodology for Global Temperature NSYSU and NCKU, respectively; H. Nesetrilova Trend Detection” on Nov. 8, 2008 at NCKU. of Czech University of Life Sciences a lecture: ” Growth models in animal breeding” on Feb. 12, 2. Visitor 2009 at NSYSU, and Chun Li of Vanderbilt Prof. W. K. Haerdle of Humboldt-Universitat University a lecture: “Powerful Association Tests Zu, Berlin visited our center from Sep. 29 to Oct. for Genome-Wide Association Studies Using 5, 2008. He has given two lectures (one in NCKU, Admixed Populations” on May 7, 2009 at NCKU. one in NSYSC, see above) and discussed research 2. Visitor ideas in financial mathematics and statistics. Also, George Tiao has visited our center from Nov.2-4, 李文雄院士 Prof. W-H Lee ( ) visited our center 2008. He has given a lecture (see above) in on Nov. 27-28, 2008. He gave a workshop (see applications of time series method and discussed below) and discussed research topics with Prof. possible statistical methodology in studying the S.-C. Chen of NCKU. And they have recently ozone hole problem. finished the draft of their joint paper. Prof. Zang Hee Cho, an academician of both the National V. Industrial Statistics Academy of Science of USA and that of Korea, Coordinator: S.-L. Jeng visited our center from Nov. 27-28, 2008 and gave lectures (see above). Prof. H. Nesetrilova of The activities from September 1, 2008 to Czech University of Life Sciences visited our August, 2009 are as follows: center from Feb. 4 -16, 2009. She gave a speech (see above) and discussed research ideas with 1. Seminar Mei-Hui Guo of NSYSU. Prof. Wei-Yan Tsai of Prof. Smiley W. Cheng of University of Columbia University visited our center on June Manitoba, Canada gave a lecture entitled: “Single 17-22, 2009. He gave a lecture entitled: ” Variable Control Charts-An Overview” on Mar. Proportional Likelihood Ratio Models” at NCKU 19, 2009 at NCKU, and Dennis K. J. Lin of Penn as well as the keynote speech (Wen-Bao Chang's State University a lecture: “Computer Keynote speech) entitled: “Statistical analysis for Experiment” on June 4 at NCKU. truncated data” in the 2009 Statistics Conference of Southern Taiwan. 2. Workshop
75 ‹‹- Highlights of the Regional Programs The ”2009 Statistics & Machine Learning (II) Lecture Notes Workshop” was held on Apr. 25-26, 2009 at [8] Probability handout (機率論講義) by Y.-S. NCKU. Totally, there were about 250 participants. Chow (2009) 3. Publications VI. Research Results: (I) Research Articles: From September 1, 2008 until the present time, [1] T.-J. Wu, X. Shi and B. Miao (2009). our program has already invited totally 12 short- Asymptotic approximation of inverse term visiting scholars (among them, five: Y.-S. moments of nonnegative random variables. Chow, George Tiao, T.-L. Lai, W.-H. Li & K.-Y. Statist. & Probab. Letters, 79, 1366-1371, SCI Liang are academicians of Academia Sinica and [2] P. Chen, L. Osadciw and T.-J. Wu (2009). one: Zang-Hee Cho is an academician of both the Multiple targets characterization of National Academy of Science of USA and that of electromagnetic vulnerability. Signal Korea); held 22 seminar talks; sponsored the 2008 Processing, (in press), SCI Bioinformatics workshop (about 120 participants), 2009 Probability workshop (about 80 [3] S.-C. Chen, J. Tzeng, T.-H. Tsai and W.-H. Li participants), 2009 Symposium in Statistics and (2009). Microarray analysis based on dynamic Probability (about 200 participants); and 2009 support and confidence association rules. Workshop in Statistics Methodology; and (submitted) co-sponsored the 2009 Statistics Conference of [4] S.-C. Chen, D. Hayden, S.S. Young and J. Southern Taiwan (about 300 participants) and the Tzeng (2009). The wavelet transform for NIR 2009 Statistics & Machine-Learning Conference prediction (submitted). (about 250 participants). Furthermore, we have [5] W.-C. Wang, R.-B. Chen and C.-L. Hsu already supported 3 young scholars to go abroad (2009). A surrogate-assisted method using for research collaborations and/or international adaptive multi-accurate function evaluations. conferences. Between them, one is an associate (submitted) professor (Ray-Bing Chen) from NUK, one is an [6] R.-B. Chen, M.-H. Guo, W.K. Hardle and associate professor (Mi-Chia Ma) from NCKU, S.-F. Huang (2009). COPICA-Independent and the other is an assistant professor (May-Ru component analysis via Copula techniques. Chen) from NSYSU. Finally, under the (partial) (submitted) support of our program, 8 papers and one lecture [7] W.-J. Huang and N.-C. Su (2009). A study of note in the form of reprints or preprints have been generalized skew-normal distribution. generated and acknowledged the support of NCTS (submitted). (South).
Highlights of the Regional Programs -›› 76 Activities of Onsite Scientists
Title Name Field Period Probability Stochastic Guan-Yu Chen 2007/08/01-2009/07/31 Processes Jiun-Cheng Chen Algebraic Geometry 2006/08/01-2009/07/31 Cheng-Hsiung Hsu Dynamical Systems 2008/08/01-2009/07/31 Ming-Chia Li Dynamical Systems 2007/08/01-2009/07/31 Wen-Ching Winnie Li Number Theory 2009/05/14-2011/07/31 Chin-Cheng Lin Analysis 2008/08/01-2009/07/31 Center Scientists 2004/08/01-2008/12/31 Song-Sun Lin Dynamical Systems 2009/08/01-2010/07/31 Wen-Hsiung Lin Algebraic Topology 2007/08/01-2009/07/31 Wen-Wei Lin Scientific Computation 2008/08/01-2010/07/31 Chin-Lung Wang Algebraic Geometry 2004/01/01-2008/12/31 Yi-Fan Yang Number Theory 2008/08/01-2009/07/31 Jing Yu Number Theory 2004/01/01-2011/07/31 Visiting Associate Andreas Schweizer Number Theory 2008/08/01-2009/07/31 Professor Chieh-Yu Chang Number Theory 2008/08/01-2009/07/31 Postdoctoral Fellow Yu-Yun Chen Mathematical Biology 2008/08/01-2009/07/31 Chih-Hung Chang Dynamical Systems 2008/08/01-2009/07/31
.1 Center Scientists month of NTU (July, 2009): Chair one talk in probability session. – France – I. Guan-Yu Chen • Analysis and Probability in Nice, 2nd session National Chiao Tung University, Assistant (June, 15-19, 2009): Invited speaker. Professor NCTS Activities Conferences • NCTS Probability Seminar (April 10, 17, 2009): – Taiwan – Speaker • The 18th South Taiwan Statistics Conference • NCTS Seminar on Probability (August 6): (June 26-27, 2009): Probability Session Chair. Speaker. • International conference at the mathematics
77 ‹‹- Activities of Onsite Scientists • NCTS Summer Mini-Course on stochastic Conferences and Visiting processes (July-August, 2009): Lecturer – United States – • AMS Fall Southeastern Section Meeting, Publications October 24~26 (2008), University of Alabama, • Guan-Yu Chen, Wai-Wai Liu and Laurent Huntsville, Alabama, U.S.A. Saloff-Coste, The logarithmic Sobolev constant • Department of Mathematics, University of of some finite Markov chains. Annales de la Kansas, U.S.A., October (2008). Faculté des Sciences de Toulouse Vol. XVII, No. 2 (2008), 239-290. – Czech – • Guan-Yu Chen and Laurent Saloff-Coste, On • Equadiff 12, International Conference on the L2-cutoff for normal Markov processes. Differential Equations, July 20~24 (2009), Submitted. Brno, Czech Republic.
Recent invited journal referee NCTS Activities • Probability theory and related fields • 2009 CTS Workshop on Dynamical Systems, co-organizer (May 21~24, 2009)
II. Jiun-Cheng Chen Publications 1. Inviscid and viscous stationary waves of gas National Tsing Hua University, Assistant flow through contracting- expanding nozzles, Professor Journal of Differential Equations, (2009), National Center for Theoretic Sciences, accepted (with J. M. Hong & W. Liu) Center Scientist 2. Viscous standing asymptotic states of Conferences and Visiting isentropic compressible flows through a – Korea – nozzle, Archive for Rational Mechanics and • KIAS (Nov, 2008): East Asia Algebraic Analysis, (2009), accepted (with J. M. Hong & geometry conference. W. Liu) – United States – 3. Diversity of traveling wave solutions in FitzHugh-Nagumo type equations, Journal of • MSRI (Feb, 2009): Jumbo algebraic geometry Differential Equations 247, (2009), 1185-1205. conference. (with C.-R. Yang & T.-H. Yang) • Harvard University (Feb, 2009): visiting Prof. 4. Pullback and forward attractors for dissipative S. T. Yau. lattice dynamical systems with additive noises, NCTS Activities Dynamical Systems-An International Journal, (2009), 139-155. (with J.-C. Ban, Y.-H. Lin & • NCTS (Taipei office) Seminar in Algebraic T.-S. Yang) Geometry, (September 2008-June, 2009) 5. Existence of periodic orbits for a system of Research Works delay differential equations, Nonlinear Analysis-Theory, Methods and Applications, • Cone Theorem via Deligne-Mumford stacks, (2009), accepted. (with S.-Y. Yang, T.-H. Yang (with H.-H Tseng), to appear in Math Ann, and T.-S. Yang) 2009. 6. Stability and bifurcation of a two-neuron • On Fano varieties with large pseudo-index, to network with distributed time delays, appear in ASPM, 2009. Nonlinear Analysis-Real World Applications, (2009), accepted. (with S.-Y. Yang, T.-H. Yang III. Cheng-Hsiung Hsu and T.-S. Yang) 7. Sub-to-super transonic steady states and their National Central University, Professor
Activities of Onsite Scientists -›› 78 linear stabilities for gas flows, (2009), My research work in recent years fall in two submitted. (with J. M. Hong and W. Liu) areas: number theory and coding theory. In number theory I am interested in zeta functions of 8. Traveling wave solutions of delayed lattice graphs and complexes arising from quotients of differential system in Lotka-Volterra type, the Bruhat-Tits buildings, the arithmetic of (2009), submitted. (with T.-H. Yang) noncongruence modular forms, and Drinfeld 9. Inviscid and viscous stationary waves of gas modular forms; in coding theory I am interested in flow through nozzles of varying area, (2009), the Elkies' modularity conjecture and the low- preprint. (with W. Liu) density parity-check codes. The publications listed 10. Traveling wave solutions for discrete-time below record a major part of my efforts in these model of delayed cellular neural networks, topics. We briefly describe the highlights of some (2009), preprint. (with J.-J. Lin) of the work. The zeta function for graphs is known since Ihara's work in 1960's. However, nothing is IV. Ming-Chia Li known for the zeta function for simplicial National Chiao-Tung University, Professor complexes of higher dimension. In [B1] we give the firrst zeta function for 2-dimensional Conferences and Visitings complexes arising from quotients of PGL(3). The – Japan – approach was more combinatorial. In the paper International Conference: New Development [B3] a different approach using representation in the study of Dynamical Systems beyond theory was given. The two different approaches Uniform-Hyperbolicity, RIMS, Kyoto University, gave complimentary interpretations of the zeta Japan, September 29-October 3, 2008. function identity, which is reminiscent of the zeta function attached to surfaces, similar to the fact Publications that the zeta function for graphs are analogous to the zeta function for curves. • Topological entropy for multidimensional perturbations of snap-back repellers and one- In the past century, there have been fantastic dimensional maps, Nonlinearity, 21 (2008), progress on modular forms for congruence 2555-2567 (with M.-J. Lyu and P. Zgliczynski) subgroups, which led to the proof of Fermat's Last Theorem. The understanding of the arithmetic for • Generalized Henon maps and Smale horseshoes noncongruence forms, however, is still of new types, Intern. J. Bifurcation and Chaos, preliminary. The main reason is due to the lack of 18 (2008), 3029-3052. (with S. Gonchenko and effective Hecke operators. On the other hand, M. Malkin) Scholl has associated l-adic Galois representations • A simple proof for persistence of snap-back to noncongruence forms. These Galois repellers, Journal of Mathematical Analysis and representations were constructed geometrically, Applications, 352 (2009), 669-671 (with M.-J. and hence according to Langlands' prediction, Lyu) they should be modular, that is, associated to the representations of certain adelic reductive groups. • On stability of forcing relations for The paper [B4] confirrms the modularity of Scholl multidimensional perturbations of interval representations for a special noncongruence maps, Fundamenta Mathematicae, to appear. group, and also establishes the so-called Atkin- (with P. Zgliczynski) Swinnerton-Dyer conjecture, which is the p-adic analogue of Hecke relations expressed in terms of V. Wen-Ching Winnie Li congruences. This is the first 3-dimensional example of such kind. Professor of Mathematics, Pennsylvania State The function field valued Drinfeld modular University forms, while similar to complex valued classical Director, National center for Theoretical modular form, in many ways, also have distinct Sciences (beginning June 1, 2009)
79 ‹‹- Activities of Onsite Scientists properties. One such property is the fact that the Dec. 19-20, 2009 to attend a number theory Hecke operators may not be diagonalizable. The conference jointly organized by Choie and paper [B5] shows that for a given congruence myself. This is the first joint conference subgroup, the Hecke operators lose their between the Pohang Mathematics Institute and diagonalizability when the weight is increased. NCTS. We expect to have more joint activities in the years to come. Activities Organized (beginning June 1, 8. Taiwan-France Workshop on Theoretical 2009) Sciences, Oct. 26, 2009. This is part of the 1. A general audience colloquium talk on "Three international co-operation program with France episodes in geometry, astronomy and physics" cosponsored by the NSC, Institut Francais de by Prof. Wu-Yi Hsiang, University of Taipei, Institut des Hautes Études Scientifiques California at Berkeley, June 22, 2009. This (IHES), Centre National de la Recherche activity was co-sponsored by the Fundamental Scientifique (CNRS), and NCTS. A group of Science Research Center of National Tsing Hua four French delegates visited various University. This talk was well-attended by institutions in Taiwan Oct 20 to 27, 2009 to undergraduate and graduate students, as well as promote further scientific co-operative faculty members in Math., Physics, and activities. During the one day workshop four Astronomy. French and four Taiwanese scientists gave 2. Special lectures on "The variation with p of the lectures. Among them, four were physicists and number of polynomial solutions mod p" by four mathematicians. There was also a two- Prof. Serre, Collége de France, July 7-11, 2009 week photo exhibition titled "The Unravelers" (four 2-hour lectures). provided by the IHES to celebrate their 50th anniversary. 3. (With L-C. Hsia, Y-F. Yang and J. Yu) More than 30 hours of intensive lectures on various Conferences (After May 12, 2009) advanced topics in June, 2009, to prepare – Taiwan – students to benefit from and take notes of • International conference at the mathematics Serre's lectures. The lecture notes will be month of NTU, July 6-10, 2009, National posted on the NCTS website. Taiwan University, invited speaker, title: Zeta 4. Mentored undergraduate student, Mr. Hao-Yun functions in number theory and combinatorics. Yang of National Taiwan University, in • NCTS Mathematics Conference in Hsinchu summer 2009. We studied materials from the Area, NCTS, June 11-12, 2009, invited speaker, book by Griffith and Harris "Principles of title: Recent progress on the arithmetic of Algebraic Geometry". noncongruence modular forms. 5. Weekly student seminar titled "Introduction to • TIMS International Conference on Modular p-adic Hodge theory", beginning October 12, Forms and Function Field Arithmetic (May19- 2009. 22, 2009 NTU), organizer. 6. Hosted the visit of Prof. Ling Long, Iowa State – Netherland – University, July 6-Aug 4, 2009. We worked together on noncongruence modular forms. • International Conference on The Theory of Automorphic Forms, June 15-19, 2009, Woud- 7. (With JoungJu Choie) A special session on schoten/Utrecht, Netherland, invited speaker, "Modular forms and related topics" in KMS- title: Modular forms for noncongruence sub- AMS meeting in Seoul, Korea, Dec. 16-17. I groups. invited Chia-Fu Yu ( professor), Yi-Fang Yang (associate professor), Ming-Lun Hsieh – Ireland – (assistant professor), and Fu-TsunWei • Ninth International Conference on Finite Fields (graduate student) from Taiwan to give talks to and Applications, July 13-17, 2009, Dublin, promote their international visibility. The same Ireland, invited plenary speaker, title: Zeta group of people will visit Postech University functions of graphs and complexes.
Activities of Onsite Scientists -›› 80 – Turkey – 5. (with Y. Meemark) Hecke operators on • International Conference on Sequences, Codes Drinfeld cusp forms, J. Number Theory 128 and Curves, September 25-29, Antalya, Turkey, (2008), 1941-1965. invited speaker, title: Zeta functions of the pseudocodewords of low-density-parity-check codes. VI. Chin-Cheng Lin National Central University, Professor Workshop / Number Theory Seminar / (after May 12, 2009) Conferences 1. China – Taiwan – International Workshop on Coding and • Workshop on Analysis (October 2008 at NCU) Cryptography, June 1-4, 2009, Zhangjiajie, China, Organizer invited speaker, title: Zeta functions of the • International Conference on Matrices and pseudocodewords of low-density-parity-check Operators (July 2009 at NSYU) codes. Invited Speaker, A fundamental principle for 2. United States the boundedness of operators on weighted Workshop on Noncongruence Modular Forms Hardy spaces and Modularity, August 17-21, 2009, Amer-ican – China – Institute of Mathematics, Palo Alto, CA, U.S.A., • International Conference on Harmonic Analysis organizer. & PDE's with Applications (May 2009 Beijing) 3. Turkey Invited Speaker, Triebel-Lizorkin spaces of Number Theory Seminar, October 5, 2009, para-accretive type and a Tb theorem Middle East Technical University, Ankara,Turkey, – Canada – invited speaker, title: Modular curves and coding theory • Canadian Mathematical Society Summer Meting (June 2009, St. John’s) Publications Invited Speaker: Hardy spaces associated with A. NCTS affiliated Schrodinger operators on the Heisenberg group 1. Modular curves and coding theory : a survey, Publications Proceedings of the Ninth International Conference on Finite Fields and Applications, • Boundedness of singular integral operators with Dublin, Contemporary Math., to appear. variable kernels (with Ming-Yi Lee, Ying-Chieh Lin, and Dunyan Yan), J. Math. Anal. Appl. 348 B. NCTS acknowledged (2008), 787-796. 1. (with Ming-Hsuan Kang) Zeta functions of • Triebel-Lizorkin spaces of para-accretive type complexes arising from PGL(3), submitted. and a Tb theorem (with Kunchuan Wang), J. 2. Zeta functions in combinatorics and number Geom. Anal. 19 (2009), 667-694. theory, Proceedings of the 4th International • A wavelet characterization for the dual of Congress of Chinese Mathematicians, weighted Hardy spaces (with Ming-Yi Lee and Hangzhou, China, 2007, International Press, to Ying-Chieh Lin), Proceedings AMS 137 (2009), appear. 4219-4225. 3. (with Ming-Hsuan Kang and Chian-Jen Wang) Zeta functions of complexes from PGL(3): a VII. Song-Sun Lin representation-theoretic approach, Israel J. Math, to appear. National Chiao-Tung University, Chair Professor of National Chiao-Tung 4. (with A. O. L. Atkin and L. Long) On Atkin University. and Swinnerton-Dyer congruence relations(2), Math. Annalen 340 (2008), No 2, 335-358. Conferences and Visitings
81 ‹‹- Activities of Onsite Scientists – U.S.A. – NSC Midterm Report, NSC 96-2115-M-007- Harvard University, Boston, August 2008. 004-MY2 (2008). – Japan – 3. W. H. Lin, “The Kervaire invariant θ6”, NSC Ryukoku University, Kyoto, November 2008. Report, NSC 96-2115-007-004-MY2 (2009).
Publications IX. Wen-Wei Lin • Spatial complexity in multi-layer cellular neural National Chiao-Tung University networks, J. Differential Equation, vol. 246, 552-580. (2009). (with Jung-Chao Ban, Chih- National Chairship Professor Hung Chang and Yin-Heng Lin). Chair Professor of Chiao Tung University • Zeta functions for higher-dimensional shifts of Conferences and Visitings finite type, to appear in International J. – China – Bifurcation and Chaos, (2009). (with Wen-Guei • Numerical Algorithm and Scientific Hu). Computation (NASC2008), Nanjing, China, November, 2008 (Invited Speaker). VIII. Wen-Hsiung Lin Visitors • Professor Edward Allen, Texas Tech. University, National Tsing Hua University, Professor TX, USA (Aug. 1 - Aug. 14, 2008) Conferences and Visiting • Professor Chun-Hua Guo, University of Regina, 1. Participation of the conference to celebrate the Canada (Mar. 1 - Jun. 30, 2009) 60th birthday of Professor Shing-Tung Yau at • Professor Shui-Nee Chow, Georgia Institute of Harward University. Technology, GA, USA (Mar. 15 - Mar. 21, Dates: Aug. 27, 2008-Sept. 1, 2008. 2009) Topic of the conferences: Geometric Analysis, • Professor Eric King-Wah Chu, Monash Present and Future University, Australia (Jul. 6 - Jul. 31, 2009) 2. Visiting Northwestern University, U. S. A. to Publications talk with Professor Mark Mahowald on the subject: Quadratic Constructions toward the 1. Vibration of Fast Trains, Palindromic Eigenvalue Problems and Structure-Preserving Kervaire invariant element θ6 via the Toda 〈 〉 Doubling Algorithms, J. Comp. Appl. Math., bracket θ5, 2ι, θ4. Vol. 219, No. 1 (2008), 237-252. (with E. K. Dates: October 19-October 24, 2009. W. Chu, T. M. Hwang and C. T. Wu)
3. Projected participation of the 3rd East Asia 2. Digital Secure-Communication Using Robust Conference on Algebraic Topology to be held Hyper-Chaotic Systems, Int. J. Bifur. and at the Vietnam National University, Hanoi, Chaos, Vol. 18, No. 11 (2008), 3325-3339. Dates: December 14-December 18, 2009. (with S. L. Chen, S. M. Chang and T. T. Hwang) Title of the talk: Some Toda brackets viewed 3. Asymptotic Synchronization of Modified from the quadratic constructions. Logistic Hyper-Chaotic Systems and its Applications, Nonlin. Anal. Real World Appl., Recent Publications Vol. 10, Issue 2 (2009), 869-880. (with S. M. 4,* 5,* 1. W. H. Lin, “Ext A (Z/2, Z/2) and Ext A ( Z/2, Chang and M. C. Li) Z/2)”, Topology and its applications, Volume 4. Structured Doubling Algorithms for Weakly 155, Issue 5 (2008), 459-496. (NSC Report, Stabilizing Hermitian Solutions of Algebraic NSC 94-2115-M-007-005) Riccati Equations, Lin. Alg. Appl., Vol. 430 2. W. H. Lin, “The Kervaire invariant 126, Part I: (2009), 1452-1478. (with T. M. Hwang) A homology theory in the Steenrod algebra”,
Activities of Onsite Scientists -›› 82 5. Solutions to a Quadratic Inverse Eigenvalue Sciences, invited speaker Problem, Lin. Alg. Appl., Vol. 430 (2009), (October 26) 1590-1606. (with Y. F. Cai, Y. C. Kuo and S. F. Xu) Research Works (in this period) 6. Convergence Analysis of the Doubling 1. (with C.-S. Lin), A function theoretic view of Algorithm for Several Nonlinear Matrix the mean field equations on tori in “Proceeding Equations in the Critical Case, SIAM Matrix of the International Conference on Geometric Anal. Appl., Vol. 31, No. 2 (2009), 227-247. Analysis (TIMS, Taipei 2007)”, Higher (with C. Y. Chiang, E. K. W. Chu, C. H. Guo, Education Press 2009 T. M. Huang and S. F. Xu) 7. Structure-Preserving Algorithms for 2. Quantum invariance under flop transitions, in Palindromic Quadratic Eigenvalue Problems “Proceeding of Geometric Analysis: Present Arising from Vibration of Fast Trains, SIAM and Future, a conference in honor of Professor Matrix Anal. Appl., Vol. 30, No. 4 (2009), Shing-Tung Yau's 60th birthday (Harvard 1566-1592. (with T. M. Hwang and J. Qian) University, Cambridge 2008)”, International Press 2009 8. Quadratic Model Updating with Symmetry, Positive Definiteness and No Spill-Over, SIAM 3. (with Y. Iwao, Y.-P. Lee and H.-W. Lin), Matrix Anal. Appl., Vol. 31, No. 2 (2009), 546- Invariance of Gromov-Witten theory under 564. (with D. Chu and M. Chu) simple flops, submitted 2009 4. (with Y.-P. Lee and H.-W. Lin) Invariance of X. Chin-Lung Wang quantum rings under ordinary flops, preprint 2009 National Taiwan University, Professor (since Singular mean field equations August 1, 2008) 5. (with C.-S. Lin) on tori, preprint 2009 National Center for Theoretic Sciences, Shiing-shen Chern Fellow and Center 6. (with S.-S. Wang) Extensions of multiply Scientist (up to 08/12/31) twisted pluri-canonical forms, preprint 2009 Conferences and Visiting – China – XI. Yifan Yang Zhijiang University (August 24 – 28): Center National Chiao Tung University, Associate of Mathematical Sciences. Professor “Arithmetic Geometry and Moduli Spaces in National Center for Theoretic Sciences, Algebraic Geometry”, invited speaker Center Scientist – Japan – (forthcoming event) Conferences Tokyo University (December 7 – 11): Graduate 1. Sp_4-modularity of Picard-Fuchs differential School of Mathematical Sciences. “GCOE equations for Calabi-Yau threefolds, Workshop International Conference on Mirror Symmetry and on number theory and physics at the Gromov-Witten Invariants”, invited speaker crossroads, Tsuda College, Japan, August 4-6, 2008. NCTS Activities 2. Construction and applications of a class of 1. NCTS(TPE)/TIMS joint seminar in Algebraic modular functions, Annual meeting of the Geometry, co-organizer Mathematical Society of the Republic of (Weekly based full year activity) China, Hsinchu, Taiwan, December 19-21, Including a lecture series on Geomov-Witten 2008. theory (April) 3. Construction and applications of a class of 2. NCTS Taiwan-France Workshop on Theoretic modular functions, Joint workshop on number
83 ‹‹- Activities of Onsite Scientists theory between Japan and Taiwan, Waseda 8. Yifan Yang, congruences of the partition University, Japan, March 9-11, 2009. function, (preprint). 4. Congruences of the partition function, East 9. Heng Huat Chan, Yoshio Tanigawa, Yifan Asia number theory conference, Tsing Hua Yang, and Wadim Zudilin, new analogues of University, China, August 19-22, 2009. Clausen’s identities arising from the theory of modular forms, (preprint). 5. Congruences of the partition function, Nankai number theory conference, Nankai University, China, August 24-28, 2009. XII. Jing Yu Visits National Tsing-Hua University 1. Tsuda College, Japan. Visit Fukuhara from 28 National Chair professor, till July 31, 2009 July 2008 to 18 August 2008. National Central University Adjunct Professor of Mathematics 2. East China Normal University, China. Visit Zhiguo Liu from 21 August 2008 to 4 Conferences September 2008. -Taiwan- 3. Waseda University, Japan. Visit Hashimoto • International Conference on Value distribution from 25 July 2009 to 16 August 2009. theory and Complex Geometry, (July 27-30, 2009 at NCTS) Organizer. NCTS Activities • International conference at the mathematics 1. NCTS number theory seminar. month of NTU, (July 6-10, 2009, National Taiwan University) Invited speaker: On Galois Research Works theory of several variables. 1. Yifan Yang, on the mean square of the • TIMS Conference on transcendence and Riemann zeta function and the divisor function field arithmetic (May 19-22, 2009 problems, Publ. Inst. Math. (Beograd), 83 NTU) (2008), 71-86. -Switzerland- 2. Shinji Fukuhara and Yifan Yang, period • Conference on Diophantine geometry in honor polynomials and explicit formulas for Hecke of G. Wuestholz, (June, 2009 at ETH) Invited operators on Gamma_0(2), Math. Proc. speaker: on Galois theory of several variables in Cambridge Philos. Soc., 146 (2009), 321-250. positive characteristic. 3. Fang-Ting Tu and Yifan Yang, defining • Mini workshop on number theory at ETH equations of X_0(2^{2n}), Osaka J. Math, 46 (February 2009) Organizer (2009), 105-113. -Japan- 4. Yifan Yang, modular units and cuspidal divisor class groups of X_1(N), J. Algebra, 322 (2009), • Waseda Conference on number theory, (March 514-553. 9-11, 2009 Tokyo) Invited speaker: On Tori and a Galois theory for special values of Gamma 5. Yifan Yang and Jeng-Daw Yu, structure of the functions in positive characteristic cuspidal rational torsion subgroups of -China- J_1(p^n), accepted by J. London Math. Soc. (pending minor revision). • International Conference on Algebra and Number (January 8-11, 2009, at Nanjing 6. Aristides Kontogeorgis and Yifan Yang, University) Invited Speaker: On Galois theory automorphism groups of hyperelliptic modular of several variables and algebraic independence curves, accepted by LMS J. Comp. Math. 7. Shinji Fukuhara and Yifan Yang, twisted Hecke Number Theory Seminar/Workshop L-values and period polynomials, accepted by -Taiwan- J. Number Theory.
Activities of Onsite Scientists -›› 84 • NCTS Number Theory Seminar (April 2009), 1 Research lecture My research interest lies in the following areas: • Seminar on Drinfeld modular forms (April and function field arithmetic, Drinfeld modules, May 2009 ), 4 lecture elliptic curves and elliptic surfaces, classical and Drinfeld modular curves,(non-)congruence • 2009 Winter School on Number Theory subgroups of SL2, value-sharing of meromorphic (February 1-5, 2009 Acer Park), 1 lecture functions. -The Netherlands- Concentrating on the academic year 2008/2009 • On Galois theory of several variables (February, and the papers listed below: 2009, Leiden University) The joint papers with Matthias Schütt discuss Publications the maximal number of connected components of a bad fiber of an elliptic surface. In positive 1. Algebraic independence of arithmetic gamma characteristic it can be significantly bigger than in values and Carlitz zeta values, (with Chieh-Yu characteristic 0. As an “elementary” application Chang, D. Thakur, and M. Papanikolas), to one obtains statements about the degree of ƒ3-g2 if appear in Advances of Math 2009. f and g are two polynomials. The second paper 2. Determination of algebraic relations among shows that the elliptic K3 surfaces that realize this special gamma values and zeta values in maximal number are unique (in any characteristic positive characteristic, (with Chieh-Yu Chang different from 2). and M. Papanikolas), to appear in International Mathematics Research Notices 2009. Inspired by some examples in Serre’s book “Trees”, in [3] we investigate the fundamental 3. On primitive roots for rank one Drinfeld domain for the action of SL2(C) on the Bruhat-Tits modules (with W.-C.Yao}, to appear in Journal tree where C is the affine coordinate ring of a of Number Theory 2009. conic without rational points. In [5] we introduce 4. Frobenius difference equations and algebraic the concepts of quasi-level and quasi-amplitudes independence of zeta values in positive of a subgroup of SL2. These carry more characteristic, (with Chieh-Yu Chang and M. information than the classical level and cusp Papanikolas), preprint 2009. amplitudes. Several applications to congruence subgroups are given (necessary conditions, relations between level and index, ..). The paper [4] shows that for any finite set of F.2 Visiting Associate Professor complex values one can construct a compact Riemann surface carrying two meromorphic functions that share these prescribed values. Name: Andreas Schweizer Value-sharing on compact Riemann surfaces with finitely many punctures is also discussed. Teaching This year I also started a collaboration with Fall 2008: Graduate Course on Function Field Prof. Yifan Yang from Chiao Tong University in a Arithmetic, 32 lectures à 90 minutes, 8 project on the torsion of elliptic curves over exercise sheets, for graduate students suffciently general function fields. from Tsing Hua University, Chiao Tong University, and National Central Publication and Preprints University 1. (with Matthias Schütt) On Davenport-Stothers February 2009: NCTS Winter School, Aspire inequalities and elliptic surfaces in positive Park, Tao Yuan County 4 lectures characteristic, Quarterly J.Math. (Oxford) 59 à 75 minutes on Drinfeld Modular (2008), 499-522 Curves 2. (with Matthias Schütt) On the uniqueness of elliptic K3 surfaces with maximal singular fibre, submitted
85 ‹‹- Activities of Onsite Scientists 3. (with A.W. Mason) Nonrational genus zero • 27 - 30 July 2009 - Conference on Value function fields and the Bruhat-Tits tree, Distribution Theory and Complex Geometry, Communications in Algebra, 37 vol. 12 (2009), Hsinchu, 4241-4258 (NCTS-preprint 2008-10-003) Invited talk “Value-sharing of meromorphic 4. Value-sharing of meromorphic functions on a functions on a Riemann surface” Riemann surface, Journal of Mathematical • 12 August 2009 - Algebra Seminar, Glasgow Analysis and Applications, to appear (NCTS- University (Scotland): preprint 2009-5-001) “On the class groups of quadratic function 5. (with A.W. Mason) The cusp amplitudes and fields”
quasi-level of a congruence subgroup of SL2 over any Dedekind domain, submitted (NCTS- Research Visit preprint 2009-8-002) 4 - 14 August 2009 - Research visit to Glasgow University (Scotland) for discussions with Prof. Conferences, Workshops, Talks A.W. Mason. The main subject was the material of • 10 September 2008 - NCTS Number Theory what is going to be our sixth joint paper, on Seminar: elliptic points of the Drinfeld modular groups. “On the torsion of elliptic curves over suffciently general function fields” • 11 September 2008 - Colloquium, Academia Sinica, Taipei: F.3 Report of Post Doctors “Shared values of meromorphic functions on a compact Riemann surface” Name: Chieh-Yu Chang • 26 November 2008 - NCTS Number Theory Seminar: Research: “On the m-rank of class groups of quadatic My main research work focuses on function fields” transcendence theory over function fields in • 1 December 2008 - Colloquium, Tsing Hua positive characteristic. In the past year, I spent University, Hsinchu: much time on revising several preprints and some “Davenport-Stothers inequalities in positive of them were recently accepted by mathematical characteristic” journals, (eg. [3]~[5] in the list of publications). On the other hand, I obtained three results this • 17 December 2008 - NCTS Number Theory year: Day: Arithmetic of Curves: Invited talk “Elliptic curves over q(T) and the The first one is about the periods of third kind Bruhat-Tits tree” for rank 2 Drinfeld modules. In [7], I define a notion of periods of third kind for rank 2 Drinfeld • 22 December 2008 - Number Theory Seminar, modules and derive explicit formulae for them. Taiwan National University, Taipei: Then I prove the algebraic independence of “Torsion of elliptic curves over suffciently periods of the first, second and third kinds for the general function fields” rank 2 Drinfeld module in question. • 6 January 2009 - Colloquium, Chiao Tong The second one is that I prove the University, Hsinchu: transcendence of the special values of the classical “Shared values of meromorphic functions on a nonzero weight quasi-modular forms with compact Riemann surface” algebraic Fourier coefficients at the algebraic points of the moduli space SL(2,Z)\H, where H is • 26 February 2009 - Colloquium, National the complex upper half plane. I also prove the Central University, Chung Li: analogous result for Drinfeld quasi-modular forms “On class groups of quadratic fields” (in positive characteristic).
Activities of Onsite Scientists -›› 86 The third one is a joint work with M. 15. Number Theory Seminar, Univ. of Waterloo, Papanikolas. The project is a continuation of our Canada, Sep. 2009 previous work (cf. [5]) to higher rank Drinfeld 16. Workshop on t-motives, Banff, Canada, Oct. modules. There are two parts in this work. One is 2009. to prove the period conjecture for Drinfeld modules, which asserts that all the algebraic Visiting: relations among the entries of the period matrix for the Drinfeld module in question are the linear • Univ. of Leiden (Netherlands) and ETH relations induced from the endomorphisms. The (Switzerland) (Feb. 8~ 22 2009) other is to prove the algebraic independence of • Univ. of Duisburg-Essen, Germany (June ~July Drinfeld logarithms of algebraic points when 2009) these values are linearly independent over the endomorphism ring of the Drinfeld module in Publications and Preprints: question. We hope to finish the writing as soon as [1] C.-Y. Chang and J. Yu, Determination of possible. algebraic relations among special zeta values in positive characteristic, Advances in Invited talks at Seminars/Workshops/ Mathematics 216 (2007), 321-345. Conferences [2] C.-Y Chang, A note on a refined version of 1. Colloquium at Dept. of Math., National Tsing Anderson-Brownawell-Papanikolas Hua Univ. Oct. 2008 criterion, Journal of Number Theory 129 2. Colloquium at Dept. of Applied Math., (2009), 729-738. National Sun Yat-Sen Univ. Oct. 2008 [3] C.-Y. Chang, M. A. Papanikolas and J. Yu, 3. NCTS Number Theory Seminar, Dec. 2008 Geometric gamma values and zeta values in positive characteristic, accepted by Int. Math. 4. Colloquium at Institute of Math., Academia Res. Notices (IMRN). Sinica, Jan. 2009 [4] C.-Y. Chang, M. A. Papanikolas, D. S. Thakur 5. Intercity Seminar, Univ. of Leiden, and J. Yu, Algebraic independence of Netherlands, Feb. 2009 arithmetic gamma values and Carlitz zeta values, accepted by Advances in Mathematics. 6. Mini Workshop on Number Theory, ETH, Switzerland, Feb. 2009 [5] C.-Y. Chang and M. A. Papanikolas, Algebraic relations among periods and 7. Joint workshop on Number Theory between logarithms of rank 2 Drinfeld Japan and Taiwan, Univ. of Waseda, Japan, modules, accepted by American Journal of March 2009 Mathematics. 8. NCTS Number Theory Seminar, April 2009 [6] C.-Y. Chang, M. A. Papanikolas and J. Yu, 9. Workshop on Algebra and Geometry, National Frobenius difference equations and algebraic Chung Cheng Univ., April 2009 independence of zeta values in positive equal characteristic, submitted. 10. Conference on Modular Forms and Function [7] C.-Y. Chang, Periods of third kind for rank 2 Field Arithmetic (in honor of Prof. Jing Yu’s Drinfeld modules and algebraic independence 60th birthday), TIMS (Taipei), May 2009 of logarithms, submitted. 11. Oberseminar, Univ. of Duisburg-Essen, Germany, July 2009 Name: Yu-Yun Chen 12. East Asian Number Theory Conference, Beijing, China, August 2009 Research: 13. Conference on Number Theory, Chern My primary research interest is community Institute, China, August 2009 ecology, with a focus on the eco-evolution of 14. NCTS Number Theory Seminar, Sep. 2009 forest phenology. My former empirical studies
87 ‹‹- Activities of Onsite Scientists provided a background of ecological theories on idea with a simulation including much of the subject and inspiration to build evolutionary stochastic effects. I plan to applied technique of models for phenology divergence. As a start, I partial differential equation to build a model of built a model of two species and a single life stage delayed enemy attack. This model, though to explore the impact of reproductive facilitation excludes the stochastic effects, yet may preserve to the coexistence of two strategies. Dr. Sze-Bi some of the properties of spatial heterogeneity. I Hsu from the Mathematics Department of Tsing hope to then trace the key effect of the newly Hua University has aided the analyses of the proposed mechanism on the species dynamics of a model in the collaboration. We not only laid out community. the analytical solutions to stable coexistence of the two phenological strategies but also found Seminar/Workshop /Conference: “rescue” effect for the inferior species of the two In the last year, I co-hosted one seminar series in our model. The manuscript was submitted to on mathematical biology with Dr. Hsu in the the Bulletin of Mathematical Biology later on. Center and participated in one of the mathematical I also collaborate with Dr. Sze-Bi Hsu and Dr. biology reading course. The seminar series was to Shu-Ming Chang from the Applied Mathematics study basic models and analyses on chemo-stat Department at the National Chao-Tung University models. Several mathematicians were invited to on a second project on a phenological model. The demonstrate mathematical analyses for certain model, called resource budget model, was topics. I was also invited to seminars in several proposed by Isagi et al. (1996) to explore institutions, workshops, and conferences. In these polymorphism of phenology in a population. occasions, I not only presented ideas from my However, the original model considered too few previous and current studies but also exchanged factors and unrealistically assumed no death and ideas with participants of these meetings and birth in the modeled forest. Improving the model started collaborations with them. Here I list the on the two short-comings was our goals. This meetings I have attended both within and outside work is underway with mathematical analysis for the Center: simpler cases and with the tool of computation for 1. Seminar series in NCTS in the past year more complex cases in the model. (1) Seminar series in mathematical biology In the test for the outcome of our theoretical (2) Reading course in mathematical biology: An work, I collaborate with Drs. I-Fang Sun from introduction to mathematical biology Tunghai University, Stephen P. Hubbell from 2. Talks given outside NCTS in the past year UCLA, and Dr. S. Joseph Wright from the (1) First Taiwan-Japan Ecology workshop at the Smithsonian Tropical Research Institute on data Taida Mathematics Center, National Taiwan collecting in the field. Field work covers forests in University Taiwan as well as in Southeast Asia. (2) Annual meeting of Taiwan Ecological My other interests in community ecology Research Network include testing other new ecological theories. One (3) Second Cross-Strait Forest Dynamics Plot of the most popular theories to explain forest symposium diversity is the density dependence hypothesis (or enemy hypothesis). The hypothesis addresses the (4) The symposium of Mathematics Month at the importance of negative density dependence on the Taida Mathematics Ceter, National Taiwan prevention of superior competitors when high University density patches of seedlings suffer higher 3. Workshop mortality rates. This hypothesis has been tested (1) Workshop on quantitative ecology, held by with many empirical data yet not all of them Academia Sinica and Tunghai University in agreed with the prediction from the theory. Fushan Botanical Garden (2007) Recently, ecologist Stephen Hubbell proposed an (2) Workshop on the application of forest idea of delayed enemy attack that may change dynamics plot database, held by the Taiwan forest dynamics and further the status of species Forest Research Institute coexistence of a community. He demonstrated the
Activities of Onsite Scientists -›› 88 Preprint applied in physics, biology and social science. The I have finished a manuscript on the model of first issue is the ergodicity of cellular automata. plant reproductive strategies. The work was We use iteration method to show that celular submitted to Bulletin of Mathematical Biology. automata that satisfy some conditions are ergodic [1, 3]. The existence and uniqueness of equilibrium measures is also an interesting issue, Name: Chih-Hung Chang we show that the equilibrium measure exists and is unique by elucidating the measure-theoretic Research: entropy, topological entropy and topological pressure [1, 3]. 1. Multi-layer Cellular Neural Networks My researches in the last year focus mainly on Seminar/Workshop /Conference: the continued issues of my Ph. D. thesis that is a I attended the following two conferences: cowork with Prof. Song-Sun Lin, Prof. Jung-Chao Ban and Ms. Yin-Heng Lin. In the previous work, 1. 2009 CTS Workshop on Dynamical Systems, we show that mosaic patterns of multi-layer 2009.5.21~2009.5.24 cellular neural networks is topologically conjugate 2. NCTS 2009 Interdisciplinary Conference on to sofic shifts. Using the well-developed theory in Applied Analysis and Mathematics, the symbolic dynamical system we give an 2009.5.11~2009.5.13 algorithm for the computation of spatial entropy and zeta function of the mosaic patterns. Publication and Preprint: Moreover, numerical result shows that the symmetry of spatial entropy fails whenever the [1] J.-C. Ban and C.-H. Chang, The topological input is considered. In [2] we give a theoretical pressure of linear cellular automata, Entropy explanation for the asymmetry of spatial entropy. 11, 271-284, 2009. Moreover, we try to investigate the monotonicity [2] J.-C. Ban and C.-H. Chang, O n t h e of spatial entropy when the radius of interaction monotonicity of entropy for multi-layer neighborhood and the number of layers are treated cellular neural networks, International J. as parameters. Bifurcation and Chaos, in press. 2. Thermodynamic Formalism [3] J.-C. Ban, C.-H. Chang, T.-J. Chen and M.-S. Another issue we are interested is the ergodic Lin, The complexity of permutive cellular properties of cellular automata, introduced by automata, submitted. John von Neumann in 1940s, that is widely
89 ‹‹- Activities of Onsite Scientists Preprints
Series I Title and Author
Ramakrishna-Khare Systems and Modularity Lifting Theorems in Higher 2009-1-01 Weights Yih-Jeng Yu
The Zeta Functions of Complexes From PGL(3): A Representation-Theoretic 2009-1-02 Approach Ming-Hsuan Kang, Wen-Ching Winnie Li and Chian-Jen Wang
On Action-Minimizing Retrograde and Prograde Orbits of the Three-Body 2009-1-03 Problem Kuo-Chang Chen and Yu-Chu Lin
Expanding Convex Immersed Closed Plane Curves 2009-1-04 Tai-Chia Lin, Chi-Cheung Poon and Dong-Ho Tsai
Nonrational Genus Zero Function Fields and The Bruhat-Tits Tree 2009-1-05 A. W. Mason and Andreas Schweizer
A Fast Non-Linear Digital Chaotic Generator in Secure Communication 2009-1-06 Shih-Liang Chen, Shu-Ming Chang, TingTing Hwang and Wen-Wei Lin
Numerical Traveling Wave Solutions of Some Nonlinear Mixed-type Lattice 2009-1-07 Di erential Equations Ching-Lang Huang and Ting-Hui Yang
The Entropy Formulas for CR Heat Equation and Its Applications on 2009-1-08 Pseudohermitian (2n+1)-Manifolds Shu-Cheng Chang and Chin Tung Wu
Immersed Equations of the Hyperbolic Surfaces 2009-1-09 Hsungrow Chan
Numerical Algorithms for Estimating the Largest Structured Singular Value 2009-1-10 of a μ-Synthesis Control System Kun-Chu Chen, Chern-Shuh Wang and Ching-Chang Yen
Structured Quadraticization and Structure-Preserving Algorithm for 2009-1-11 Palindromic Polynomial Eigenvalue Problems Tsung-Ming Huang, Wen-Wei Lin and Wei-Shuo Su
Preprints -›› 90 Series I Title and Author
A Palais-Smale Approach the Two Coupled Nonlinear Schrӧdinger Equations 2009-1-12 Hsiung-yu Wang and Tsung-fang Wu
Structured Condition Number for Palindromic Polynomial Eigenvalue 2009-1-13 Problems Yueh-Cheng Kuo
A Div-Curl Decomposition for the Local Hardy Space 2009-1-14 Der-Chen Chang, Galia Dafni and Hong Yue
Periods of Third Kind for Rank 2 Drinfeld Modules and Algebraic 2009-1-15 Independence of Logarithms Chieh-Yu Chang
Transition to Quantum Turbulence in a Bose-Einstein Condensate Through 2009-1-16 the Bending-Wave Instability of a Single-Vortex Ring T.-L. Horng, C.-H. Hsueh and S.-C. Gou
Value-Sharing of Meromorphic Functions on a Riemann Surface 2009-1-17 Andreas Schweizer
Stationary Wave Patterns Generated by An Impurity Moving with 2009-1-18 Supersonic Velocity Through a Bose-Einstein Condensate T.-L. Horng, S.-C. Gou, T.-C. Lin, G. A. El, A. P. Itin and A. M. Kamchatnov
On the L2-Cutoff for Normal Markov Processes 2009-1-19 G.-Y. Chen and L. Saloff-Coste
The p-Faber-Krahn Inequality Noted 2009-1-20 Jie Xiao
Palindromic Quadratization and Structure-Preserving Algorithm for 2009-1-21 Palindromic Matrix Polynomials of Even Degree Tsung-Ming Huang, Wen-Wei Lin and Wei-Shuo Su
Synchronization and Asynchronization in a Lattice of Coupled Lorenz-Type 2009-1-22 Maps Wen-Wei Lin, Shih-Feng Shieh and Yi-Qian Wang
The Palindromic Generalized Eigenvalue Problem A*x = λAx: Numerical 2009-1-23 Solution and Applications Tiexiang Li, Chun-Yueh Chiang, Eric King-wah Chu and Wen-Wei Lin
Double Vogan Diagrams and Semisimple Symmetric Spaces 2009-1-24 Meng-Kiat Chuah and Jing-Song Huang
91 ‹‹- Preprints Series I Title and Author
Pompeiu Problem on Products of Heisenberg Group 2009-1-25 Der-Chen Chang and Wayne Eby
A Null Space Free Jacobi-Davidson Iteration for Maxwell's Operator 2009-1-26 Tsung-Ming Huang, Yin-Liang Huang, Wen-Wei Lin and Wei-Cheng Wang
Symmetry Preserving Eigenvalue Embedding in Finite-Element Model 2009-1-27 Updating of Vibrating Structures Joao B. Carvalho, Biswa N. Datta, Wen-Wei Lin and Chern-Shuh Wang
Two-Dimensional Quantum Turbulence in a Nonuniform Bose-Einstein 2009-1-28 Condensate T.-L. Horng, C.-H. Hsueh, S.-W. Su, Y.-M. Kao and S.-C. Gou
The Cusp Amplitudes and Quasi-Level of a Congruence Subgroup of SL2 2009-1-29 over any Dedekind Domain A. W. Mason and Andreas Schweizer
Spillover Phenomenon in Quadratic Model Updating 2009-1-30 Moody T. Chu, Biswa Datta, Wen-Wei Lin and Shufang Xu
Note on Golden Means, Nonlinear Matrix Equations and Structured 2009-1-31 Doubling Algorithms Chun-Yueh Chiang, Eric King-Wah Chu and Wen-Wei Lin
Congruences of the Partition Function 2009-1-32 Yifan Yang
Twisted Hecke L-Values and Period Polynomials 2009-1-33 Shinji Fukuhara and Yifan Yang
The Complexity of Permutive Cellular Automata 2009-1-34 Jung-Chao Ban, Chih-Hung Chang, Ting-Ju Chen, Mei-Shao Lin
Digital Secure-Communication Using Robust Hyper-Chaotic Systems 2009-1-35 Shih-Liang Chen, Shu-Ming Chang, Wen-Wei Lin and Tingting Hwang
Asymptotic Synchronization of Modified Logistic Hyper-Chaotic Systems 2009-1-36 and Its Applications Shu-Ming Chang, Ming-Chia Li and Wen-Wei Lin
Coupled Neural Network Loops with Delays (I) 2009-1-37 Chih-Wen Shih and Jui-Pin Tseng
Preprints -›› 92 Series I Title and Author
Geometric GammaA ValuesA and Zeta Values in Positive Characteristic 2009-1-38 Chieh-Yu Chang, Matthew A. Papanikolas and Jing Yu
Frobenius Difference Equations and Algebraicn Independence of Zeta Values 2009-1-39 in Positive Equal Characteristic Chieh-Yu Chang, Matthew A. Papanikolas and Jing Yu
Synchronized Reproduction Promotes Species Coexistence through 2009-1-40 Reproductive Facilitation Yu-Yun Chen and Sze-Bi Hsu
On Fano Varieties with Large Pseudo-Index 2009-1-41 Jiun-Cheng Chen
Spatial Disorder of Soliton Solutions for Discrete Nonlinear Schrӧdinger 2009-1-42 Equations in a 2D Lattice Shih-Feng Shieh
Delayed Transiently Chaotic Neural Networks and Their Application 2009-1-43 S. S. Chen
An Efficiency Study of Polynomial Eigenvalue Problem Solvers for Quantum 2009-1-44 Dot Simulations Tsung-Ming Huang, Weichung Wang and Chang-Tse Lee
The Kervaier Invariant θ6 2009-1-45 Wen-Hsiung Lin
Condition Numbers of Multiple Eigenvalue for Matrix Polynomial 2009-1-46 Eigenvalue Problems Yueh-Cheng Kuo
A Generalized Mac Scheme on Curvilinear Domains 2009-1-47 Yin-Liang Huang, Jian-Guo Liu and Wei-Chen Wang
On Hyperbolic Dynamics of Multidimensional Systems with Homoclinic 2009-1-48 Tangencies of Arbitrary Orders Sergey Gonchenko and Ming-Chia Li
93 ‹‹- Preprints Series II Title and Author
On The Rank of A Cograph 2009-2-01 Gerard J. Chang, Liang-Hao Huang and Hong-Gwa Yeh
A Note on The Stability and Uniqueness for Solutions to The Minimal Surface 2009-2-02 System Yng-Ing Lee and Mu-Tao Wang
Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean 2009-2-03 Curvature Flows Yng-Ing Lee and Mu-Tao Wang
Hamiltonian Stationary Cones and Self-Similar Solutions in Higher 2009-2-04 Dimension Yng-Ing Lee and Mu-Tao Wang
Self-Similar Solutions and Translating Solitons for Lagrangian Mean 2009-2-05 Curvature Flow Dominic Joyce, Yng-Ing Lee and Mao-Pei Tsui
Mean Curvature Flow in Higher Co-Dimension 2009-2-06 Kuo-Wei Lee and Yng-Ing Lee
Mass Formula for Supersingular Abelian Surfaces 2009-2-07 Chia-Fu Yu and Jeng-Daw Yu
Stationary Wave Patterns Generated by An Impurity Moving With 2009-2-08 Supersonic Velocity Through A Bose-Einstein Condensate T.-L. Horng, S.-C. Gou, T.-C. Lin, G.A. El, A.P. Itin, and A.M. Kamchatnov
Finiteness Properties of Differential Polynomials 2009-2-09 Tsiu-Kwen Lee
Prime Radicals of Constants of Algebraic Derivations 2009-2-10 Chen-Lian Chuang and Tsiu-Kwen Lee
Partially Defined $Sigma$-Derivations on Semisimple Banach Algebras 2009-2-11 Tsiu-Kwen Lee and Cheng-Kai Liu
An Identity with Generalized Derivations 2009-2-12 Tsiu-Kwen Lee and Yiqiang Zhou
Regularity and Morphic Property of Rings 2009-2-13 Tsiu-Kwen Lee and Yiqiang Zhou
Preprints -›› 94 Series II Title and Author
On Finiteness of Endomorphism Rings of Abelian Varieties 2009-2-14 Chia-Fu Yu
Traveling Wave Front for A Two-Component Lattice Dynamical System 2009-2-15 Arising in Competition Models Jong-Shenq Guo and Chang-Hong Wu
Uniquely Morphic Rings 2009-2-16 M. Tamer Kosan, Tsiu-Kwen Lee and Yiqiang Zhou
Right Ideals Generated by an Idempotent of Finite Rank 2009-2-17 Tsiu-Kwen Lee and Yiqiang Zhou
Geometry of The Siegel Modular Threefold with Paramodular Level 2009-2-18 Structure Chia-Fu Yu
Eisenstein Congruence on Unitary Groups and Iwasawa Main Conjectures 2009-2-19 for CM Fields Ming-Lun Hsieh
Ordinary P-Adic Eisenstein Series and P-Adic L-Functions for Unitary 2009-2-20 Groups Ming-Lun Hsieh
The Algebraic Functional Equation of Selmer Groups for CM Fields 2009-2-21 Ming-Lun Hsieh
Ramakrishna-Khare Systems and Modularity Lifting Theorems in Higher 2009-2-22 Weights Yih-Jeng YU
Special Fibers of Shimura Curves and Steinberg Representations 2009-2-23 Yih-Jeng YU
Blowing Up at Zero Points of Potential for An Initial Boundary Value 2009-2-24 Problem Jong-Shenq Ggo and Masahiko Shimojo
95 ‹‹- Preprints Series III Title and Author
Circular Degree Choosability 2009-3-01 S. Norine and X. Zhu
Circular Choosability Via Combinatorial Nullstellensatz 2009-3-02 S.Norine,T.Wong and X.Zhu
Adapted List Coloring of Graphs and Hypergraphs 2009-3-03 A. V. Kostochka and X. Zhu
Fractional Chromatic Number of Distance Graphs Generated by Two 2009-3-04 Interval Sets Daphne Liu and Xuding Zhu
Game Colouring Cartesian Product of Graphs 2009-3-05 Xuding Zhu
The 6-relaxed Game Chromatic Number of Outerplanar Graphs 2009-3-06 Jiaojiao Wu and Xuding Zhu
Rootless Pairs of EE8-Lattices 2009-3-07 R.L. Griess Jr. and C. H. Lam
Transitivity of Jordan Algebras of Linear Operators: On Two Questions by 2009-3-08 Gruenenfelder M. Chebotar, W.-F. Ke and V. Lomonosov
W-Algebras in Lattice Vertex Operator Algebras 2009-3-09 Ching-Hung Lam, C. Dong,and H. Yamada
A Note on Polynomial Rings over Nil Rings 2009-3-10 M. A. Chebotar, W.-F. Ke, P.-H. Lee and E. R. Puczylowski
Algorithms for Infinite Quadratic Programming in Lp Spaces 2009-3-11 S. Y. Chen and S. Y. Wu
An Algorithm for Semi-Infinite Transportation Problems 2009-3-12 S. Y. Chen and S. Y. Wu
Unique Continuation for The Elastic Transversely Isotropic Dynamical 2009-3-13 Systems and Its Application Ching-Lung Lin, Gen Nakamura, and Mourad Sin
Strong Lefschetz Property under Reduction 2009-3-14 Chiang, R.; Xia, Eugene Z
Preprints -›› 96 Series III Title and Author
Explicit Connections with SU(2)-Monodromy 2009-3-15 Xia, Eugene Z.
Colouirng Games on Outerplanar Graphs and Trees 2009-3-16 H. Chang and X. Zhu
Bipartite Subgraphs of Triangle-Free Subcubic Graphs 2009-3-17 X. Zhu
An Upper Bound on Adaptable Choosability of Graphs 2009-3-18 Mickaal Montassier, Andre Raspaud and Xuding Zhu
Adaptable Choosability of Planar Graphs with Sparse Short Cycles 2009-3-19 Albert Guan abd Xuding Zhu
Multi-Colouring of Mycielski Graphs 2009-3-20 Wensong Lin, Daphne Liu and Xuding Zhu
Game Circular Colouring of Graphs 2009-3-21 Wensong Lin and Xuding Zhu
Adaptabel Colouring of Graph Products 2009-3-22 Pavol Hell, Zhishi Pan, Tsai-Lien Wong and Xuding Zhu
Game Colouring of the Square of Graphs 2009-3-23 Louis Esperet and Xuding Zhu
Adaptable List Colouring of Planar Graphs 2009-3-24 Louis Esperet, Mickael Montassier and Xuding Zhu
Bipartite Density of Triangle Free Subcubic Graphs 2009-3-25 Xuding Zhu
Distinguishing Number of Group Actions 2009-3-26 Tsai-Lien Wong and Xuding Zhu
Colouring Graphs with Bounded Generalized Colouring Number 2009-3-27 Xuding Zhu
The Independent Arcs of Acyclic Orientations of Complete R-Partite Graphs 2009-3-28 G. J. Chang, C.-Y. Lin, and L.-D. Tong
W-Algebras Related to Parafermion Algebras 2009-3-29 C. Dong, C.H. Lam and H. Yamada
97 ‹‹- Preprints Series III Title and Author
Frame Stabilizers for Framed Vertex Operator Algebras Associated to 2009-3-30 Lattices Having 4-Frames C.H. Lam, H. Shimakura
The Structure of Parafermion Vertex Operator Algebras 2009-3-31 C. Dong, C.H. Lam, Q. Wang and H. Yamada
Quantum Codes from Hadamard Matrices. Linear and Multilinear Algebras 2009-3-32 W.-F. Ke, K. F. Lai and R. B. Zhang
The Cardinality of Some Symmetric Differences 2009-3-33 P.-Y. Huang, W.-F. Ke and G. F. Pilz
Matrix Maps over Planar Nearrings 2009-3-34 W.-F. Ke, J. Meyer and G. Wendt
Dihedral Groups and Sums of EE8-Lattices 2009-3-35 Ching-Hung Lam and R.L. Griess Jr.
Conjugate Dual Problems in Constrained Set-Valued Optimization and 2009-3-36 Applications S. J. Li, C. R. Chen and S. Y. Wu
Optimality Conditions for Vector Optimization Problems 2009-3-37 N. J. Huang, J. Li and S. Y. Wu
An Algorithm Based on The Generalized D-gap Function for Equilibrium 2009-3-38 Problems L. P. Zhang and S. Y. Wu
Improved Smoothing Newton Methods for $P_0$ Nonlinear Complementarity 2009-3-39 Problems L. P. Zhang and S. Y. Wu
Characteristic Functions of Quantum Graphs 2009-3-40 Chun-Kong Law and V. Pivovarchik
New Approach for The Nonlinear Programming with Transient Stability 2009-3-41 Constraints Arising from Power Systems X. J. Tong, S. Y. Wu and R. J. Zhou
A New Smoothing Newton-Type Algorithm for Semi-Infinite Programming 2009-3-42 C. Ling, Q. Ni, L. Qi and S. Y. Wu
Preprints -›› 98 Series III Title and Author
An Explicit Algorithm for Linear Semi-Infinite Programming Problem with 2009-3-43 Second-Order Cone Constraint S. Hayashi and S. Y. Wu
A Numerical Approach to Infinite-Dimensional Linear Programming in L1 2009-3-44 Spaces S. Ito, S. Y. Wu, T. J. Shiu and K. L. Teo
A New Approach to Supply Chain Network Equilibrium Models 2009-3-45 L. P. Zhang and S. Y. W
An Infinite-Dimensional Mathematical Programming Approach to Separation 2009-3-46 in Lp (X, A, μ) M. Lόpez, S. Y. Wu, C. Ling and L. Qi
Inverse Nodal Problem and Ambarzumyan Problem for The P-Laplacian 2009-3-47 Chun-Kong Law, W.C. Lian, and W.C. Wang
99 ‹‹- Preprints Appendix I. Visiting Mathematicians 2009
Name Field of Interest Period of Visit Appendix Ⅰ Stefan Liebscher Dynamical Systems 2008/09/01-2008/09/30 (Ferie University Berlin)
Shunsuke Hayashi Applied Mathematics 2008/09/15-2008/09/28 (Kyoto University)
Hua-Liang Chang Geometry 2008/09/24-2008/10/02 (SISSA, Treiste)
Hubert Kiechle Algebra 2007/09/24-2007/10/02 (University of Hamburg)
Wolfgang Haerdle Statistics 2008/09/30-2008/10/02 (Humboldt-Universitat Zu)
Tai-Peng Tsai PDE 2008/10/14-2009/06/30 (University of British Columbia)
Sharad Goel Probability 2008/10/27-2008/11/05 (Yahoo! Research)
George C. Tiao Statistics 2008/11/02-2008/11/04 (The University of Chicago)
King-Fai Lai Applied Mathematics 2008/11/10-2008/11/13 (The University of Sydney)
Johannes Hendrik Meyer Algebra 2008/11/15-2008/11/30 (University of the Free State)
Akihiro Munemasa Algebra 2008/11/25-2008/12/04 (Tohoku University)
Zang-Hee Cho Statistics 2008/11/27-2008/11/28 (Gachon Medical School)
Wen-Hsiung Li Statistics 2008/11/27-2008/11/28 (Academia Sinica)
Masaaki Harada Algebra 2008/11/28-2008/12/03 (Yamagata University)
Tsuyoshi Miezaki Algebra 2008/11/28-2008/12/03 (Kyushu University)
Manabu OURA Algebra 2008/11/28-2008/12/04 (Yamagata University)
Hiroki Shimakura Algebra 2008/11/28-2008/12/03 (Aichi University of Education)
Appendix Ⅰ -›› 100 Name Field of Interest Period of Visit
Marco Lopez Applied Mathematics 2008/12/01-2008/12/07 (Alicante University) Appendix Ⅰ Der-Chen Chang Analysis 2008/12/04-2008/12/24 ( Georgetown University )
Robert Griess Algebra 2008/12/07-2008/12/10 (Michigan University)
Jianya Liu Number Theory 2008/12/07-2008/12/26 (Shandong University)
Shuichi Jimbo Differential Equations 2008/12/11-2008/12/24 (Hokkaido University)
Yashinari Hamahata Number Theory 2008/12/13-2008/12/17 (Tokyo University of Science)
James Grover Ecology and Math. Modeling 2008/12/15-2009/01/12 (University of Texas, Arlington)
Kiichiro Hashimoto Number Theory 2008/12/15-2008/12/21 (Waseda University)
Yukiko Sakai Number Theory 2008/12/15-2008/12/21 (WasedaUniversity)
Atsuki Umegaki Number Theory 2008/12/15-2008/12/21 (Waseda University)
Simon Levin Mathematical Biology 2008/12/17-2008/12/24 (Princeton University)
Mikhail Chebotar Ring Theory 2008/12/18-2009/01/03 (Kent State University)
Victor Lomonosov Operator Theory 2008/12/18-2009/01/03 (Kent State University)
Dihua Jiang Geometry 2008/12/18-2008/12/31 (University of Minnesota)
Andrew Yau Scientific Computation 2008/12/18-2008/12/20 (Tsinghua University, Beijing)
Bei Hu PDE 2008/12/21-2009/01/02 (University of Notre Dame)
Tetsuhiro Moriyama Geometry 2008/12/21-2009/01/03 (The University of Tokyo)
101 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Vincent Maillot Algebraic Topology and (Intitut de Math. de Jussieu, 2008/12/23-2009/01/10 Algebraic Geometry Appendix Ⅰ Université Paris 7)
Manabu Akaho Geometry 2008/12/25-2008/12/30 (Tokyo Metropolitan University)
Takahiko Yoshida Geometry 2008/12/25-2009/01/03 (Meiji University)
Mikhail Chebotar Algebra 2008/12/26-2008/12/31 (Kent State University)
Do Young Kwak Scientific Computation 2008/12/26-2009/01/15 (KAIST)
Victor Lomonosov Algebra 2008/12/26-2008/12/31 (Kent State University)
Ka-Fai Yiu (The Hong Kong Polytechnic Applied Mathematics 2008/12/26-2008/12/30 University)
Yuan Lou PDE and Mathematical Biology 2008/12/27-2009/01/23 (Ohio State University)
Quo-Shin Chi (Washington Differential Geometry, 2009/01/01-2009/05/31 University in St. Louis) Algebraic Geometry
Zhenyue Zhang Scientific Computation 2009/01/04-2009/01/12 (Zhe Jiang University)
King-Fai Lai Applied Mathematics 2009/01/06-2009/01/10 (The University of Sydney)
Douglas B. West Extremal, structural, and (University of Illinois Urbana- algorithmic questions in discrete 2009/01/07-2009/01/13 Champaign) mathematics
Arnd Scheel PDE 2009/01/07-2009/01/16 (University of Minnesota)
Tze Leung Lai Statistics 2009/01/08-2009/01/10 (Stanford University)
Claude Tardif (Royal Military College of Graph theory 2009/01/08-2009/02/08 Canada)
Applied Mathematics, Ting-Hui Yang Dynamical System, 2009/01/15-2009/02/15 (Tamkang University) Scientific Computation
Appendix Ⅰ -›› 102 Name Field of Interest Period of Visit
Yuen-Cheng Kuo Scientific Computation 2009/01/16-2009/02/15 (NUK) Appendix Ⅰ Shyan Shiou Chen Scientific Computation 2009/01/17-2009/02/20 (NTNU)
Hung-Yuan Fan Scientific Computation 2009/01/17-2009/02/20 (NTNU)
Tsung-Min Hwang Scientific Computation 2009/01/17-2009/02/20 (NTNU)
Shin-Feng Shieh Dynamical System, 2009/01/17-2009/02/20 (NTNU) Applied Mathematics
Kingfai Lai Number Theory 2009/01/19-2009/01/20 (University of Sidney)
Chern-Shuh Wang Scientific Computations 2009/01/19-2009/02/15 (NCKU)
Liang-Chung Hsia Number Theory 2009/02/01-2009/07/31 (NCU)
Seok Jong Lee Fuzzy 2009/02/02-2009/02/22 (Chungbuk National University)
Teruo Asanuma Algebra 2009/02/03-2009/02/22 (Toyama Univerity)
Helena Nesetrilova (Czech University of Life Statistics 2009/02/04-2009/02/16 Sciences)
Sangho Kum Evacuation planning 2009/02/05/-2009/02/07 (Chungbuk National University)
Yongdo Lim (Kyungpook National Positivity in Lie theory 2009/02/05-2009/02/07 University)
Gue Myung Lee Vector Optimization 2009/02/05-2009/02/07 (Pukyong National University)
Peng Lu Geometric Analysis 2009/02/05-2009/04/06 (University of Oregon)
Keiichi Watanabe (Nihon University, Algebra 2009/02/09-2009/02/14 Japan)
Wu Jie Shi Algebra 2009/02/09-2009/02/15 (Soochow University)
103 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Zhong Ming Tang Algebra 2009/02/09-2009/02/15 (Soochow University) Appendix Ⅰ François Hamel Elliptic and parabolic non-linear 2009/02/10-2009/02/15 (University of Aix-Marseille III) partial differential equations
Tetsu Mizumachi PDE 2009/02/15-2009/02/21 (Kyushu University)
Bueno Filho, J. S. S. (Universidade Federal de Lavras- Statistics 2009/02/15-2009/03/04 UFLA)
Eunok Jung Applied Mathematics 2009/02/18-2009/02/21 (Konkuk University)
Do Wan Kim Applied Mathematics 2009/02/18-2009/02/21 (Hanyang University )
Yongsam Kim Applied Mathematics 2009/02/18-2009/02/21 (Chung-ng University )
Hiroshi Matano PDE 2009/02/18-2009/02/23 (University of Tokyo)
Victor Isakov PDE 2009/02/21-2009/02/27 (Wichita State University)
Hideyuki Miura PDE 2009/02/22-2009/03/06 (University of Tokyo)
Masaki Hoshino PDE 2009/02/23-2009/02/26 (Tohoku University)
Kota Ikeda PDE 2009/02/23-2009/02/28 (Tohoku University)
Tohru PDE 2009/02/23-2009/02/26 (Tohoku University )
Tatsuki Kawakami PDE 2009/02/23-2009/02/26 (Tohoku University)
Harunori Monobe PDE 2009/02/23-2009/02/26 (Tohoku University )
Michiaki Onodera PDE 2009/02/23-2009/02/26 (Tohoku University)
Shota Sato PDE 2009/02/23-2009/02/26 (Tohoku University)
Appendix Ⅰ -›› 104 Name Field of Interest Period of Visit
Eiji Yanagida PDE 2009/02/23-2009/02/26 (Tohoku University) Appendix Ⅰ Makoto Maejima Probability 2009/02/25-2009/03/04 (Keio University, Japen)
Takahiro Aoyama Probability 2009/02/25-2009/03/04 (Tokyo University of Science)
Chunhua Guo Scientific Computation 2009/03/01-2009/06/30 (University of Regina)
J. Carlos Gomez-Larrañaga (Centro de Investigación en Algebra 2009/03/01-2009/03/12 Matemáticas)
Karl Endel Petersen Ergodic theory 2009/03/10-2009/03/25 (University of North Carolina)
Naoki Chigira Algebra 2009/03/11-2009/03/15 (Kumamoto University)
Hiroshi Suzuki (International Chiristian Algebra 2009/03/11-2009/03/15 University)
Hiroyoshi Yamaki Algebra 2009/03/11-2009/03/15 (Kumamoto University)
Shui-Nee Chow Dynamical Systems 2009/03/15-2009/03/21 (Georgia Institute of Technology)
King-Fai Lai p-adic automorphic forms 2009/03/18-2009/03/19 (NCKU)
Victor Ginzburg Geometry 2009/03/21-2009/04/04 (University of California)
Jean-Pierre Fouque (University of California at Santa Financial Mathematics 2009/03/22-2009/03/28 Barbara)
Yukihiro Seki PDE 2009/03/24-2009/03/31 (University of Tokyo)
Xuding Zhu circular chromatic number 2009/03/28-2009/03/29 (NSYU)
Otto Van Koert Geometry 2009/04/07-2009/04/13 (Hokkaido University)
105 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Klaus Niederkruger (Ecole Normale Supérieure de Geometry 2009/04/07-2009/04/13
Appendix Ⅰ Lyon)
G. L. Zhang Algebra 2009/04/15-2009/04/20 (Shanghai Jiao Tong University)
King-Fai Lai p-adic automorphic forms 2009/04/15-2009/04/16 (NCKU)
Zhiguo Liu Number Theory 2009/04/15-2009/04/30 (East China Normal University)
Hirokazu Ninomiya Reaction-diffusion system, 2009/04/20-2009/04/23 (Ryukoku University) blowup, pattern formation
Yiqiang Zhou (Memorial University of Rings and Modules 2009/04/23-2009/05/22 Newfoundland)
Wojbor A. Woyczynski (Case Western Reserve Probability theory 2009/04/26-2009/05/09 University)
Ke Zhu (The Chinese University of Hong Geometry 2009/04/27-2009/05/11 Kong)
Robert Griess Algebra 2009/04/30-2009/05/30 (University of Michigan)
Sergey Gonchenko (Nizhny Novgorod State Dynamical System 2009/05/01-2009/05/31 University)
Der-Chen Chang Analysis 2009/05/05-2009/08/04 (George Town University)
Qin YUE (Nanjing University of Algebraic Number Theory 2009/05/08-2009/06/05 Aeronautics and Astronautics)
Jarslaw Grytczuk Discrete Mathematics 2009/05/10-2009/05/25 (Jagiellonian University)
Zhaojun Bai Scientific Computation 2009/05/11-2009/05/13 (University of California)
Goong Chen Dynamical System 2009/05/11-2009/05/13 (Texas A&M University)
Appendix Ⅰ -›› 106 Name Field of Interest Period of Visit
Yihong Du Mathematical Biology 2009/05/11-2009/05/13 (University of New England) Appendix Ⅰ Zhaosheng Feng (University of Texas-Pan PDE Non-linear Analysis 2009/05/11-2009/05/13 American)
Yu Huang (Sun Yat-Sen University, Dynamical System 2009/05/11-2009/05/13 Guanzhou)
Tien-Yien Li Dynamical System 2009/05/11-2009/05/13 (Michigan State University)
Tsujii Masato Dynamical System 2009/05/11-2009/05/13 (Kyushu University)
Jakub Przybylo (AGH University of Science and Discrete Mathematics 2009/05/11-2009/05/23 Technology)
Xiaoqiang Zhao (Memorial University of Dynamical System 2009/05/11-2009/05/13 Newfoundland)
Jianxin Zhou Scientific Computation 2009/05/11-2009/05/13 (Texas A&M University)
Yongzhi Steve Xu Applied Mathematics 2009/05/12-2009/05/26 (University of Louisville)
Dinesh Thakur Number Theory 2009/05/13-2009/05/27 (University of Arizona)
Matt Papanikolas Number Theory 2009/05/15-2009/06/13 (Texas A&M University)
Pei-Yu Tsai Arithmetic Geometry 2009/05/15-2009/07/31 (Harvard University)
Kazumi Tanuma Elasticity, Inverse Problems 2009/05/17-2009/05/23 (Gunma University)
Paul Waltman Dynamical Systems 2008/05/18-2008/05/24 (Emory University)
Richard Moeckel Dynamical System 2009/05/19-2009/05/25 (University of Minnesota)
Andrea Venturelli Dynamical System 2009/05/19-2009/05/29 (University of Avigonon)
107 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Wu-Yi Hsiang Transformation groups, (University of California, 2009/05/20-2009/07/31 Differential geometry Appendix Ⅰ Berkeley)
Huyi Hu Dynamical System 2009/05/20-2009/05/26 (Michigan State University )
Wen Huang (Chinese University of Science Dynamical System 2009/05/20-2009/05/25 and Technology)
Bang-He Li Topology , Harmony Analysis 2009/05/20-2009/06/30 (Chinese Academy of Sciences)
Ya-Qing Li Harmony Analysis , Distribution 2009/05/20-2009/06/30 (Chinese Academy of Sciences) Theory
Kening Lu Dynamical System 2009/05/20-2009/05/25 (Brigham Young University )
Alain Chenciner (University Paris VII and Dynamical System 2009/05/22-2009/06/10 IMCCE )
Ming-Hsian Kang Number Theory 2009/05/22-2009/06/10 (Penn. State University )
Jiaping Wang Geometric Analysis & PDE 2009/05/22-2009/06/01 (University of Minnesota)
F. Breuer Number Theory 2009/05/24-2009/05/28 (University Stellenbosch)
Ye-Kai Wang Geometry 2009/05/26-2009/08/14 (Columbia University)
Yared Nigussie Discrete Mathematics 2009/06/01-2009/06/20 (East Tennessee State University)
Ching-Jui Lai Geometry 2009/06/03-2009/07/31 (University of Utah)
Shin-Yao Jow Algebraic geometry 2009/06/05-2009/07/18 (University of Michigan)
Shihshu Walter Wei Differential Geometry 2009/06/09-2009/07/14 (The University of Oklahoma)
Yuan-Shih Chow Statistics 2009/06/10-2009/06/12 (Columbia University)
Yi Hu Algebraic Geometry 2009/06/10-2009/07/09 (University of Arizona)
Appendix Ⅰ -›› 108 Name Field of Interest Period of Visit
Xiao Jie Geometric Harmonic Analysis, (Memorial University of 2009/06/12-2009/06/28 PDE Newfoundland) Appendix Ⅰ
Baojun Bian PDE 2009/06/15-2009/06/16 (Tongji University)
Yongdo Lim (Kyungpook National Positivity in Lie theory 2009/06/15-2009/06/16 University)
Sangho Kum Evacuation planning 2009/06/15-2009/06/16 (Chungbuk National University)
Wenyang Zhang Statistics 2009/06/16-2009/07/02 (University of Bath)
Wei-Yann Tsai Statistics 2009/06/17-2009/06/22 (Columbia University)
Shyan Shiou Chen Scientific Computation 2009/06/19-2009/09/18 (NTNU)
Hung-Yuan Fan Scientific Computation 2009/06/19-2009/09/18 (NTNU)
Tsung-Min Hwang Scientific Computation 2009/06/19-2009/09/16 (NTNU)
Yuen-Cheng Kuo Scientific Computation 2009/06/19-2009/09/18 (NUK)
Shin-Feng Shieh Dynamical System, Applied 2009/06/19-2009/09/18 (NTNU) Mathematics
Tsung-fang Wu Nonlinear PDE 2009/06/19-2009/09/18 (NUK)
Arjun K. Gupta (Bowling Green State Statistics 2009/06/23-2009/06/30 University)
Yu-Shen Lin Geometry 2009/06/24-2009/08/01 (Harvard University)
Chih-Kang Chu Nonparametric statistics, Time 2009/06/25-2009/06/28 (National Dong Hwa University) series data
Wolfgang Haerdle (Humboldt-Universität zu Statistics 2009/06/25-2009/06/29 Berlin)
109 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Steve Marron (University of North Carolina at Statistics 2009/06/25-2009/06/28
Appendix Ⅰ Chapel Hill)
Susan R. Wilson Statistics 2009/06/25-2009/06/28 (Australian National University)
Yen-Hsi Richard Tsai (The University of Texas at Computational and Applied Math 2009/06/26-2009/07/17 Austin)
Kung-Yee Liang Statistics 2009/06/26-2009/07/23 (Johns Hopkins University)
Chiu-Chu (Melissa) Liu Differential Geometry 2009/06/28-2009/07/11 (Columbia University)
Tin-Yau Tam Matrix theory and Lie groups 2009/06/29-2009/07/08 (Auburn University)
Sun-Yung Alice Chang Differential Geometry 2009/07/01- 2009/07/11 (Princeton University)
Ronald Graham Discrete Mathematics 2009/07/01-2009/07/09 (University California)
Fan Chung Graham (University California, San Discrete Mathematics 2009/07/01-2009/07/09 Diego)
Wen-Wei Li Representation Theory 2009/07/01-2009/08/15 (Universite Paris 7)
Chern-Shuh Wang Scientific Computations 2009/07/01-2009/09/15 (NCKU)
Paul Yang Differential Geometry 2009/07/01-2009/07/11 (Princeton University)
Stephen Shing-Toung Yau Algebra 2009/07/01-2009/07/05 (University of Illinois)
Mu-Tao Wang Differential Geometry 2009/07/02-2009/07/11 (Columbia University)
Lani F. Wu (The University of Texas Biomathematics 2009/07/02-2009/07/19 Southwestern Medical Center at Dallas)
Appendix Ⅰ -›› 110 Name Field of Interest Period of Visit
Steven Altschuler (The University of Texas Biomathematics 2009/07/02-2009/07/19 Southwestern Medical Center at Appendix Ⅰ Dallas)
Heng Huat Chan (National University of Number Theory 2009/07/02-2009/07/14 Singapore)
Mihai Paun Algebraic Geometry 2009/07/04-2009/07/10 (Université Nancy)
Jean-Pierre Serre Number Theory Algebra and 2009/07/04-2009/07/14 (College de France) Geometry
Jean-Pierre Tignol (Université catholique de Algebra and Number Theory 2009/07/04-2009/07/08 Louvain)
Jaroslaw Wlødarczyk Algebraic geometry 2009/07/04-2009/07/10 (Purdue University)
Pinyuen Chen Statistics 2009/07/05-2009/07/06 (Syracuse University)
Christy Jane-Lan Chuang-Stein (Stat. Research & Consulting Statistics 2009/07/05-2009/07/12 Center, Pfizer Inc.)
Osamu Fujino Algebraic Geometry 2009/07/05-2009/07/08 (Kyoto University)
Shinobu Hosono Differential Geometry 2009/07/05-2009/07/10 (The University of Tokyo)
Tailen Hsing Statistics 2009/07/05-2009/07/11 (University of Michigan)
White noise theory, Stochastic Hui-Hsiung Kuo differential equations, Probability 2009/07/05-2009/07/11 (Louisiana State University) on infinite dimensional spaces
Wieslaw Z. Krawcewicz PDE 2009/07/05-2009/07/22 (University of Alberta)
Statistical genetics, Shaw-Hwa Lo Bioinformatics, 2009/07/05-2009/07/13 (Columbia University) Survival Analysis
Ue-Li Pen (Canadian Institute for Computational and Applied Math 2009/07/05-2009/07/12 Theoretical Astrophysics)
111 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Mei-Chi Shaw PDE 2009/07/05-2009/07/10 (University of Notre Dame) Appendix Ⅰ Chuu-Lian Terng Differential Geometry 2009/07/05-2009/07/12 (University of California)
Tai-Peng Tsai PDE 2009/07/05-2009/07/11 (University of British Columbia)
Pit-Mann Wong Differential Geometry 2009/07/05-2009/07/12 (University of Notre Dame)
Stephen S. T. Yau (University of Illinois at Algebraic geometry 2009/07/05-2009/07/13 Chicago)
Shih-Hsien Yu (National University of PDE 2009/07/05-2009/07/10 Singapore)
Eric Chu Scientific Computation 2009/07/06-2009/07/31 (Monash University)
Jing - Song Huang Representation Theory, (Hong Kong University of 2009/07/06-2009/07/11 Lie Theory Science and Technology)
Kuang-Kuo Gordon Lan Statistical Science 2009/07/06-2009/07/11 (Johnson & Johnson)
Shuo-Yen Robert Li (The Chinese University of Hong Discrete Mathematics 2009/07/06-2009/07/08 Kong)
Ling Long Number Theory 2009/07/06-2009/08/04 (Iowa State University)
Qing Nie Computational and Applied Math 2009/07/06-2009/07/09 (University of California, Irvine)
Claes Olof Runborg (NADA, Royal Institute of Numerical Analysis 2009/07/06-2009/07/12 Technology(KTH))
Ju-Kang Yu Algebra and Number Theory 2009/07/06-2009/07/11 (Purdue University)
Lung-Chi Chen Probability 2009/07/07-2009/07/17 (Fu Jen U. and U.B.C.)
Mei-Ling Ting Lee Statistics 2009/07/07-2009/07/13 (University of Maryland)
Appendix Ⅰ -›› 112 Name Field of Interest Period of Visit
Houman Owhadi (California Institute of Multi-scale analysis 2009/07/07-2009/07/11
Technology) Appendix Ⅰ
Yuan Yu PDE 2009/07/07-2009/07/14 (University of Washington)
Jiu - Kang Yu Number Theory and 2009/07/07-2009/07/17 (Purdue University) Representation Theory
YanYan Li PDE 2009/07/08-2009/07/11 (Rutgers University)
Eiji Yanagida PDE 2009/07/08-2009/07/12 (Tohoku University)
Chiu-Yen Kao Computational and Applied Math 2009/07/08-2009/08/05 (The Ohio State University)
Keke Zhang Computational and Applied Math 2009/07/08-2009/07/15 (University of Exeter)
Ching-Shui Cheng (University of California, Statistics 2009/07/08-2009/07/12 Berkeley)
Wen-Jang Huang (National University of Statistics 2009/07/08-2009/07/10 Kaohsiung)
Ruey S. Tsay Statistics 2009/07/08-2009/07/10 (University of Chicago)
Jane-Ling Wang Statistics 2009/07/08-2009/07/14 (University of California, Davis)
Chien-Fu Jeff Wu Statistics 2009/07/08-2009/07/11 (Georgia Institute of Technology)
Naihua Duan Statistics 2009/07/09-2009/07/15 (University Columbia)
Julian Lopez Gomez (Complutense University of Applied Mathematics 2009/07/15-2009/08/15 Madrid )
Kai-Wen Lan Number Theory 2009/07/15-2009/08/29 (Princeton University)
Applied Mathematics, Ting-Hui Yang Dynamical System, 2009/07/15-2009/09/15 (Tamkang University) Scientific Computation
113 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Tsao-Hsien Chen (Massachusetts Institute of Representation Theory 2009/07/21-2009/08/21
Appendix Ⅰ Technology)
Edmund Y. M. Chiang Complex Analysis 2009/07/21-2009/07/30 (USTHK)
Min Ru Complex Analysis 2009/07/21-2009/07/30 (University of Houston)
N. Sibony Complex Analysis 2009/07/24-2009/07/30 (University Paris-Sud)
Karen Anne Chandler (University of California at Number Theory 2009/07/25-2009/07/30 Riverside)
Xiaobo Liu Differential Geometry 2009/07/25-2009/07/30 (University of Notre Dame)
Ta Thi Hoai An Number Theory 2009/07/26-2009/07/30 (Hanoi Institute of Math.)
Jih-Hsin Cheng Differential Geometry 2009/07/26-2009/07/30 (Academia Sinica)
M. Dulock Complex Analysis 2009/07/26-2009/07/30 (University of Houston)
M. Ionel Complex Geometry 2009/07/26-2009/07/30 (University of Toledo)
Aaron Levin (Centro De Giorgi, Scuola Number Theory 2009/07/26-2009/07/30 Normale Superiore)
Giorgio Patrizio Complex Geometry 2009/07/26-2009/07/29 (University of Firenze)
Yum-Tong Siu Complex Geometry 2009/07/26-2009/07/28 (Harvard University)
Paul Vojta Number Theory 2009/07/26-2009/07/30 (University of California)
Julie Tzu-Yueh Wang Number Theory 2009/07/26-2009/07/30 (Academia Sinica)
Bun Wong Several Complex Variables, (University of California, 2009/07/26-2009/07/30 Complex differential Geometry Riverside )
Appendix Ⅰ -›› 114 Name Field of Interest Period of Visit
Pit-Mann Wong Complex Geometry 2009/07/26-2009/07/30 (University of Notre Dame) Appendix Ⅰ Zhao Xianyu (Chinese Academy of Science Complex Analysis 2009/07/26-2009/07/29 Institute of Mathematics)
Stephen S. T. Yau Complex Geometry 2009/07/26-2009/07/29 (University of Illinois)
Aaron Nung Kwan Yip Applied Mathematics 2009/08/13-2009/08/14 (Purdue University)
Shaohua Pan Continuous optimization, (South China University of 2009/08/13-2009/08/14 Nonsmooth analysis Technology)
Chang-Qing Hu Differential Geometry 2009/08/17-2009/09/18 (Soochow University)
Thomas Yizhao Hou (California Institute of Applied Mathematics 2009/08/18-2009/08/21 Technology)
Yang Fang Number Theory 2009/08/25-2009/12/25 (Penn. State University)
Jonas Kibelbek Number Theory 2009/08/25-2009/12/25 (Penn. State University)
Chenying Wang Number Theory 2009/08/25-2009/12/25 (Penn. State University)
Matt Papanikolas Number Theory 2009/08/28-2009/09/16 (Texas A & M Universtiy)
Yi-Fan Yang Number Theory 2009/08/30-2009/09/12 (NCTU)
Edmund R. Puczylowski Ring Theory 2009/09/05-2009/10/02 (University of Warsaw)
Shunsuke Hayashi Applied Mathematics 2009/09/06-2009/09/29 (Kyoto University)
King-Fai Lai Automorphic Forms 2009/09/10-2009/09/11 (NSYU)
Muhammet Tamer KOŞAN Ring and Module Theory 2009/09/15-2009/10/07 (Gebze Institute of Technology)
Kazunaga Tanaka Dynamical System 2009/09/17-2009/09/23 (Waseda University)
115 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
Yuan-Shih Chow Statistics 2009/09/18-2009/09/18 (Columbia University) Appendix Ⅰ Edmund Puczylowski Algebra 2009/09/18-2009/09/24 (University of Warsaw)
Yair Censor Optimization theory 2009/09/23-2009/10/06 (University of Haifa)
Kung-Yee Liang Statistics 2009/09/24-2009/09/25 (The Johns Hopkins University)
Ming Jiang Biomedical imaging 2009/09/27-2009/10/11 (Peking University)
Rongfeng Sun (National University of Probability Theory 2009/10/13-2009/10/17 Singapore)
Ruibin Zhang Algebra 2009/10/18-2009/11/14 (University of Sydney)
Wu-Yi Hsiang Transformation groups, (University of California, 2009/10/19-2009/11/06 Differential geometry Berkeley)
Zheng-rong Liu (South China University of Probability 2009/10/19-2009/10/25 Technology)
Min Wu (South China University of Probability 2009/10/19-2009/10/25 Technology)
Quandi Wang (South China University of T Probability 2009/10/19-2009/10/25 echnology)
Yong-Sheng Li (South China University of Probability 2009/10/19-2009/10/25 Technology)
Sheng-Lin Zhou (South China University of Probability 2009/10/19-2009/10/25 Technology)
Kang Qindge Graph Theory 2009/10/19-2009/10/21 (Hebei Normal University)
Ernst-Ulrich Gekeler Number Theory 2009/10/20-2009/11/19 (University of Saarlandes)
Appendix Ⅰ -›› 116 Name Field of Interest Period of Visit
Gilles Lachaud Number Theory Algebraic 2009/10/20-2009/10/27 (CNRS) Geometry Appendix Ⅰ Jean-Pierre Bourguignon Number Theory 2009/10/22-2009/10/27 (IHES)
Shin Kiriki Dynamical System 2009/10/31-2009/11/23 (KyotoUniversity)
Katsutoshi Shinohara Dynamical System 2009/10/31-2009/11/09 (University of Tokyo)
Lorenzo J. Diaz Dynamical System 2009/11/01-2009/11/22 (PUC-Rio)
Siye Wu (University of Colorado, Mathematical Physics 2009/11/01-2009/11/13 Boulder)
Qin Sheng Numerical Methods for PDEs 2009/11/05-2009/12/06 (Baylor University)
Krishnaiyan Thulasiraman Discrete Mathematics 2009/11/07-2009/11/14 (University of Oklahoma)
Sandeep Sen (Indian Institute of Technology Discrete Mathematics 2009/11/08-2009/11/12 Delhi)
S. Arumugam (National Center for Advanced Discrete Mathematics 2009/11/08-2009/11/13 Research in Discrete Mathematics)
R. Balakrishnan Discrete Mathematics 2009/11/08-2009/11/13 (Bharathidasan University)
Ambat Vijayakumar (Cochin University of Science Discrete Mathematics 2009/11/08-2009/11/13 and Technology)
P. Paulraja Discrete Mathematics 2009/11/08-2009/11/13 (Annamalai University)
R. Sampath Kumar Discrete Mathematics 2009/11/08-2009/11/13 (Annamalai University)
A. Muthusamy Discrete Mathematics 2009/11/08-2009/11/13 (Periyar University)
T. Karthick (Indian Institute of Technology Discrete Mathematics 2009/11/08-2009/11/13 Madras)
117 ‹‹- Appendix Ⅰ Name Field of Interest Period of Visit
S. Francis Raj Discrete Mathematics 2009/11/08-2009/11/13 (Bharathidasan University) Appendix Ⅰ T. Tamizh Chelvam (Manonmaniam Sundaranar Discrete Mathematics 2009/11/08-2009/11/13 University)
Manoj Chanjat Discrete Mathematics 2009/11/08-2009/11/13 (University of Kerala)
Subir Ghosh (Tata Institute of Fundamental Discrete Mathematics 2009/11/08-2009/11/14 Research)
Partha Pratim Goswami (Tata Institute of Fundamental Discrete Mathematics 2009/11/08-2009/11/14 Research)
Ramesh Krishnamurti Discrete Mathematics 2009/11/08-2009/11/14 (Simon Fraser University)
Eric Chu Scientific Computation 2009/11/15-2009/12/31 (Monash University )
Jerry Lloyd Bona (University of Illinois at PDE 2009/11/19-2009/12/10 Chicago)
Yiqian Wang Dynamical System 2009/11/21-2009/11/27 (Nanjing University)
Marco A. Lopez Applied Mathematics 2009/11/22-2009/12/06 (Alicante University)
Li Guo Number Theory 2009/12/02-2009/12/09 (Rutgers University, Newark)
Antoine Probability Theory and Wavelets Ayache (Laboratoire Paul 2009/12/03-2009/12/18 Theory Painlevé)
Mickael Montassier Discrete Mathematics 2009/12/04-2009/12/17 (University of Bordeaux)
Andre Raspaud Discrete Mathematics 2009/12/04-2009/12/17 (University of Bordeaux)
Inchi Hu (Hong Kong University of Statistics and Probability 2009/12/07-2009/12/13 Science and Technology)
Sergei Yu. Pilyugin Differential equation 2009/12/07-2009/12/21 (St.Petersburg State University)
Appendix Ⅰ -›› 118 Name Field of Interest Period of Visit
Irina Markina Real Analysis 2009/12/12-2009/12/25 (University of Bergen) Appendix Ⅰ Alexander Vasiliev Complex and Applied Analysis 2009/12/12-2009/12/25 (University of Bergen)
Jun-cheng Wei Nonlinear Partial Differential (The Chinese University of Hong 2009/12/18-2009/12/23 Equations Kong)
Dong-Hui Li Applied Mathematics 2009/12/20-2010/01/20 (Hunan University)
Lek-Hrng Lim (University of California, Computational Sciences 2009/12/20-2010/01/03 Berkeley)
Tian Ma Nonlinear Analysis 2009/12/20-2010/01/20 (Si Chuan University)
Fugee Tsung (Hong Kong University of Statistics and Probability 2009/12/20-2009/12/22 Science and Technology)
Ilie Grigorescu Statistics and Probability 2009/12/24-2010/01/07 (University of Miami)
Joongul Lee Algebraic number theory 2009/12/28-2010/01/03 (Hongik University)
Xiaojun Chen (The Hong Kong Polytechnic Applied Mathematics 2010/03/14-2010/03/27 University)
119 ‹‹- Appendix Ⅰ NCTS 2008.9-2009.12 Conference, Workshop, School & Special Lecture
Time Conference & Workshop Place Appendix Ⅱ
NCTS One-day Workshop for Summer Students Presentation Organizers: Kuo-Chang Chen (NTHU) Lecture Room of Sept. 4, 2008 Meng-Kiat Chuah (NTHU) NCTS, National Shu-Yen Pan (NTHU) Tsing Hua Univ. Dong-Ho Tsai (NTHU) Jyh-Haur Teh (NTHU) Jing Yu (NCTS & NTHU)
2008 NCTS & NCTU Joint Course on Mathematics Sept. 15, 2008- National Chiao in the Atmospheric and Oceanic Fluids January 15, 2009 Tung University Instructor: Hung-Chi Kuo (NTU)
Lecture Room of Sept. 16, 2008- 2008 NCTS Fall Course Function Field Arithmetic NCTS, National January 16, 2009 Instructor: Andreas Schweizer (NCTS) Tsing Hua Univ.
Sept. 17, 2008- 2008 NCTS Fall Course on Applied Math National Chiao January 15, 2009 Organizer: Wen-Wei Lin (NCTU). Tung University
Lecture Room of Sept. 17, 2008- 2008 NCTS Fall Course Abelian Varieties NCTS, National January 16, 2009 Organizer: Jing Yu (NCTS & NTHU) Tsing Hua Univ.
Workshop on algebraic combinatorics Speakers: Yeong-Nan Yeh(Academia Sinica, Taiwan) R204, 2F, NCTS, November 19-21, 2008 Jun Ma( Academia Sinica, Taiwan) NCKU Hungyung Chang ( Academia Sinica, Taiwan) Organizer: Ching Hung Lam (NCKU)
2008 Bioinformatics Workshop Speaker: Audio-Visual Academician Wen-Hsiung Li Room 62115, 1F, November 27, 2008 (Biodiversity Research Center, and Genomics Research Dept. of Statistics, Center, Academia Sinica ) NCKU Organizer: Tiee-Jian Wu (NCKU)
Appendix Ⅱ -›› 120 Time Conference & Workshop Place
Mini-Workshop in Algebraic Combinatorics Speakers:
Masaaki Harada (Yamagata University/JST Presto) Appendix Ⅱ Manabu Oura ( Kochi University, Japan ) R204, 2F, NCTS, November 29, 2008 Akihiro Munemasa ( Tohoku University, Japan ) NCKU Tsuyoshi Miezaki ( Kyushu University, Japan ) Hiroki Shimakura ( Aichi University of Education, Japan ) Organizer: Ching Hung Lam (NCKU)
Fujisan One-day Workshop in Geometry and Topology Speakers: R204, 2F, NCTS, December 27, 2008 Manabu Akaho (Tokyo Metropolitan University, Japan) NCKU Tetsuhiro Moriyama (University of Tokyo, Japan) Takahiko Yoshida (Meiji University, Japan) Organizer: River Chiang (NCKU)
Symposium in Statistics and Probability Speaker: Tze Leung Lai Audio-visual Room January 9, 2009 (Academician of Academia Sinica, Taiwan / Dept. of 62331, 3F, Dept. of Statistics, Stanford University, USA) Statistics, NCKU Organizer: Tiee-Jian Wu (NCKU)
2009 Workshop on Graph Theory Organizers: Gerard J. Chang (National Taiwan University, Taiwan) Dept. of Applied Pavol Hell (Simon Fraser University, Canada) Mathematics, January 10-14, 2009 Ko-Wei Lih ( Academia Sinica, Taiwan) National Sun Yat- Jarik Nesetril (Charles University, Czech Republic) sen University, Li-Da Tong (NSYSU, Taiwan) Kaohsiung, Taiwan Tsai-Lien Wong (NSYSU, Taiwan) Xuding Zhu (NSYSU, Taiwan)
Miniworkshop for Optimization Speakers: Hadjisavvas Nicolas (University of the Aegean, Greece) Nguyen Dong Yen(Vietnamese Academy of Science R204, 2F, NCTS, January 14, 2009 and Technology, Vietnam) NCKU Chong Li (Zhejiang University, China ) Nguyen Huy Chieu (Vinh University, Vietnam) Jian-Wen Peng (Chongqing Normal University, China) Organizer: Soon-Yi Wu (NCKU)
NCTS Mathematical Modeling & Scientific National Chiao January 19-20, 2009 Computation Tung University Organizer: Ming-Chih Lai (NCTU)
121 ‹‹- Appendix Ⅱ Time Conference & Workshop Place
2009 NCTS Winter School on Number Theory Aspire Park, February 1-5, 2009 Appendix Ⅱ Organizer: Jing Yu (NCTS & NTHU) Taoyuan
2009 Mini Workshop on Optimization (1) Speakers: Sangho Kum (Chungbuk National University, Korea) Gue Myung Lee (Pukyong National University, Korea) National Taiwan Feb. 6, 2009 Yongdo Lim (Kyungpook National University, Korea) Normal University Jein-Shan Chen (National Taiwan Normal University) Chun-Hsu Ko (I-Shou University) Shaohua Pan (South China University of Technology)
Miniworkshop of Algebra Speakers: Room 308, New Teruo Asanuma (Toyama University, Japan) Mathematics Feb. 10-13, 2009 Ming-Chang Kang (National Taiwan University) Building, National Wujie Shi (Suzhou University, China) Taiwan University Zhongming Tang (Suzhou University, China) Keiichi Watanabe (Nihon University, Japan)
2009 NCTS One-Day Workshop on Modeling and National Chiao February 12, 2009 Computing in MRI Tung University Organizer: Wen-Wei Lin (NCTU)
2009 NCTS One Day Workshop on Interface National Chiao February 19, 2009 Problems Tung University Organizer: Ming-Chih Lai (NCTU)
Taiwan-Japan Joint Workshop on Partial Differential Equations Lecture Room of February 23-26, 2009 Organizers: NCTS, National Jann-Long Chern (NCU, Taiwan) Tsing Hua Univ. Eiji Yanagida (Tohoku University, Japan)
2009 NCTS Spring Course -Abelian Varieties and Diophantine Approximations Lecture Room of Instructors: March 11 -June17, 2009 NCTS, National Jing Yu (NCTS & NTHU) Tsing Hua Univ. Julie Tzu-Yueh Wang (Academic Sinica) Liang-Chung Hsia (NCU)
Appendix Ⅱ -›› 122 Time Conference & Workshop Place
Mini-Workshop on Finite Groups Speakers:
Koichiro Harada (NCKU and Ohio State University) Appendix Ⅱ R204, 2F, NCTS, March 13, 2009 Hiroyoshi Yamaki(Kumamoto University, Japan) NCKU Hiroshi Suzuki ( International Christian University ) Naoki Chigira ( Kumamoto University, Japan ) Organizer: Ching Hung Lam (NCKU) Mini-workshop on Contact Geometry Speakers: Otto van Koert(Hokkaido University, Japan ) R204, 2F, NCTS, April 12, 2009 Klaus Niederkruger (Ecole Normale Superieure de NCKU Lyon, France) Shu-Cheng Chang(NTU, Taiwan) Organizer: River Chiang (NCKU)
Lecture Room of NCTS Lie Theory Workshop April 23, 2009 NCTS, National Organizer: Meng-Kiat Chuah (NTHU) Tsing Hua Univ.
R62x05, B1, The Fifth Statistics and Machine Learning College of April 25-26, 2009 Workshop Management, Organizer: Shuen-Lin Jeng (NCKU) NCKU
Room 4011, Xi-Wan Combinatorial Workshop Series 2009 May 1 & 8, 2009 Faculty of Organizer: Xuding Zhu (NSYSU) Sciences, NSYSU
NCTS 2009 Interdisciplinary Conference on Applied Analysis and Mathematics Organizers: Lecture Room of May 11- 13, 2009 Goong Chen (Texas A&M University) NCTS, National Ming-Chih Lai (NCTU) Tsing Hua Univ. Chang-Shou Lin (NTU) Wen-Wei Lin (NCTU) Miniworkshop on Graph Colouring Speakers: Jarek Grytczuk (Jagiellonian University, Poland) Room 4011, May 17, 2009 Jakub Przybyło (AGH University of Science and Faculty of Technology, Poland) Sciences, NSYSU Tsai-Lien Wong (NSYSU, Taiwan) Organizer: Xuding Zhu (NSYSU, Taiwan) 2009 NCTS Mini Course on Geometric Analysis Lecture Room of Organizers: May 18-July 27, 2009 NCTS, National Der-Chen Chang (NCTS & Georgetown Univ.) Tsing Hua Univ. Chiung-Jue Sung (NTHU)
123 ‹‹- Appendix Ⅱ Time Conference & Workshop Place
2009 NCTS Workshop on Dynamical Systems
Appendix Ⅱ Organizers: Kuo-Chang Chen (NTHU) Lecture Room of May 21-24, 2009 Cheng-Hsiung Hsu (NCU) NCTS, National Jung Juang (NCTU) Tsing Hua Univ. Ming-Chia Li (NCTU) Chih-Wen Shih (NCTU)
2009 Probability Workshop Speaker: Audio-visual Room Kung-Yee Liang (Academia Sinica / Dept. of June 11, 2009 62331, 3F, Dept. of Biostatistics, School of Public Health, The Johns Statistics, NCKU Hopkins University) Organizer: Tiee-Jian Wu (NCKU)
Mini Workshop on Optimization (2) Speakers: Baojun Bian (Tongji University, China) Sangho Kum (Chungbuk National University, Korea) National Taiwan June 15, 2009 Yongdo Lim (Kyungpook National University, Korea) Normal University Jen-Yen Lin (National Chiayi University) Jeng-Huei Chen (National Cheng-Chi University) Chia-Hui Huang (Kainan University)
NCTS Preparation Seminar for Serre's Lecture Organizers: Lecture Room of June 22-26 , 2009 Yifan Yang (NCTU) NCTS, National Liang-Chung Hsia (NCU) Tsing Hua Univ. Wen-Ching Winnie Li (NCTS)
International The 18th South Taiwan Statistics Conference Conference Hall, June 26-27, 2009 Speaker: Wei-Yann Tsai (Columbia University, USA ) FL 11, Info-Library Building, NSYSU
Appendix Ⅱ -›› 124 Time Conference & Workshop Place
NTU Mathematics Month Speakers: H. Brezis (Rutgers University) Appendix Ⅱ I. Daubechies (Princeton University) B. Engquist (University of Texas, Austin) R. Graham (University of California, San Diego) P. Hall (University of Melbourne) Y.-T. Lee (Academia Sinica; Nobel Prize in Chemistry) National Taiwan June 29 - July 18, 2009 E. Lieb (Princeton University) University F.-H. Lin (New York University) D.-H. Phong (Columbia University) R. Schoen (Stanford University) J.-P. Serre (College de France) Y.-T. Siu (Harvard University) S. R. S. Varadhan (New York University) S.-T. Yau (Harvard University) E. Zelmanov (University of California, San Diego)
Lecture Room of Lecture Series by Jean-Pierre Serre July 7, 9 , 10, 11, 2009 NCTS, National Instructor: Jean-Pierre Serre (Collège de France) Tsing Hua Univ.
NCTS 2009 Summer Course on Discrete Mathematics Instructors: National Chiao July 1-August 20, 2009 Chiuyuan Chen (NCTU) Tung University Hong-Bin Chen (NCTU) Chih-Wen Weng (NCTU)
2009 NCTS Short Course in Monotone Dynamical Systems with Applications Lecture Room of July 7-August 11, 2009 Organizers: NCTS, National Changyuan Cheng (NPUE) Tsing Hua Univ. Sze-Bi Hsu(NTHU) Feng-Bin Wang (NTHU)
NCTS Summer Mini-Course on Stochastic Processes Organizers: National Chiao July 7-August 25, 2009 Guan-Yu Chen (NCTU) Tung University Yuan-Chung Sheu (NCTU)
2009 NCTS & NTHU (Statistics) Summer Short Lecture Room of Course: Multistratum Fractional Factorial Designs NCTS, National July 16-August 6, 2009 Instructor: Ching-Shui Cheng (University of California, Tsing Hua Univ. Berkeley)
125 ‹‹- Appendix Ⅱ Time Conference & Workshop Place
Mathematical Models and Scientific Research Speaker: Hung-Chi Kuo R203, 2F, NCTS, July 21-24, 2009 Appendix Ⅱ (Dept. of Atmospheric Sciences, NTU, Taiwan) NCKU Organizer: Chern-Shuh Wang (NCKU) Conference on Value Distribution Theory and Complex Geometry Organizers: Lecture Room of July 27-30, 2009 Min Ru (University of Houston) NCTS, National Paul Vojta (U.C. Berkeley) Tsing Hua Univ. Julie Tzu-Yueh Wang (Academia Sinica) Jing Yu ( NCTS & NTHU) 2009 Workshop in Statistics Methodology:An Overview on Likelihood-based Inferential Procedures I & II Audio-visual Room Speaker: Sept. 24, 2009 62331, 3F, Dept. of Kung-Yee Liang (Academia Sinica / Dept. of Statistics, NCKU Biostatistics, School of Public Health, The Johns Hopkins University) Organizer: Tiee-Jian Wu (NCKU)
Workshop on Theory and Applications of Mathematical Analysis Speakers: Min Wu (South China University of Technology, China) Jyh-Hao Lee (Academia Sinica) Shenglin Zhou (South China University of Technology, China) Jein-Shan Chen (National Taiwan Normal University) Room 308, New Bing Li (National Taiwan University) Mathematics October 21-22, 2009 Quandi Wang (South China University of Technology, Building, National China), Taiwan University Gerard Jennhwa Chang (National Taiwan University) Zhengrong Liu (South China University of Technology, China) Kin-Ming Hui (Academia Sinica) Ngai-Ching Wong (National Sun Yat-sen University) Yongsheng Li (South China University of Technology, China) Narn-Rueih Shieh (National Taiwan University)
NCTS Taiwan-France Workshop on Theoretical Sciences Lecture Room of Organizers: October 26, 2009 NCTS, National Arnaud Lalo (Institut Francais de Taipei) Tsing Hua Univ. Wen-Ching Winnie Li (NCTS & Penn. State) Chung-Yu Mou (NCTS & NTHU)
Appendix Ⅱ -›› 126 Time Conference & Workshop Place
NCTS Lectures on Number Theory Lecture Room of October 23-November Instructor: Ernst-Ulrich Gekeler (Universitat des NCTS, National
13, 2009 Appendix Ⅱ Saarlandes) Tsing Hua Univ.
NCTS Dynamics Day-focusing on non-hyperbolic systems Organizers: National Chiao November 6, 2009 Jonq Juang (NCTU) Tung University Ming-Chia Li (NCTU) Chih-Wen Shih (NCTU)
Taiwan-Japan Joint workshop on Numerical Analysis and Scientific Computation Speakers: Hisashi Okamoto (Kyoto University, Japan) Feng-Nan Hwang (National Central University) Room 101, New Nobito Yamamoto (The Univ. of Electro- Mathematics November 7-8, 2009 Communications, Japan) Building, National Naoshi Nishimura (Kyoto University, Japan) Taiwan University Hiroshi Kokubu (Kyoto University, Japan) Kaname Matsue (Kyoto University, Japan) Hitoshi Imai (Tokushima University, Japan) Hiroshi Fujiwara (Kyoto University, Japan) Kazuki Niinou (Kyoto University, Japan)
India-Taiwan Conference on Discrete Mathematics Speakers: S. Arumugam (National Center for Advanced Research in Discrete Mathematics, India) R. Balakrishnan (Bharathidasan University) Subir Ghosh (Tata Institute of Fundamental Research) A. Vijayakumar (Cochin University of Science and Technology) P. Paulraja (Annamalai University) Room 204, R. Sampath Kumar (Annamalai University) Condensed Matter A. Muthusamy (Periyar University) Science and November 9-12, 2009 T. Karthick (Indian Institute of Technology Madras) Physics Building S. Francis Raj (Bharathidasan University) , National Taiwan T. Tamizh Chelvam (Manonmaniam Sundaranar University University) K. Thulasi Raman (University of Oklahoma) Manoj Chanjat (University of Kerala) Subhas Chandra Nandy (Indian Statistical Institute) Partha Pratim Goswami (Tata Institute of Fundamental Research) Ramesh Krishnamurti (Simon Fraser University) Sandeep Sen (Indian Institute of Technology
127 ‹‹- Appendix Ⅱ Time Conference & Workshop Place
2009 Workshop on Nonlinear Analysis and Optimization
Appendix Ⅱ Speakers: Shigeo Akashi (Tokyo University of Sciences, Japan) Sompong Dhompongsa (Chiang Mai University, Thailand) T. Ibaraki (Nagoya University, Japan) Do Sang Kim (Pukyong National University, Korea) National Taiwan November 25-27, 2009 Jong Kyu Kim (Kyungnam University, Korea) Normal University Yasunori Kimura (Tokyo Institute of Technology, Japan) Liqun Qi, (The Hong Kong Polytechnic University, Hong Kong) Wataru Takahashi (National Sun Yat-sen University) Sangwoon Yun (Korea Advanced Institute of Science and Technology, Korea) 2009 Taiwan-Norway Joint Workshop on Geometric Analysis and Mathematical Physics Organizers: Lecture Room of December 15-16, 2009 Chiung-Jue Sung (NTHU) NCTS, National Alexander Vasilev (University of Bergen, Norway) Tsing Hua Univ. Irina Markina (University of Bergen, Norway) Der-Chen Chang (Georgetown University, USA)
Appendix Ⅱ -›› 128 Physics Division Report of the Division Head
General Remarks programs, it is aiming to stimulate better research and foster greater collaboration among researchers Taiwan in the 3rd phase. Most importantly, through the participation of international researchers in the CTS enters the operation of the 3nd activities of focus groups, the visibility of phase early this year. The 6-year theoretical researches in Taiwan can be further endorsement from National Science Council increased. Therefore, we expect more intensive (NSC) has enabled the center for long-term international exchanges with theoretical scientists planning. In the 3rd phase, NCTS follows the from all over the world, in particular with other format established in the 2nd phase with the main world renowned research centers of theoretical project being located at National Tsing Hua sciences in the 3rd phase. University (NTHU), subproject I being at National Before we report academic activities and Taiwan University (NTU), and subproject II being highlights of researches in 2009, I want to take located at National Cheng-Kung University this opportunity to welcome Professor Ling-Fong (NCKU). In addition to NTHU and National Li (李靈峰) from Carnegie Mellon University, Chiao Tung University (NCTU), National Central who has kindly accepted the offer to head the University (NCU) joins and co-hosts the main Division. Professor Li will inaugurate in January project. For physics programs, subproject I is led 2010. In the following, we shall first describe the 侯維恕 by Professor Wei-Shu Hou ( ) from the operation structure for the 3rd phase. Detailed Physics Department of NTU, while the subproject reports on each focus group and topical program 盧炎 II is currently led by Professor Yan-Tien Lu ( can be found on the NCTS web-site http://phys. 田 ) from the Physics Department of NCKU. The cts.nthu.edu.tw/. annual budget allocation of NCTS in the 3rd phase will be determined based on annual review. Organization Structure In 2009, about one-third and one-sixth of the NCTS annual budget are channeled through The operation of the Physics Division is Subproject I and Subproject II at NCKU, conducted with the help of the executive respectively. The rest of the NCTS budget is committee. Division head and PIs of subprojects allocated in the main project. (Professors Wei-Shu Hou and Yan-Tien Lu) are default members in the committee. In 2009, the In the 3rd phase, the Division continues to rest members are Professor Pei-Long Chen (陳培 implement focus groups as the main academic 亮, NCU), Professor Yung-Chung Chen (陳永忠, program. In addition, the Division will also play a Tunghai University), Professor Chon-Saar Chu more dominant role by selecting important topics (朱仲夏, NCTU), Professor Guang-Yu Guo that may lead to works with wide impact and (郭光宇, NTU), Professor Kin-Wang Ng (吳建宏, organize these topics as topical programs. The Academia Sinica (AS)), Professor Shiow-Fon main project and subprojects support all activities Tsay (蔡秀芬, National Sun Yat-sen University) of focus groups together, while the NCTS and physics review-panel convener of NSC scientific personnel, and the additional NCTS (Professors Chia-Seng Chang (張嘉升, AS) and sponsored functions, such as topical programs and Jow-Tsong Shy (施宙聰, NTHU)). Members of the joint programs between Physics and Executive Committee represent various fields in Mathematics Division are supported by the main theoretical physics, providing opinions and project. Through the organization of nationwide suggestions based on their expertise, and serving
Report of the Division Head -›› 130 as the second reviewers of applications and Pohang on quantum condensation. Six delegates recruitments submitted to NCTS. supported by NCTS attended the program. The workshop extended for 2 weeks and is aiming for In addition to the executive committee, an inducing possible cooperated researches. During annual review will be performed each year in the rd the period of the workshop, the interaction among 3 phase. The annual review for 2009 will take Taiwan delegates and other foreign participants place on Dec. 26. The function of the annual was intensive. Some projects were initiated. To review committee takes over that of the nd continue the joint effort and projects, the same performance evaluation panel in the 2 phase joint workshop will be held at NCTS in August except that it is formed by NSC. In addition, the 2010 with anticipated number of participants review committee gives recommendation on being around 20. Another joint workshop with budget of the following year to NSC. APCTP is the workshop on multiferroics which Scientific Activities will be held in early January of 2010 in Taiwan. This workshop will bring theorists and Except for a couple of mini-workshops experimentalists together both from Taiwan and organized by center staff scientists, the majority of abroad and is aiming to induce timing cooperated the scientific activities in the physics division are researches in the subject of multiferroics. planned and carried out by the NCTS affiliated focus groups. All NCTS sponsored activities have In addition to the existing international been posted on the NCTS web-site at http://phys. cooperation, NCTS is also exploring possible cts.nthu.edu.tw/ as soon as it is planned, and also cooperation with theoretical institutes in France. stayed on the web-site afterwards as a future For this purpose, a Taiwan-France workshop on reference. In addition to focus groups, the theoretical sciences was held in October. This is a Division selected Laser/Maser Plasma Science as workshop organized jointly with the mathematical a topical program with emphasized on physics of division. Four French delegates with two laser-wake plasma. The coordinator is Prof. Shih- physicists came to join the workshop. The Hung Chen of NCU. The program is jointly workshop ends with a mutual understanding organized with a strong local experimental group between NCTS and France to organize joint (with 100-TW laser available) led by Prof. academic program in the future. 汪治平 Jyhpyng Wang ( ) from AS. With efforts To nurture young theorists in various fields, 14 from both theorists and experimentalists, the schools on different subjects were organized in program is aiming to further promote visibility 2009. In particular, the Division organized a and cooperated researches of researchers in the summer school on theoretical physics for area of large-scale laser/maser plasma simulation. undergraduates in July. It was aiming to attract In 2009, in addition to focus groups and good students to join theoretical researches. There topical programs, three initiative programs (Build- were 66 undergraduate students from various up of Theory Support for LHC Physics, Establish universities in Taiwan participating in this 2-day GPU-based Supercomputing Platform, and Theory school. The school was met with a lot of and Simulation of Plasmonic Meta-materials) are undergraduate students who show great interest in proposed and operated by subproject I. Even theoretical physics. It appears that the school though these programs do not follow the normal provides a good opportunity for undergraduate procedure that programs were proposed and students to appreciate theoretical physics and we operated in the division, they will be also shall continue it in 2010 with more careful reviewed and the reports of their activities will designing lectures involved. In addition, a summer also be described in the following report. course on quantum field theory was also organized by the Center. This course was mainly A number of activities in 2009 were performed lectured by Prof. Ling-Fong Li from Carnegie through international collaborations with foreign Mellon University and provides an entry point for physics centers. In particular, a joint KITP-type students who want to join researches on particle workshop with Asia Pacific Center for Theoretical physics. Physics (APCTP) was organized in August at
131 ‹‹- Report of the Division Head Highlights of Researches models. These works were published in Phys. There are quite a number of excellent research Lett. B678, 293 (2009); JCAP910, 001 (2009); results generated by activities of NCTS. In the Phys. Lett. B675, 77 (2009); Phys. Lett. B678, followings, I shall highlight representatives. 168, (2009); Mod. Phys. Lett. A24, 2139, (2009) Details of highlights for individual focus group and have been cited well. In addition to these can be found in the following report. published work, two discussion sessions on experimental data and theoretical ideas were also In a joint effort to understand the recently organized with LHC Physics Focus group and observed gigantic spin Hall effect in FePt/Au cosmology and astrophysics Focus group were 郭光 system at room temperature, Guang-Yu Guo ( also organized. Some of the models proposed may 宇 , NTU) and his cooperators revealed the orbital- be further tested at the LHC. dependent Kondo effect in Fe impurity in Au by performing ab initio electronic structure Recruitment and Scientific Staff calculations for various transition metal impurities There are several members departing from the in gold. In particular, they demonstrated that the Physics Division in 2009. Among the recent giant hall effect is due to resonant skew scattering departures, Dr. David Adams, a visiting assistant enhanced by multi-orbital Kondo effect. This professor of NCTS at Taipei office, was recruited fascinating result relates the spin Hall effect to the by Nanyang Technological University as an classic Kondo problem in condensed-matter assistant professor. Dr. Shih-Yuin Lin (林世昀) physics. It was published in Phys. Rev. Lett. 102, joined as an assistant research scholar in National 036401 (2009) and was selected as a viewpoint in Cheng Kung University. Other departure includes Physics. Dr. Chih-Hao Chen (陳志浩), who joins Institute In another joint work of Ying-Jer Kao (高英哲, of Systems Biology and Bioinformatic at NCU. NTU) and his coworkers, it is demonstrated that, To maintain viable supporting scientific using Zn-doped La2CuO4 as an example, a personnel, the Physics Division continues to spinless impurity doped into a non-frustrated recruit staff scientists in the past year. The antiferromagnet can induce substantial frustrating recruitment in 2009 is quite fruitful. In particular, interactions among the spins surrounding it. This Professor Ling-Fong Li has agreed to lead the work results from past effort of members for division. Professor Li will inaugurate in Jan. 2010. developing numerical methods for strongly In addition, four new members have joined the correlated physics and is published in Phys. Rev. Physics Division: Dr. Eibun Senaha (Particle Lett. 102, 167201 (2009). The result has provided Physics), Dr. Takayuki Hirayama (String), Dr. Pei- the key to resolve long-standing discrepancies Jen Lin (林佩真, Condensed Matter Physics), and between experimental data and earlier theories and 陳俊仲 is expected to provide a common mechanism for Dr. Chun-Chung Chen ( , Soft Condensed other correlated oxides as well. Matter Physics). In 2009, there are seven long- term visiting professors joining the Division. During the past two years, triggered by Among them, Professor Abdesslam Arhrib evidences of dark matter from Pamela, ATIC, and (visiting associate Professor, High Energy FERMI-LAT data, showing that there are excesses Physics) joined the Physics Division at Taipei in cosmic e+ and e-, tremendous work has been office. Professors Vidar Gudmundsson (visiting devoted to explain these excesses. Members in the professor, condensed matter physics) and Ling- LHC Physics Focus group and cosmology and Fong Li join the Division at Hsinchu. The astrophysics Focus group were able to catch the Division also made an offer to Dr. Ming-Chiang research front and had published important papers Chung (張明強, condensed matter physics), who on this subject. One of the possible sources for will join the center in Feb. 2010. these excesses is from dark matter annihilation or Finally, through the Center Scientist program, dark matter decay. A number of members in these t h e P h y s i c s d i v i s i o n h a s r e n e w e d t h e focus groups have proposed model independent appointments of Professors Kingman Cheung (張 analysis of dark matter properties, dark matter 敬民, NTHU), Yuen-Nan Chen (陳岳男, NCKU), decay models, and dark matter annihilation and David Lin (林及仁, NCTU) as center
Report of the Division Head -›› 132 scientists. The appointment of Prof. Cheung is community, I am confident that the Center has the renewed at senior level and is demanded by the potential to mature into a world class center for leadership in his research field, while Profs. Chen theoretical sciences. and Lin are renewed as Junior Center Scientists. Since this is my last report as the Division Head, I would like to take this opportunity to Conclusions and Acknowledgement thank many colleagues in Taiwan for their support As noted at the beginning, in the year 2009, during the past two years. I would especially like NCTS is going into the 3rd phase with 6-year to thank Professor Chon-Saar Chu for helping me endorsement from NSC. In the 3rd phase, the in taking care of numerous administrative work. I Physics Division also made some adjustment in am confident that under the new leadership of organization to strengthen the coherence of Professor Ling-Fong Li, the NCTS Physics operations. After 12-year operation, the Physics Division will enjoy success for the following Division now has more experience about years. successful operational strategies. The Division will continue to operate based on its current strength and improve areas that have not been Chung-Yu Mou (牟中瑜) doing well. With continued support from the November 2009 government and strong support from the physics
133 ‹‹- Report of the Division Head Highlights of Programs Complex Systems and Soft Matter
Focus Group on Critical Phenomena and Complex Systems
Coordinator: Chin-Kun Hu (Academia Sinica; email: [email protected]) Committee Members: Hu-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), Wen-Jer Tzeng (Tamkang 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), Ming-Chya Wu (Academia Sinica)
I. Brief Description Department of Physics of National Kaohsiung Normal University, Ming-Chang Huang (黃敏 章) at Department of Physics of Chung-Yuan Christian University, Tai-huang Huang (黃太 煌 A. he purpose of this FG is to develop ) at Institute of Biomedical Sciences of 姜一民 ideas and methods in statistical and Academia Sinica, I-Min Jiang ( ) at nonlinear physics, then apply such ideas and Department of Physics of National Sun Yat-sen 李柏翰 methods to complex physical, biological, and University, Po-han Lee ( ) at The social problems. The focus research topics Affiliated Senior High School of National 林財 include (1) Theoretical models of critical Taiwan Normal University, Chai-Yu Lin ( 鈺 phenomena, chaos, and pattern formation, (2) ) at Physics Department of National Chung 林榮信 Structures, folding, aggregation, and evolution Cheng University, Jung-Hsin Lin ( ) at of biological macromolecules, (3) Modeling Research Center for Applied Sciences & and analysis of complex network and signals. Institute of Biomedical Sciences of Academia 羅煜聘 The activities of this FG can be found at Sinica, Yu-Pin Luo ( ), Department of “Activity” of LSCP website: http://proj1. Electronic Engineering of National Formosa 施奇廷 sinica.edu.tw/~statphys/. U n i v e r s i t y, C h i - T i n S h i h ( ), Department of Physics of Tunghai University, B. The key researchers of this FG include (1) 曾文哲 張書銓 Wen-Jer Tzeng ( ) at Department of Shu-Chiuan Chang ( ) at Physics Dept. Physics of Tamkang University, Dr. Ming- of National Cheng-Kung University, Chi-Ning 吳明佳 陳企寧 Chya Wu ( ) at Research Center for Chen ( ) at Physics Department of Adaptive Data Analysis of National Central National Dong-Hwa University, Dr. Yi-Chiuan U n i v e r s i t y, J u i-L i n g Yu (余瑞琳) a t Chen (陳怡全), Institute of Mathematics of 鄒忠毅 Department of Applied Mathematics of Academia Sinica, Chung-I Chou ( ) at Providence University, Zicong Zhou (周子聰) Department of Physics of Chinese Culture at Department of Physics of Tamkang University, Ming-Chung Ho (何明宗) at
Highlights of Programs -›› 134 University.(2) Long term visitos: D. Y. Lando Short term visitors can be found from speakers from Belarus National Academy of Sciences, of BioComplex-Taiwan-2009 and Workshops BELARUS; N. Sh. Izmailian from Yerevan listed in II.A. We are collaborating with visitors State University in Armenia; David B. Saakian on following problems. from Yerenan Physics Institute in Armenia, (3) [1] Po-han Lee, T. Hwa (U.C. San Diego), A. E. Postdoctoral fellow: Shura Hayryan, Yao-Chen Allahverdyan (Yerevan Physics Inst) and Hung, Wen-Jong Ma and Karen Petrosyan at C.-K. Hu will collaborate to study Inst of Phys. Of Academia Sinica; Chia-Hei polymorphism and sympatric speciation in Yang at Department of Physics of Tunghai bacteria. Univ.; Chung-ke Chang at Institute of Biomedical Sciences, Academia Sinica (4) [2] Shura Hayryan, Ming-Chya Wu and Chin- Ph.D. students: Chun-Ling Chang at Natl Kun Hu in collaboration with Prof. Nikolay V. Central Univ, Hsin-Ling Jiang at Natl-Hsing Dokholyan’s group at North Carolina are Hua Univ, Chien-Zhong Wang at Natl Chung establishing database and website for three- Hsin Univ, Shi-Jie Wang at Natl Chung Hsin dimensional structures of microRNA. Univ. [3] Ming-Chya Wu, Yao-Chen Hung, Shi-Jie Wang, Chin-Kun Hu, in collaboration with Z. II. Activities R. Struzik and Y. Yamamoto at University of A. Academic Activities (see “Activities” at http:// Tokyo are analyzing physiological signals to proj1.sinica.edu.tw/~statphys/). identify health problems in human subjects. [1] We organized a series of four 2009 NCTS [4] Hsin-Ling Jiang, Wen-Jong Ma, Yun-Ru Chen Workshops on Critical Phenomena and (Genomics Res Center of AS), Rita Chen Complex Systems on 27 & 30 March, 12, 13 (Inst. Bio. Chem., AS), and Chin-Kun Hu in &15 June, 24, 27 & 28 July, and 25 & 28 collaboration with Mai-Suan Li (Polish September 2009. Academy of Sciences) and Hisashi Okumura [2] We are organizing BioComplex- (Institute for Molecular Science at Okazaki,) Taiwan-2009:2009 Taiwan International to work on protein folding and aggregation Workshop on Biological Physics and Complex problems. Systems at AS on 10-13 December and at [5] Jui-Ling Yu and Prof. Olga. S. Rozanova of Chung-Yuan Christian University on 14-15 Department of Math. at Moscow State December 2009. University are establishing a mathematical B. Train young-generation physicists: model for predicting the trajectory of typhoon on curved space. [1] Shu-Chiuan Chang, Chi-Ning Chen, Chai-Yu Lin, and Jui-Ling Yu, Wen-Jer Tzeng visited [6] Chi-Ning Chen and Prof. Jonathan Dushoff NCTS (North) in the summer break of 2009. (Department of biology, McMaster University, CANADA) are working on a model for [2] Ph.D. student Mr. Shi-Jie Wang visited disease spreading. University of Tokyo for one week to collaborate with Prof. Nobuyasu Ito’s group at [7] Ming-Chang Huang and Prof. N. Sh. Department of Applied Physics on analysis of Izmailian from Yerevan State University in complex human network. Armenia are working on lattice models of critical phenomena. (3) Ph. D student Hsin-Ling Jiang visited Institute for Molecular Science at Okazaki, Japan for IV. Highlights of Research Results one month to collaborate with Prof. Hisashi A. Highlights of Research Results: Okumura’s group on protein folding and aggregation. 1. Development of a theory of biological polymorphism under periodic fast varying III. Visitors and International environments [A. E. Allahverdyan and C.-K. Collaborations Hu, Phys. Rev. Lett. 102, 058102 (2009).].
135 ‹‹- Highlights of Programs 2. Classification of human ventricular fibrillation talks, Shu-Chiuan Chang, Chung-I Chou, Wen- ECG (Electrocardiography) time series into Jer Tzeng and Zicong Zhou gave invited talks three types (uniform UF, concave CC, and at “The 5th Cross Strait Conference on convex CV) by using phase statistics approach Statistical Physics” at Nanjing Normal Univ. and find that UF and CC types have about the on 13-15 August 2009. same probability of survival and non-survival, CV type has zero probability of survival [M.-C. V. Publications Wu, et al. Phys. Rev. E 80, Nov. (2009)]. Only list 2009 papers. Selected ones are good 3. Establishment of database and website for enough. three-dimensional structures of micoRNA in A. Papers with NCTS as the affiliation. collaboration with Prof. Nikolay V. Dokholyan’s group at North Carolina. 1. D. B. Saakian, C. K. Biebricher,and C.-K. Hu, Phase diagram for the Eigen quasispecies 4. Using a formula by F. Y. Wu to express the theory with the truncated fitness landscape, Potts model partition function as a sum over Phys. Rev. E 79, 041905 (2009). spanning subgraphs, S.-C. Chang proved some properties of the partition function concerning 2. O. S. Rozanova, J.-L. Yu, and C.-K. Hu, factorization, monotonicity, and zeros. It Typhoon eye trajectory based on a follows that the Tutte polynomial can also be mathematical model: comparing with generalized. [ J. Phys. A: Math. Theor. 42, observational data, Nonlinear Anal. Real World 385004 (2009)]. Appl. (2009) B. Invited Presentations: 3. S.-C. Chang, Spanning trees on two- dimensional lattices with more than one type of 1. Chin-Kun Hu gave (1) a plenary talk on vertex, J. Phys. A: Math. The. 42, 015208 “Molecular models of the origin of life and (2009) (21 pages) biological evolution” at “The First International Conference on Complex 4. C.-Y. Lin, A Renormalization-group Approach Sciences: Theory and Applications (Complex to the Manna Sandpile, Phys. Rev. E, submitted 2009)” at University of Shanghai for Science (2009). and Technology in Shanghai, China on 23-25 B. Papers acknowledged NCTS supports: February 2009, (2) an invited talk “Some universal patterns in human activities” at 1. A. E. Allahverdyan and C.-K. Hu, Replicators APFA7 Satellite Workshop: “Can we simulate in fine-grained environment: Adaptation and the whole human society?” at Yayoi polymorphism, Phys. Rev. Lett. 102, 058102 Auditorium of the University of Tokyo, On 6 (2009). March 2009, (3) an invited talk on “Molecular 2. C.-K. Chang, Y.-l. Hsu, Y.-H. Chang, F.-A. dynamics approach to relaxation and Chao, M.-C. Wu, Y.-S. Huang, C.-K. Hu, T.-H. aggregation of polymer chains” at the Huang, Multiple nucleic acid binding sites and workshop “Frontiers of Non-equilibrium intrinsic disorder of SARS coronavirus Physics: Fundamental theory, glassy and nucleocapsid protein - implication for granular materials, and computational physics” ribonucleocapsid protein packaging, J. at Kyoto University on 21 July-21 August Virology 83, 2255-2264 (2009). 2009, (4) a plenary talk at “The 5th Cross Strait 3. A. E. Allahverdyan, Zh.S. Gevorkian, C.-K. Conference on Statistical Physics” at Nanjing Hu, and Th.M. Nieuwenhuizen, How Normal University on 13-15 August 2009. adsorption influences DNA denaturation, Phys. 2. Ming-Chya Wu and Ming-Chang Huang gave Rev. E 79, 031903 (2009). invited talks at Oversea Chinese Physicist 4. J. S. Kim, B. Kahng, and D. Kim, Association (OCPA) Conference at Lanzhou, Disassortativity of random critical branching China on 3-7 August 2009. trees, Phys. Rev. E 79, 067103 (2009). 3. Ming-Chung Ho and I-Min Jiang gave plenary 5. M.-C. Wu, E. Watanabe, Z. R. Struzik, C.-K.
Highlights of Programs -›› 136 Hu, and Y. Yamamoto, Phase statistics 10. S.-C. Chang and R. Shrock, Some exact approach to human ventricular fibrillation, results on the Potts model partition function Phys. Rev. E 80, Nov (2009), in a magnetic field, J. Phys. A: Math. The. 42, 385004 (2009) (5 pages) 6. H.-J. Fang, Y.-Z. Chen, M. S. Li, M.-C. Wu, C.-L. Chang, C.-k. Chang, Y.-l. Hsu, T.-h. 11. H. L. Chen, C.-c. Hsu, M.-H. Viet, M. S. Li, Huang, H.-M. Chen, T.-Y. Tsong, and C.-K. C.-K. Hu, C.-H. Liu, F. Luk, E. Chang, A. Hu. Thermostability of the N-terminal RNA- Wang, M.-F. Hsu; W. Fann and R. Chen, binding domain of the SARS-CoV Studying the fast folding kinetics of an nucleocapsid protein: Experiments and antifreeze protein RD1 using a photolabile numerical simulations, Biophys. J. 96, 1892- caging strategy and time-resolved 1901 (2009). photoacoustic calorimetry on a nanosecond timescale, J. American Chem. Society, 7. J. Busa, S. Hayryan, C.-K. Hu, J. Skrivanek, submitted. and M.-C. Wu, Enveloping triangulation method for detecting internal cavities in 12. W.-J. Ma and C.-K. Hu, Molecular dynamics proteins and algorithm for computing their approach to relaxation and aggregation of surface areas and volumes, J. Comp. Chem. 30, polymer chains, to be published. 346-357 (2009). 13. M.S Li, N. T. Co, C.-K. Hu and D. 8. N. Sh. Izmailian and C.-K. Hu, Boundary Thirumalai. Factors governing fibrillogenesis conditions and amplitude ratios for finite-size of polypeptide chains, Phys. Rev. Lett., corrections of a one-dimensional quantum spin submitted. model, Nucl. Phys. B 808, 613 (2009) 14. Y.-C. Hung and C.-K. Hu. Stochastic 9. B. C. Bag and C.-K. Hu, Current inversion resonance in p53 regulatory network, Phys. induced by colored non-Gaussian noise, J. Stat. Rev. Lett., submitted Phys., p02003 (2009).
137 ‹‹- Highlights of Programs Focus Group on Soft Matter Physics
Coordinator: Hsuan-Yi Chen (National Central University; email: [email protected]), Paul Hoong-Chien Lee (National Central University; email: [email protected]), Ming-Chih Shih (National Chung Hsing University; email: [email protected]) Committee Members: Hsien-Da Huang (National Chiao Tung University), Hsueh-Fen Juan (National Taiwan University), Pik-Yin Lai (National Central University), Chun-Yi Lu (National Taiwan University), Sy-Sang Liaw (National Chung Hsing University), Jiunn-Ren Roan (National Chung Hsing University), Kai-Jung Chi (National Chung Hsing University), Jeng-Tze Yang (National Chung Hsing University)
I. Brief Description interdisciplinary nature of our FG, some members are from departments of life sciences and mathematics. The main research topics of the members of our he key members of this focus group FG include: include: 1. Neuron and other cell culture networks Bio-soft Matter (BSM): 2. Biomembranes, cytoskeleton, and other Pik-Yin Lai (NCU Phys), Peilong Chen (NCU biomaterials including spider webs Phys), Hsuan-Yi Chen (NCU Phys), Heng-Kwong 3. Pattern formation and nonlinear dynamics, Tsao (NCU ChemEng), Ya-Wei Hseuh (NCU including time sequences analysis Phys), Chien-Jung Lo (NCU Phys), Chi-Lun Lee 4. Complex fluids, including granular matter (NCU Phys), Chi-Keung Chan (Academia Sinica Phys), Keng-Hui Lin (Academia Sinica Phys), 5. Biomemchanics, for example the effect of Kwan-Tai Leung (Academia Sinica Phys). Pterostigma on insect locomotion and fluid dynamics of biological sniffers Nonlinear Dynamics (NLD): 6. Evolutionary dynamics and biofilms Sy-Sang Liaw(Physics, NCHU); Jiunn-Ren 7. The evolution of genome Roan (Physics, NCHU); Kai-Jung Chi(Physics, 8. Biological networks and brain NCHU); Ming-Chih Shih(Physics, NCHU); I-Min Tso(Life Science, THU); Jiann-Hwa II. Activities Chen(Molecular Biology, NCHU); Chao-Nien Regular meeting Chen (Math, NCUE); Jeng-Tze Yang (Entomology, NCHU); Ming-Huang Wu (Physics, Seminars: Thursday 12:00-13:00 at NCU (BSM) NCHU) and Tzyy-Leng Horng(Applied Math, This series of seminars are given mostly by FCU). students and some times by PIs. The diverse Systems Biology (SB): research background in this group has led to discussions on topics such as nonequilibrium Hoong-Chien Lee (NCU Systems Biol), Ming- phenomenon in cold liquids, collective behavior Sheng Wang (NCU Systems Biol & Phys), Sun- of bacteria cultures, nonlinear dynamics in fluids, Chong Wang (NCU Systems Biol), Jung-San and mostly recently, because the establishment of Huang (NCU Systems Biol), Li-Ching Wu (NCU a new experimental group on the motile behavior Systems Biol), Hsuan-Cheng Huang (YMU of E. Coli by Prof. Lo, many different aspects of Biomed Info). the biophysics of E. Coli (motors, mutations, and Besides PIs, there are totally about 10 postdocs chemotaxis behavior) were discussed in the and 50 graduate students in our FG. Because the seminars.
Highlights of Programs -›› 138 Colloquiums: Thursday 11:00-12:00 at NCU (SB) This 2-day workshop, the 5th since 2005, features about 10 lecturers, all PIs from the This series of colloquiums are given mostly by Institute of Physics, Academia Sinica, NCU experts in Taiwan and around the world. The Physics and Systems Biology. 40-50 students newest focus in recent talks is the systems (mostly undergraduates, some graduate biological research related to cancer treatment and students, and even a couple of professors) cancer fundamental research. attended this workshop. The talks are Biophysical Journal Club: Thursday 12:00-13:00 introductory, related to the recent research (NCHU) activities of these PIs. The goal is to attract Biophysical Journal Club was initiated in 2004, more young people to the field of biophysics and it has been continued and thriving and systems biology. successfully with the support of this FG. BJC has • Biophysics workshop: Evolutionary Biology – attracted broad attendance from various Observation, Experiment and Mathematical disciplines. The mailing list of BJC continues Models, Hui-Sun Forest Station, Nan-Tou, Oct. growing. About 20 to 40 people attend the Club at 29-Nov. 1 each gathering. Details of the BJC activity We focus on the science of evolutionary subjects can be found at http://140.120.11.15/ dynamics and the related applications in vedio/biophysics/Chinese/journal%20club/ behaviors of biological systems. Four activity.htm prestigious speakers are invited: Dr. Hisashi Group meeting for nonlinear phenomena: Ohtsuki, Dr. Stuart A. West, Dr. Joan E. Friday 10:30-13:00 (NCHU) Strassmann, and Dr. David C. Queller. About Two main topics are under intense discussion 90 audiences attended the workshop. every week. One is granular physics and the other • Bio-soft matter and systems biology days, Jan. the application of fractal to real non-stationary 25-28, 2010 (scheduled). data. The group has made some achievements As the 5th workshop of this kind since 2005, we including two papers published this year. will invite people who work in bio-soft and Workshops systems biology in Taiwan to this 3-day Some of the workshop activities are described workshop, presenting their recent research in the following. work to other colleagues and to graduate students. Besides educational purpose, this • Summer School in Fluid Dynamics, National workshop will also feature discussion sessions Central University, Aug.10-21. that aim at discussing on-going work of the About 30 undergraduate students from PIs. We expect about 25 PIs and 80 students to Mainland China and Taiwan attended this participate this event. As it used to be, there intense school. The topics range from will be intensive and stimulating discussions. elementary fluid mechanics to modern topics in turbulence, nano-fluidic devices, and III. Visitors and International polymeric fluids. Besides getting a chance to Collaborations learn this important (but neglected in main- Many PIs in our FG has international stream courses) field of physics from about 10 collaborations. For example, many scientists have lecturers, and working hard on the homework visited the group led by Prof. H.C. Lee (NCU), problems (about 2-3 questions were assigned together they have generated many high-quality to the students each day), the students also research results. The total number of international benefit much from the fresh learning attitude of visitors in the year 2009 is 21. The following is friends from the other side of the Formosa only a part of recent international collaborations. strait. 1. Physics of Biological surfaces: Chi (NCHU), • NCU Biophysics camp, National Central Shih (NCHU), and Gorb (Kiel Univ, Germany) University, Oct. 10-11 Prof. Chi has invited Prof. S. Gorb, the group
139 ‹‹- Highlights of Programs leader of evolutionary biomaterials group at cardiac myocytes are not correlated at early Kiel University, for a series of biophysics times, but get synchronized as the cultures workshop. Together, they tend to explore the mature. This synchronization can be feasibility of study physical properties of understood by a Kuramoto model with a time- biological surfaces. Prof. Gorb will visit increasing coupling strength. It is found that Taiwan and conduct collaborative pilot studies the growth of the coupling strength between in April 2010. clusters is linear, while the overall wave dynamics of the system is controlled by the 2. Sand flow through a vertical pipe: Liaw passive fibroblast in the system. (NCHU), Liu (NCHU), Shih (NCHU), Matsushita (Chuo Univ, Japan) 2. In H-C Lee (NCU) group: The inverse- symmetry of complete genome is studied, the The initial experimental idea was proposed by results suggest segmental and whole-genome Prof. Matsushita during his previous visit, the inverse duplications are important mechanisms experimental facility was immediately setup in genome growth and evolution, probably and experiments were continued. Many because they are efficient means by which the interesting phenomena were observed and a genome can exploit its double-stranded model capable of simulating the density flow structure to enrich its code-inventory. of the sand in the pipe was established. 3. In Liaw (NCHU) group: A method to calculate 3. Nonequilibrium dynamics of bio-soft matter: the fractal dimensions of the time series from a Chen (NCU), Mikhailov (FHI-MPI, Germany); geometric point of view by evaluating the Chen (NCU), Prost (ESPCI & Curie Inst, turning angles at every point is proposed. The France), and Joanny (Curie Inst, France) method can be applied easily to existing non- A new theoretical framework for the dynamics stationary data abundant in natural, economic, of lipid bilayers that contain ion pumps was and medical sciences. constructed by HY Chen and A.S. Mikhailov, When the vibration amplitude and filling several new instabilities are predicted in a fraction of granular particles in a container are recent preprint. In another research program, appropriately set, the particles will form a HY Chen, J. Prost, and J-F Joanny together compact cluster. An intruder to this cluster of proposed a new theory for the dynamics of identical particles will migrate in a specific actin polymerization under compression. The direction according to its size and mass. A theory explains recent oscillations observed in mechanism is proposed to explain this an experiment carried by the group led by J. phenomenon, which was called in the literature Israelavichili at UCSB. the horizontal Brazil nut effect. 4. Dynamics of cardiac cell culture: Lai (NCU), 4. In Chi (NCHU) group: In the study of spider Chan (Academia Sinica), Osipov (Russia) et al. web mechanics, Prof. Chi, Prof. I-Min Tso and This is a collaboration that began at 2007. Chen-Pan Liao discovered that wind New experiment/theory on the cardiac cell disturbances can affect the structural and cultures have been done, result results are material properties of spider webs. In greater described in the next section. wind the webs are not only stronger but also have reduced wind drag, which can prevent the IV. Highlights of Research Results webs from breakage. Research results mentioned in “international 5. In Shih (NCHU) group: In the study of collaborations” are not listed below. Some other membrane interaction with large molecules, we research results are: found molecules can preferentially participate 1. In Lai (NCU)/Chan (Academia Sinica) group: in membrane domains. This selectivity could Synchronization of heterogeneous systems play an important factor in the subcellular consist of oscillatory and passive elements, localization of molecules which could be such as in cardiac myocytes/fibroblasts critical to its therapeutic outcome or cellular co-cultures, are studied . The beatings of the toxicity.
Highlights of Programs -›› 140 V. Selected Publications especially vulnerable to changes in the [1] Quantitative measure of randomness and relative orientation of H1 and its S1 flank, order for complete genomes, S-G Kong , W-L C-Y Tseng, C-P Yu, and H-C Lee, Euro. Fan, H-D Chen, J. Wigger, A.E. Torda, and Biophys. J. Biophys. Lett., 38, 601, (2009). H-C Lee, Phys. Rev. E, 79, 061911 (2009) [7] 11. Sy-Sang Liaw* and Feng-Yuan Chiu, [2] Surface response of spherical core-shell “Fractal dimensions of time sequences”, structured nanoparticle by optically induced Physica A388, 3100 (2009) . elastic oscillations of soft shell against hard [8] 12. Fei Fang Chung, Sy-Sang Liaw*, and core, S. I. Bastrukov, Pik-Yin Lai, I. V. Chia-Yi Ju, “Brazil nut effect in a rectangular Molodtsova, H. K. Chang, and D.V. Podgainy, plate under horizontal vibration, Granular Surf. Rev. & Lett. 16, p.1~6 (2009). Matter 11, 79 (2009). [3] Granular Gases in Compartmentalized [9] 13. Yunn-Fang Ho, Ming-Huang Wu, Bor- Systems, Pik-Yin Lai, M. Hou, and C. K. Hen Cheng,Yar-Wen Chen, Ming-Chih Shih*. Chan , J. Phys. Soc. Jpn. (invited review) 78, “Lipid-mediated Preferential Localization of 041001-1~9 (2009). Hypericin in Lipid Membranes” Biochem. [4] Synchronization in growing heterogeneous Biophys. Acta 1788, 1287-1295 (2009) media, W. Chen, S. C. Cheng, E. Avalos, O. [10] 14. Liao, C.-P., Chi, K.-J., and I.-M. Tso. Drugova, G. Osipov, Pik-Yin Lai, and C. K. 2009. The effects of wind on trap Chan, Europhys. Lett. 86, 18001-p1~5(2009). architectural and mechanical properties of a [5] Bursting of Neurons induced by inhibitory sit-and-wait predator. Behavioral Ecology, mechanism, Y. S. Chou, Pik-Yin Lai, and C. doi:10.1093/beheco/arp119 (Advance Access K. Chan, Chin. J. Phys., to be published published online on August 18, 2009) [6] Integrity of H1 helix in prion protein revealed by molecular dynamic simulations to be
141 ‹‹- Highlights of Programs Highlights of Programs Condensed Matter Physics
Working Group on Quantum Phenomena in Condensed Matter Physics A. Focus Group on Mesoscopic Physics and Strongly Correlated Systems Coordinator: Chung-Hou Chung (National Chiao Tung University; email: [email protected]), Hsiu-Hau Lin (National Tsing Hua University; email: [email protected]) Committee members: Chon-Saar Chu (National Chiao Tung University), Chang-Ming Ho (Tamkang University), Chung-Der Hu (National Taiwan University), Di-Jing Huang (National Synchrotron Radiation Research Center), Juhn-Jong Lin (National Chiao Tung University), Wen-Chin Wu (National Taiwan Normal University)
I. Brief Description lasting conference series on mesoscopic and spin physics. In addition, we also organized a summer school in August to attract and train interested students into condensed matter physics. An he goal of our focus group is to promote informal workshop CMP2009 to bring in domestic research topics in mesoscopic physics and researchers was also organized in August. strongly correlated electron systems, with These workshops and conferences have particular emphasis on quantum transport, brought in useful techniques in renormalization multiferroic materials, spintronics and group, Green’s function approach to quantum nanostructures. The sign-up members for our focus transport, non-equilibrium approach to quantum group are over 70 and around 1/3 of the members criticality, dynamical properties in spintronics and have been actively participating the group others. Meanwhile, active group memebers build activities. up collaborations with visitors listed below. II. Activities With limited travel supports, we manage to We have organized 8 workshops/miniprograms support 10 graduate students and postdocs to on functional renormalization group, quantum attend international conferences. This channel of transport, spin dynamics in nanostructures and supports is precious for the talented young bloods others, including two joint workshops with and their exposure to the international community APCTP in Korea on the subject of exotic quantum has given them a glimpse about the outside world. condensation and strongly correlated systems in In addition, we hope to attract young talents into low dimensions. condensed matter physics via summer school, workshops/miniprograms and journal clubs. In the coming spring, we have planned two international conferences. The first one is III. Visitors and International co-organized with APCTP (February 2010) on Collaborations multiferroic materials. The second one is the long-
Highlights of Programs -›› 142 We have 1 long-term visitor and 8 short-term Spintronics visitors this year. Chon-Saar Chu continues his long-term Chung-Hou Chung developed collaboration collaboration with Malshukov [Phys. Rev. Lett. with Woelfle at Karlsruhe and Vojta at Yale on the 95, 107203 (2005)] and investigate the general quantum phase transition associated with the theory for spin Hall effects. Focusing upon the Kondo breakdown mechanism. Right now, Dresselhaus-type intrinsic spin-orbit interaction, Chung-Hou is in the exchange program to Yale they look for the symmetry, or asymmetry, working together with Vojta and others. Hsiu-Hau characteristics in two magnetic-field orientations: Lin collaborates with Lee at Pohang on magnetic along and transverse to the stripe [Phys. Rev. B materials and with Hikihara at Hokkaido on 78, 155302]. They also study the interplay graphene and related materials. He also developed between the Rashba and cubic-k Dresselhaus spin- a long-term collaboration with Tang at New orbit interactions and obtain the spin accumulation Hampshire on low dimensional electron systems. and spin polarizations at the edges and in the bulk Chon-Saar Chu continues his long-term as well [Phys. Rev. B 79, 195314 (2009)]. Hsiu- collaboration with Malshukov from Moscow on Hau Lin develops the theory for carrier-mediated spin Hall effects in various geometries. ferromagnetism and collaborates with experimental group in Taiwan [Appl. Phys. Lett. Shun-Jen Cheng starts collaboration with 92, 242501 (2008)] and in Korea [Appl. Phys. Climente in Spain (June-August 2009) via a Lett. 94, 042509 (2009)]. In particular, the non- miniprogram on spin dynamics. Juhn-Jong Lin collinear exchange coupling between multilayers works with visitor Prof. Lien from Vietnam (May is computed theoretically and explains the 2009) on transport in nanostructures. Hsiu-Hau experimental observations extremely well [Phys. Lin and Chung-Hou Chung plan to build a team Rev. B 79, 140412(R) (2009)]. on functional renormalization group and start collaborating with Prof. Honerkamp (Jan 2009) Multiferroic materials from Germany recently. This ongoing Di-Jing Huang and Chung-Yu Mou work on collaboration also leads to interaction with Prof. the experimental and theoretical sides of the Lee at Berkeley and Dr. Wang at MIT, trying to multiferroic materials. Di-Jing Huang’s group apply the same technique to recently discovered reports the unexpected evolution [Phys. Rev. Lett. iron pnictide superconductors. 102, 067601 (2009)], with thermal and magnetic- field (H) variations, of the interrelation between IV. Highlights of Research Results the polarization P, magnetization M, and spiral Quantum transport wave vector Q in CoCr2O4, which has a Chung-Hou Chung collaborates with Woelfle ferrimagnetic conical-spiral magnetic order. In the at Karlsruhe and Vojta at Yale on the quantum related material LiCu2O2, they find a large phase transition associated with the Kondo interchain coupling which suppresses quantum breakdown mechanism [Phys. Rev. Lett 102, fluctuations along spin chains, and a quasi-2D 216803 (2009)]. They apply the nonequilibrium short-range magnetic order prevails at renormalization group (RG) approach to study temperatures above the magnetic transition [Phys. transport of the system and clarify several Rev. Lett. 101, 077205 (2008)]. These important issues concerning quantum criticality observations unravel the fact that the ground state out of equilibrium. Hsiu-Hau Lin and his students of LiCu2O2 possesses long-range 2D-like investigate the conductance through a single incommensurate magnetic order rather than being impurity in carbon nanotubes and find that it a gapped spin liquid as expected from the nature sensitively depends on the impurity strength and of quantum spin-1/2 chains. the bias voltage [Appl. Phys. Lett. 95, 082104 Nanostructures and low dimensional systems (2009)]. The interplay between the current- carrying scattering states and the evanescent Shun-Jen Cheng works on the theory of diluted modes lead to rich phenomena including resonant magnetic semiconductors in nanorod morphology backward scattering, perfect tunneling, and charge [Phys. Rev. B 77, 115310 (2008)] and also accumulations. investigates magnetic anisotropy in magnetic
143 ‹‹- Highlights of Programs colloidal quantum dots doped with transition [3] Huang WM, Tang JM, Lin HH, Power-law metals [Phys. Rev. B 79, 245301 (2009)]. Shun- singularity in the local density of states due to Jen Cheng collaborates with experimental groups the point defect in graphene, PHYSICAL and finds the diamagnetic shifts for different REVIEW B 80, 121404(R) (2009) exciton complexes confined in small InAs [4] Liu CW, Liu S, Kao YJ, et al., Impurity- quantum dots [Phys. Rev. Lett. 101, 267402 Induced Frustration in Correlated Oxides, (2008)]. In addition, the developed theory is PHYSICAL REVIEW LETTERS 102, applied to explain experimental data in 167201 (2009) semiconducting GaN nanorods [Appl. Phys. Lett. [5] Chang RS, Chu CS, Mal'shukov AG, 95, 051905 (2009); Appl. Phys. Lett. 94, 251912 Competing interplay between Rashba and (2009)]. Hsiu-Hau Lin collaborates with Tang at cubic-k Dresselhaus spin-orbit interactions in New Hampshire on the impurity effect in spin-Hall effect, PHYSICAL REVIEW B 79, graphene [Phys. Rev. B 80, 121404(R) (2009)] 195314 (2009) and find an unexpected anomalous scaling in the local density of states. He also collaborates with [6] Chang PY, Lin HH, Conductance through a Jeng at Academia Sinica and Hikihara at single impurity in the metallic zigzag carbon Hokkaido on the correlation effects in graphene nanotube, APPLIED PHYSICS LETTERS nanoribbons [Phys. Rev. B 79, 035405 (2009)]. In 95, 082104 (2009) addition, he studies the spin-wave excitations near [7] Cheng SJ, Magnetic anisotropy in symmetric graphene edges [Phys. Rev. B 78, 161404(R) magnetic colloidal quantum dots doped with (2008)] and finds a novel relativistic few Mn2+ impurities, PHYSICAL REVIEW ferromagnetic magnon without its relativistic B 79, 245301 (2009) partner. [8] You JS, Huang WM, Lin HH, Relativistic The authors of these highlighted works have ferromagnetic magnon at the zigzag edge of been invited to various workshops and graphene, PHYSICAL REVIEW B 78, international conferences. In particular, both 161404 (2008) Chung-Hou Chung and Hsiu-Hau Lin have been [9] Huang SW, Huang DJ, Okamoto J, et al., invited to participate the Low Dimensional Magnetic ground state and transition of a Electron Systems program at Kavli Institute for quantum multiferroic LiCu2O2, PHYSICAL Theoretical Physics in Santa Barbara and REVIEW LETTERS 101, 077205 (2008) presented their work on quantum transport and [10] Chung-Hou Chung, Gergely Zarand, and graphene this year. Peter Woelfle, Two-stage Kondo effect in double quantum dots: Perturbation theory V. Selected Publications and Numerical Renormalization Group [1] Choi YJ, Okamoto J, Huang DJ, et al., analysis, Phys. Rev. B 77, 035120 (2008). Thermally or Magnetically Induced [11] C. D. Hu, Relationship between Polarization Reversal in the Multiferroic ferroelectricity and Dzyaloshinskii-Moriya CoCr2O4, PHYSICAL REVIEW LETTERS interaction in multiferroics and the effect of 102, 067601 (2009) bond-bending, Phys. Rev. B 77, 174418 [2] Chung CH, Le Hur K, Vojta M, et al., (2008). Nonequilibrium Transport at a Dissipative [12] Wang LY, Chu CS, Mal'shukov AG, Quantum Phase Transition, PHYSICAL Asymmetries in intrinsic spin-Hall effect in REVIEW LETTERS 102, 216803 (2009) low in-plane magnetic field, PHYSICAL REVIEW B 78, 155302 (2008)
Highlights of Programs -›› 144 Working Group on Quantum Phenomena in Condensed Matter Physics B. Focus Group on Numerical Methods for Strongly Correlated Physics Coordinator: Ying-Jer Kao (National Taiwan University; email: [email protected]) Committee members: Yong-Chung Chen (Tunghai University), Chung-Hou Chung (Nation Chiao Tung University), Chang-Ming Ho (Tamkang University), Di-Jing Huang (National Synchrotron Radiation Research Center), Jiunn-Yuan Lin (National Chiao Tung University), Chien-Hua Pao (National Chung Cheng University), Horng-Tay Jeng (Academia Sinica), Wen-Chin Wu (National Taiwan Normal University)
I. Brief Description 2. 2009 Condensed Matter Summer School, August 31-September 2, 2009 (Tainan) 3. CMP2009: NCTS Condensed Matter Summer Workshop, September 3-4, 2009 (Tainan) he “Numerical Methods on Strongly Correlated Physics” (NMSCP) is a focus 4. Conference on Computational Physics 2009, group under the Quantum Phenomena in the December 15-19, 2009 (Kaohsiung) Condensed Matter Physics Working Group. It was 5. Workshop on Quantum Information Science formed to provide a platform for condensed matter and Quantum Manybody Physics (Tainan) theorists who are specializing and/or interested in 6. Bi-weekly Meeting of NMSCP Focus Group numerical simulations to facilitate interaction and (Taipei & Hsin-Chu) collaboration. In addition, activities and visitor programs are designed to provide opportunities Activity (1) is a one-day workshop on for researchers to establish international numerical simulations in strongly correlated collaborations. In addition, travel funds are systems, where international speakers and local available to provide financial support to students researchers exchange ideas and establish future and junior researches to attend international collaborations. Activity (2) & (3) are co-organized conferences. An executive committee of ten under the CMP WG. Activity (2) is designed to members from major institutes is formed to educate graduate students to familiarize them with coordinate these activities and oversee the usage necessary techniques. The summer school also of the fund. serves as a platform for students from different universities to interact with each other. Activity In addition to the executive committee, there (3) is the second year of the CMP workshop, are twenty-two active faculty members and twenty where we provide an environment to establish an junior members (postdocs and senior graduate informal workshop among experts. We aim to students). The focus research topics are (1) create a stage where people can concentrate on a Quantum Information Theory Inspired Numerical specific topic in physics for several days with an Methods, (2) Spin Hall Effect, Topological informal atmosphere, so the initiation of Insulators, Multiferroics and Oxides (3) Quantum collaborations can be facilitated. This year’s major Transport in Nanodevices (4) Superconductivity, themes were spin transport and strongly Supersolidity and Magnetism. correlation in ab initio methods. Activity (4), II. Activities CCP2009, is one of the most important international conferences hosted in Taiwan, and During the past one-year period, our focus our focus group helped part of the organization. In group organized or sponsored following activities, addition, we will organize a workshop on 1. Mini-workshop on Numerical Methods in Quantum Information Science and Quantum Strongly Correlated Systems 2009, May 23, Manybody Physics (Activity (5)), following this 2009 (Taipei) conference. Activity (6) focuses on two special
145 ‹‹- Highlights of Programs topics of Quantum Monte Carlo and Real-space Po-Chung Chen and Min-Fong Yang have Renomalization Group. Seminars are held developed one particular entanglement based biweekly in Taipei and Hsin-Chu alternatively numerical method for strongly correlated systems. with participants from institutes in both areas. In In this approach, the variational ground state addition, live webcast is provided for participants wave-function is in the form of tensor product from remote sites. This informal seminar is state. They use 2D iTEBD to optimize the trial intended to motivate junior researchers to identify wave function, and then use TERG to evaluate the and discuss on research topics. More information expectation values. They demonstrate this method can be found at http://sites.google.com/sites/ can reach high accuracy for first-order transition, nmscp. and then use it to study the frustrated spin-dimer model and identify the regime of super-solid III. Visitors and International phase. Hence extend the usability of the method to Collaborations the frustrated models.[1] Chen was invited to give A. Internatonal Visitors: (Dec 09-Nov 09 ) a talk at APCTP Advanced Program on Quantum Condensation in Pohang. Igor Hubert (Simon Frasier U., Canada) Sujit Sarkar (India), Anders Sandvik (Boston U.), Ling Ying-Jer Kao and his coworkers proposed a Wang (Boston U.). method for contracting the tensor network in two dimensions, based on auxiliary tensors B. International Collaborations: accomplishing successive truncations of 8-index 1. Ming-Che Chang (NTNU) + Qian Niu (UT tensors for 2×2 plaquettes into 4-index tensors. Austin) on non-canonical dynamics with Berry The scheme is variational. Test results for the phase effects. quantum phase transition of the transverse-field Ising model confirm that even the smallest 2. Ying-Jer Kao (NTU) + Anders Sandvik possible tensors produce much better results than (Boston), Roger Melko (Waterloo) on the simple product state. Kao was invited to talk numerical approaches based on tensor on Recent trends in Strongly Correlated Systems, networks for frustrated systems. Kalkota, India. 3. Wen-Chin Wu (NTNU) + Igor Herburt (Simon Ming-Che Chang and Min-Fong Yang study Frasier University, Canada) on issues regarding the magnetization for the classical graphene. antiferromagnetic Ising model on the Shastry- 4. Chien-Hua Pao (CCU) + Mark Jarrell Sutherland lattice using the tensor (Louisiana State University) on DCA studies of renormalization-group approach. For a range of BCS-BEC crossover. temperature and coupling constant, they find a single magnetization plateau at one third of the 5. Horng-Tay Jeng (AS) + M. A. van Hove saturation value.[2] (Hong-Kong), Xiao Hu, Toshiya Hikihar (Japan), H. Berger (Switzerland), Z. Hu B. Spin Hall Effect, Topological Insulators, (Germany), and E. W. Plummer (USA). Multiferroics and Oxides 6. Yung-Chung Chen (THU) + Yong-Baek Kim Guang-Yu Guo and coworkers performed ab (Toronto). initio electronic structure calculations for various transition metal impurities in gold, and they reveal 7. Chao-Cheng Kaun (AS) + Hong Guo (McGill) orbital-dependent Kondo effect in Fe impurity in to study the spin transport in nanostructures. Au, demonstrating that the gigantic spin Hall 8. Yu-Cheng Lin (NCCU) + Heiko Rieger effect observed recently in FePt/Au system at (Germany) on entanglement in quenched room temperature is due to resonant skew disordered systems. scattering enhanced by multi-orbital Kondo effect. [3] This paper was selected as a viewpoint in IV. Highlights of Research Results Physics. Spin Hall effect has recently become an A. Quantum Information Theory Inspired issue of intensive interests both theoretically and Numerical Methods experimentally. A fascinating point of this work is
Highlights of Programs -›› 146 that the spin Hall effect is related to the classic cascade of jumps in the order parameter Kondo problem in condensed-matter physics. Guo (supercurrent and superfluid as a function of the was invited to give an invited talk on Ab Initio superfluid velocity for diameters d < 10-15 nm
Studies of Spin Hall Effect, in International and sufficiently low temperatures T < 0.3-0.4 TC.
Workshop on Advances on Spintronic Materials: When approaching TC, the jumps are smoothed Theory and Experiment, Duisburg, Germany, Nov. into step-like but continuous drops. In the 26-28, 2008, in CECAM Workshop on Orbital mesoscopic regime, the quantum-size cascades are Magnetization in Condensed Matter, Lausanne, fully washed out. Below this regime the critical
Switzerland, June 15-17, 2009, and in current density jC exhibits the quantum-size International Workshop on Novel Topological oscillations with pronounced resonant States in Condensed Matter Physics, Hong Kong, enhancements: the smaller the diameter, the more June 21-24, 2009. significant is the enhancement. Thickness fluctuations of real samples will smooth out such Horng-Tay Jeng and his coworkers used ab oscillations into an overall growth of jC with initio calculations to study a variety of subjects, decreasing nanowire diameter. such as ferromagnetism in armchair graphene nanoribbons[4], they show that the inclusion of Shih-Jye Sun considers the substrate coupling mutual repulsions leads to drastic changes and the effect to transport in nanographene ribbon. He ground state turns ferromagnetic in a range of finds that the coupling between the substrate and carrier concentrations. Their ?ndings highlight the the nanographene ribbon increases the conduction crucial importance of the electron-electron of the nanographene ribbon when compared with interaction and its subtle interplay with boundary a non-substrate-coupled nanographene ribbon, topology in graphene nanoribbons. The resultant especially at small coupling; eventually, the large ferromagnetic state with metallic conductivity has coupling suppresses the conduction.[7] potential applications in spintronics at nanoscale. D. Superconductivity, Supersolidity and [4] Magnetism Ming-Che Chang and Min-Fong Yang study Wen-Chin Wu and coworkers have extended the optical signature of topological insulator. The their earlier work to study the spin-polarized axion coupling in topological insulators couples point-contact spectroscopy in electron-doped electric polarization with magnetic field, and cuprate superconductor (EDSC).[8] They consider magnetization with electric field. As a result, the the interplay between the spin polarization and the usual laws of electromagnetic wave propagation AF order in a d-wave superconductor. It is shown are modified. They find that, because of the axion that there exists midgap surface-state contribution coupling, in order to realize the Brewster-angle to the conductance to which Andreev reflections condition, the incident polarization should be are largely modified due to the interplay between rotated away from the plane of incidence. This the exchange field of ferromagnetic metal and the offers a convenient way to determine the axion AF order in EDSC. Low-energy anomalous angle by optical measurement.[5] Chang was conductance enhancement can occur which could invited to talk at IFF Spring school on further test the existence of AF order in EDSC. Spintronics: From GMR to Quantum Information, 2009, Juelich, Germany, and CECAM workshop Yong-Chung Chen and his coworkers use on Orbital Magnetization in Condensed Matter, numerical quantum and variational Monte Carlo 2009, Lausanne, Switzerland. to investigate the interplay between commensurate lock-in and incommensurate supersolid phases of C. Quantum Transport in Nanodevices the hard-core bosons at half-filling with Chao-Cheng Kaun and coworkers study the anisotropic nearest-neighbor hopping and interplay between the transverse discrete modes repulsive interactions on triangular lattice.[9] with a longitudinal supercurrent in a They find that for finite-size systems, there exist a superconducting nanowire.[6] They find the series of jumps between different supersolid superconductor-to-normal transition induced by a phases as the anisotropy parameter is changed. longitudinal superflow of electrons occurs as a The density ordering wave vectors are locked to
147 ‹‹- Highlights of Programs commensurate values and jump between adjacent V. Selected Publications supersolids. In the thermodynamic limit, however, [1] P. Chen, C.-T. Lai, and M.-F. Yang, J. Stat. the magnitude of these jumps vanishes leading to Mech., P10001 (2009). a continuous set of novel incommensurate [2] M. C. Chang, and M. F. Yang, Phys. Rev. B supersolid phases. 79, 104411 (2009). Ying-Jer Kao and coworkers demonstrate that, [3] G. Y. Guo, S. Maekawa, and N. Nagaosa, using the example of Zn-doped La2CuO4, a Phys. Rev. Lett. 102, 036401 (2009). spinless impurity doped into a non-frustrated [4] H. H. Lin et al., Phys. Rev. B 79, 035405 antiferromagnet can induce substantial frustrating (2009). interactions among the spins surrounding it. This counterintuitive result is the key to resolving [5] M. C. Chang, and M. F. Yang, Phys. Rev. B discrepancies between experimental data and 80, 113304 (2009). earlier theories. This mechanism should be [6] M. D. Croitoru et al., Phys. Rev. B 80, 024513 common to other correlated oxides as well.[10] (2009). Kao was invited to talk at “Recent trends in [7] S. J. Sun, J. Phys. Cond. Matt. 21, 235302 Strongly Correlated Systems”, Kalkota, India. (2009). [8] P. M. Chiu, C. S. Liu, and W. C. Wu, Phys. Rev. B 79, 064509 (2009). [9] S. V. Isakov et al., Euro. Phys. Lett. 87, 36002 (2009). [10] C. W. Liu et al., Phys. Rev. Lett. 102, 167201 (2009).
Highlights of Programs -›› 148 Focus Group on Computational Materials Research
Coordinator: Ching Cheng (National Cheng Kung University; email: [email protected]) Committee members: Chun-Ming Chang (National Dong Hwa University), Feng-Chuan Chuang (National Sun Yat Sen University), Guang-Yu Guo (National Chengchi University & National Taiwan University), Hung-Chung Hsueh (Tamkang University), Chao-Cheng Kaun (Academia Sinica), Ming-Hsien Lee (Tamkang University), Min-Hsiung Tsai (National Sun Yat Sen University), Shiow-Fon Tsay (National Sun Yat Sen University)
I. Brief Description HC Hsueh (TKU) for ExcS, FC Chuang (NSYSU) for NM, CM Chang (NDHU) for QMC and CC Kaun(AS) for QT, and another six senior members of the group, i.e. GY Guo (NTU), MH Lee (TKU), TC Leung (CCU), MH Tsai (NSYSU), SF Tsay he primary purpose of this program is to (NSYSU), and C. Cheng (the coordinator of enhance the domestic research capacity in CMRFG, NCKU). The missions of the committee the computational material science based on the are to allocate the budget, to initiate research first-principles quantum mechanical methods activities, to invite the long-term and short-term through promoting interactions and collaborations visitors and to recommend candidates (Ph.D. among local members as well as between local student or junior scientist) to attend international members and international noted scholars, and school, conference, or workshop through the also through attracting outstanding young financial support of CMRFG. researchers into this field. The CMR focus group presently consists of II. Activities more than 50 members, including 40 faculties and The activities supported by CMRFG are listed 14 postdoctors. According to the interests and the according to the following three categories 1) existing expertises of the members, we have workshops for all members 2) schools 3) study- identified four frontiers to concentrate on, i.e. group meetings. calculations of the electronic excited states 1. 7/1-7/3 2009 : 9th Workshop on First- (ExcS), nanomaterials (NM), quantum Monte Principles Computational Materials Physics Carlo methods (QMC), and quantum transport (QT). Study-group meetings initiated by the 7/6-7/10 2009: The 1st Workshop of High- members involved in these four topics become Performance Computing on Nanoscale one of the main backbone activities in promoting Materials Research 2009 collaborations among members as well as 2. 5/16-5/17 2009 : The school on first-principles stimulating new ideas and in-depth discussions. computational materials research -- So are the corresponding leading international introductory level visitors with the held comparable minischools. The Ph.D. students, postdoctors and the junior 6/06-6/07 2009 : The school on first-principles faculty members are encouraged to attend the computational materials research -- relevant international conferences, workshops and introductory level schools. 7/06-7/10 2009 : The school on first-principles The focus group is run by a committee whose computational materials research -- advanced members consists of four coordinators in charge lever of the activities related to the four frontiers, i.e. 12/27 2009: Minischool of LDA+U and GW
149 ‹‹- Highlights of Programs methods (CCU), is held in National Center for High- Performance Computing. The summer, organized 3. 4/17 2009 : QMC study group meeting by T. C. Leung (CCU), is held in NCTS (south). 5/02 2009 : Excited-state study group meeting Both schools include the practical hands-on 5/08 2009 : Nanomaterials study group sessions. The responses from both students and meeting non-specialist researchers are much positive as there are more than one hundred participants in 6/26 2009 : Excited-state study group meeting the spring school and more than fifty participants 7/06 2009 : QMC study group meeting in the summer school. 7/21 2009 : QMC study group meeting • Excited State study group Meeting and Minischool of LDA+U and GW methods 9/11 2009 : Excited-state study group meeting Four study-group meetings are held for the last 11/06 2009 : Excited-state study group meeting eight months. The discussions are mainly on the 11/11 2009 : QMC study group meeting applications of the present available methods, i.e. the GW methods (VASP and Berkeley GW), the 11/20 2009 : Nanomaterials study group Bethe-Salpeter methods (Berkeley GW) and the meeting time-dependent DFT (Turbomol), for the excited- • The 9th Workshop on First-Principles state study of the bulk materials and Computational Materials Physics nanomaterials. This program-wide workshop was held on July • Quantum Monte Carlo study group Meeting 1-3, 2009 in Cheng Ching Lake of Kaohsiung. Four study-group meetings are held for the last The aim of this workshop is to promote eight months. The discussed topics cover 1) interactions and collaborations among local generation of norm-conserving pseudopotentials members. The CMRFG Committee also takes this with the Opium package 2) atomic or molecular opportunity to learn about the general interests of absorption on surfaces using QMC methods 3) the community in order to organize beneficial magnetic moments of small metallic clusters using activities for the members in the future. All QMC methods 4) generation of Wannier functions participants, particularly PhD students and postdoctors, are encouraged to give a talk in this III. Visitors and International workshop. Collaborations • The 1st Workshop of High-Performance Examples of collaborations between CMRFG Computing on Nanoscale Materials Research members are listed as follows : This workshop is also a program-wide one as 1. CM Chang (NDHU), C Cheng (NCKU) and most of the CMRFG members involve more or CM Wei (AS) on the applications of the less in the studies of nanoscale systems. The Quantum Monte Carlo methods. emphasis is especially on the possible combinations of the less CPU time-consuming 2. HT Jeng (AS) , CY. Ren (NKNU) and CS. methods for larger systems with the accurate first- Hsue (NTHU) on the Orbital Ordering in principles methods to identify the crucial transition-metal oxides and developing a mechanisms for the investigated issues. specialized ab initio code for surface problems. • Schools on First-Principles Computational 3. BR Wu (CGU) and TC Leung (CCU) on the Materials Research electronic and optical properties of ribbon under external electric field. To help the newcomers in this field overcome the hurdle in the beginning, both the introductory- 4. GY Guo ( NTU), TC Leung (CCU) and HC level spring school and the advanced-level Hsueh (TKU) on the ab initio study for the summer school on the first-principles excited state of nanomaterials. computational materials research are organized. 5. CC Kaun (AS) and TS Tang (NUU) on the The spring school, lectured by T. C. Leung
Highlights of Programs -›› 150 quantum transport in graphene nanoribbons experts are expected to lead to concrete and and in nanomachines. eminent research results as the pursuit all the time International collaborations are listed as follows : of the NCTS. (1) Excited State study group meetings 1. GY Guo (NTU) and N Nagaosa (Japan) on the intrinsic spin Hall effect. The group explores the applicability of the established codes for the electronic excitation 2. TC Leung (CCU) and CT Chan (HongKong) using the GW, the Bethe-Salpeter and the time- on the optical properties of nanomaterials. dependent DFT methods. Investigations are 3. CM Wei (AS) and N. Drummond (UK) on the applied to the covalent and ionic insulators as well applications of the Quantum Monte Carlo as the nanosystems. Extensions of these studies to methods. optical spectrum and absorption spectrum are also 4. HC Hsueh (TKU) and SG Louie (USA) on the developed. quasiparticle excitations in nanomaterials. (2) Quantum Monte Carlo study-group meetings 5. CC Kaun (AS) and G Hong (Canada) on the To successfully apply the QMC methods to the spin transport in nanostructures systems consisting of the extensive range of the 6. CC Kaun (AS) and FM Peeters (Belgium) on elements in the periodic table, the generation of the interplay of the transverse discrete modes the physical and cpu-time-affordable norm- with a longitudinal supercurrent in a conserving pseudopotentials is explored and superconducting nanowire achieved. The current effort is mainly on the generation of the maximally localized Wannier IV. Highlights of Research Results functions from the DFT calculations in order to construct a much better initial many-body The community of the first-principles wavefunction for the DMC calculations. In the electronic calculations for materials of this mean time, the effect of the exchange and country has flourished in the last few years. The correlation on the magnetic moments of magnetic number of faculty members in the community clusters and the stability of the surface absorption started by less than ten is now reaching forty. The of atoms and simple molecules are also members benefits extremely from the interactions undergoing investigations. through the activities supported by the NCTS. That the members share their individual expertise (3) Nanomaterials study-group meetings within the community without reservation also The major issues of these meetings are to advances the community’s strength as a whole. identify the way in making use of the advantages How these could lead directly to the concrete of the capable but coarser methods together with research results, e.g. journal publications or the accurate first-principles methods to resolve invited talks, is not as straightforward to identify problems in considerably large-size systems. as might have been implied in the performance evaluations required by the funding agency. Not V. Selected Publications to mention that those concrete research results [1] GY Guo, S Maekawa and N Nagaosa, Phys. also benefit mostly from the personal NSC Rev. Lett., 102, 036401 (2009). projects of the members as well as, for some, the joint projects. [2] TW Chen and GY Guo, Phys. Rev. B 79, 125301 (2009). However, for the last eight months, the [3] ZR Xiao and GY Guo, J. Chem. Phys., 130, majority of the members have benefited 214704 (2009). enormously by the study-group meetings of the focused topics supported by the CMRFG which [4] S Ju, TY Cai, and GY Guo, J. Chem. Phys., could not be acquired from other resources 130, 214708 (2009). otherwise. Continuous supports of these meetings [5] ZZ Zhu, JC Zheng, GY Guo, Chem. Phys. with extensions through invitations and potential Lett., 472, p99 (2009). collaborations with the international leading [6] TH Cho, WH Su, TC Leung, W Ren, CT
151 ‹‹- Highlights of Programs Chan, Phys. Rev. B 79, 235123 (2009). [12] Y. H. Chiu, Y. H. Lai, J. H, Ho, D. S. Chuu, [7] J. P. Chou, H. Y. T. Chen, C. R. Hsing, C. M. and M. F. Lin, Phys. Rev. B 77, 045407 Chang, C. Cheng, and C. M. Wei, Phys. Rev. (2008). B 80, 165412 (2009). [13] C. M. Chang, C. Cheng, C. M. Wei, J. Chem. [8] GY Guo, S Murakami, TW Chen, and N Phys., 128, 124710 (2008). Nagaosa, Phys. Rev. Lett., 100, 096401 [14] F.C. Chuang, Chia-Hsiu Hsu, C.-Z. Wang, (2008). and K.-M. Ho, Phys. Rev. B 77 153409 [9] S. Ju and Guo GY, J. Chem. Phys., 129, (2008). 194704 (2008). [15] PA Lin, HT Jeng, and CS Hsue, Phys. Rev. B [10] S. Ju and G. Y. Guo, Appl. Phys. Lett. 92, 77, 085118 (2008). 202504 (2008). [16] CK Yang, Appl. Phys. Lett. 92, 033103 [11] I. J. Wu and G. Y. Guo , Phys. Rev. B 78, (2008). 035447 (2008). [17] C Cheng, Phys. Rev. B 78, 132403 (2008).
Highlights of Programs -›› 152 Highlights of Programs Particles and Fields
Focus Group on Cosmology and Particle Astrophysics
Coordinator: Pisin Chen (National Taiwan University; email: [email protected]) Committee members: Chuan-Hung Chen (National Cheng Kung University), Chao-Qiang Geng (National Tsing Hua Univeristy), W-Y. Pauchy Hwang (National Taiwan University), Wolung Lee (National Taiwan Normal University), Guey-Lin Lin (National Chiao Tung University), Guo-Chin Liu (Tamkang Univeristy), Kin-Wang Ng (Academia Sinica)
Summary • Invitation of short-term foreign visitors to give lectures at summer or winter school • Encouraging and promoting cooperation and/or joint research projects among domestic research s a new comer in NCTS, the Focus Group groups on Cosmology and Particle Astrophysics (FGCPA) has been very active during 2009. For • Training of graduate students and post-docs the weekly activities, it has been divided into three through their attendance of international schools Local Chapters, in Taipei, Hsinchu and Tainan, or visits to foreign research institutes on the respectively, for seminars and working group longer-term basis meetings. We further held Quarterly Meetings in • Invitation of distinguished cosmologists and Taipei, where the June meeting was held jointly particle astrophysicists for 3-month or longer- with the FG on Gravitation, while the December term visits (See the list of potential visitors). meeting will be a Joint Retreat with the FG on • Establishing exchange programs with foreign LHC. The highlight of the first-year activities is research organizations and conducting exchange perhaps the Summer School on Cosmology activities. Targeted sister institutions include organized jointly with the NTU Leung Center for KIPAC (Stanford), KIC (Cambridge), IPMU Cosmology and Particle Astrophysics (LeCosPA). (University of Tokyo), and KIAA (Peking About 150 students from all over Taiwan attended University). this Summer School. When looking back, it is evident that the mutual support between FGCPA In addition to the Core Members, there are and LeCosPA has been instrumental in the build- about 20 professors and researchers, 10 post-docs, up of the very active research of this field in 12 PhD students, 10 Master students participate in Taiwan. this FG. FGCPA has been pursuing the following 5 I. Brief Description research topics jointly with LeCosPA: The goals of FGCPA are as follows. 1. Large Scale Structure of the Universe (LSS): • Organization of summer or winter school to Keiichi Umetzu (organizer) offer short-term CPA courses to students and researchers 2. Baryon Asymmetry of the Universe (BAU): Chao-Qiang Geng (organizer)
153 ‹‹- Highlights of Programs 3. Dark Energy Phenomenology: Je-An Gu Triggered by the intriguing anomalous cosmic (organizer) ray spectrum observed by PAMELA and ATIC detectors, and the new discovery made by 4. Alternative Models for Cosmic Expansion: Sidney et al. (Nature 2008) where, based on Wolung Lee (organizer) the analysis of the dynamics of 300 galaxies, it 5. Cosmic Rays and Neutrinos: Guey-Lin Lin was claimed that the conventional CDM (cold (orgainzer) dark matter) model was in doubt, we organized this mini-workshop to explore their II. Activities implications. 1. Seminars • Mini-Workshop on Extreme Intensity Laser Taipei Chapter: This seminar series is located at and Science, Dec. 2009 NTU and organized by Pauchy It has been suggested since 1990s that the ultra Hwang. It has been holding high intensity fields in lasers and particle seminars every week except accelerators may be a useful tool for the during the Summer. laboratory investigations of astrophysics such Hsinchu Chapter: This bi-weekly seminar series is as the nature of black hole Hawking radiation, located at NTHU/NCTS. It is the plasma wakefield acceleration for the organized jointly by Chao- production of ultra high energy cosmic rays Qiang Geng (NTHU) and Guey- (UHECR), etc. Recently the European Union Lin Lin (NCTU). has funded a new project, ELI (Extreme Light Infrastructure), to build the world’s highest Tainan Chapter: This series is located at NCKU intensity laser. One of its goals is to investigate and organized by Chuan-Hung laboratory astrophysics. This mini-workshop is Chen. organized to explore the possibility of Taiwan- Since there are relatively fewer ELI collaboration. FG members in southern Taiwan, 5. Summer School it was decided that this series is held non-regularly and jointly The First Summer School on Cosmology was with the existing seminar series in jointly organized by FGCPA and LeCosPA and the Physics Department of was held at NTU in June 2009. In order to NCKU. maximize the effectiveness of students’ learning, we decided to use Chinese instead of English as 2. Working Groups the language for all lectures. Several ethnic Among the 5 Working Groups, except that the Chinese international experts in cosmology, BAU WG organized by Chao-Qiang Geng is including Prof. Lizhi Fang (U. Arizona), were conducted in Hsinchu, the rest are in Taipei. Since invited in addition to other experts in Taiwan as the issues involved in the Dark Energy lecturers. About 150 students from all over Taiwan Phenomenology and the Alternative Models for had attended the School. Among them about 60% Cosmic Expansion WGs, it was eventually were graduate students and post-docs, and the decided that the two WGs activities be combined remaining 40% were upper level undergraduate into one, where Je-An Gu is the organizer. students. Students who were admitted to the 3. Joint Retreats School did not have to pay the registration. Their room-and-board for the four-day event was also Our FG has organized two Joint Retreats with fully covered by the School. Many students could the FG on Gravitation led by Hoi-Lay Yu (AS) not believe the generosity of the School and had and with the FG on LHC led by Xiao-Gang He cherished such an unprecedented learning (NTU) in June and December, respectively. opportunity. 4. Workshops 6. Attendance of International Conferences • Mini-Workshop on Dark Matter Crisis, Jan. • A PhD student was sent to the International 2009 Conference on Cosmic Rays (ICRC) in Poland,
Highlights of Programs -›› 154 where he made a presentation. PAMELA anomaly. • Two post-docs attended the 11 th Marcel • Pisin Chen, Guey-Lin Lin and their PhD student Grossmann Conference in Paris in July. Two Feng-Yin Chang (now post-doc at LeCosPA) other post-docs gave presentations at the OCPA collaborate with R. Sydora (U. Alberta, Canada) Conference, Lanzhou. and R. J. Noble (SLAC) on plasma wakefield acceleration for the production of ultra high • Two Master students and one senior undergrad energy cosmic rays. student gave oral presentation on their research at the 2009 CosPA Symposium in Melbourne, 3. Sister Institutions Australia in November. During 2009, three world-renown institutions: • The Coordinator of FGCPA has given plenary KIPAC (Stanford), IPMU (U. Tokyo) and talks at major international conferences ICRANet (Italy) have signed collaboration including the OCPA Conference in Lanzhou MOUs with LeCosPA. Although FGCPA cannot (Aug. 2009), LEI Conference in Romania (Oct. sign such documents with foreign institutions, it is 2009), The 1st Galelio-Xu Guangqi Conference expected to also benefit from such formal in Shanghai (Oct. 2009), Italian-Korean agreements through its close connections with Conference on Relativistic Astrophysics (Nov. LeCosPA. 2009). He also gave seminars at Imperial College London, University of Oxford, VI. Highlights of Research Results University of Cambridge. • ATIC/PAMELA Anomaly from Fermionic Decaying Dark Matter III. Visitors and International Collaborations Two of our FG’s Core Members, Chuan-Hung Chen and Chao Qiang Geng, collaborated and With the very high degree of overlap between proposed to resolve the ATIC/PAMELA anomaly FGCPA and LeCosPA in terms of research topics by allowing the dark matter to be biased towards and members, many international visitors and decaying into leptons. They showed that the collaborations are shared, with benefits to both. observed P/A anomaly can be explained by the 1. Visitors three body decay of the neutral lepton N2 with the 2 17 mass M ≥1.5 TeV and the lifetime 10 s << τ2 Distinguished international visitors include ≤1026 s. One of the advantages of their mechanism Lizhi Fang (U. Arizona), Remo Ruffini (U. Rome is that there are no requirements for the and ICRANet), Joseph Silk (U. of Oxford), degeneracy of masses and unnaturally small Gerard Mourou (ENSTA, Paris), Sergei Bulanov couplings or any other enhancement factors. (JAEA, Kyoto). • Magnetowave Induced Plasma Wakefield 2. International Collaborations Acceleration for Ultra High Energy Cosmic • Collaboration between Ron Adler (Stanford Rays University) and Pisin Chen (NTU), Fabio Pisin Chen, Guey-Lin Lin and their PhD Scardigli (NTU) and Christine Gruber (NTU & student Feng-Yin Chang (now post-doc at Linz U., Austria) on the pre-inflation LeCosPA) collaborate with R. Sydora (U. Alberta, cosmology. Canada) and R. J. Noble (SLAC) on plasma • Collaboration between Pauchy Hwang (NTU) wakefield acceleration for the production of ultra and Sang Pyo Kim (Korea) on nonlinear QED high energy cosmic rays. Through particle-in-cell effects under Schwinger field. (PIC) simulations, they demonstrated the viability 20 • Collaboration between Pisin Chen and Johann of producing UHECR at energies ~10 eV at Rafelski and his students on the quantum astrophysical sites such as the AGNs. Their paper vacuum structure and cosmology. was published in Phys. Rev. Lett. In March 2009, which was further selected as one of the six papers • Continuing collaboration of Chao Qiang Geng in the Physics Highlights section in the April issue and Odintsov (Barcelonia, Spain) and on of Physics Today. particle astrophysics, in particular on the ATIC/
155 ‹‹- Highlights of Programs • New Approach to Testing Dark Energy Models V. Publications by Observations [1] “Constraints on the Phase Plane of the Dark Je-An Gu, Chien-Wen Chen and Pisin Chen Energy Equation of State” Je-An Gu, Chien- proposed a new model-independent method for Wen Chen, Pisin Chen, accepted for testing different dark energy models. They publication in Phys. Lett. B (2009); published three papers on this idea in New J. arXiv:0905.2738. Phys, Mod. Phys. Lett. A, and Phys. Lett. B. In [2] “ATIC/PAMELA anomaly from fermionic particular, they found that dark energy models decaying Dark Matter” Chuan-Hung Chen, including the cosmological constant, phantom, Chao-Qiang Geng, Dmitry V. Zhuridov, Phys. non-phantom barotropic fluids, and monotonic Lett. B675: 77 (2009). up-rolling quintessence are ruled out at the 68.3% [3] “Neutrino Masses, Leptogenesis and confidence level based on the current Decaying Dark Matter” Chuan-Hung Chen, observational data. Down-rolling quintessence, Chao-Qiang Geng, Dmitry V. Zhuridov JCAP including the thawing and the freezing models, is 0910:001 (2009). consistent with the current observations. All the [4] “Resolving Fermi, PAMELA and ATIC above-mentioned models are still consistent with Anomalies in Split Supersymmetry without the data at the 95.4% confidence level. R-Parity” Chuan-Hung Chen, Chao-Qiang Geng, Dmitry V. Zhuridov, Preprint: arXiv:0905.0652 [5] “Resolution to Neutrino Masses, Baryon Asymmetry in Leptogenesis and Cosmic-Ray Anomalies” C. H. Chen, Preprint: arXiv:0905.3425 [6] “Sommerfeld Enhancement from Unparticle Exchange for Dark Matter Annihilation” C.H. Cen and C.S. Kim, Preprint: arXiv:0909.1878
Highlights of Programs -›› 156 Focus Group on Gravitation
Coordinator: Hoi-Lai Yu (Academia Sinica; email: [email protected]) Committee members: Hing-Tong Cho (Tamkang University), Da-Shin Lee (National Dong Hwa University), James M. Nester (National Central University), Chopin Soo (National Cheng Kung University)
I. Brief Description avoid the obstruction in the Parikh–Wilczek derivation of Hawking radiation. Much effort has been focusing on the student training programs which is a unique program of his has been an exciting year for the the Gravitation focus group among other focus gravitation focus group. Let us first groups in the community. More than 15 students highlight some of the developments, beginning were encouraged and supported to participate in with, studies in the stochastic gravity on de Sitter international conference abroad. With the help of spacetime, which have revealed the fluctuation of Prof. Y. K. Lau from The Applied Mathematics the corresponding Hawking radiation. Also, work Institute, Academia Sinica, Beijing, more than 10 on higher-dimensional Kerr black holes has been students each year were able to participate in the focusing on the analysis of the quasinormal modes gravitation related summer school/institute and the emission of particles in the Hawking program hosted by China. We believe this will radiation. The investigation of gravitational help the student not only to expand their energy and gauge theories of gravity, being one of knowledge spectrum and opportunities but also to the main academic activities in our focus group, become more mature at an early stage of their had also gained tremendous momentum and academic careers. important results, especially concerning, theories with torsion, using the covariant Hamiltonian In 2010 our focus should host: International formalism developed by our colleagues in recent Association for Relativistic Dynamics (IARD) years. In particular, they have been looking into 2010. how to choose the quasi-local reference/ 29th May – 1st June, 2010 we shall host the displacement, the energy of cosmologies, and the IARD, and more than 70 distinguished post-Riemannian cosmological effects of gauge Relativitists and gravity related researchers from theories of gravity. Our numerical relativity abroad are expected to participate in the colleagues have improved the flexibility of the IARD2010. FMR/AMR in their code, including the moving- box method, the higher-order 3D Hermite II. Activities interpolation for the interface between different The following major activities were carried out levels of grid. One of the triumphs is to evolve a last year on top of our regular/irregular journal binary black hole from its quasi-circular initial club meetings at the Institute of Physics, data in the in-spiral stage, through the plunge Academia Sinica and Department of Physics at stage, to its final merger and extract the complete National Central University, National Cheng Kung gravitational radiation. In the investigation of and National Dong Hwa University. Lorentz symmetry which is manifested as a local gauge symmetry in curved spacetime, the (1) APCTP-NCTS International School/ generalizations of the Painleve–Gullstrand slicing Workshop on Gravitation and Cosmology, th th which are not spatially flat but remain regular at Pohang, Korea, 16 January-20 ; http:// the horizons have been introduced which can apctp.org/conferences/2009/IWGC2009/
157 ‹‹- Highlights of Programs This was the third joint international school/ Wu) were arranged to visit and conduct workshop of the sort in Cosmology and research at Princeton University, the Gravitation. This time hosted by APCTP and University of Maryland , Tuft University, the co-sponsored by NCTS and Institute of Physics, International Center for Gravitation Research Academia Sinica. The meeting was not only at the University of Pennsylvania and the helpful in reinforcing collaborative research Perimeter Institute, Canada. Several important activities among Asia Pacific area within a flight papers (see the highlights and publication list distance of two hours but also in attracting below) in the cutting edge were published talented young researchers to contribute. The main during these activities. purpose of this meeting is to introduce to students (ii) With the help of Prof. Y.K. Lau, more than 13 and researchers the latest developments in graduate students (from NCU, NDHU and gravitation, semi-classical and quantum gravity. NCKU) were arrange to attend the gravitation We had 16 graduate students, postdocs and 11 workshop at the Institute of Applied local faculties fly to Pohang, Korea to participate Mathematics, Academia Sinica, Beijing and to in the school/workshop. About 35 students/ participate in related research programs (i.e. faculties from the Asia Pacific area, Europe and Summer School at Wuhan, June, 2009) during the United States participated in the meeting. The the summer annually in the last four years. school lectures which were catered to bring to the (iii) Joint School/Workshop in Gravitation in the students the conceptual foundations and technical Asia-Pacific is aimed not only to bring to know-how to the latest development in the researchers the latest developments and to gravitation related areas. promote collaborations but also to bring to the (2) 4 th Sept-5th Sept. Mini-Workshop on graduate students a wide spectrum of Cosmology and Gravitation at Tamkang knowledge and technical know-how at an University early stage of their academic career. The joint meetings will rotate between Taiwan, China, The main purpose of the workshop is for Korea and Japan. The 2011 meeting will be participants to present ideas of on-going and hosted by Shanghai Normal University. future research projects on cosmology and gravitation. It was hoped that this would stimulate (iv) Combine with resources from the Institute of discussions and initiate further collaborations Physics, Academia Sinica, our FG had among participants. successfully brought to the community (3) 29 March, 2009 Mini-workshop on distinguished researchers for long stays (one Gravitation and Cosmology to three months) which had benefited not only our faculties but also graduate students This workshop was organized by colleagues at through seminar, discussions and National Central University during Prof. Friedrich collaborations. Among them are : Hehl’s (University of Cologne) visit to our focus (a) Prof. Larry Ford from Tuft University who group. had triggered works on the instabilities of rd (4) 13 June, Joint Meeting of NCTS FG on De Sitter space through the gauge invariant Gravitation and FGCPA at NTU Ricci tensor. This is the first joint meeting between our FG (b) Prof. Friedrich Hehl from University of and the FGCPA. The main purpose of the meeting Cologne resulted in (1) rekindling an old is to communicate ideas and initiate possible joint research project that will lead to 2 collaborations between our FG and the FGCPA. publications, (2) catalyzing the revision of another of Prof. Nester’s dormant works lll. Visitors and International (now accepted), and (3) generating a new Collaborations line of inquiry into gauge theories of (i) With the help of Profs. L. Ford and B.L. Hu gravity with odd parity terms (drafts of 2 our postdocs (S.Y. Lin, C.S. Chou and C.H. papers now exist).
Highlights of Programs -›› 158 (c) During Dr. Shan Bai's visit in Taiwan, we symmetric metrics by physical Lorentz have developed the code of the initial data boosts. With these generalized PG metrics, in thespectral method in order to simulate problematic contributions to the imaginary the evolution in various scenarios. With the part of the action in the Parikh–Wilczek code we will be able to specify different derivation of Hawking radiation due to the mass ratios, different spin magnitudes, and obstruction can be avoided. Generalized PG coordinate separations once the code is coordinates for stationary axisymmetric completed. Dr. Shan Bai's visit will help the spacetimes are also explicitly constructed; students in their waveform extraction. and the results are applied to the Kerr- Newman family of rotating black hole (d) Dr. ZhouJian Cao has done a lot of solutions. The generalizations are all free of improvement on the various flexibility of coordinate singularities at the horizon(s). the FMR/AMR in our code, including the moving-box method, the higher-order 3D (viii) A general expression for quasilocal energy Hermite interpolation for the interface flux for spacetime perturbation is derived between different levels of grid during his from covariant Hamiltonian formulation visit to Taiwan. using functional differentiability and symplectic structure invariance, which is lV. Highlights of Research Results independent of the choice of the canonical (i) Investigate the gravitational energy within variables and the possible boundary terms small regions of spacetime, one initially puts into the Lagrangian in the diffeomorphism invariant theories. The (ii) Develop normal frames for use in small energy flux expression depends on a regions of spacetime, displacement vector field and the 2-surface (iii) Further develop the Poincare gauge theory under consideration. cosmologies by including the 0- mode, (ix) Have shown that for untrapped or marginal (iv) Improve the various flexibility of the FMR/ surfaces, fixing the area element on the AMR in our code, including the moving-box 2-surface boundary (rather than the induced method, the higher-order 3D Hermite 2-metric) is enough to have a functionally interpolation for the interface between differentiable Hamiltonian. The analysis different levels of grid. provides a natural choice of the evolution vector which reduces to the Kodama vector (v) Evolve a binary black hole from its quasi- in spherical symmetry. This vector plays a circular initial data in the inspiral stage, similar role for the stationary untrapped through the plunge stage, to its final merger. boundary conditions that the stationary During the simulation, we also extract the Killing vector plays for stationary black complete gravitational radiation. The PhD holes. When the vector is null, these student, JuiPing Yu keeps working on the boundary conditions reduce to those given by extraction of the waveform. the isolated horizons. (vi) Developed the code of the initial data in the (x) Have constructed an effective field theory for spectral method in order to simulate the a condensate of cold Fermi atoms whose evolution in various scenarios. With the code scattering is controlled by a narrow Feshbach we will be able to specify different mass resonance. Have shown from first principles, ratios, different spin magnitudes, and it permits a hydrodynamic description of the coordinate separations once the code is BEC-BCS crossover from which the equation completed. of state, intimately related to the speed of (vii) Generalizations of PG slicings which are not sound, can be derived. spatially flat but which remain regular at the (xi) The saturation mechanism of the velocity horizons are introduced. These metrics can be dispersion in a suparohmic environment is obtained from standard spherically found to be distinctly different from that in an
159 ‹‹- Highlights of Programs ohmic environment. The stochastic force [8] J. M. Nester, L. L. So and T. Vargas, “Energy arising from the supraohmic environment is of homogeneous cosmologies” Phys. Rev. D shown to have both positive and negative 78(2008), 044035. correlations, thus leading to the saturation of [9] C. Y. Lin and C. Soo, “Generalized Painleve- the velocity dispersion. Gullstrand Metrics”, Phys. Lett. B671(2009), (xii) The study of the detailed spatial dependence 493. of entanglement dynamics between two [10] R.S. Tung and H. L. Yu, “Quasi-Local Energy Unruh-DeWitt detectors at rest separated in a Flux of Spacetime Perturbation”, Phys. Rev. fixed distance and coupled to a common D78(2008), 104010. relativistic quantum field(This work was [11] R. S. Tung, “Stationary untrapped boundary selected for the May 2009 issue of Virtual conditions in general relativity”, Class. Journal of Quantum Information). Quantum Grav. 25(2008), 085005. [12] R. S. Tung, “Energy and angular momentum V. Publications in strong gravitating systems”, International [1] Hing-Tong Cho, Kin-Wang Ng, and I-Chin Journal of Modern Physics A, 24(2009), Wang, “Scalar field fluctuations in 3538-3544. Schwarzschild-de Sitter space-time”, [13] Y.Y. Charng, D. S. Lee, C.N. Leung, K.W. arXiv:0905.2041 [astro-ph.CO] (2009). Ng, “Affleck-Dine Baryogenesis and [2] Z.J. Cao, H.J. Yo, and J.P. Yu, Phys. Rev. Inflation”, Phys. Rev. D 80(2009), 063519. D78(2008), 124011. [14] C.Y. Lin, D.S. Lee and R. J. Rivers, “The [3] J.M. Nester, “Normal frames for general Non-universal behaviour of Cold Fermi connections” to appear in Ann.Phys. (Berlin), Condensates with Narrow Feshbach 1--8 (2009). Resonances”, Phys.Rev. A 80(2009), [4] H. Chen, F.H. Ho, J.M. Nester, C.H. Wang 043621. and H.J.Yo, “Cosmological dynamics with [15] J.T. Hsiang, T.H. Wu, and D.S. Lee, propagating Lorentz connection modes of spin “Brownian motion of a charged particle zero” J. Cosmology Astroparticle Phys. under electromagnetic fluctuations at finite 10(2009),027. temperature ( to appear in Found. [5] L. L. So and J. M. Nester, “Positive small- Phys.2009). vacuum-region gravitational-energy [16] S.-Y. Lin and B. L. Hu, “Temporal and spatial expressions'' Phys. Rev. D79(2009), 084028. dependence of quantum entanglement from a [6] L. L. So, J. M. Nester, and H. Chen, “Energy- field theory perspective”, Phys. Rev. D momentum density in small regions: the 79(2009), 085020. classical Pseudotensors” Class. Quantum Grav. 26(2009) 085004. [7] L. L. So and J. M. Nester, “Gravitational Energy-Momentum in Small Regions According to the Tetrad-Teleparallel Expressions” Chin. J. Phys. 47(2009), 10.
Highlights of Programs -›› 160 Focus Group on Lattice QCD and Hadron Physics
Coordinator: Ting-Wai Chiu (National Taiwan University; email: [email protected]) Committee members: Jiunn-Wei Chen (National Taiwan University), Chung-Wen Kao (Chung-Yuan Christian University), David Chi-Jen Lin (National Chiao-Tung University), Cheng-Pang Liu (National Dong-Hwa University)
I. Brief Description III. Visitors and International Collaborations The list of visitors can be found from our focus group website (http://phys.cts.ntu.edu.tw/en/) and n LQCD, the scientific goals are (a) the international collaborations can be found from pursuing large-scale unquenched our publication list shown below. The calculations with optimal domain-wall quarks and collaboration between TWQCD and JLQCD, a building up the capacity for large scale computing well known collaboration formed by an elite with the new GPU technology (b) using lattice group of LQCD theorists, was formed since 2006. gauge field theories to explore physics beyond This collaboration has worked out many important standard model. In hadronic physics, the goals are results, with totally 9 papers published in PRL(2), (a) understanding QCD viscosities and their PRD(6), and PLB(1). C.J. David Lin has also relations to phase transitions (b) understanding the formed collaboration with an Oska U. group on impact of box diagrams in radiative corrections to walking technicolor and an Taiwan-UK-US high precision hadronic experiments. (c) collaboration on b-baryon simulations. C.W. Kao Systematic time reversal violation studies of has collaborated with Vanderhaeghen in Mainz; nuclear and atomic systems. C.P. Liu has just come back to Taiwan for one year and has maintained his collaborations with II. Activities many institutes abroad. Lots of activities have been organized to induce new ideas and collaborations: IV. Young Researchers (1) Weekly meetings: In addition to training young researchers with platforms set up by the focus group activities, the (a) Hadron physics at NTU, video focus group has supported Yao-Yuan Mao conferencing with NDHU and NCKU (b) (research assistant) to attend Lattice 2009 (he also TWQCD collaboration at NTU (c) Lattice QCD attended 2009 Les Houches School with full journal club (d) Seminars Series at NDHU support from Les Houches), Kenji Ogawa (biweekly), co-funded by LQCDHP and (postdoc) to visit KEK, and Yen-Fu Liu (Ph. D. Cosmology focus groups student) to visit Prof. Tetsufumi Hirano at (2) Schools and Workshops: University of Tokyo for 2 weeks for collaboration. (a) Nucleon Structure (April 27) (b) The 13th J.W. Chen’s students were admitted to Caltech, Taiwan Nuclear Physics Summer School (June Duke and SUNY for physics Ph. D. programs in 29-July 4) http://phys.cts.ntu.edu.tw/nuclear/2009/ 2009. (c) The 2009 Taipei Workshop on Lattice QCD (December 13-15) http://twqcd09.phys.ntu.edu. V. Highlights of Research Results tw/ . A. Lattice QCD The nuclear summer school has attracted (a) Large-scale simulations of unquenched around 100 participants. lattice QCD with optimal domain-wall quarks:
161 ‹‹- Highlights of Programs The TWQCD collaboration led by Ting-Wai (d) Physics related to the LHC-b program Chiu has made a breakthrough in applying the Chi-Jen David Lin has collaboration with new GPU technology in large scale computing. It colleagues in the US and the UK on the physics is the first group around the world to use a GPU related to the LHC-b program which would allow cluster (with 120 Teraflops peak) to perform large- us to probe the possible right-handed coupling scale LQCD simulations and is one of the three structure in physics beyond the Standard Model. groups (together with RBC/UKQCD, JLQCD) Presently, we already calculated the spectrum of that can perform large scale unquenched baryon containing one b quark and found it simulations of lattice QCD with exact chiral consistent with experiment. Calculations for symmetry. relevant matrix elements are being performed. (b) Theoretical prediction of newly discovered B. QCD viscosities Y(4140) In the last few years, Jiunn-Wei Chen has In 2007, TWQCD published a paper “X(3872) initiated a series of investigations of viscosities in lattice QCD with exact chiral symmetry” [T.W. and phase transitions. His paper “Phase transitions Chiu and T.H. Hsieh, Phys. Lett. B646 (2007) 95]. and perfectness of fluids in weakly coupled real In this paper, they investigated the mass spectrum scalar field theories” [ Jiunn-Wei Chen, Mei of 1^{++} exotic mesons with quark content Huang, Yen-Han Li, Eiji Nakano and Di-Lun (c-cbar-q-qbar), using molecular and diquark- Yang, Phys. Lett. B670:18-21,2008] is selected by antidiquark operators. For (c-cbar-u-ubar) the web of science as one of the highly cited operators, they observed a resonance with mass papers last year. In that paper, the simplest around 3891(17)(21) MeV, which is naturally theoretical model with different kinds of phase identified with X(3872) discovered by Belle in transitions is used to rigorously study the relation 2003. Furthermore, they also predicted a heavier between phase transitions and the perfectness of exotic meson resonance with 1^{++}, with quark fluids. It was found that, for the first time, the content (c-cbar-s-sbar), and mass 4143(19)(25) same behavior observed in all the known systems MeV. (there are more than 30 of them) can be On March 17, 2009, CDF announced the reproduced in a theoretical study. It is a follow up discovery of a new exotic state Y(4140). Since study of another paper supporting that the quark Y(4140) decays into J/Psi(3100) and phi(1020), it and gluons plasma that existed a few microsecond is likely that Y(4140) is the exotic (c-cbar-s-sbar) after the big bang is a near perfect fluid. Their state TWQCD have predicted in 2007! Private result appeared in the 2007 US Nuclear Science communications with CDF revealed that the C Long-Range Plan as part of the near perfect fluid parity of Y(4140) is likely to be positive. If story which was featured as the first one of the confirmed, it will be a big triumph of TWQCD. eight recent accomplishments. (c) New strong interactions at TeV scale C. Extraction of the strangeness of the proton In the last few years, Chi-Jen David Lin has In the last few years, Chung Wen Kao has established collaboration with a Osaka University initiated a series of the extraction of the group of led by Professor Tetsuya Ogoni on strangeness of the proton to include state of the art walking technicolour scenario. It is a popular “box diagram” contributions. In their previous possibility for dynamical electroweak symmetry work “The Two-Photon-Exchange and gamma breaking in which flavour-changing neutral Z-Exchange Corrections to parity-Violating current processes are suppressed naturally Elastic Electron-Proton Scattering’’, Phys. Rev. (dynamically). Presently, many researchers are Lett .99:262001,2007, CWK and collaborators looking for candidate strongly-coupled gauge challenged the widely used approximation of the theories for this scenario, which requires a quasi box diagrams by evaluating directly the two- non-trivial infrared fixed point. From our boson exchange effects in a hadronic model and in simulations, we have evidence that SU(3) gauge a partonic model. Their result shows that the two- theory with 12 flavours develops such a fixed boson exchange effects have complicated point. dependence on the kinematics variables and
Highlights of Programs -›› 162 therefore should not be approximated as a [6] “Mixed Action Effective Field Theory: an constant as previous analysis did. This discovery Addendum”, J.W. Chen, M. Golterman, D. has a wide impact on precision measurements O'Connell and A. Walker-Loud, Phys. Rev. where theoretical radiative corrections are critical D79 (2009) 117502. for data interpretation. They have estimated this [7] “U_A(1) Anomaly in Hot and Dense QCD effect on the extracted value of the proton and the Critical Surface”, J.W. Chen, K. strangeness recently and are finishing up a state of Fukushima, H. Kohyama, K. Ohnishi and U. the art analysis on this quantity. Raha, Phys. Rev. D80 (2009) 054012. [8] “pi-pi Scattering in Twisted Mass Chiral VI. Outlook Perturbation Theory”, M. I. Buchoff, J. W. In addition to continue studying the rich Chen and A. Walker-Loud, Phys. Rev. D79 manifestations of QCD in hadronic matter, an (2009) 074503 emerging theme of this focus group is the study of [9] “Universality of mixed action extrapolation new physics (physics beyond the stand model) formulae”, J.W. Chen, D. O'Connell, A. either directly related to (walking Technicolor, Walker-Loud, JHEP 04, 090 (2009) Higgs-Yukawa systems, AdS/CFT) or complimentary to (time violation and box [10] “Bulk viscosity of a gas of massless pions”, diagrams corrections to low energy precision J.W. Chen, J. Wang, Phys. Rev. C79: 044913 tests) LHC physics. TWQCD’s ability to perform (2009). large-scale simulations of unquenched LQCD [11] “A new scheme for the running coupling with optimal domain-wall quarks is also very constant in gauge theories using Wilson exciting and is expected to produce more state of loops”, E. Bilgici, A. Flachi, E. Itou, M. the art results. Kurachi, C.-J. D. Lin, H. Matsufuru, H. Ohki, T. Onogi, T. Yamazaki, Phys. Rev. D80 VII. Selected Publications (2009) 034507. [1] “Topological Susceptibility to the One-Loop [12] “Bottom hadron mass splittings in the static Order in Chiral Perturbation Theory”, limit from 2+1 flavour lattice QCD”, W. TWQCD Collaboration (Yao-Yuan Mao and Detmold, C.-J. David Lin, M. Wingate, Nucl. Ting-Wai Chiu), Phys. Rev. D80 (2009) Phys. B818 (2009) 17. 034502. [13] “Extraction of charged pion polarizabilities [2] “Topological susceptibility in 2+1 flavors from radiative pion photoproduction in lattice QCD with domain-wall fermions”, Heavy Baryon Chiral perturbation Theory”, TWQCD Collaboration (Ting-Wai Chiu et C.W. Kao, B.E. Norum, K. Wang, Phys. Rev. al.), Phys. Lett. B671 (2009) 135. D79 (2009) 054001. [3] “Lattice calculation of strong coupling [14] “Magnetic susceptibility of QCD vacuum at constant from vacuum polarization functions”, finite density”, S. Nam, H.-Y. Ryu, M. M JLQCD and TWQCD Collaborations (E. Musakhanov, H.-C. Kim , J. Korean Phys. Shintani et al.). Phys. Rev. D79 (2009) Soc. 55 (2009) 429. 074510. [15] “Contribution of Two-Boson-Exchange with Delta(1232) Excitation to Parity-Violating Elastic Electron-Proton Scattering”, K. [4] “Non-perturbative renormalization of bilinear Nagata, H. Q. Zhou, C.W. Kao, S.N. Yang, operators with dynamical overlap fermions”, Phys. Rev. C79 (2009) 062501. JLQCD and TWQCD Collaborations (J. Noaki et al.), arXiv:0907.2751, to appear in Phys. Rev. D (2009). [5] “Pion form factors from two-flavor lattice QCD with exact chiral symmetry”, JLQCD Collaboration and TWQCD Collaboration (S. Aoki et al.), Phys. Rev. D80 (2009) 034508.
163 ‹‹- Highlights of Programs Focus Group on LHC Physics
Cheif coordinator: Xiao-Gang He (National Taiwan University; email:[email protected]) Coordinators: Chuan-Hung Chen (National Cheng Kung University), Kingman Cheung (National Tsing Hua University), Cheng-Wei Chiang (National Central University), Keiw-Chou Yang (Chung-Yuan Christian University), Tzu-Chiang Yuan (Academia Sinica)
I. Brief Description II. Activities To bring all interested researchers to be more coherently involved in related research activities, the focus group is conducting several types of he large hadron collider (LHC) at CERN activities: will be in operation soon. LHC physics a. We have formed natural working group at will become one of the most important fields in different universities AS, CYCU, NCKU, particle physics in the next 10 to 20 years. The NTHU and NTU, involving faculty members purpose of this focus group, the LHC Physics and Postdocs, visitors and students. Seminars Focus Group, is to bring out all the existing are conducted on weekly bases. This year we theoretical efforts, to establish close working have had 109 seminars in total so far. These relations with our experimental groups, and also seminars benefited our researchers and students to train young researchers and students in this area in many ways. to play an important role in this field. Our focuses, as stated in our proposal, are in the following b. Beside local natural working group seminars, directions: we have also set up mechanism to organize special mini-workshops to report new research • Investigation of physics of electroweak results from group members and also symmetry breaking and international visitors, and to have quick • Higgs mechanism response to new discoveries. This year we • Physics beyond the standard model. already had two rapid responding meetings on dark matter and 3 mini-workshops (2 already • Probing the nature of dark matter conducted and another will be held on 12/12). • Flavor physics and CP violation These meetings are held at different university. These activities also enabled our theoretical We formed our coordinator team involving researchers to have more chances to interact active researchers from different universities with with experimentalists. one person as the chief coordinator taking care of details. The current chief coordinator is Xiao- c. We also organize conferences and schools to Gang He. The next five years’ chief coordinators, attract international visitors and to train our in order, are: Tzu-Chiang Yuan (AS), Cheng-Wei young students. This year we organized, as th Chiang (NCU), Keiw-Chou Yang (CYCU), co-organizers, two conferences: the 8 Particle th Chuan-Hung Chen (NCKU) and Kingman Cheung Physics Phenomenology, and the 4 (NTHU). International Symposium on Symmetries in Subatomic Physics. And two schools: the Our members come from all over Taiwan particle physics Spring School, and the summer containing 25 faculties (18 theorists and 7 School. experimentalists), 15 post doctoral fellows, and about 30 master and Ph.D students. d. One of the main purposes of NCTS is to train young-generation physicists. We have made our efforts in this direction. We have used the
Highlights of Programs -›› 164 NCTS multi-year senior visitor program more than one institutes in Taiwan. Our members invited Professors Tony Zee and We-Yi Keung have been invited to give talks at international to visit us and to work with some of our conferences more than 10 times, and also more members and give mini-courses to our graduate than 5 contributed talks. We highlight students. We also used our limited money to achievements according to the topics proposed in support students, postdocs and young faculties reverse order in the following. to attend international conferences to give • Flavor physics and CP violation talks. This year, we will send at least 1 student and 3 postdocs to conferences. We have Taiwan has strong tradition working in the established an international exchange program field of flavor physics and CP violation, in with KEK theory group in Japan. This year we particular in B related flavor physics and CP have sent 4 of our researchers to KEK. violation. Since LHC has LHCb program and also Belle II may well continue in the future, we III. Visitors and International should keep enough efforts in this area. Collaborations Hai-Yang Cheng, Chun-Khiang Chua, Keiw- International collaboration is one of our Chou Yang and their groups have been strengths. Many of our members have concentrate on CP violation in B(Bs) to two international collaborators. We have more than15 mesons and two baryons. They found that some of international collaborations working on topics them to be very sensitive probe of new physics. related to our physics problems from the China, They carried out an updated QCD light cone Europe, Japan, Korea and USA.. calculation of B→Vγ decay and found that their results from their method are in good agreement Using limited resources from our FG budget, with data. we have invited more than 20 international visitors to come to Taiwan to work with our Cheng-Wei Chiang and his collaborators have members. We have used the NCTS multi-year model independent analysis of B to PP and PV senior visitor program invited Professors Tony decays. By performing global fits, they find that Zee and We-Yi Keung to visit us and to work with current data can be satisfactorily explained within some of our members and give mini-courses to the Standard Model (SM). The analysis can our graduate students. provide an independent constraint on the unitarity triangle at a precision level comparable to other We do not limit ourselves just to invite methods. They also found that the famous B to Kπ international collaborator to come to Taiwan for puzzle, using latest data, no longer provides collaborations, we also used our limited money to compelling reasons for the need of new physics. support students, postdocs and faculties to attend Hsiang-nan Li also anlysised K pi puzzle recently. international conferences to give talks aiming at forming new collaborations. This year, we plan to Chuan-Hung Chen, Chao-Qiang Geng and send at least 1 student and 3 postdocs to their group have shown that new physics can conferences. have significant effects on B(B_s) mixing and also on b to q l \bar l. We have established an international exchange program with KEK theory group in Japan. This • Probing the nature of dark matter year we have sent 4 of our researchers to KEK. This year is an exciting year for dark matter study. Last year Pamela and ATIC, and this year IV. Highlights of Research Results FERMI-LAT data show that there are excesses in As a result of our efficient operation, we have cosmic e+ and e-. One of the possible sources for been able to move on to physics problems studies these excesses is from dark matter annihilation or and to stimulate collaborations quickly. We are dark matter decay. Our focus group has responded very pleased to report that we have made rapidly from several fronts, model independent progresses in most areas proposed to study. analysis of dark matter properties, dark matter Among the papers by group members more than decay and annihilation models. Chuan-Hung 20 papers were written with authors come from Chen, Kingman Cheung, Chao-Qiang Geng, Xiao-
165 ‹‹- Highlights of Programs Gang He, Tzu-Chiang Yuan and their groups have Supersymmetry is another very well motivated written, in a short time, 9 papers. Our papers are theory. Recently people have been interested in well cited. We also organized two discussion another way of extending the minimal MSSM by sessions on experimental data and theoretical adding dimension five operator to the theory ideas jointly with Cosmology and Astrophysics without enlarging particle contents. Kingman Focus group. Some of the models proposed may Cheung and his group have studied the impact of be further tested at the LHC. such an extension. They found that it has a • Physics beyond the standard mode and significant impact on the scenario of the Higgsino- *Investigation of physics of electroweak dominated neutralino state being the lightest symmetry breaking and Higgs mechanism supersymmetric particle (LSP). It increases the mass difference between the LSP and the lightest Higgs search is the main goal of the LHC. chargino as well as that between the LSP and the Naturally it is one ofhte focus for our group. second-lightest neutralino and therefore enhances Xiao-Gang He and his group have studied the LHC discovery potential. possible beyond the SM effects which may change LHC offers a possibility to directly test the the SM properties, such as enhanced invisible seesaw mechanism which explains why neutrinos Higgs decay modes from unparticle or dark are so much lighter than their charged partners. In matter. New search strategies may be needed. a series of papers, Xiao-Gang He and his There may be also new types of Higgs particles. collaborators showed that there are new solutions Recently Cheng-Wei Chiang and Akroyd have which can have large mixing providing the hope studied how a doubly charged Higgs boson of the of testing the seesaw mechanism at the LHC. triplet Higgs in Type-II seesaw can be search for They also found that the Type-III seesaw model and studied at hadron colliders. They found that proposed by professor He and his collaborators in there is strong correlation between neutrino mass 1989, can be better tested at the LHC (For more hierarchy and Majorana phase. This work detailed descriptions see the report to NSC). establishes one direct link between LHC physics and the neutrinos. V. Publication Z’ physics. This is a new boson particle We have published 41 SCI papers (18 with resulting from extended gauge groups beyond the NCTS in the addresses and 23 with SM. This is probably one of the most motivated acknowledgment to NCTS), and have written 21 new particles beyond the SM. This year Cheng- preprints submitted to SCI journals for publication Wei Chiang, Kingman Cheung, Xiao-Gang He, (11 with NCTS in the addresses and 10 with Tzu-Chiang Yuan and their groups have attacked acknowledgement to NCTS), and 3 conference related studies from flavor violating, collider proceedings. (See publication list in the report to signature and also model building aspects. We are NSC), The Focus group has allowed us to react working out some of the best ways to search for quickly of new developments. We are confident to such a particle. In a related study, Kingman make even better progresses in the future. We Cheung and Tzu-Chiang Yuan proposed a W' hope to have continued support at the same level. boson that couples to down and top quarks can give rise a large enough forward-backward asymmetry to explain recent CDF data.
Highlights of Programs -›› 166 Focus Group on Strings
Coordinator: Chiang-Mei Chen (National Central University; email: [email protected]) Committee members: Chuan-Tsung Chan (Tung Hai University), Kazuyuki Furuuchi (National Center for Theoretical Sciences), Choon-Lin Ho (Tamkang University),Pei-Ming Ho (National Taiwan University), Hsien-chung Kao (National Taiwan Normal University), Jen-Chi Lee (National Chiao Tung University), Feng-Li Lin (National Taiwan Normal University), Yi Yang (National Chiao Tung University).
I. Brief Description cosmology inspired from string theories. Our progress will be summarized later. Our group also encourages and supports postdocs and students to attend international ur FG in this year includes the following conferences and workshops. In January 2009, we postdocs members: Hirotaka Irie, Hiroshi organized the first international Taiwan String Isono, Tomohisa Takimi, Wen-Yu Wen (Nat’l Theory Workshop focused on the topics of black Taiwan U), Shou-Huang Dai, Pei-Wen Kao, holes physics and the holographic principle. The Shoichi Kawamoto, Chen-Pin Yeh (Nat’l Taiwan second Workshop has been arranged in December Normal U), Dmitry Orlov, Jia-Rui Sun (Nat’l of this year at Taiwan Normal University. We Central U), Takayuki Hirayama, Dan Tomino, hope to keep this workshop annually as a Chih-Wei Wang (NCTS), Keijiro Takahashi, significant event of our FG. This activity can Yoshihiro Mitsuka (Nat’l Chiao Tung U), Wen- advance the visibility of the Taiwan string Tsan Lin (Tamkang U). There are also about nine community. student members. The String FG activities are organized to II. Research Activities enhance the interaction and collaboration among 1. Weekly string seminars at NTU the group members, and to establish intense http://web.phys.ntu.edu.tw/string/index.htm international connections in particular with the Japanese and Korean string communities. The weekly seminars at NTU are a core Following the tremendous efforts of the previous activity of our group initiated in 1996. The coordinators, Pei-Ming Ho, Jen-Chi Lee and schedule is arranged in the Friday afternoon which Hsien-chung Kao, our members have benefited is the most convenient time that our group considerably from the FG activities, such as members can attend. The talks are given either by regular seminars, topic working groups, and group members or by invited visitors from surely from discussions with our reputable overseas to present their recent works. It usually visitors. Form the local/international collaborated lasts for two hours, so that the details of the work publications, the achievements of the String FG is can be explained to some extent and participants obviously appreciable. have enough time to ask questions. After the seminar, members would usually stay for further The research topics of our group members are discussion with the speaker or with one another. primarily in four directions: (i) using the Lie this has been important for generating 3-algebra to investigate the structure of M-theory, collaborations and bonding among the group (ii) analyzing the high energy string scatterings to members. reveal the hidden symmetry in string theories, (iii) exploring the AdS/CFT duality and its application, 2. Biweekly high energy seminar at NTNU in particular to QCD, condensed matter and http://home.phy.ntnu.edu.tw/~highenergy/ superconductor physics, (iv) gravity and
167 ‹‹- Highlights of Programs This series of seminars includes topics such as Moreover, in this year, we improve our cosmology and particle physics so that the group connections with the string communities in Korea members have a chance to interact with physicists and Mainland China. We would like to strengthen from other fields. Many foreign visitors visiting these connections and extend to other Asian NTU also spend a few days in NTNU for giving countries. additional talks or further discussions. A summary of the information about our 3. Biweekly high energy seminar at NTHU visitors from 2005 can be found at http://web. phys.ntu.edu.tw/string/visitors.html. http://phys.cts.nthu.edu.tw/~string/index.html Our faculty and postdocs members in the IV. Highlights of Research Results Hsinchu area are increasing. Regular seminars 1. Lie 3-Algebra and Multiple M2-branes have been arranged since 2007. Our visitors invited by the members there usually stayed at Based on previous substantial progress, Pei- NCTS. Some of other visitors would like to visit Ming and his cooperators from Japan have NCTS for a few days. Moreover, many lectures extended the connection between D-branes in were arranged by Kazuyuki Furuuchi (there are 5 string theory and the multiple membrane theory of lectures this year) on various interesting topics. Bagger-Lambert-Gustavsson (BLG) to its full extent through discoveries of new Lie 3-algebras. 4. Taiwan String Theory Workshop It is a new development in Mathematics as well as http://phys.cts.ntu.edu.tw/string/2009/ in Physics. Their paper [8] is a “highly cited paper” according to ISI Web of Science in the The first international Taiwan String Theory “Essential Science Indicators” database. The Workshop was organized by Kazuyuki Furuuchi, space-time covariant formulation of BLG model Shoichi Kawamoto and Feng-Li Lin on 19 - 21 was explored and a simple model was suggested. January at Taiwan University. The main topics focus on the aspects of black hole, AdS/CFT and 2. High Energy String Scatterings holographic principles. Five invited speakers from The program of investigating the connection Europe, USA, Japan and Korea lectured on between high-energy scattering amplitudes and frontier progress. This has been helpful for our hidden symmetry in string theory is a long term members to discuss with experts on mainstream project from 2003 based on Jen-Chi’s earlier developments. We plan to continue this workshop works in the 90’s. Our FG members have annually. The second workshop has been arranged published about 20 papers on this subject. This on 20 - 23 December at Taiwan Normal research topic generates intense collaborations in University which has been extended to have a 4 which about half of our members are involved. days program, and 9 invited speakers will attend. 3. AdS/CFT Duality and Its Applications III. Visitors and International AdS/CFT correspondence and its possible Collaborations applications to field theories has become a Inviting favorable visitors and collaborators to creditable focused topic in the string community. visit is one principle program of our FG. A At the critical points, notable rescaling dominate part of our budget is spent on this symmetries emerge in various physical problems purpose. In particular, the string focus group has such as in condensed matter, superconductor etc. maintained a steady and close connection with the It is very difficult to calculate non-perturbative Japanese string community. Many of our visitors, aspects in the original field theory. However, the mainly from Japan, come by their own airfare and AdS/CFT correspondence provides a total we only need to support their local expanses. This different approach which allows us to deal with is way we can have about thirty overseas visitors such problems. Many of our members are working each year in the past few years. In addition, many on this subject cooperating with members of other of our members have been invited to visit several NCTS FGs. institutes. A lot of collaborations have been 4. Gravity and Cosmology generated through these academic exchanges.
Highlights of Programs -›› 168 Gravity and cosmology are close related to JHEP 0903:045 (2009) [arXiv:0901.2003 string theories. In particular, investigation of black [hep-th]]. hole physics has motivated many important [9] Chao Wang, Song He, Mei Huang, Qi-.Shu physical ideas, e.g. the holographic principle. It is Yan and Yi Yang, “Scalar Mesons and also expected to be a crucial step toward the glueballs in Dp-Dq hard-wall models,” quantum gravity. Our FG members have e-Print: arXiv:0902.0864 [hep-th]. considered higher curvature corrections on black [10] Hirotaka Irie, “Fractional supersymmetric hole physics and investigate the microscopic Liouville theory and the multi-cut matrix description of black hole entropy. models,” Nucl. Phys. B819 (2009) 351 In the 24 papers done by our FG members, 6 [arXiv:0902.1676 [hep-th]]. papers are international joint work. Moreover, the [11] Kazuyuki Furuuchi and Dan Tomino, working group on little string theory organized by “Supersymmetric reduced models with a Chuan-Tsung Chan starts to produce a paper. symmetry based on Filippov algebra,” JHEP 0905:070 (2009) [arXiv:0902.2041]]. V. Publications [12] Wen-Yu Wen, “Holographic descriptions of [1] Chiang-Mei Chen, Yuan Tsai and Wen-Yu (near-)extremal black holes in five Wen, “Giant Magnons and Spiky Strings on dimensional minimal supergravity,” e-Print: S3 with B-field,” Prog. Theor. Phys. 121, arXiv:0903.4030 [hep-th]. 1189 (2009) [arXiv:0809.3269 [hep-th]]. [13] Chuan-Tsung Chan and Wei-Ming Chen, [2] Feng-Li Lin and Shang-Yu Wu, “Non- “High Energy Symmetry of Bosonic Open relativistic Holography and Singular Black String Theory in the Light-like Linear Hole,” Phys. Lett. B679: 65-72 (2009) Dilaton Background,” accepted by JHEP, [arXiv:0810.0227 [hep-th]]. e-Print: arXiv:0905.2322 [hep-th]. [3] Sheng-Lan Ko, Jen-Chi Lee and Yi Yang, [14] Koji Hashimoto, Takayuki Hirayama and “Kummer function and High Energy String Deog Ki Hong, “Quark Mass Dependence of Scatterings,” e-Print: arXiv:0811.4502 [hep- Hadron Spectrum in Holographic QCD,” th]. e-Print: arXiv:0906.0402 [hep-th]. [4] Takayuki Hirayama and Dan Tomino, [15] Kazuyuki Furuuchi and Tomohisa Takimi, “Membrane scattering from Bagger-Lambert “String solitons in the M5-brane theory,” JHEP 0908:071 (2009) worldvolume with a Nambu-Poisson [arXiv:0812.1866 [hep-th]]. structure and Seiberg-Witten map,” JHEP [5] Sheng-Lan Ko, Jen-Chi Lee and Yi Yang, 0908:050 (2009) [arXiv:0906.3172 [hep-th]]. “Patterns of high energy massive string [16] Chuan-Tsung Chan and Wei-Ming Chen, scatterings in the Regge regime,” JHEP “Massive Vertex Operators and Conformal 0906:028 (2009) [arXiv:0812.4190 [hep-th]]. Algebra of the Bosonic Open String Theory [6] Shoichi Kawamoto, Tsunehide Kuroki and in Flat Space-time,” e-Print: Akitsugu Miwa, “Boundary condition for arXiv:0907.5347 [hep-th]. D-brane from Wilson loop, and gravitational [17] Chuan-Tsung Chan and Wei-Ming Chen, interpretation of eigenvalue in matrix model “Vertex Operators and Scattering Amplitudes in AdS/CFT correspondence,” Phys. Rev. of the Bosonic Open String Theory in the D79:126010 (2009) [arXiv:0812.4229 [hep- Linear Dilaton Background,” e-Print: th]]. arXiv:0907.5472 [hep-th] [7] Chiang-Mei Chen and John E. Wang, [18] Hsien-Chung Kao and Wen-Yu Wen, “Holographic Duals of Black Holes in Five- “Absorption cross section in warped AdS(3) dimensional Minimal Supergravity,” e-Print: black hole revisited,” JHEP 0909:102 (2009) arXiv:0901.0538 [hep-th]. [arXiv:0907.5555 [hep-th]]. [8] Pei-Ming Ho, Yutaka Matsuo and Shotaro [19] Chuan-Tsung Chan, Hirotaka Irie, Sheng-Yu Shiba, “Lorentzian Lie (3-)algebra and Darren Shih and Chi-Hsien Yeh, toroidal compactification of M/string theory,”
169 ‹‹- Highlights of Programs “Macroscopic loop amplitudes in the multi- [22] Pei-Ming Ho and Xue-Yan Lin, “A UV cut two-matrix models,” accepted by Nucl. completion of scalar field theory in arbitrary Phys. B [arXiv:0909.1197 [hep-th]]. even dimensions,” e-Print: arXiv:0910.3287 [20] Jen-Chi Lee, Yi Yang and Sheng-Lan Ko, [hep-th]. “Stirling number identities and high energy [23] Chiang-Mei Chen, Dmitri V. Gal'tsov, string scatterings,” e-Print: arXiv:0909.3894 Nobuyoshi Ohta and Dmitry G. Orlov, [hep-th]. “Global solutions for higher-dimensional [21] Chiang-Mei Chen, Jia-Rui Sun and Shou- stretched small black holes,” e-Print: Jyun Zou, “The RN/CFT Correspondence arXiv:0910.3488 [hep-th]. Revisited,” e-Print: arXiv:0910.2076 [hep- [24] Shoichi Kawamoto and Feng-Li Lin, th]. “Holographic Anyons in the ABJM Theory,” e-Print: arXiv:0910.5536 [hep-th].
Highlights of Programs -›› 170 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: Chung-Hou Cheng (National Chiao Tung University), Ying-Cheng Chen (Academia Sinica), Te-Kuei Fang (Fu-Jen Catholic University), Shin-Chuan Gou (National Changhua University of Education), Jiang-Nan Liu (Fu-Jen Catholic University), Wei-Chi Liu (National Taiwan Normal University), Yi-Wei Liu (National Tsing Hua University), Wen-Chin Wu (National Taiwan Normal University)
I. Brief Description laser, cold atom experiments, and quantum Group size: optics etc. II. Activities Cross-Strait AMO Workshop: ctive faculty members are about 20, In Oct. 2008, we hosted a cross-strait Atomic- including experimentalists. Molecular and Optical Physics Workshop in Goal: National Central University, organized by Tai- Shun Yih. We invited several important theorists 1) To encourage more cooperation between as well as experimentalists in AMO fields from faculty in this community, including mainland China to interchange research results cooperation between theorists and and experiences. It was very successful and experimentalist. therefore will be held again in the Institute of 2) To attract more researchers/ students to join to Physics, Chinese Academy of Science, in Dec. form a stable research environment. 2009. We plan to make it a regular annual meeting so that more interchange or connection can be 3) To enhance the research quality by actively made in the AMO community of Taiwan and cooperating with international frontier Mainland China. researchers. International Workshop: Research direction: In the end of March 2009, we held an (1) Strongly correlated effects in cold atoms/ International Workshop on Ultracold Atoms and molecules, Molecules in National Tsing-Hua University, (2) Dynamical properties of Weakly interacting organized by Daw-Wei Wang. We invited several Bose gases, world-leading-edge theorists and experimental groups to introduce their work on ultracold atoms (3) Atomic structure theory and spectroscopy. and molecules. This includes Eugene Demler Besides these three major subjects, we also (Harvard), John Bohn (JILA), Masahito Ueda partially support researches in high intensity (Tokyo U.), Miguel Cazalilla (DIPS, Spain),
171 ‹‹- Highlights of Programs Tilman Pfau’s group (Stuttgart), H. Nergel’s group join this community. (U. Innsbruck) and Jun Ye’s group (JILA) etc. In the afternoon of 3/27, we had a satellite meeting III. Visitors and International for our local researchers to present their works in cooperation front of our invited speakers and got valuable Visitor in the past year: In the previous year feedback. Most of our speakers also stayed for a (Nov. 2008-Oct. 2009), we invited Prof. Eugene few days longer to interact with other researchers Demler (Harvard), John Bohn (JILA), Masahito or to visit other institutes (NTHU,NCTS, IAMS Ueda (Tokyo U.), Miguel Cazalilla (DIPS, Spain), and NCTU). We believe it was a successful to stay NCTS/NTHU for a few days before or workshop and will continue it. after the International Workshop of ultracold Group-participation of ICTP cold atom atoms/molecules. We had a chance to discuss conference: various directions with local community. We also invited Prof. Guo-zheng Wu from Tsing-Hua U. In May 2009, we organize a group of people (5 (Bejing) as a long term visitor (three months). professors, 2 postdocs, and 4 students) to Prof. Wu is an expert in molecular dynamics and participate the Ultracold atom conference in Raman spectroscopy, and provides two short-term International Center for Theoretical Physics classes about group theory and chaotic dynamics. (ICTP), Trieste, Italy. Our focus group provided In June, we also invited Mr. Pingnan Ma, a financial support for three junior researchers student of Fu-Chun Chang and M. Troyer in Hong (postdocs and junior professor). We also got Kong University. Ma gave a series of lectures connected with Prof. G. Shlyapnikov as well as about worm algorithm in quantum Monte Carlo Prof. E. Demler etc. for deeper discussion. Such method. In Oct., we invited Prof. Makoto Tsubota format can encourage local researchers to share (Osaka City U., Japan), who is a world expert in the same vision and enhance the possible quantum fluids and will collaborate with Prof. collaboration in an advanced topics. Shih-Chuan Gou in NCUE. Besides, we also had a Sending students outside for learning quantum chance to invite Dr. K.-K. Ni (JILA) in Nov. to Monte Carlo method: talk about her pioneering experimental work in In July 2009, we sent two students in NTHU to polar molecules, which has been one of the most go to Hong Kong U. to learn a powerful numerical important subjects in ultracold atom systems. method, quantum Monte Carlo in worm Finally, Dr. Yu-Ju Lin from NIST also visited us algorithm. After three weeks, we could build up and presented her important work of artificial our own code and becomes one of a few groups in gauge field in cold atoms. the world (3-5) to have such world’s fastest QMC International cooperation: D.-W. Wang code to exactly calculate many-particle quantum (NTHU) recently has collaboration with Prof. E. phases of bosonic particles in optical lattice. We Demler (Harvard) on dipolar atoms, with G. are going to have the first quantitative comparison Shyalpnikov (LPTMS) on supersoilid phase in in the world between ab inito calculation and in polar molecules, with Cheng Chin and Pingnan situ experiments (data is from Cheng Chin’s group Ma on the first comparison between QMC and the in U. of Chicago). in situ experiments near quantum phase transition, AMO Summer School: and with prof. S. Das Sarma (UMCP) on fermionic polar molecules. Prof. Chung-Hou th In Sep. 2009, we held the 6 AMO summer Chung (NCTU) has a collaboration with Yong school in Institute of Atomic and Molecular Study, Baek Kim (U. Toronto) on the supersolid phase in organized by Wang-Yao Cheng. This year, besides frustrated system. Prof. T.-K, Fang (FJU) of active researchers in the AMO field, we also collaborates with Prof. T.-N. Chang (USC) in invited several speakers from the AMO-related atomic structure theory. Prof. Shih-Chuan Gou industry to share the potential application of AMO collaborates with Prof. Makoto Tsubota (Osaka knowledge to this society. From students’ City U., Japan) on quantum turbulence in cold feedback, we know that this format worked very atoms. well, and will attract more perspective students to
Highlights of Programs -›› 172 IV. Highlight of Research Results the system size is increased. In the thermodynamic Exotic quantum phases of cold atoms and polar limit, we argue that the supersolid phase will molecules: become a real “ imcommensurate” phase where the ordering wave-vector is an irrational number. In recent years, systems of cold polar Quantum Turbulence in Cold atoms: molecules have been one of the most fast growing subject in cold atoms. D.-W. Wang has formed a Quantum turbulence (QT) in the trapped BEC theoretical group in NTHU to explore various has been addressed in the last few years. Recently, aspects of ultracold polar molecules. Recent S.C. Gou and collaborators have studied the important results include (1) the first theoretical hydrodynamic properties of the trapped BEC by prediction about inter-tube correlation in 1D solving the time-dependent Gross-Pitaevskii (GP) double tube systems [1], (2) the first complete equation [7-9], focusing on the dynamics of quantum phase diagram of multi-tube systems [2], turbulent flow in a 2D trapped BEC. In our recent (3) the first exact pseuso-potential for a general results, we have found that 2D quantum power-law potential in 2D system [3]. More works turbulence in trapped BEC is characterized by the are submitted to Phys. Rev. Lett. but not listed k -5/3 and k -4 scaling laws (where k is the here. wavenumber) rather than the k-5/3-k-3 ones (i.e. the Spinor condensate in optical lattice: well-known Kraichnan-Batchelor theory in 2D classical turbulence). We will then examine the M.-C. Chung and S. Yip (Academia Sinica) hydrodynamic behavior of 2D superflow in have been studying spin-1 Bose gas in optical various systems, including the dipolar BEC, two- lattice, in particular atoms with component BEC, spinor BEC, and the Fermi 23 “antiferromagnetic” interactions such as Na superfulids. [4,5]. Due to the rather peculiar effective spin- Atomic structure and spectroscopy: spin interaction, the spin ordering in such a lattice is very different from ordinary anti-ferromagnets. The efforts of his joint theoretical (T. K. Fang In the absence of magnetization, nematic at Fujen University, his Ph. D. student, J. H. Chen, (quadrupolar) ordering is expected. Phase and T. N. Chang at USC) and experimental (T. S. diagrams at both zero and finite temperatures are Yih and his experimental team at NCU) project constructed. In addition to the nematic phase, focus on the study of multi-electron effect in there are also partially polarized and fully photon-atom interaction. A detailed investigation magnetic phases. To investigate the possibility of on resonance spectra of Ca and Sr for an extended reaching the nematic state, the entropy of the energy region [10] using a B-splined based system is compared with the Bose gas without the complex rotation method was carried out with lattice. It is shown that reaching this exotic state very good agreement between theory and should be relatively easy experimentally. experiment. The publication of this work leads to Supersolid phase in triangular optical lattice: the confirmation of Ph. D. degree of J. H. Chen at Fujen University. The extension of this work to C.H. Chung and collaborators (NCTS visitors) resonance spectra in the presence of external showed via Variational Monte Carlo, Quantum electric field has also been carried out. The Monte Carlo (QMC) and spin-wave theory that preliminary result shows, again, good agreement there exits supersolid phase in the Bose-Hubbard between theory and experiment. In addition, a model with hard-core bosons on the anisotropic joint experimental (T. S. Yih at NCU, his Ph. D. triangular lattice over a wide range of parameter student J. I. Luo and a few others at NSRRC) and space in frustration [6]. The QMC results indicate theoretical (T. N. Chang at USC) investigation on the supersolid ordering wave-vector q is pinned to “column density and temperature effects on certain rational numbers as the frustration is photoionization and photoabsorption spectra” has tunned. Different ordering wave-vectors are led to new physical insight which resolves the separated by series first-order jumps in superfluid long standing difficulty on the disagreement density. The superfluid density as a function of between theory and experiment and also among frustration becomes more and more continuous as number of high precision experiments for the
173 ‹‹- Highlights of Programs extra narrow atomic resonances in He. This work known AMO theorist and is a frequent visitor of is also a part of the Ph. D. project of Mr. J. I. Luo NCTS. Prof. Lin is going to have a long-term at NCU. collaboration with Prof. Tsing-Fu Jiang (NCTU) Developing numerical method for strongly on high intensity laser-atom interaction since interacting bosons: summer 2009. However, since Prof. Lin is not officially associated with Taiwan’s community, we (1) D.-W. Wang and R.-K. Lee developed the first feel it is not appropriate to emphasize his large size numerical methods based on important work here in this year. We expect Prof. Truncated Wigner Approximation to study the Jiang’s collaboration with him will bring fruitful quantum fluctuation effects of many-body results in the next few years for our AMO focus dynamics. Using this method, they submitted group. the first paper in the world to investigate the quantum many-body dynamics of the time-of- V. Selected Publications flight experiment, which is the most important [1] C.-M. Chang, et. al., Phys. Rev. A, 79, 053630 tool in cold atom experiments. (2009) (2) D.-W. Wang and P.-C. Chen sent students to [2] Y.-P. Huang and D.-W. Wang, Phys. Rev. A. Hong Kong U. to learn worm algorithm of 80, 053610 (2009) quantum Monte Carlo calculation, the world’s [3] S.-M. Shih and D.-W. Wang, Phys. Rev. A, most efficient code in large size simulation. 79, 065603 (2009) Their ab inito results can be used to directly compare to the in situ experimental data in [4] M. C. Chung and S. K. Yip, Phys. Rev. A 79, Cheng Chin’s group (U. Chicago), showing 053617 (2009) the world’s first quantitative comparison [5] M. C. Chung and S. K. Yip, arXiv:0904.4110, between theory and experiment in quantum accepted by Phys. Rev. A. many-body physics of cold atoms (paper in [6] S. V. Isakov, et al., Europhys. Lett. 87, 36002 preparation). (2009) (3) D.-W. Wang also collaborate with Pingnan Ma [7] T.-L. Horng, C.-H. Hsueh and S.-C. Gou*, on variational Monte Carlo method, which has Phys. Rev. A 77, 063625 (2008) been applied to the strongly interacting [8] T.-L. Horng, et al., Phys. Rev. A 79, 053619 fermionic system to investigate the important (2009) problem of itinerary ferro-magnetism of [9] T.-L. Horng, et al., Phys. Rev. A 80, 023618 ultracold atoms. (2009) High Intensity laser atom interaction: [10] J. H. Chen, T. K. Fang, C. C. Chu, T.S. Yih Besides of the research work above, there are and T. N. Chang, Phys. Rev. A 80, 042509 also important works by Prof. Chi-Dong lin in (2009) Kansas State University. Prof. Lin is a world-wide
Highlights of Programs -›› 174 Focus Group on Plasma Science
Coordinators: Chio-Zong Cheng (National Cheng Kung University; email: [email protected]) Committee members: Lin-Ni Hau (National Central University), Kwo-Ray Chu (National Tsing Hua University), Ker-Chung Shaing (National Cheng Kung University), Chio-Zong Cheng (National Cheng Kung University)
I. Brief Description 2. Lin I (NCU) 3. Lin-Ni Hau (NCU) 4. Ling-Hsiao Lyu (NCU) oals: 5. Yuh-Ren Lin-Liu (NCU) 6. Kwo-Ray Chu (NTHU) 7. Chwung- Shan Kou (NTHU) 1. Organize an annual Plasma Science Workshop; 8. Tsun-Hsu Chang (NTHU) 2. Organize a summer/winter school to offer short 9. Ker-Chung Leou (NTHU) courses to students and researchers; 10. Ker-Chung Shaing (NCKU) 3. Invite short-term foreign visitors to give lectures in summer/winter school or NCTS 11. Kuan-Ren Chen (NCKU) sponsored or co-sponsored Plasma Science 12. Han-Tzong Su (NCKU) Workshop; 13. Kai-Ti Wang (NCKU) 4. Encourage participation in the Joint 14. Rue-Ron Hsu (NCKU) Conference of Asia Fusion Association and 15. Sunny W. Y. Tam (NCKU) Asia Pacific Plasma Theory Conference (APPTC) to be held in Aomori, Japan in 16. Eiichirou Kawamori (NCKU) October, 2009; 17. Ya-Hui Yang (NCKU) 5. Encourage cooperation and/or joint research 18. Yasutaro Nishimura (NCKU) projects among domestic research groups; 19. Yung-Chiang Lan (NCKU) 6. If the funding is available, we plan to invite Focused Research Topics: distinguished foreign plasma theory The focused research topics include basic researchers for a 3-month or longer term magnetized plasma physics with applications in Taiwan visit; magnetic confinement fusion plasmas and space 7. If the funding is available, we plan to establish plasmas. and conduct exchange programs with distinguished foreign plasma research II. Activities organizations. A. We organized the 2009 Plasma Science Names of Coordinators: Summer School, which was held at National Chio-Zong Cheng Cheng Kung University during Aug. 24-28, 2009. In total, 17 lecturers, who are experts on Names of Group Committee Members or Key different plasma science area, are invited from Members: Academia Sinica, National Central University The following list is in alphabetic order of first (NCU), National Chung Cheng University name. (CCU), and National Cheng Kung University (NCKU) to give lectures in the school. The 1. Chin-Ching Tzeng (INER - Institute of Nuclear lectures provide overviews of the major Energy Research) applications of plasma science and technology
175 ‹‹- Highlights of Programs to undergraduate and graduate students who USA): Dr. Nikolai Gorelenkov of Princeton show interest in this field. Four research Plasma Physics laboratory will visit NCKU assistants of Academia Sinica and National during Nov. 29, 2009 – Jan. 1, 2010 to Tsing Hua University (NTHU) and 45 students collaborate on energetic particle physics in from NCU, NTHU, CCU, NTU, and NCKU tokamak plasmas with Prof. C. Z. Cheng and participated in this summer school. About 20 the faculty and staff of Plasma and Space students also presented poster papers to Science Center, NCKU. Dr. Gorelenkov is a discuss and exchange their research results and world-leading theoretist in tokamak fusion ideas with other students and invited lecturers. plasmas with expertise on (1) the stability of Toroidal Alfven Eigenmodes (TAEs), B. The 2009 International Workshop on Frontiers Compressional Alfven Eigenmodes (CAEs), In Space and Fusion Energy Sciences and other Afven eigenmodes in tokamaks; (2) (FISFES), which is co-sponsored by NCTS, the stability of ballooning modes; and (3) will be held at NCKU during Nov. 30 – Dec. 3, kinetic-MHD model of magnetized plasmas. 2009. There will be 52 oral paper presentations Dr. Gorelenkov will also attend the 2009 and 25 poster papers. Experts in space plasma FISFES Workshop to give an invited talk. He and fusion sciences around the world will will also interact with research staff and gather in Taiwan and 32 world-leading plasma students at NCKU. Because of limited budget experts from foreign institutions will attend the of the Plasma Focus Group in 2009 from workshop and give invited talks. It is a great NCTS we provide Dr. Gorelenkov with a very opportunity for our young scientists and small partial support of his housing expense students to learn new trends in frontiers of by using the NCTS fund. space and fusion plasma sciences and technologies and exchange ideas with these B. Professor Kuei-Jen Lee (professor of scholars. In total, about 70 scientists and 30 Department of Communication Engineering in students have registered to attend this event. Oriental Institute of Technology): Prof. Lee was invited as a domestic visitor during the C. The biweekly seminars and meetings on winter vacation in 2009. Prof. Lee is an expert “Subwavelength photonics with nano- on simulation and designing of optical devices, structured plasmonic metamaterials” were photonic crystal simulation, etc. During the organized by Prof. Kuan-Ren Chen. visit, she started the collaborative work of the Subwavelength photonics is a research area of near-field characterization by subwavelength multi-disciplines, involving physics, electro- plasmonic double slits with Professor K. R. optics, materials, mechanical, chemical Chen, Professor K. Y. Kim and Mr. J. S. Hong. engineering and many other disciplinary. After the visit, they presented two papers Currently, the active participants include seven entitled ‘Near-field characterization on light NCKU professors and their students under the interference formed by subwavelength above mentioned disciplines. External and plasmonic double slit of finite length using 3D internal speakers are invited with topics FDTD method’ and ‘Near-field including nanoimprinting, field enhancement characterization on light emanated from in metal nanoparticle arrays, subwavelength subwavelength plasmonic double slits’ in the focusing, nano-structure fabrication, etc. 4th International Conference on Besides the benefits of introducing new fields Electromagnetic Near Field Characterization and new techniques that the routine seminars and Imaging (ICONIC 2009), Taipei, Taiwan. and meeting brought, they also provide an opportunity for the collaborators to meet and discuss with each other. IV. Highlights of Research Results Because the NCTS headquarter informed us to III. Visitors and International use the very limited budget of the Plasma Focus Collaborations Group (about NT$ 90,000 out of NT$600,000 total budget) to support the Sub-wavelength A. Nokolai Gorelenkov (Princeton Plasma photonics research activity led by Prof. Kuan-Ren Physics laboratory, Princeton University,
Highlights of Programs -›› 176 Chen, we have only NT$480,000 left to conduct to attend the 2009 Fall AGU meeting, which is our main focused plasma science activity. We held at San Francisco during Dec. 14-18, 2009. have concentrated our activity in organizing a Dr. Marty Chou will present a paper on “Modeling plasma science summer school and an of Saturn’s magnetosphere based on satellite international workshop on space and fusion observation data.” Dr. Marty Chou is also in the plasma sciences. We have also established process of completing a paper on “Equilibrium collaboration with Dr. Nikolai Gorelenkov of model for Saturn’s magnetosphere” for Princeton Plasma Physics Laboratory, who will submission to J. Geophysical Research in visit Taiwan during Nov. 29, 2009 – Jan. 1, 2010 November, 2009. to collaborate on theory of energetic particles in tokamak fusion plasmas, and we will use NCTS V. Publication fund to provide partial support of the housing [1]. M. Chou and C. Z. Cheng, A 2D equilibrium expense for Dr. Gorelenkov. We also plan to model for Saturn’s magnetosphere, to be provide NCTS foreign travel fund to support Dr. submitted to J. Geophys. Res. (2009). Marty Chou, an NSC postdoc stationed at NCKU,
177 ‹‹- 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 Huan University), Chi-Yee Cheung (Academia Sinica), Chung-Hsien Chou (National Cheng Kung University), Li-Yi Hsu (Chung-Yuan Christian University), Chopin Soo (National Cheng Kung University), Zheng-Yao Su (National Center for High-Performance Computing), Wei-Min Zhang (National Cheng Kung University)
I. Brief Description is an emerging research and education frontier that has generated a great deal of interests and stimulated novel potential applications for the last decade. The 4th workshop on QST brought he main mission of the QIS focus group is together both theorists and experimentalists in to build a platform of communication and this area to give lectures and present their discussion for researchers in this area in Taiwan. recent findings. One of the major aims was to In the last few years, we have brought QIS promote and enhance research activities, researchers in Taiwan to work and discuss interactions and collaborations among the research together and to hold activities, such as participants. scientific seminars, workshops and short-term 2. To enhance the international visibility, we schools. We have also been seeking to establish participate in organizing "Conference on links and exchanges as well as to initiate Computational Physics 2009" in Kaohsiung collaborations with other QIS researchers during Dec. 15 ~ 19, 2009. There will be two worldwide. sessions for Quantum Information Science. Focused research topics: High-profile foreign researchers in this field, Prof. J. I. Cirac, Prof. R. Fazio, Prof. G. Vida, Quantum Decoherence, Quantum Prof. A. P. Young and Prof. H. Q. Lin, will give Measurement, Quantum Entanglement, Quantum lectures not only in the conference, but also in Computation and Quantum Communication. the following workshop to be held from Dec. 19 ~ 20, 2009 at NCKU. Therefore, it is II. Activities and Beneficiaries expected to attract many participants, including • Activities faculties, postdocs, and students. 1. “The 4th Workshop on Quantum Science and 3. The workshop in December is jointly organized Technology” at Taichung, Sep. 9 ~ 11 (2009). by two focus groups: QIS focus group and 2. Workshop on Quantum Information Science NMSCP focus group. The aim of this and Many-Body Physics, NCKU, Dec. 19 ~ 20 workshop is to bring together researchers from (2009). quantum information science and quantum many-body physics, to discuss recent advances 3. Mini-workshops and seminars at NCKU, NTU, in quantum many-body systems from the and CYCU. perspectives of quantum information science. It • Beneficiaries is expected that new ideas can be generated via such an interdisciplinary activity. 1. The Quantum Science and Technology (QST) • Training of young-generation physicists
Highlights of Programs -›› 178 1. Financial supports for international Prof. Yan (Hong-Kong) and Prof. Jin conferences (Hangzhou) Projects or Activities: (1) Mrs. Nien-En Wang (NCKU), Chung-Chin Transient quantum transport problems in Jian (NTU) and Shang-Yu Huang (NTU). nanoscale devices. The 3rd Int. Workshop on Solid-State Quantum Computing & Hong Kong Forum QIS members: Prof. C. Y. Cheung on Quantum Control Collaborators: Prof. Zhang (Anhui) (2) Supports students to attend the conference Projects or Activities: CCP2009 in Kaohsiung. Quantum teleportation. III. Visitors and International QIS members: Prof. L. Y. Hsu Collaborations Collaborators: • Visitors Dr. Hsieh (Japan) Projects or Activities: 1. Prof. B. L. Hu, Univ. of Maryland, USA (June Entanglement in entanglement-assisted 2009) quantum low-density parity-check codes. 2. Dr. Mintert, Universitat Freiburg (Sep. 17, QIS members: Prof. L. Y. Hsu 2009 ~Sep. 25, 2009) Collaborators: 3. Dr. D. E. Chang, California Institute of Prof. Long (Beijing) Technology, USA (Feb. 11 ~19, 2009) Projects or Activities: Quantum secret-sharing protocol. 4. Prof. Makhlin, Landau Institute for Theoretical Physics, Russia (Feb. 12, 2009 ~Feb. 14, 2009) QIS members: Prof. C. H. Chou and Prof. Y. N. Chen 5. Prof. Cabello, Universidad de Sevilla, Spain Collaborators: (Feb. 12, 2009 ~Feb. 14, 2009) Prof. Buchleitner (Freiburg) 6. Dr. Lambert, Riken, Japan (Feb. 9, 2009 ~ Feb. Projects or Activities: 15, 2009) (1) Research Visit: Prof. Chou and Prof. Chen visited Freiburg (July 2009). Dr. Mintert 7. Prof. X.Z. Yuan, Shanghai Jiao Tong visited NCKU (Sep. 2009). University, China (Jul. 28, 2009~ Sep. 5, (2) Mr. G. Y. Chen (student to Prof. Y. N. 2009) Chen) visited Freiburg for one year. • International Collaborations QIS members: Prof. Y. N. Chen QIS members: Prof. W. M. Zhang Collaborators: Collaborators: Prof. Nori and Dr. Lambert (Riken) Prof. Aharony and Prof. Entin-Wohlman Projects or Activities: (Isarel) Research visiting: Prof. Y. N. Chen and Dr. Projects or Activities: Lambert. Focus on Quantum measurement. Dephasing problem in quantum transport and QIS members: Prof. H.-S. Goan molecular electronics. Collaborators: QIS members: Prof. W. M. Zhang Prof. X.Z. Yuan and Prof. K. D. Zhu (Shanghai Collaborators: Jiao Tong U.) Prof. Gurvitz (Isarel) and Prof. Li (Beijing) Projects or Activities: Projects or Activities: Research visit: Prof. X.Z. Yuan visited NTU Magnetic field switching in parallel quantum (August 2009) dots and related problems. QIS members: Prof. W. M. Zhang IV. Highlights of Research Results Collaborators: • Research results
179 ‹‹- Highlights of Programs I. Decoherence and Measurements 2. Entanglement dynamics in relativistic motions and macroscopic quantum 1. Mon-Markovian decoherence theory for phenomena double-dot charge qubit: In the work[10] collaborated with Dr. S.Y. Lin We developed a non-perturbation theory for at NCTS and Prof. B.L. Hu of UMD, we describing non-markovian decoherence started to study the entanglement dynamics of dynamics of electrons in nanoscale devices. We two harmonic oscillators coupled to a extended the Feynman-Vernon influence background field with one in uniform functional theory to fermionic environments acceleration. This is an important ingredient and derive an exact master equation for the for the establishment of relativistic quantum reduced density matrix of electrons in the information theory. In our nonperturbative double dot for a general spectral density at treatment, the field will be evolving with the arbitrary temperature and bias. This should be detectors as a combined close system. a big breakthrough since Hu and co-workers in Maryland Univ derived the first exact master III. Quantum Computation and Quantum equation for quantum Brownian motion Communication (bosonic environment) in 1992 after Feynman 1. Optimal control of quantum gates for and Vernon proposed the influence functional quantum computation theory in 1963. [1]. We apply the gradient ascent pulse engineering 2. Detecting non-Markovian plasmonic band (GRAPE) optimization approach to find gaps in quantum dots using electron control parameter sequence in near time- transport optimal way for a high-fidelity controlled-NOT We show how two non-Markovian effects, (CNOT) gate in silicon-based donor spin band edge and retardation, could be observed quantum computer architectures. This CNOT in such a system. Combined with a quantum- gate has an error of about 10-6, below the error dot p-i-n junction, these effects could be threshold required for fault-tolerant quantum readout via current-noise measurements. We computation, and its operation time of 100ns is also discuss how these effects can occur in about 3 times faster than 297ns of the proposed similar systems with restricted geometries, global control scheme. It also relaxes such as phononic cavities and photonic crystal significantly the stringent distance constraint of waveguides. This work links two previously two neighboring donor atoms of 10~20nm separate topics: surface plasmons and current- reported in the original Kane's proposal to noise measurements. [6] ~30nm in which surface control gates may be II. Quantum Entanglement built with current fabrication technology. [11] 2. Criterion for faithful teleportation with an 1. Field Induced Spin Supersolidity in arbitrary multiparticle channel Frustrated Spin-1/2 Spin-Dimer Models: We present a general criterion which allows We have developed one particular one to judge if an arbitrary multiparticle entanglement based numerical method for entanglement channel can be used to teleport strongly correlated systems. In this approach, faithfully an unknown quantum state of a given the variational ground state wave-function is in dimension. We also present a general the form of tensor product state. We use 2D multiparticle protocol applicable for all iTEBD to optimize the trial wave-fucntion, channel states satisfying this criterion. [14] then use TERG to evaluate the expectation values. We first demonstrated that the method 3. Deterministic dense coding and faithful can reach high accuracy for first-order teleportation with graph states transition. We then use it to study the frustrated We propose schemes to perform the many-to- spin-dimer model and identify the regime of one deterministic dense coding and one-to- super-solid phase. Hence extend the usability many faithful teleportation with multipartite of the method to the frustrated models. [8]
Highlights of Programs -›› 180 graph states. The sufficient and necessary V. Publications condition of a viable graph state can be stated [1] Matisse W. Y. Tu and Wei-Min Zhang, Phys. as follows. For the associated graph, the Rev. B 78, 235311 (2008). reduced adjacency matrix of the Tanner-type [2] Feng Li, Xin-Qi Li, Wei-Min Zhang, S.A. subgraph between senders and receivers should Gurvitz, (EPL, 2009, in press). be invertible. Out results can be generalized to any stabilizer state, which is local equivalent to [3] Matisse W. Y. Tu, M. T. Lee, Wei-Min Zhang, some graph state. [16] Quantum Inf. Process, 8, 631 (2009). [4] J. H. An, M. Feng and Wei-Min Zhang, 4. Quantum direct communication with mutual Quantum Infom. Comput. 9, 0317 (2009). authentication [5] N. Lambert, Y. N. Chen, R. Johansson, F. We propose a new protocol capable of Nori, Phys. Rev. B 80, 165308 (2009). achieving secure quantum direct [6] Y. N. Chen, G. Y. Chen, Y. Y. Liao, N. communication with authentication. Our Lambert, and F. Nori, Phys. Rev. B 79, protocol does not require a direct quantum link 245312 (2009). between any two users, who want to communicate with each other. This may be an [7] Y. N. Chen, G. Y. Chen, D. S. Chuu, and T. appealing advantage in the implementation of a Brandes, Phys. Rev. A 79, 033815 (2009). practical quantum communication network. [8] Pochung Chen, Chen-Yen Lai, and Min-Fong [17] Yang, arXiv:0910.5081. • Invited presentations [9] C. M. Chang, C. Y. Lai, W. C. Shen, Pochung Chen, and D. W. Wang, Phys. Rev. A 79, 1. Prof. C. H. Chou (July 14, 2009) and Prof. Y. 053630 (2009). N. Chen (July 16, 2009), Science seminars at [10] S. Y. Lin, C. H. Chou, and B. L. Hu, Phys. Universitat Freiburg. Rev. D 78, 125025(2008). 2. Prof. W. Zhang, Prof. C. H. Chou and Prof. [11] D.-B. Tsai, P.-W. Chen, and H.-S. Goan, H.-S. Goan, August (2009), The 6th joint Phys. Rev. A 79, 060306 (R) (2009). meeting of Chinese physicists worldwide, [12] Md. M. Ali and H.-S. Goan, J. Phys. A 42, Lanzhou, China 385303 (2009). 3. Prof. W. Zhang and Prof. H.-S. Goan, [13] W. Zhang, Y.M. Liu, Z.J. Zhang, C.Y. December (2009), The 3th International Cheung, Accepted by Optics Communi. Workshop on Solid-State Quantum Computing, (2009). Hong Kong. [14] C.Y. Cheung and Z.J. Zhang, Phys. Rev. A 80, 022327 (2009). [15] C.Y. Huang, I. C. Yu, F. L. Lin, and L. Y. Hsu, Phys. Rev. A 79, 052306 (2009). [16] Li-Yi Hsu and Keng-Shuo Wu, Phys. Rev. A 80, 042324 (2009). [17] C.-A. Yen, S.-J. Horng, H.-S. Goan, T.-W. Kao, Y.-H. Chou, Quantum Infom. Comput. 9, 0376 (2009).
181 ‹‹- Highlights of Programs Highlights of Programs
Topic Program on Laser/Maser Plasma Science
Coordinator: Shih-Hung Chen (National Central University; email: [email protected] ) Committee members: Kwo-Ray Chu (National Tsing Hua University), Wei-Cheng Huang (National Central for High-Performance Computing), Yu-Ren Linliu (National Central University), Ling-Hsiao Lyu (National Central University), You-Hsien Shiau (National Chengchi University), Gih-Yih Tsaur (Tunghai University), Jyhpyng Wang (Academia Sinica)
I. Brief Description been resulted in great advancements. The recent investigations conducted in NTHU group also awake a general interest on a relatively dormant subject, gyrotron backward wave oscillator (gyro- he Laser/Maser Plasma Science Topical BWO). Program is coordinated by Prof. Shih- Facilitated by these two groups, a “theoretical Hung Chen from National Central University. The study and simulation group” which has intensive program plays a major role to integrate the related collaborations with the two groups is forming. The theoretical research and training activities of two new group comprises participants from several research groups, whose research topics include the research institutions and universities. The laser plasma physics and relativistic electronics. operations of this group are concordant with the The first group, High-Field Physics and goals and vision of the NCTS program. Over the Ultrafast Technology Laboratory at the Institute of past few years, the group has built capacities of Atomic and Molecular Sciences, Academia Sinica, the theoretical analysis and the large-scale constructed a high-quality 10-terawatt laser simulation for the study of the laser/maser plasma system in 2004 and complete the construction of a science. The forming of the topical program can 100-TW laser at National Central University by provide a more solid foundation and operation the end of 2007. They utilized the laser facility to mechanism for the theoretical and simulation conduct pioneering experiments in high-field group. science. These three groups represent the local The second group, High Frequency community of laser/maser plasma science, and Electromagnetic Laboratory at National Tsing Hua they have gained lots of scientific achievements of University, has been devoted to the study of the the international visibility. The proposed laser/ Electron Cyclotron Maser during the past twenty maser plasma science topical program intends to years. They have taken the lead in the establish a plateform to serve the community and international microwave/plasma community by to couple all sub-areas through common interest in addressing these physics groundwork that have simulation, theory and education, and to interact with experimentalists under the support of NCTS.
Highlights of Programs -›› 182 The key members include Prof. Kwo Ray Chu supplementary training activity, which fills the (National Tsing Hua University), Prof. Yu-Ren gap left by the cancellation of the original summer Linliu (National Central University), Prof. school in the year, for the topical program. During Jyhpyng Wang (IAMS, Academia Sinica), Prof. the summer school, we also invited Prof. Zeng- Gin-Yih Tsaur (Tunghai University), Ling-Hsiao Ming Sheng (Shanghai Jiao Tong University, P. R. Lyu (National Central University), Weicheng China) to visit National Central University and Huang (Ntl. Center for High-performance discuss about the recnet progresses of the Computing) and Prof. You- Hsien Shiau (National computational study of the laser-based proton Chengchi University). There are 11 researchers/ accelerators with him. professors, 2 post doctors, 10 Ph.D. students and The other important activity is 2009 Plasma 17 Master students joined in the program. Science Summer School held by Plasma and The laser/maser plasma physics is the area to Space Science Center, National Cheng Kung study the highly nonlinear and highly relativistic University during Aug. 24 - 28. The school system. The coupling between the electromagnetic provided a wide spectrum of plasma-related field and various degrees of freedom of plasma is courses, including the fusion technology, space highly nonlinear, hence parametric instabilities are plasma physics, laser plasma science and ubiquitous. Whether the effects are useful or micorwave techniques et al. Our students can detrimental, it is essential to control these learn different plasma-related research topics, instabilities. The onset of instability can usually be which can stimulate them to study their own studied analytically by perturbation techniques, problems with a broader point of views. but the saturation or stabilization of these effects In order to complement the local plasma may not. Computer simulation can serve as physics courses, we invited Prof. Liu Chen numerical experiments to explore the control (University of California, Irvine, USA) to give methods with low cost and great flexibility in the lectures on nonlinear plasma physics during May parameter space. The nonlinear theory is an 1, May 4 and Sep. 1 - 4. The contents of the essential guideline and acts as the complementary lectures include most essential topics for the tool for the study of these problems. In the nonlinear analysis of the plasma physics, e.g. program, the focused research topics includes the nonlinear mode-mode coupling, parametric laser wakefield electron accelerators, laser-based interactions, and drift wave turbulence et al. The proton accelerators, radiaiton sources based on the nonlinear analysis can provide more precise laser-plasma interactions and electron cyclotron guideline for the computer simulation and resonance and plasma-based nonlinear optics et al. experimental designs, as compared to the linear theory. Laser/Maser Plasma interaction is a highly II. Activities nonlinear problem, the lectures provide the The major activity of the topical program is the students and researchers a starting point to apply laser plasma summer shcool. Due to the the nonlinear analysis on the study of Laser/Maser reorganiztion of the courses of the summer school plasma science. and some similar summer shools were held in Taiwan during the summer vacation, the annual We also held a particle-in-cell training course summer shool was cancelled this year. Even during Jul. 21 - 23. The purpose of the training thoguh, some of key members were helping course is to help students and researchers get organize 4th Asia Summer School and familiar with the simulation technique and start to Symposium on Laser-plasma Acceleration and apply the particle simulation on their research Radiation (http://www.hope.nthu.edu.tw/4th_ works after the course. ASS/), which was held at NSRRC of Taiwan In order to keep our students and researchers during Aug. 17 - 21, 2009. They also gave lectures updated with the newly development of the laser/ at the summer school. The students and maser plasma science, we held a journal club by researchers learned the fundamental knowledge of reporting the newest publications on the journals laser plasma physics and the newest development of high impact from Mar. 2009. The activities are of the field. So the Asia summer school is a still regularly held at National Central University.
183 ‹‹- Highlights of Programs III. Visitors and International discussed the possibility of future collaboration on Collaborations the laser fusion project. Prof. Liu Chen came to visit us during the The topical program supported the visit of Dr. beginning of May and Sep., 2009. He gave Mikhail Glyavin (Russian Academy of Sciences) lectures at National Central University during his at National Tsing Hua University during Jun. 9 - stay and had discussions with local researchers 13, 2009. Dr. Glyavin was hosted by Prof. T. H. about the apllication of the nonlinear analysis on Chang and his major research work is to develop the study of the laser/maser plasma interactions. the terahertz radiation sources based on the We decided to start the collaborations from the electron cyclotron maser (gyrotron). Recently, Dr. analysis of the gyrotron backward-wave Glyavin developed a pulsed magnetic field up to oscillators (gyro-BWO) and obtain the possible 40 Tesla, which was applied to generate high- physical reasons for its non-stationary behaviors. power coherent terahertz radiation (Phys. Rev. The experiences of the nonlinear analysis will be Lett. 100, 015101 (2008)). He gave a talk, which extended to other topics, e.g. the relativistic high title is "review of powerful pulsed terahertz harmonics generation from the interactions gyrotrons," at NCTS on Jun. 10. between the laser and solid targets et al. We are collaborating with Prof. Ang Lay Kee IV. Highlights of Research Results (Nanyang Technological University, Sigapore) and 1. A versatile three-beamline two-wavelength Dr. Koh Wee Shing (Institute of High) to study the 100-TW laser system with high stability and space charge effects in a LWFA. The research spatiotemporal quality has been constructed in works require the extension of the electrostatic National Central University. The laser will be model for evaluating the space charge limiting used for the development of advanced laser- current to the relativistic electromagnetic model. wakefield electron acceleration, proton Our computer simulation results can provide a acceleration, soft x-ray laser, high-harmonic guideline for the improvement of their old theory. generation, plasma nonlinear optics, etc. (Hsu- We invited Dr. Koh Wee Shing to visit NCU and Hsin Chu, invited talk at 2009 Cross-Strait our discussions made the works well-organized. Symposium on the Fusion Energy and Plasma Dr. Koh also introduced his team works on the Science, CSS- FEP) study of surface plasmonics, and we plan to apply 2. Relativistic optical rectification is analyzed by the particle simulation on the study of the utilizing the analytical solutions of the three- nonlinear behavior of the surface plasmonics. dimensional collective electron motion driven We also collaborate with Prof. Chuan Sheng by a high-intensity pulsed Gaussian beam. Liu (University of Maryland, USA) on the study Under the paraxial expansion the slowly of the LWFA and laser-based proton accelerators, varying components in the nonlinear and the recent works have been submitted to oscillation of electron density and electric Physics of Plasmas. The theoretical analysis for current are extracted from the solutions first, the beam energy scaling of the LWFA will be then they are used in the Maxwell equations as published soon. the source terms to calculate the terahertz electromagnetic fields as functions of the The joint works with scientists in the Institute spatiotemporal amplitude of the pulsed of Plasma Physics, Chinese Academy of Sciences, Gaussian beam. The analysis compares well Hefei, are to develop a fully relativistic Fokker- with available experimental data and computer Planck code for studying electron cyclotron wave simulations, and demonstrates the general heating in tokamak, an axisymmetric magnetic scheme of paraxial expansion for the analysis confinement device for magnetic fusion energy of relativistic nonlinear optical interactions. research. The code can also be used to study the (Jyhpyng Wang, presented at OCPA6, problems of electron transport in fast-ignition LanZhou, China, 2009) plasmas in laser fusion. Professor Z. M. Sheng of the Institute of Plasma Studies, Shanghai Jiao 3. We are studying the thermal relaxation Tong University visited us in August. We have phenomenon due to electron-ion collision in
Highlights of Programs -›› 184 fully ionized plasmas by using a 1-dimensional V. Publications PIC simulation code. The collision is modeled [1] Beam Energy Scaling of a Stably Operated by successive small-angle scatterings of Laser Wakefield Accelerator, Shih-Hung Chen electrons by a fixed positive ion background et al, submitted to Physics of Plasmas. using a Monte-Carlo procedure. The [2] Relativistic optical rectification driven by a breakdown of the ND2 law in the 1-D high-intensity pulsed Gaussian beam, Gin-yih simulation is also observed. The phenomenon Tsaur and Jyhpyng Wang, Phys. Rev. A 80, of numerical thermalization in the PIC 023802 (2009). simulation of a Lorentz plasma is investigated. The thermalization time of the simulation is reduced in the presence of the additional Monte-Carlo collision which simulates the electron-ion pitch angle scattering. (Yu-Ren Linliu, invited talk at 2009 Cross-Strait Symposium on the Fusion Energy and Plasma Science, CSS- FEP)
185 ‹‹- Highlights of Programs Highlights of Programs
Initiative (sub-project I): Establish GPU-based Supercomputing Platform
Coordinator: Ting-Wai Chiu (National Taiwan University; email: [email protected]) Committee members: Tzi-Hong Chiueh, Ying-Jer Kao (National Taiwan University)
I. Brief Description Center for Quantum Science and Engineering (CQSE)[http://cqse.ntu.edu.tw] on the innovative idea of establishing a GPU cluster as a supercomputing platform in large-scale scientific uring the last two years, the GPU computations. The 2009 budget of GPU initiative (Graphic Processing Unit) on a graphic only constitutes of the hardware money. It has card has emerged as a powerful device for high- been used in acquiring 4 units of Supermicro performance computing, even though it was servers, as the hosts of the 8 units of Nvidia Tesla primarily designed for the graphic display and S1070 (with 32 GPUs, and 32 x 4 Gbytes). Our computer games. With a price of NT$14,000, a objective in 2009 is to set up the hardware, and to graphic card (e.g., Nvidia GTX285) can deliver develop the CUDA codes for the large-scale greater than 100 Gflops (sustained) computing computations in lattice QCD, quantum spin power, which is 10-100 times faster than a single systems, and cosmology. CPU. The reason behind the overwhelming floating-point capability of GPU is that GPU is II. Activities designed for intensive and highly parallel In “The 2009 Taipei Workshop on Lattice QCD computations (i.e., graphics rendering ), in which (December 13-15)” http://twqcd09.phys.ntu.edu. more transistors are devoted to data processing tw/ , we have invited the renown GPU expert, Dr. rather than data caching and flow control. Thus a Mark Harris to give a series of lectures on CUDA GPU cannot stand alone in a computer system, but programming and optimization. Dr. Mark Harris’s only works as a powerful floating-point lectures will attract a lot of participants from coprocessor of the CPU. With a GPU card, one many other fields in science and engineering. can immediately turn any PC into a personal supercomputer. This opens up a great opportunity III. Highlights of Research Results for many scientific and engineering problems (A) The GPU supercomputer at CQSE which require enormous amount of number- crunching power. Recall that in the past 50 years, We have successfully set up the GPU cluster at every 10 times jump in computing power CQSE (see Fig. 1), constituting of 16 units of motivated new ways of computing, which in turn Nvidia Tesla S1070 (with total 16 x 4 GPUs, 16 x led to many scientific breakthroughs. 64 Gbytes, and peak 64 Teraflops) connecting to 16 servers (with total 16 x 2 Intel Quadcore CPUs, The goal of the NCTSn GPU initiative is to and total 16 x 32 Gbytes). This is the first GPU collaborate with the Subproject 5 of the NTU supercomputer successfully installed in Taiwan. It
Highlights of Focus Group -›› 186 We proposed an alternative large-scale structure formation model, where the dark matter particles are very light such that they are condensed in the Bose-Einstein state. It essentially solves the time-dependent Schrodinger equation with a self-consistent, time-dependent gravitational potential. This work incorporates some critical solvers developed in (1), such as the Poisson solver and the AMR scheme. We have finished the coding and testing of this code in Nov. 2009, and are ready to execute a few production-run simulations in the near future.
(D) Tensor Network Method for Quantum Spin System We have developed efficient tensor contraction codes for tensor network method to study frustrated spin systems in two and three dimensions. We have achieved at least 20x speedup for the tensor contraction kernel, and we are in the process of finalizing the full version Fig. 1 The GPU supercomputer at the Center of Quantum code. Science and Engineering (E) Large-scale simulation of unquenched lattice has been in production runs since February 2009. QCD We have developed highly efficient CUDA We have developed a highly efficient CUDA (Compute Unified Device Architecture ) codes for code for Monte Carlo simulation of lattice QCD the computationally challenging problems in with exact chiral symmetry, attaining sustained quantum chromodynamics (QCD), quantum spin 140 Gflops for a single GPU. Also, we are the first systems, and astrophysics. With our GPU group around the world performing a large scale supercomputer, we have attained 8 Tflops simulation of lattice QCD with a GPU cluster. So (sustained) at a price NT$5,000,000. Thus we can far, there are only 3 lattice groups tackle many large scale computations, without (RBC+UKQCD, JLQCD, and TWQCD) around using the prohibitively expensive supercomputers. the world who are capable to simulate lattice QCD Note that the price/performance ratio of our GPU with exact chiral symmetry. supercomputer is less than 1/100 of a conventional supercomputer (e.g. IBM BlueGene/L), and only IV. Outlook 1/10 of the power consumption of the IBM BlueGene/L. One of the main objectives of 2010 is to develop highly efficient CUDA codes for (B) AMR for Fluid and Gravity MultiGPUs under MPI and OpenMP, for lattice We have developed a generic parallel GPU QCD, quantum spin systems, and cosmology. We acceleration Adaptive-Mesh-Refinement (AMR) plan to hire a postdoc under the Subproject 5 of code for fluid and gravity, with the application to CQSE, and 2-3 graduate research assistants, cosmology large-scale structure formation. It is focusing on innovative numerical algorithms and the first of its kind in computational physics, and CUDA optimization. We outline our 2010 work it has been accepted for publication in plan as follows. Astrophysical Journal Supplement (Impact (1) We will organize intensive training courses factor=13). aiming for graduate students and postdocs. (C) Large-Scale Structure Formation Model Our purpose is to speed up the learning processes of programming GPU, and build a
187 ‹‹- Highlights of Focus Group team of researchers who will become the core impossible in the CPU version of our code of the future GPU research. due to the massive CPU time needed. In addition, we will develop GPU version of (2) For the Adaptive-Mesh-Refinement (AMR) classical Monte Carlo codes, which has been code for fluid and gravity, we will incorporate proven successful in Ising models. Our goal is the dark matter particles in this hydro+gravity to further push the methods to systems with code as well as to improve the fluid solver impurities and frustration. with a higher-order Riemann scheme. (6) For the Monte Carlo simulation of lattice (3) We will continue the production run of time- QCD with exact chiral symmetry, we will dependent Schrodinger equation with a self- continue the production runs for the consistent and time-dependent gravitational (2+1)-flavor QCD with optimal domain-wall potential, where the mesh refinement will quarks. Also, we will develop the CUDA code achieve up to 10 levels (with 2**10 finer for the study of a Technicolor theory with Nf meshes) at the highly collapsed regions so as techniquarks, to find out whether there is a to resolve the core property of dark matter conformal window at large Nf, which is one halos. In addition, a stellar disk will be of the most interesting topics in the strong included in the dark matter halo to examine interaction physics, relating to the Large how well a stellar disk may survive in the Hadron Collider (LHC). presence of the halo density granulations arising from the uncertainty principle. V. Publications (4) We will port the computational intensive [1] “GAMER: a GPU-Accelerated Adaptive codes from CPU to GPU. For example, to Mesh Refinement Code for Astrophysics”, identify the unbound particles in a N-particle Hsi-Yu Schive, Yu-Chih Tsai, Tzihong system, where of order N**3 computations Chiueh, to be published in Astrophysical are required, with N ranging from 10**5 to Journal Supplement (2009). 10**6. [2] “TWQCD’s dynamical DWF project”, T.W. (5) We will use our efficient tensor contraction Chiu, T.S. Guu, T.H. Hsieh, C.H. Huang, Y.Y. CUDA codes to study the frustrated J1-J2 Lee, Y.Y. Mao, K. Ogawa, P.K. Tseng, to be Heisenberg model by increasing the virtual published in PoS (LAT2009)034. dimension and lattice sizes of systems. This is
Highlights of Focus Group -›› 188 Initiative (sub-project I): Build-up of Theory Support for LHC Physics
Coordinator: George Wei-Shu Hou (National Taiwan University; [email protected])
I. Brief Description part of the NTU 拔尖 Project “Scaling the Particle Frontier”, which can be viewed as the matching fund from NTU for this Initiative through MOE. No new routine seminar activity is directly oal: As titled. introduced, as one enjoys the forum of contact Coordinator: George W.S. Hou already established in the past, the Particle Key Members: Xia o-G a n g H e, F r a n c e s c a Physics Journal Club held at Monday lunch time at NTU, and sponsored by LHC FG. This JC is an Borzumati (NTU拔尖), Johan Alwall (NCTSn); unusual setting in Taiwan, where both theorists also Hsiang-nan Li and Tzu-Chiang Yuan of AS and experimentalists are present in good numbers, Plus: close contact with experimental colleagues ranging from mature researchers to beginning (mostly CMS) Kai-Feng Chen, Paoti Chang, students. It was established during the Belle era, Minzu Wang, Bob Hsiung (NTU) Yuan Chao, which is exemplary for the good TH-EXP cross- Rong-Shyang Lu, Paolo Bartalini (NTU拔尖) fertilization. In anticipation of the LHC era , the Yuan-Hann Chang, Shin-Shan Yu, Chia-Ming Kuo JC was broadened to Particle Physics a few years (NCU) Song-Ming Wang of AS in ATLAS ago. The NTUHEP group receives significant Group Size: above, plus postdocs, visitors and funding from NSC and NTU, and has significant students, altogether over a dozen theorists manpower base. The purpose of this TH-LHC (matching with NTU拔尖Project "Scaling the Initiative is to try to replicate the success of the Particle Frontier", where the Coordinator is the Belle era, into the LHC era, to put Taiwan on the CI) map of LHC physics. Research Focus (from Phase-III 6-year proposal A special goal for 2009, as written in the of NCTS): 6-year proposal filed in late 2008 (see http://phys. Before 2012 cts.ntu.edu.tw/data/proposal.pdf), is to hold the Second Workshop on Beyond 3 Generation Help find t' and b' quarks at LHC, and Standard Model elucidate associated Flavor and CP Violation physics (other topics of course pursued). http://indico.cern.ch/conferenceDisplay. py?confId=68036 Before 2015 which is now scheduled to be held January Help elucidate the impact on CPV for BAU, 14-16 2010 on NTU campus (original date was EWSB and New Resonances, and prepare for December, but in deference to a workshop at Super B factory and ILC. CERN, it was shifted to January; this is still within the approved 2009 budget extension to II. Activities 3/2010). This is a follow-up on the first workshop, Unlike the FGs of past 5 years, the Initiative is http://indico.cern.ch/conferenceDisplay. a new concept or approach at NCTS North/ py?confId=33285, held at CERN in Sept. 2008. Physics. The purpose of this “TH-LHC Initiative” The current workshop is now subtitled “New is to bring in strong enough theory manpower, to Fermions at the Crossroads of Tevatron and enhance contact with cutting edge experiment for LHC”, because of the slow start of LHC. The mutual benefit. It also complements the Theory small scale workshop will bring in over two dozen
189 ‹‹- Highlights of Focus Group international researchers with active interests in We are delighted especially with the studying and understanding the 4th generation, to exceptional catch of Dr. Johan Alwall, a establish an “international consortium” (wording MadGraph/MadEvent author and expert, and a from 6-year proposal), with Taiwan as a main hub very good and broad particle phenomenologist, to for activity. It should be emphasized that join the TH-LHC Initiative for a 5-year term (3+2 practically all international participants will be years, as per 6-year proposal) starting 1/2010. Dr. attending the workshop using their own funds. Alwall first arrived during summer 2009 as a This is one thing we wish to introduce into Taiwan visitor from SLAC. We managed to attract him to in general, and NCTS funded meetings in stay for the 5-year assistant fellow job, rather than particular — people attend our workshop because the 3-year postdoc position that he would have it is of interest, not because their expenses are continued on to at Fermilab. This in a way already paid for ! puts NCTS North’s TH-LHC Initiative on the map. We have received very strong We also wish to emphasize that, the reason for th recommendations, in particular to help/allow Dr. targeting the 4 generation study for experiment, Alwall nurture a small start-up research group, and with heightened theory support from NCTS which is precisely the design goal of our original North, is laid out clearly in the 6-year proposal, 6-year proposal, and the timing cannot be better which received favorable review in 12/2008. for the scheduled restart of LHC for high energy With new manpower brought in during 2009 collisions in early 2010. The 5 year period of under the Initiative, we have studied CP violating 2010-2014 could be the start of a Golden Age, for asymmetries in b' → s decays, 4th generation us to take part in. As stated by one recommender decaying to dark matter, a comprehensive study of (Kaoru Hagiwara of KEK), he himself would visit b' and t' decay modes and rates, and initiated how Dr. Alwall to collaborate, and through Dr. Alwall, to distinguish 4th generation from SUSY if a a web of international collaborations and signal is found. Note that the latter two are joint exchanges with SLAC, Fermilab, IPMU, UC efforts between theory and experiment. New Irvine, UC Louvain, etc., would be established projects have also been initiated to understand and cultivated, which would be on top of our neutron EDM, study of possibility of large existing contacts. Yukawa driven EWSB on a lattice (how to define th As planned in the 6-year proposal, two 5-year the problem), elucidate CPV strength with 4 term positions have been advertised for the generation, etc. Some of these may already come TH-LHC Initiative, which appeared in the June to fruition in 2010. 2009 issue of Physics Today. This has been Students, postdocs and junior colleagues have reemphasized recently on HEPIC/SPIRES, and been sent to attend schools like Les Houches, or transmitted personally to a few leading Japanese conferences like EPS-HEP, and visiting places like colleagues, to attract Japanese applicants (which is UC Irvine, Caltech, or IPMU Tokyo, and KEK. happening). We wish to get the best applicant we can! Since the NCTS North budget, as pre- III. Visitors and International allocated by the 6-year Phase-III ad hoc review Collaborations panel of NSC at end of 2008, can support only one The two main intermediate-term visitors during 5-year term under the TH-LHC Initiative, 2009 are: Prof. Abdesslam Arhrib (April– matching from NTU university side would be October), a long time collaborator with many sought for the second position. This is one major theorists in Taiwan, including the Coordinator, responsibility of the NCTS North director, which Prof. Hou; and Dr. Johan Alwall (August, and is also the Coordinator of this Initiative. October–December; see below). Short term Please do appreciate that the aim of NCTS visitors are variably sponsored between TH-LHC North TH-LHC Initiative is to be internationally Initiative, LHC FG, and CTS of NTU (college visible, rather than just “national”. This is the true funded), where examples are Chung Kao, Hsin- nature of particle physics itself, and Taiwan ought Chia Cheng, Ian Low, and Masaya Kohda and to be not self-limiting. Teruki Kamon.
Highlights of Focus Group -›› 190 IV. Highlights of Research Results proposal as the reason for focus, beyond just The highlight result of 2009 is the insight work supporting the set experimental agenda of the joint of the Coordinator, Prof. Hou, on the 1015 NTU-NCU analysis effort at CMS, is now well enhancement of possible CP violation strength, tested in front of world-wide erudite audiences. To as one extends from 3 generation Kobayashi- quote from the 6-year proposal: Maskawa model (2008 Nobel Prize) to a 4th I f 4 th generation is ruled out (will take ~ 5 generation: The KM structure can provide years) by our combined Exp/TH efforts, the sufficient CPV for generating the (visible) accumulated manpower would have a foothold Universe. In accord with the experimental strategy on the developments of LHC physics, i.e. of 漢中策略 (laid down in early 2006; see 6-year whatever may emerge on Mass Generation, proposal), people still frown on the 4th generation, and pursue what we have learned. But clearly, hence the paper is published in Chinese Journal of in preparing in advance for uncovering the 4th Physics (47, 134 (2009)). But it is our judgment generation, if we help find it and elucidate its that this observation alone makes the 4th generation properties and impact, NCTS-North/Physics extremely attractive. Prof. Hou has focused his would no doubt become a world-renowned work in the past 4 years on insights of B physics Center. No other way can approach this level and CP Violation in regards the 4th generation, and of recognition. the work is now quite visible. The prediction for → But of course, the manpower build-up is not large and negative CP phase in Bs J/ψ φ is th currently being vigorously pursued by the CDF limited to 4 generation physics. Not only we would carry out a broad agenda interfacing with and Dzero experiments at Fermilab, and will soon 拔 be superseded by the LHCb experiment at LHC. LHC FG (as well as the theory arm of the NTU 尖計畫), the purpose is to bring the NCTS North The Coordinator, Prof. Hou, has taken 2009 setting into the LHC era, which would last at least “campaigning” worldwide for the 4th generation for the next 20 years. cause, giving seminars and colloquia, many of which invited, at IPMU, Washington (Seattle), V. Selected Publications SLAC, Virginia, William and Mary, Fermilab, [1] The aforementioned Chin. J. Phys. 47, 134 Chicago, Ecole Polytechique, CERN, Osaka, (2009) would likely become eminent (and in a Bonn, UC Irvine, UCLA, and Caltech; and Taiwan journal). Another worthy work is domestically at AS, NTU, NTHU, NCU and Phys. Rev. D 80, 076005 (2009). Several NCKU. Presentations have also been given in manuscripts would appear by December conferences and workshops at CERN, and at review time. ICHEP08 and FPCP09, with associates giving presentations at EPS-HEP09, as well as [2] The Coordinator, Prof. Hou, also published a domestically. In general, the broad impact picture book volume in the Springer Tracts in Modern Physics in 2009, titled Flavor Physics and the is very well received, with people appreciatively th calling the talk “excellent”. Of course, it remains TeV Scale, where the case for a 4 generation that there are still few believers, despite the from flavor physics and CP violation is also outlined and emphasized from B physics and success of the talks, because of a deeply-ingrained → prejudice (which is cashed in as basis for the especially b s CP violation data. But this experimental 漢中策略) against the 4th generation. monograph was written largely in 2008, and So, the basic broad idea, outlined in 6-year NCTS was not directly acknowledged.
191 ‹‹- Highlights of Focus Group Initiative (sub-project I): Theory and Simulation of Plasmonic Metamaterials
Coordinator: Guang-Yu Guo (National Chengchi University/National Taiwan University; email: [email protected]) Committee members: Michitoshi Hayashi, Ming-Wen Chu (National Taiwan Univ.)
I. Brief Description individual Ag and Au nanoparticles (NPs). The plasmonics critically relies on the detailed knowledge of electric near fields associated with various surface-plasmon modes on metallic NPs. urface plasmon polaritons (SPPs) are The STEM-EELS routinely provides the electromagnetic waves confined to a nanometer spatial resolution by focusing a metal-dielectric interface and coupled to the subnanometer electron beam (~2 Å) on NPs and quantized collective oscillation of free charge analyzing the energy losses of the electrons to the carriers. The low-dimension nature of SPPs and NPs. A nanometer-scale resolution is difficult to the strong electromagnetic field at the interface attain by conventional optical approaches such as are responsible for a number of fascinating scanning near-field optical microscopy that phenomena in fundamental science and exciting marginally attains a spatial resolution of ~20 nm. opportunities for technological applications such While experiments plunge ahead, they need as enhancing Raman scattering by astronomical strong theory support. Having identified this orders, enabling extraordinary transmission of direction as promising, and with Taipei taking the light through nanoholes, guiding electromagnetic lead, we wish to enhance Theory Support, to waves with SPPs beyond the diffraction limit. hopefully make a difference over 5-6 years. Therefore, plasmonic nanostructures have been attracting an enormous amount of experimental Therefore, the main purpose this year is to and theoretical interest worldwide in recent years. build up internationally competative Theory Support for Plasmonic Metamaterials. To this end, Indeed, a large number of experimental groups we have proceeded in two directions: (1) to hunt in Taiwan, in particular, the prominent groups of for quality overseas scientists to work in the Cheng-Hsuan Chen (NTU-CCMS), Yang-Fang NCTSn as either long term fellows/postdocs or Chen and Ding-Ping Tsai (NTU-Physics) in NTU, short term visiting scientists, and (2) to build up have already begun to conduct research in in-house expertise of theory and simulation of plasmonics-related nano-sciences and plasmonic metamaterials. nanotechnologies in recent years. Indeed, Yang- Fang Chen’s group at NTU were able to II. Activities manipulate surface plasmon resonance electrically Build-up of the in-house theoretical team: for the first time in Au nanorod-liquid crystal devices. Through the composite of semiconductor To provide a platform for in-house professors, nanorods and metal nanoparticles, they postdocs and students to have discussions, to demonstrated that a suitable band alignment exchange ideas and to learn related theoretical between metal and semiconductor, the band gap methods and experimental techniques, we have emission of semiconductor nanorods can be organized a series of monthly informal meetings greatly enhanced, while defect emission can be since last May (2009). For example, in the first suppressed to noise level. Cheng-Hsuan Chen’s meeting, G.-Y. Guo gave a review on open source group has established the combined technique of computer codes for plasmonic metamaterials scanning transmission electron microscopy simulations, explaining the advantages and (STEM) in conjunction with electron energy-loss disadvantages of several commonly used methods spectroscopy (EELS) and its applications for including plane wave expansion (photonic band mapping and probing plasmonics modes in structure) (MIT MPB), finite difference time-
Highlights of Focus Group -›› 192 domain (FDTD) (MEEP), Mie theory and Moroz. M.-W. Chu and G.-Y. Guo have been multiple-scattering theory (KKR) (Wave- jointly training a student to develop a theory for scattering.com), and discrete dipole approximation describing interaction of relativistic electron beam (DDSCAT). In the same meeting, M.-W. Chu also with plasmons on metal surfaces. Ding-Ping Tsai gave a talk on their latest STEM-EELS results also has one postdoc and one PhD student which would need theoretical calculations to learning how to simulate nanoplasmonics using understand. the FDTD method. Encouragingly, after intensive work in the past several months, our team In the meeting last June, M. Hayashi gave a members have mastered a few basic theories and review on current status of understanding of the computational methods, and are ready to work detailed mechanism of surface enhanced Raman with our experimental colleagues as well as our scattering (SERS), one of the key issues in the distinguished foreign visitors to tackle some field of nanoplamonics. He also outlined how one fascinating issues in the field of plasmonics and can resolve some of the fundamental issues metamaterials. concerning SERS by performing ab initio quantum mechanical [e.g., time-dependent density functional theory (TD-DFT)] calculations. G.-Y. III. Visitors and International Guo, on the other hand, spent some time Collaborations explaining in detail how the DDA and the Through connections with international friends associated DDSCAT code work. He illustrated this and colleagues, we have been able to invite well by presenting his own calculations for a few Ag known scientists in the field, V. Klimov (PN and Au nanoparticle clusters. Lebedev Physics Institute) (Sept. 15-Nov. 23, 2009) and A. Alexander Moroz (wavescattering. As mentioned above, plasmonics and com) (Oct. 2-23, 2009). Their visits have been metamaterials are currently a very hot field and very helpful and fruitful. Both of them gave at therefore there are many experimental and least two seminars/lectures each in both NTU and theoretical groups in other Taiwan institutions NTNU. Furthermore, they have had intensive actively working on it. Therefore, in Oct. 2-3, discussions and exchanged ideas with both 2009, we organized a workshop titled Plasmonics experimentalists and theoreticians alike from both in Metal Nanoparticles: Experiment and Theory, NTU and other institutions. For example, A. to provide an opportunity for domestic scientists Moroz is a world expert using the KKR methods to present latest results, to exchange ideas and to study electromagnetic responses of nanoparticle experience, and lastly but not the least, to educate clusters and photonic crystals. During his stay, he our young researchers (students, postdocs and met with the students in NTU-Physics many even faculty members). The workshop was very times, teaching them how to use the KKR method. successful and was attended by more than 60 participants from all over Taiwan. In the last week of this month, Che-Ting Chan of Hong Kong Univ. of Science and Technology, Since last April (2009), we have been actively will visit NCTSn. During his stay, C.-T. Chan will training our young researchers with widely used give two lectures titled Using transformation theoretical methods and also ourselves with new optics to create illusion and the physical theoretical techniques. For example, M. Hayashi properties of plasmonic lattices in the forthcoming has been teaching one student, one research Mini-school on Plasmonic Metamaterials in NTU. assistant and one postdoc how to perform excited Furthermore, Mark Stockman of Georgia State state calculations for metallic nanoparticle- Univ. will visit NCTSn and NTU-Physics in mid- molecular systems in order to understand fully the December for about nine days. microscopic mechanism of SERS. G.-Y. Guo has been teaching two students how to use the DDA IV. Highlights of Research Results and KKR methods to calculate electromagnetic responses of metallic nanoparticle clusters. The 1. Fundamental properties of clusters of strongly students who are learning the KKR method, also interacting plasmonic nanoparticles benefited greatly from the three-week visit of A. Main characteristic features of plasmonic
193 ‹‹- Highlights of Focus Group resonances depend critically on shape. These techniques for single molecule detection. The features allow tuning interaction between requirement for single molecule detection using nanoparticles and light and molecules. A best way Raman spectroscopy is that the cross section is to control plasmon resonances is clusters of enhanced by a factor of 1014-1015. These huge simple nanoparticles. It was shown already that enhancements have been achieved using silver cluster of two nanospheres has unique optical nanoparticles in conjunction with resonance properties which cannot in principle be achieved enhancements due to a molecular electronic in single nanoparticles. Cluster of three and more transition. Although SERS was discovered several nanoparticles are also of great interest. During the decades ago, a complete picture of the present visit of V. Klimov in NCTSn, we have enhancement mechanism is not available, due to together investigated optical properties of three its highly complicated experimental conditions. cylinder clusters by using both approximate Electronic structure methods are ideal tools. Even analytical theory and numerical DDA calculations. so, due to the complicated metal cluster geometry, Fascinatingly, we found that in contrary to it is not clear how plasmon-like excitation forms common point of view the decreasing of system and what is the origin of such excitations. size results in transformation of dark modes into Our focus here is placed on constructing model very bright one. This interesting finding is systems that can provide a clear physical view of presented in a manuscript which is almost ready how plasmon-like excitations of a metal cluster for submission. The cluster samples of three Ag affect optical properties of the adsorbed molecule. cylinders are being made and will be investigated We take pyrazine as an adsorbate molecule and using the STEM-EELS by C. H. Chen and M.-W. Nan or Agn as metal cluster systems. We have Chu’s experimental team in the CCMS-NTU in constructed a clear physical model of the the coming months. interaction between plasmon-like excitations and 2. Plasmonic metamaterials with negative the adsorbed molecule and also established a full refraction and related effects quantum mechanical approach to this issue. We have explored recent TD-DFT methods and time- The development of plasmonic metamaterials dependent coupled-perturbated Kohn-Sham started from the idea of negative refraction and equation technique to calculate electronic perfect lens in 2000 by J. Pendry. Despite fast excitation properties and dynamic polarizabilities. development of this area the initial idea of perfect We are now able to investigate the most recent lens is still very controversial and paradoxical. It issue on how plasmon affects optical properties of was shown recently that a perfect lens cannot be adsorbed molecular systems including emission realized in principle. Moreover during the present and non-radiative electronic transitions. A full visit of V. Klimov in NCTSn, we have together quantum mechanical study on this issue is crucial demonstrated that another important idea of to the experimentalists who have been trying to negative refraction media (antimatter theorem) by modify the optical properties of the adsorbed J. Pendry and his coworkers also has very limited molecules by controlling plasmon of metallic region of applicability (far fields only). Our nano-structures. results show the crucial role of surface plasmons in left-handed materials (LHM) and pave the way 4. STEM-EELS probe of metal nanoparticles to develop new applications on the base of full A major expenditure in the experimental front control of surface plasmons in LHM (preparation in the past year has been the establishment of the of entangled states for quantum computing and to combined technique of STEM and EELS, and its effective excitation of nanosized light sources for applications for mapping and probing plasmonics plasmonic computer of next generation). A modes in individual Ag and Au nanoparticles manuscript on these results is being prepared. (NPs). An electron beam can excite SPs by 3. Quantum mechanics treatment of interaction coupling to their evanescent-field components of plasmons with molecular systems close to the NP surface and yields detailed information on the spatial distribution of the SPs. Surface-enhanced Raman scattering has This STEM-EELS technique, therefore, gives rise opened the possibilities of using Raman
Highlights of Focus Group -›› 194 to a very powerful tool for studying SP properties [2] H. Y. Xie, P. T. Leung, D. P. Tsai, “General of NPs, which often exhibit a range of distribution validity of reciprocity in quantum mechanics,” in sizes and shapes. STEM-EELS overcomes the Phys. Rev. A 78, 64101 (2008). averaging problems encountered in macroscopic [3] K. M. Lin and G. Y. Guo, “Uncoupled modes optical measurements and gives us the unique and all-angle negative refraction in walled capability of performing local spectroscopy on honeycomb photonic crystals”, individual nano-object with (sub-)nanometer J. Opt. Soc. Am. B 25, C75 (2008). spatial resolution. We have demonstrated the 2009: applications of STEM-EELS in unveiling (a) various SP modes in individual and coupled Ag [1] H. Y. Xie, P. T. Leung and D. P. Tsai, “General and Au NPs in the near-infrared to UV regimes proof of optical reciprocity for nonlocal and (b) UV-range surface resonances in electrodynamics,” J. Phys. A: Math. Theor. semiconductors. 42, 045402 (2009). Plasmonics has been a field of extensive [2] H. Y. Xie, P. T. Leung, D. P. Tsai, “Molecular research focuses since over two decades, whereas decay rates and emission frequencies in the STEM-EELS for SPs investigations was not vicinity of an anisotropic metamaterial,” Solid realized until 2007. Our STEM-EELS facility is, State Commun. 149, 625 (2009). to date, the first and only STEM in Taiwan and [3] K. P. Chiu, K. F. Lai, S. C. Yen, D. P. Tsai, one of the very few STEMs in the world (4) “Surface plasmon polariton coupling between capable of carrying out high resolution EELS. The nano recording marks and their effect on electron monochromator is characterized by a optical read-out signal,” Opt. Rev. 16, 326 superb energy resolution (~0.14 eV), and a weak (2009). elastic tail that enables one to tackle electronic [4] H. Y. Xie, P. T. Leung, D. P. Tsai, excitations down to the near-infrared spectral “Clarification and extension of the optical regime (~1 eV). Up to date, only four STEM- reciprocity theorem,” J. Math. Phys. 50, EELS groups in the world can perform plasmonics 072901 (2009). researches. [5] K. P. Chiu, N. L. Wu, C. S. Wu, Y. H. Fu, C. H. Chu, H. Y. Chung, F. H. Chen, L. D. Lin, V. Publications L. H. Huang, C. D. Shue, and D. P. Tsai, 2008: “Plasmonic nanostructures for photo-catalytic [1] K. P. Chiu, K. F. Kai, D. P. Tsai, “Application reactors,” Proceedings of SPIE 7392, 73920B of surface polariton coupling between nano (2009). recording marks to optical data storage,” Optics Express 16, 13885 (2008.)
195 ‹‹- Highlights of Focus Group Research Activities of Individuals
Research Activities on High Energy Physics
Abdesslam Arhrib (University of AbdelMalek Essaadi; email: [email protected]) Visiting associate professor, 2009/4/17~2009/10/26
uring my stay at National Center for measure different CPV phase combinations, and theoretical Sciences in National Taiwan form the traditional agenda of New Physics CPV University, I have been working on diderent search in flavor sector. The study of b' → s decays projects in collaboration with scientists from would open up the genuine, new chapter of very National Taiwan University (NTU), National heavy flavor sector for CPV studies. Furthermore, Tsing Hua University (NTHU) and National although it is of DCPV type, unlike DCPV in B → Cheng Kung University (NCKU). decays but like TCPV in Bs J/ψφ (there is no longer the exquisite TCPV mechanism for b'), the My research has concentrated on strong phases in b' → s transitions are calculable. phenomenological studies relevant to Large Hadron Colliders (LHC). I have been We have shown that, asymmetries could reach → → investigating phenomenology of various 30% for b' sZ and b' sH for mb' ≈ 350 GeV extentions of Standard Model such as: Models and light Higgs, while it could reach above 50% → → with sequential fouth generation of quarks and for b' sγ and b' sg, and extend to higher mb' leptons, Supersymmetric Models as well as . The branching ratios are of order 10−3–10−5, and Models with an extended Higgs sectors such as CPV measurement would require tagging. Once two Higgs Doublet Models (2HDM) and triplet measured, however, the CPV phase canbe Higgs models. extracted withlittletheoretical uncertainty[1,2]. In collaboration withW.-S. Hou, we investigate In collaboration with R. Benbrik (NCKU), Direct CP Violation in Standard Model with Kingman Cheung (NTHU) and T.-C. Yuan sequential Fourth Generation quarks. With the (Academia scenica) we have studied the Higgs eminent start of LHC, we believe that it is time to boson efects on third-generation squark-pair survey the situation for CPV studies in 4th production in proton-proton collision at the CERN generation quark decays, in particular through b' Large Hadron Collider. We anticipate the → s transitions both in FCNC decay such as b' → contributions from the Higgs exchanges will be sX, X = γ, Z, H and gluon as well as in tree level 1 substantial at large tan β region, where the → 3 decay such as b' → sW+W −, with an smallness of the bottom-parton luminosity can be intermediate by up type quark q = u, c, t, t'. The compensated by enhancement of the bottom CPV studies in b' → s t r a n s i t i o n s i s Yukawa coupling. We found that substantial complementarity with low energy studies such as enhancement can be obtained through s-channel → → 0 0 Bs J/ψφ, or KL π ṽν, or in D mixing. The exchanges of Higgs bosons at large tan β, at which merit of CPV studies in b' → s transitions is its the enhancement mainly comes from bb,̄ bc̄, and c complementarity with low(er) energy studies such b̄ initial states. We compute the complete set of → → 0 as B s J/ψφ, or K L π ṽν mixing. These electroweak (EW) contributions to all production
Research Activities of Individuals -›› 196 channels. We found that the EW contributions can Invited Seminars be significant and can reach up to 25% in more • “Probing tripleHiggs couplings at colliders” general scenarios and at the resonance of the seminargiven at National Central University, heavy Higgs boson [3]. The size of Higgs th 17 june 2009. enhancement is comparable or even higher than • “Direct CP Violation in fourth generation the PDF uncertainties and than must be included in any reliable analysis. quark decays” seminar given at National Taiwan Universit, 12th October 2009 In collaboration with R. Benbrik, C.-H. • “Probing triple Higgs couplings at colliders” Chen(NCKU) and R.Guedes and R. Santos seminar given at National Tsing Hua (Southampton Univerity) we have investigated University, May 2009. double Higgs production at the LHC in the framework of the general two Higgs Doublet Model (2HDM). We include consider all CP-even double Higgs production, that is, References pp → h0h0, h0H, H0H0. We present the regions of [1] A.Arhrib andW.-S.Hou, “CP violationinFourth the parameter space of a general CP-conserving GenerationQuarkDecays”, Phys. Rev. 2HDM where this process is large enough to be D80:076005, 2009 probed at the LHC taking into account in our [2] A. Arhrib and W.-S. Hou, “Direct CP calculation the various experimental constraints Violation in Fourth Generation b'→s on the 2HDM parameters as well as the tree-level Transitions at High Energy Collider” unitarity and vacuum stability constraints on the November 2009, in press various parameters of the Higgs potential. We [3] A.Arhrib, R.Benbrik, K.Cheung and T.-C. have shown that in some cases, even after Yuan, “Higgs boson enhancement effects on imposing all constraints, cross sections are still squark-pair production at the LHC”, large enough to allow for a determination of November 2009, in press 2HDM triple Higgs couplings. In other cases only [4] A. Arhrib, R. Benbrik, R. Guedes and R. a deviation from the SM can be measured and Santos, “Double Neutral Higgs production in other processes would be needed to complete the the Two-Higgs doublet model at the LHC”, picture. We have given particular attention to the JHEP 0908:035, 2009 decoupling limit where the lightest Higgs mimics the SM Higgs and look for the possible non- decoupling effects [4]. Conferences presentations • “Direct CP Violation in fourth generation quark decays” talk given at second LHC meeting, 24th October 2009 • “Double Higgs production in the CP conserving Two Higgs Doublet Model” talk given at PPP08, NCKU Tainan 22th May 2009
197 ‹‹- Research Activities of Individuals Research Activities on Algorithm Developing for Microarray Data Analyses
Chih-Hao Chen (Institute of Systems Biology and Bioinformatic, National Central University; email: [email protected]) Postdoctoral researcher, 2007/11/01~2009/08/31
uring the period I worked for NCTS, I high-resolution (more than 500K probes) arrays; focused on developing algorithms for this parameter has a thoroughly tested and high-resolution microarray analysis. My research strongly recommended default value. was initially aimed at improving existing In fact, the two user tunable parameters are all algorithms, in respect of computation speed, the parameters there is in SAD. There are no memory use and accuracy, for copy number other hidden parameters in the formulation. In variation (CNV) analysis for high-resolution other words, SAD does not contain within it a microarrays. I achieved my goal with a novel difficult-to-access “black box” (there are of course algorithm: Segmentation Analysis of DNA (SAD). lines of coding). In comparison, GLAD employs The manuscript for SAD is almost ready and, as more than a dozen parameters, some of whose the first attempt, will soon be submitted to Nature meaning are obscure. Methods for publication. A software package for the public is now downloadable at http://www. Because SAD employs exact mathematical sybbi.ncu.edu.tw/public_software.htm. relations and takes advantage of the scale- independence of the variance of array errors, it is SAD’s unique and outstanding features make it extremely fast. For a 1M-probe microarray it is by far the best -- faster, more user friendly, more two orders of magnitude faster than its closest compact, easier to understand, higher accuracy -- competitor, CBS [2], and more than three orders package for CNV analysis. These advantages of magnitude faster than GLAD [3] and CGHseg derive from a simple fact: the formulation of the [4]. Its speed advantage increases with array size SAD algorithm is based on simple and rigorous because unique among algorithms for similar task applications of statistical principles, measurement SAD scales linearly with array size. theory, and precise mathematical relations, and nothing else. Our extensive testing shows that SAD is no less accurate than its competitors. It gets better, SAD makes two (related) assumptions about comparatively, when signal to noise ratio on the data property: the normal distribution of and array worsens -- caused by stromal contamination, scale-independence of the variance of array errors. for instance. These are fully supported by microarray data. No further assumptions, implicit or explicit, are made Because the statistical nature of SAD in the formulation. An example of making an formulation and because all decisions are implicit assumption concerning data property determined by the one essential parameter, which occurs when data smoothing is practiced. An is a t-value, all SAD results are assigned example of the explicit kind is the assumption of quantitative statistics. This is another feature of the existence of hidden variable as in the case of SAD that is unique among algorithms for similar Hidden Markov Model [1]. tasks. As a result of the simplicity of the formulation In summary, SAD is formulated on solid SAD is extremely user-friendly. It has only two statistical principles and mathematical relations, it user-defined parameters. One is essentially a is simple and accessible, and it delivers the goods t-value which determines the resolution of the in terms of being user friendly, fast, accurate, and analysis. The other is a segment length which produces results with solid statistics. With all largely determines how fast the program runs for these attributes we believe SAD is a breakthrough in both theory and practice, and it has the potential
Research Activities of Individuals -›› 198 of making an important contribution to the field of [4] Picard, F., Robin, S., Lavielle, M., Vaisse, C. microarray analysis, and therefore to our & Daudin J. (2005) A statistical approach for understanding of human diseases.. array CGH data analysis. BMC Bioinforma., 6, 27.
References [1] Fridlyand,J. et al. (2004) Hidden Markov models approach to the analysis of array CGH data. J. Multivariate Anal., 90, 132–153 [2] Venkatraman, E.S. and Olshen, A.B. (2007) A faster circular binary segmentation algorithm for the analysis of array CGH data. Bioinformatics, 23, 657-663. [3] Hupé, P., Stransky, N., Thiery, J., Radvanyi, F. & Barillot, E. (2004) Analysis of array CGH data: from signal ratio to gain and loss of DNA regions. Bioinformatics, 20, 3413–3422.
199 ‹‹- Research Activities of Individuals 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, 2009/2/1~now
have been in the Center as a Center bump-like structures. Scientist since November 2006. I am also In the work [1], we point out that the excess in the convener for the focus group on the LHC the ATIC data in fact consists of 1-peak plus Physics. My research area is in particle physics 1-hump structure. The peak is from 300-800 GeV phenomenology. In the following, I highlight while the bump from 80-300 GeV. A possible some works done in 2009. explanation is that the dark matter particle in the Introduction Universe undergoes both annihilation and decay. The annihilation gives rise to the peak around 600 The Large Hadron Collider (LHC) is going to GeV while the decay is responsible for the small start at the end of 2009. It will be the place for the bump around 80-300 GeV. The resulting positron next big discovery. More than half of the fraction observed at PAMELA is a combination of resources in high energy community will be put annihilation and decaying contributions. Through into it. Together with other planned cosmology a χ2 analysis we show that the fitting using a experiments, testing new ideas beyond the single mode (either annihilation or decay) is far standard model (SM) will be the major activities less satisfactory than the double mode (both in the next 10–20 years. My role is to link up annihilation and decay). The study shows that a theory and experiments. In the last year, I have dark matter particle of about 640 GeV with a accomplished a number of works on monochromatic annihilation spectrum and a soft supersymmetry, Higgs physics, dark matter, and decaying spectrum is the best simultaneous fit to cosmology. In the following, I highlight a few the PAMELA and ATIC data. In the figure, we topics that I feel very exciting. show the fits to the data of PAMELA and ATIC. Dark Matter Beyond the MSSM Dark matter has almost been confirmed by a An interesting scenario is the Higgsino-like number of cosmological and astrophysical LSP, which can arise from a number of observations. It is vital for structure formation supersymmetry breaking models, e.g., focus-point and make for the mass difference between matter supersymmetry models or whenever the µ and baryonic matter observed by WMAP. parameter is much smaller than the Bino and However, the nature of dark matter is totally Wino masses. In the minimal supersymmetric unknown, except for its nonbaryonic nature. standard model (MSSM), the Higgsino-LSP Recently, there are a number of astrophysical scenario implies nearly-degenerate Higgsino experiments hinting the signals of dark matter states: Coannihilation is too efficient so that the annihilation, notably PAMELA, ATIC, and observed CDM relic density requires a rather FERMI-LAT. The PAMELA Collaboration has heavy Higgsino state with mass around 1--1.2 reported an unexpected rise of positron fraction at TeV. Moreover, the mass degeneracies between the energy range of 10-100 GeV, unlike the ~ 0 the LSP (χ 1) and the lighter chargino/second- power-law falling background. However, similar ~ ± ~ 0 lightest neutralino (χ 1/χ 2) generate too soft decay enhancement of the anti-proton flux was expected products for detecting the states but not seen by PAMELA provides a challenging ~ ± ~ 0 χ 1 and χ 2 at the LHC. Thus, the Higgsino-LSP puzzle. The ATIC data showed an excess of in the MSSM posts a difficult scenario at the galactic cosmic-ray electrons/positrons at energies LHC. of 300 - 800 GeV, showing a peak-like and a
Research Activities of Individuals -›› 200 Iquarkonium We may encounter some new physics that we really do not expect, e.g.,unparticle proposed in 2007. The new physics proposed is the existence of a new strongly interacting nonabelian SU(3)
sector with the mass of the new fermions MQ' >> Λ' of the new sector. This sector is similar to the usual QCD but without the presence of light quarks. It is therefore very different from the usual QCD phenomenologically. In a work [3], we studied the phenomenology of such a scenario
with Λ' < ΛQCD and the mass of the new fermions, aka iquarks, is O(100) GeV. Phenomenology of this hypothetical QCD can be drastically different from the real world where light quarks do exist and one must have to worry about the spontaneous chiral symmetry breaking. For instance, heavy quarks are connected by unbreakable long and stable string flux tube since there is no light quark pairs popped up from the vacuum as the heavy quarks are being pulled apart. The size of the string flux tube is of order -1 In a work [2], we showed that the modest Λ' and it can be macroscopic for 100 eV ≤ Λ' ≤ 2 10 keV, or mesoscopic for 10 keV ≤ Λ' ≤ MeV, or addition of a dimension-5 λ(HuHd) /M to the MSSM superpotential, a scenario beyond MSSM microscopic for MeV ≤ Λ'. In general, one also (BMSSM) alleviates the difficulties of the assume Λ' is smaller than the ΛQCD such that the Higgsino-LSP scenario. It has been discussed that new color degree of freedom bears the name non-renormalizable and high-dimensional infracolor (IC). operators in new physics models can yield In the macroscopic Λ' scenario that once the important consequences in low energy ǪǬ is produced, they would be linked by a long phenomenology. This dimension-5 term, string roaming inside the detector. The infracolor 2 λ(HuHd) /M, lifts up the degeneracy between the dynamics can allow the ǪǬ bound state to survive ~ 0 ~ ± ~ 0 states χ 1 and χ 1/χ 2, thus enhancing the discovery for distances of order centimeter and preventing potential of the chargino and neutralino decays them from annihilation. In the mesoscopic Λ' with more energetic charged leptons or pions than scenario, the ǪǬ pair will appear as a single entity the decays in the MSSM. In addition, the inside the detector. On the other hand, if Λ' is ~ ± ~ 0 coannihilation of the LSP with χ 1 or χ 2 is reduced microscopic, the ǪǬ pair will lost most of their substantially such that a light Higgsino-LSP with a kinetic energy and angular momenta by emitting mass around 100 GeV can accommodate the iglueballs and/or light QCD hadrons like pions WMAP data on the CDM relic density. before annihilation. In the latter case in which Furthermore, the direct detection can be brought iquarks are QCD-colored, it leads to a hadronic below the current experimental limits due to fireball along with the other SM decay products of heavier Higgs boson mass. Thus, the BMSSM the iquarkonium. poses a lot of interesting consequences, which are Iquarks in the above model can be copiously due to the presence of higher dimensional terms in produced at the LHC, not via normal QCD the theory. Further investigations on other aspects interactions, but via electroweak interactions. The are also vital to test such higher dimensional iquarks are stable with respect to the collider time terms. scale, and linked by a string. Depending on the value of Λ' the iquarks will lose energy by
201 ‹‹- Research Activities of Individuals emitting iglueballs and bremsstrahlung until the iquark pair linked by the string come together and form a iquarkonium. The life time of the iquarkonium then depends on the annihilation rates into SM particles. In accord with the normal quarkonium, the life time of iquarkonium is inversely proportional to the square of the wave- function at the origin. The life time and decay patterns of the iquarkonium can therefore provide useful information about the quantum numbers of iquarks and the dynamics of the new strong interacting gauge group. Inflation Chia-Min Lin and I have worked on a number of papers on inflation models. Current data from WMAP have put cosmology into a precision regime, which can discriminate various inflation models or put severe constraints on models. We have considered a number of models in these papers, like hilltop inflation models, supernatural inflation models, D-term inflation, and supernatural A-term inflation models. I will skip the details here due to space limitation.
References [1] K. Cheung, P.Y. Tseng and T. C. Yuan, Phys. Lett. B 678, 293 (2009). [2] K.Cheung, S. Y. Choi and J. Song, Phys. Lett. B 677, 54 (2009). [3] K. Cheung, W. Y. Keung and T. C.Yuan, Nucl. Phys. B 811, 274 (2009). [4] C.M. Lin and K. Cheung, JCAP 0903, 012 (2009); JCAP 0906, 006 (2009); Phys. Rev. D79, 083509 (2009).
Research Activities of Individuals -›› 202 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 2009 my research activity in NCTS has the larger a is, the shorter the disentanglement been on quantum information science and time. Finally, in the non-Markovian regime, the particle physics. The work on quantum strong impact of vacuum fluctuations experienced information science is quantum entanglement locally by each detector destroys their dynamics in relativistic motions and macroscopic entanglement right after the coupling is switched quantum phenomena. The work on particle on. physics is about physics beyond the standard Currently, we are now studying the model and cosmology. decoherence and disentanglement issues from the So far most of the discussions on quantum angle of quantum fields in curved spacetime. entanglement dynamics are non-relativistic and Some pioneer work had been done about with an implicit assumption that the background decoherence in particle creation processes, and we spacetime is globally Minkowski. In the work[1] are focusing on the evolution of quantum collaborated with Dr. S.Y. Lin at NCTS and Prof. entanglement in particle creation which have not B.L. Hu of UMD, we started to study the been explored in detail. We are considering the entanglement dynamics of two harmonic entanglement dynamics of particle creation in flat oscillators coupled to a background field with one spacetime under changing background field in uniform acceleration. This is an important first[2] and will move to more interesting case for ingredient for the establishment of relativistic dynamical background spacetime. quantum information theory. In our Recently I am also interested in the polariton nonperturbative treatment, the field will be Bose-Einstein condensate(BEC). Polaritons are evolving with the detectors as a combined close quasiparticles formed from electronic excitations system. coupled to photons in a microcavity. A number of The results from our calculations show that the BEC-like effects have been observed in this type interaction between entangled UD detectors and of system, including bimodal momentum-space the field does induce quantum disentanglement distribution with a narrow peak at zero between the two detectors. We found that the momentum, spatial condensation in a macroscopic disentanglement time is finite in all cases studied, trap, long-range off-diagonal order, existence of namely, there is no residual entanglement at late quantized vortices, linear Bogoliubov excitation times for two spatially separated detectors, one spectrum, and flow without dispersion. The stationary and another uniformly accelerating, in remarkable feature is that the polariton condensate (3+1)D Minkowski space. Around the moment of is not in thermal equilibrium however there are so full disentanglement there may be some short- many canonical features of Bose-Einstein time revival of entanglement within a few periods condensate can still be onserved in polariton of oscillations of the detectors (equal to the condensate. We are applying non-equilibrium field inverse of their natural frequency). In the theory methods to treat this macroscopic quantum ultraweak coupling limit, the leading-order phenomena. behavior of quantum entanglement in Minkowski During this year I also did some work on time is independent of Rob's proper acceleration particle physics. a . When a gets sufficiently large, the disentanglement time from Alice's view would be There are some solid evidences for the physics longer for a larger a. From Rob's view, however, beyond the Standard Model (SM) of particle
203 ‹‹- Research Activities of Individuals physics. One is the observations of neutrino charged scalars and phase space suppression of oscillations which has established that neutrinos the three body decay. Finally, the possibility of have very small masses. The low energy low-scale leptogenesis can be achieved if the accelerator experiment of the muon anomalous hierarchical Yukawa couplings among the new magnetic moment also gives another hint for the particles are satisfied. This scenario can be tested physics beyond the SM. Besides that there are also at LHC and/or future experiments. Currently we evidences from early Universe cosmology and are working on some phenomenological astronomy: the existence of dark matter and implications of the model on cosmology. matter-antimatter asymmetry of the Universe. The observed baryon asymmetry of the Universe can not be explained within the SM with one CP violating phase. Despite the great success of References standard big-bang nucleosynthesis, it has been [1] S.Y. Lin, C.H. Chou, and B.L. Hu, noted that the prediction for the ratio of 7Li/H and Disentanglement of two harmonic oscillators the isotopic ratio 6Li/7Li do not agree with current in relativistic motion, Phys. Rev. D 78, observations, called the "lithium problems". They 125025(2008). do not have an astrophysical solution in a [2] B.L. Hu , C.H. Chou, and S.Y. Lin, in complete manner at present. preparation. In the work[3] done in collaboration with Dr. [3] C.S. Chen, and C.H. Chou, Neutrino masses, C.S. Chen at NCKU, we try to address all of these muon g-2, dark matter, lithium problem, and issues within a single framework. Our model is an leptogenesis at TeV-scale, extension of the radiative seesaw mechanism of arXiv:0905.3477[hep-ph], submitted to Phys. neutrino mass with extra scalars and leptonic Lett. B. fermions. By imposing a Z2 symmetry, all the new particles can only appear in pairs through the
loops due to the Z2-odd parity assignment. The neutrino masses can be generated via one-loop effects at the TeV scale, in additional to the loop suppression factor the tiny neutrino mass scale is controlled by the mixing between charged scalars in our scenario. Similar mechanism will also contribute to muon anomalous magnetic moment which is easily fitted into the current deviation between the experimental data and SM prediction.
The lightest neutral Z2-odd particle provides the dark matter candidate in our model. The model also contains a long-lived charged particle requested by the scenario of CBBN where the long lifetime is due to the small mixing between
Research Activities of Individuals -›› 204 Research Activities on Strings
Kazuyuki Furuuchi (email: [email protected]) Staff scientist, 2007/8/1~present
n this academic year I studied M-theory I also made another related investigation on branes based on the BLG model of the M5-brane: An action of a 5-brane was multiple membranes. M-theory is a hypothetical constructed by Ho-Imamura-Matsuo-Shiba by theory which is expected to provide unified starting from the BLG model and choosing the description of five types of ten-dimensional Nambu-Poisson bracket as the Lie 3-algebra, then superstring theory. However, only some parts of expanding around certain background. They its structure in some specific limits are currently conjectured that it is related to previously understood. One of the expected features of constructed M5-brane theory in a constant three- M-theory is that supersymmetric membranes and form background via a generalization of the so 5-branes, extended in 2 and 5 spatial directions called Seiberg-Witten map. To make a step respectively (we will call them M2-branes and forward for the proof of this conjecture, in Ref. M5-branes, respectively), are the fundamental [3], with Tomohisa Takimi (NTU), I constructed building blocks of the theory. In the case of supersymmetric string-like soliton solutions of the D-branes which played crucial roles in the 5-brane action of Ho et. al. in the lowest order in understanding of non-perturbative aspects of the expansion of a deformation parameter which is string theory, the Lie algebra structure of multiple related to the three-form background. This D-brane system was a characteristic new feature. solution was compared with the string soliton of From this experience, we expect that if we find the previously known M5-brane using the the characteristic algebraic structure of multiple Seiberg-Witten map, and we found an agreement M2-brane system, we will understand M-theory at this order. This result provides a non-trivial better. From the end of 2006 to the end of 2007, support for the conjecture of Ho et. al., and sheds Bagger-Lambert and Gustavsson constructed a insights into the theory of M5-branes. model for multiple super-membranes which has a novel gauge symmetry based on Lie 3-algebra (Filippov n algebra with n =3), a natural extension References of the Lie algebra. Last academic year I studied [1] Kazuyuki Furuuchi, Sheng-Yu Darren Shih, the space-time supersymmetry algebra of the Tomohisa Takimi, "M-Theory Superalgebra Bagger-Lambert-Gustavsson model (BLG model) From Multiple Membranes" JHEP 0808:072 with Sheng-Yu Darren Shih (NTU, at the time) (2008). and Tomohisa Takimi (NCTU, at the time). The conclusion was that though the BLG model is not [2] Kazuyuki Furuuchi and Dan Tomino, manifestly space-time supersymmetric, it actually "Supersymmetric reduced models with a has a symmetry which is closely related with the symmetry based on Filippov algebra," JHEP space-time supersymmetry. This result suggests 0905:070 (2009). that there exists some space-time covariant [3] Kazuyuki Furuuchi and Tomohisa Takimi, formulation of the BLG model. To understand this "String solitons in the M5-brane worldvolume point, in Ref. [2], together with Dan Tomino at with a Nambu-Poisson structure and Seiberg- NCTS, I constructed simple models which has a Witten map," JHEP 0908:050 (2009). symmetry based on the Lie n-algebra, and classified the dimension of the space-time in which the model is manifestly space-time supersymmetric. This investigation is also motivated as a search for an extension of the type IIB matrix model which was proposed as a constructive definition of type IIB superstring theory, and which is based on the Lie algebra. We comment on an interesting interplay between Lie n-algebra symmetry and supersymmetry, which is an analogue of what happens in the type IIB matrix model.
205 ‹‹- Research Activities of Individuals Research Activities on Strings
Takayuki Hirayama (email: [email protected]) Postdoctoral researcher, 2007/9-/1~present
have been working on non perturbative describes the interactions between quarks and effects of string theory. I have published gluons. Since the interaction becomes strong in two papers with my collaborators in the academic low energy, it is difficult to analyze. In low year of 2008. energy, the chiral symmetry is dynamically broken by the quark condensate, and quarks make In the paper [1], I have analyzed the so-called composites, i.e. mesons and baryons. These Bagger-Lambert theory which is expected to be a dynamics cannot be computed from perturbative low energy effective theory of multi-membranes QCD approach. Therefore it is important to find in M-theory. String theory is defined another approach. In string theory, there is a perturbatically and a non-perturbative definition conjecture which claims the equivalence between of string theory is expected be a theory of a string theory or supergravity on a curved space membrane in eleven dimensional spacetimes, and a quantum field theory without gravity like M-theory. (string theory is a theory of string in ten QCD. The example which have been studied dimensional spacetimes.) We only have poor intensively is the duality between Type IIB string knowledge of M-theory, and do not even have an theory in a space of 5 dimensional Anti-de Sitter action! Recently, Bagger and Lambert proposed space times 5 dimensional sphere and the four an action in three dimensions which possesses the dimensional N=4 supersymmetric Yang-Mills properties of multi-membranes. Thus I and my theory. This duality is a weak-strong duality in a collaborator analyzed this action and studied a sense that a weak string coupling region of Type scattering of membranes perturbatically in order IIB string theory is dual to a strong gauge to compute the potential between the membranes. coupling region of Yang-Mills theory. Therefore This potential must be identified Newton potential this AdS/CFT correspondence offers a quite and then we can read out the target spacetime powerful tool of computing a strongly coupled dimensions from the power low of potential. This gauge theory from a weakly coupled gravity study is important for checking whether Bagger- theory. I have been challenging to construct the Lambert theory is really a theory of multi- gravity dual description of QCD. One successful membranes in eleven dimension ( M-theory is model was constructed by Sakai and Sugimoto defined in eleven dimensions). Our finding is that which is based on D-branes in string theory. the target space dimension is ten, not eleven [1]. Though their model is successful, the pion, which We find that the membrane propagating between is associated with the chiral symmetry breaking, is two membranes always wrap on one space massless although the pion has a mass about 140 direction so that this direction cannot be sensed. Mev. I and my collaborators studied how to Therefore Bagger-Lambert theory does not introduce the pion mass, i.e. the quark mass in the capture all the properties which multi membrane academic year 2007. In the paper [2], we then should have, although it really has possessed some studied how much the masses of mesons and of them. We also discussed in the paper that the baryons are shifted by the presence of quark missing one space direction can be probed by non- masses. We gave the formulae to compute their perturbative process (monopole instanton). values and compared the results with the data In the paper [2], I have studied quark mass from lattice calculations. We found that our values dependence of hadrons using a holographic dual are consistent with lattice results and thus our gravitational description of QCD (Quantum model is a good candidate for the holographic Chromo Dynamics). QCD is a gauge theory which dual of QCD. Since the model is known to have
Research Activities of Individuals -›› 206 many other unsuccessful points, it is important to improve our model.
References [1] Membrane scattering from Bagger-Lambert theory. Takayuki Hirayama, Dan Tomino. Published in JHEP 0908:071,2009. e-Print: arXiv:0812.1866 [hep-th] [2] Quark Mass Dependence of Hadron Spectrum in Holographic QCD. Koji Hashimoto, Takayuki Hirayama, Deog Ki Hong. Submitted to PRD. e-Print: arXiv:0906.0402 [hep-th]
207 ‹‹- Research Activities of Individuals Research Activities on Symmetry Breaking in Hadron Physics
Hiroaki Kohyama (email: [email protected]) Postdoctoral researcher, 2008/8/1~present
008 in NCTS is devoted to the study on For the purpose to study the critical point, we symmetry breaking in hadron physics. perform numerical analysis by varying the current Quarks and gluons are believed to be the quark masses. In the 3 flavor (up, down and elementary particles which can not be divided strange) NJL model, the phase transition in the anymore. Under the cold and dilute environment, massless limit is of the first order, being the quarks and gluons are confined into hadrons and consequence of symmetry. On the other hand, the never be observed as free particles. However, at transition for intermediate quark masses is the high temperature, quarks and gluons can get crossover due to the effect of masses which enough energy to escape from hadron confinement explicitly break the chiral symmetry. This defines and they can be free particles. This state is called the critical boundary which separates the first quark gluon plasma which is seen at the extreme order transition region and the crossover region. condition in high energy experiments. The drastic This boundary is important because it determines change of sate of this kind is called the phase the order of the phase transition at the physical transition which is closely related to the current quark masses. In Ref.[1], we have studied phenomena of symmetry breaking. In the case of the critical boundary at finite temperature and\or confinement-deconfinement phase transition, density by using the extended NJL model with symmetry is broken in confinement phase and it is density dependent UA(1) anomaly. We found that restored in deconfinement phase. Thus the idea of the region of the first order phase transition the symmetry breaking is crucial key to shrinks according to the chemical potential at low understand the critical phenomena. chemical potential. The result obtained in our paper is consistent to the recent Lattice QCD In principle, all phenomena related to the studies. This may indicate that the QCD phase quarks and gluons should be described by the transition does not have the critical point, which Quantum Chromodynamics, the fundamental means that the phase transition is always the theory of quarks and gluons. The ultimate goal of crossover. QCD is to explain all strongly interacting phenomena for all energy scale, high and low. QCD is the asymptotically free theory and coupling strength becomes small at high energy, Reference which means that a perturbative calculation works [1] J.-W. Chen, K. Fukushima, H. Kohyama, K. well in high energy region. However it is difficult Ohnishi, U. Raha, UA(1) anomaly in hot and to perform a perturbative calculation due to large coupling constant in low energy region, and we dense QCD and the critical surface, Phys. usually have to rely on some effective models of Rev. D 80, 054012 (2009). QCD. The effective model that I studied in this year is the Nambu Jona-Lasinio (NJL) model. The NJL model has the same symmetry properties of QCD and successfully describes the chiral symmetry breaking at low temperature and density and its restoration at high temperature and\or density. It is also applicable to the study of the QCD critical point in the phase diagram with temperature and quark chemical potential. The QCD critical point is the point where the first order phase transition ends and the phase transition becomes the crossover above the critical temperature.
Research Activities of Individuals -›› 208 Research Activities on Particle Physics
Jae Sik Lee (email: [email protected]) Assistant research scholar, 2008/7/1~present
ike as in the previous years, my main The minimal supersymmetric model to achieve research activity during 2009 has been this goal is the Next-to-Minimal Supersymmetric concentrated on the phenomenology of the Standard Model (NMSSM) which adds one more Minimal Supersymmetric extension of the gauge singlet to the MSSM. We have made a team Standard Model (MSSM). But, I believe I will for the NMSSM phenomenology with explicit CP remember this year a little differently since I have violation. The team consists of Prof. Kingman studied several topics which are not the typical Cheung, Mr. Tie-Jiun Hou, Dr. Eibun Senaha, and MSSM ones. The list contains myself [2]. We have done the calculation of the Higgs mass spectrum and the mixing by including (i) Standard Model Higgs boson [1] the higher-order corrections beyond the one-loop (ii) Singlet extension of the MSSM [2] level and Mr. Hou presented the results at the (iii) Supersymmetric Nambu--Jona-Lasinio recent LHC workshop at NCKU, see the model [3] workshop homepage, http://phys.cts.ntu.edu.tw/ If I should choose the most important work of workshop/2009/981024LHCP/. We are going to mine in the year of 2009, it should be the work on develop this subject by including the low-energy reconstructing the SM Higgs boson at the LHC precision experiments to explain the matter- [1]. In the paper, we examine the prospect to antimatter asymmetry of our Universe. The measure the Higgs boson mass using the recently relevant LHC phenomenology is the most introduced kinematic variable, the M_T2-Assisted attractive in the coming years. On-Shell (MAOS) momentum. We show that the MAOS scheme provides a systematic Together with the members of the Physics approximation to the invisible neutrino momenta department of the National Central University, in in the Higgs-boson decay into a dileptonically which I had been affiliated before I came over to decaying W-boson pair. Through a full Monte NCTS (Hsinchu), we have studied a possibility of Carlo (MC) simulation, it is demonstrated that the dimension-five operators with strong couplings in MAOS Higgs mass distribution, constructed with the superpotential as an alternative origin of the the MAOS neutrino momenta, shows a clear peak particle masses [3]. We named the model at the true Higgs boson mass when an event cut Holomorphic Super Nambu--Jona-Lasinio Model selecting higher value of M_T2 is employed. Our (HSNJL) The approach provides a new direction results indicate that the MAOS Higgs mass can be for modeling dynamical symmetry breaking in a useful also for the discovery or exclusion of the supersymmetric setting. In particular, we adopt the Higgs boson in certain mass range. One of the idea to formulate a model that gives rise to the co-authors (Prof. Suyoung Choi) of the paper is an MSSM as the low energy effective theory with experimenter and he is now analysing the D0/ both Higgs superfields as composites. This work Tevatron data using the suggested method. This will mature in near future by including work has been done with my Korean colleagues comprehensive study of the model and exploring and this would consist part of a Ph.D thesis of the its full theoretical aspects. last author, Mr. Park. Other than the above non- or less-MSSM like Actually, the MSSM has a weak point known studies, we have published a paper on the electric as the mu problem. For a supersymmetric model and anomalous magnetic dipole moments of the to be phenomenologically viable, the size of the muon in the MSSM [4]. This work might be a mu parameter should be around the scale of 1 TeV. sequel to my previous comprehensive work on the
209 ‹‹- Research Activities of Individuals electric dipole moments in the MSSM [5]. In the collider, Phys. Rev. D 80, 073010 (2009) paper, we study the electric dipole moment [2] Kingman Cheung, Tie-Jiun Hou, Jae Sik Lee, (EDM) and the anomalous magnetic dipole Eibun Senaha, NMSSM Higgs sector with moment (MDM) of the muon in the CP-violating explicit CP violation, in preparation MSSM. We take into account the general one-loop [3] Dong-Won Jung, Otto C.W. Kong, Jae Sik graphs and the dominant two-loop diagrams. We Lee, Holomorphic Supersymmetric Nambu- improve earlier calculations by incorporating Jona-Lasinio Model, e-Print: arXiv:0906.3580 CP-violating Higgs-boson mixing effects and the [hep-ph] resummed threshold corrections to the Yukawa couplings of the charged leptons as well as that of [4] Kingman Cheung, Otto C.W. Kong, Jae Sik the bottom quark. The analytic correlation Lee, Electric and anomalous magnetic dipole between the muon EDM and MDM is explicitly moments of the muon in the MSSM, JHEP presented at one- and two-loop levels and, through 0906:020,2009. several numerical examples, we illustrate its [5] John R. Ellis, Jae Sik Lee, Apostolos Pilaftsis, dependence on the source of the dominant Electric Dipole Moments in the MSSM contributions. We have implemented the analytic Reloaded, JHEP 0810:049,2008. expressions for the muon EDM and MDM in an [6] J.S. Lee, M. Carena, J. Ellis, A. Pilaftsis, updated version of the public code CPsuperH2.0 C.E.M. Wagner, CPsuperH2.0: an Improved [6]. Computational Tool for Higgs On the other hand, together with my UK Phenomenology in the MSSM with Explicit colleagues, I studied the exotically decaying CP Violation, Comput.Phys. MSSM Higgs bosons at hadron colliders [7]. Commun.180:312-331,2009. Specifically, we suggest a new scenario for the [7] J.S. Lee, Y. Peters, A. Pilaftsis, C. search of strangephilic MSSM Higgs bosons at the Schwanenberger, Strangephilic Higgs Bosons Tevatron and the LHC, in which all neutral and in the MSSM, e-Print: arXiv:0909.1749 [hep- charged Higgs bosons decay predominantly into ph] pairs of strange quarks and into a strange and a [8] D0 Collaboration, V. Abazov et al., Search for charm quark, respectively. The proposed scenario charged Higgs bosons in top quark decays, is realized within a particular region of the MSSM e-Print: arXiv:0908.1811 [hep-ex] parameter space and requires large values of [9] Jae Sik Lee, Manifestations of CP Violation in tan(beta), where threshold radiative corrections the MSSM Higgs Sector, AIP Conf. are significant to render the effective strange- Proc.1078:36-41,2009 quark Yukawa coupling dominant. Experimental searches for neutral Higgs bosons based on the identification of b-quark jets or tau leptons may miss a strangephilic Higgs boson and its existence could be inferred indirectly by searching for hadronically decaying charged Higgs bosons. A part of the scenario has already been searched by D0 at the Tevatron [8]. Finally, I report my invited plenary talk to the 16th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY08) has been published as in Ref.[9].
References [1] Kiwoon Choi, Suyong Choi, Jae Sik Lee, Chan Beom Park, Reconstructing the Higgs boson in dileptonic W decays at hadron
Research Activities of Individuals -›› 210 Research 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, 2009/2/1~2011/1/31
Introduction Dynamical electroweak symmetry breaking Walking technicolour is one of the candidates that generate electroweak symmetry breaking at Since I joined the NCTS in 2007, I have TeV scale without the need for the Higgs particles. been working on projects in physics It is a strongly-coupled gauge theory, hence lattice related to the Large Hadron Collider using large- gauge theory can play an important role in this scale numerical simulations in Lattice Gauge research avenue. In the walking-technicolour Theory. This is reflected in two main research scenario, the coupling constant in the gauge avenues that I am pursuing. First, I am studying theory increases over a range of scale when the the scenario of electroweak symmetry breaking energy is decreased, then it becomes "frozen". At via strongly-coupled gauge theories at TeV scale. the very low energy regime, it starts increasing Second, I am performing calculations for decay again, such that conformal symmetry and chiral amplitude of baryons containing a b quark, which symmetry are broken dynamically. The system is the main subject of the LHC-b experimental then develops an energy gap which generates the project. spectrum. Hardware The reason why such a scenario is required is due to the need to dynamically suppress the The start-up equipment fund for my position flavour-changing neutral currents (FCNC) in was granted in the summer of 2007, from the physics beyond the Standard Model. A walking National Science Council and Faculty of Sience, theory is likely to produce large anomalous National Chiao-Tung University. From August dimensions for the operators that generate the 2007 to December 2007, I played the main role in Standard Model fermion masses. This can then lift the purchase of a PC cluster using this start-up the scale at which flavour emerges, hence fund. The cluster was delivered between January suppress the FCNC. It is not easy even just to and April 2008. Now it contains twenty-six find a theory which has the "walking" feature and computing nodes. Each node has two quad-code dynamical symmetry breaking at low energy. CPUs and sixteen gigabites of memory (with error Exploratory result using the step-scaling method checking). Twenty-two of these nodes are was reported by Appelquist and collaborators connected via a Double-Data-Rate (up to 20 recently [1]. These authors calculated the coupling gigabits per second) infiniband switch. The other constant in the so-called Schroedinger functional four are on a gigabit network. In addition to the scheme for QCD-like theories with large numbers computing nodes, we have a six-terabite disc array of flavours. They discovered that the coupling for storage. constant would stop running for a range of scale in Recently, I started to set up facilities for high- some of these theories. However, the coupling performance computing using GPU. In November constant not physical, hence depends on the 2009, I organised a one-day NCTS (on NCTU renormalisation scheme in which it is calculated. campus) training course for programming skills Therefore it is important to check the claim by on such equipments. Appelquist et al. in at least another scheme.
211 ‹‹- Research Activities of Individuals 2 shows the quenched feasility study of the TPL scheme. Figure 3 exhibits the data in the case of 12 flavours, where x-axis is the lattice spacing (left-hand size is coarser), y-axis is proportional to the coupling constant and different symbols correspond to various lattice sizes. From this plot, it is evident that the long-distance regime may contain an infrared fixed point.
I have formed a collaboration with physicists in Professor Tetsuya Onogi's group at Osaka University. We are studying the scale dependence of the coupling constant in these theories iusing the Creutz-ratio scheme, as well as the Twisted- Polyakov-line (TPL) scheme. In the Creutz-ratio scheme, We fix the scheme by keeping constant the ratio between the Wilson-loop size and the lattice size. This specifies the scheme. We then perform calculations at various lattice sizes and extrapolate to the continuum limit at each step. The lattice size is the renormalisation scale in this procedure. Since this is a new scheme, we have performed exploratory numerical study of the Physics of the b-baryon coupling constant in the quenched prroximation for QCD and found that it worked well [2], since A b-baryon is composed of three valence it could reproduce the perturbative results in the quarks, namely, a b-quark and two light quarks. region where perturbation theory would apply. The rare decay channels in which a non-stranged Figure shows the result of this calculation, where b-baryon decays into a stranged baryon plus a the x-axis is the scale and the y-axis is the photon or a lepton pair are sensitive to new coupling constant. physics effects involving the mixing of quarks via right-handed coupling structure that is absent in the Standard Model. This structure cannot be probed by existing experiments performed with the B mesons which do not carry spin. With William Detmold and Matthew Wingate, I have set up a programme to pin down the relevant matrix elements in the above decay channel as our final goal. In our programme, we use the dynamical gauge configurations generated and kindly lent to us by the RBC Collaboration. The lattice size is 24-cube times 64, with lattice spacing around 0.1 fm. The 2+1 flavours of dynamical quarks in these RBC configurations are domain wall For the simulations with 12 flavours, we go for fermions. We also use the same fermions for our the TPL scheme, since the required lattice size is valence light quarks. For the heavy quark, we use smaller in this scheme, compared to the Creutz- the static approximation where the heavy-quark ratio scheme. From our preliminary result [3], mass is infinite. The most time-consuming step in there is evidence that the theory flows into an this programme is to generate light-quark infrared fixed point in this scheme as well. Figure
Research Activities of Individuals -›› 212 propagators. We have accumulated many such [2] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, propagators using my PC cluster and other C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi computing resources in the USA. and T. Yamazaki, "A New scheme for the running coupling constant in gauge theories As the first step towards the calculation of rare using Wilson loops", Phys.Rev. decay matrix elements of b-baryons, we have D80:034507,2009. studied the spectrum of these baryons. In particular, we are investigating the light-quark [3] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, mass dependence of the spectrum. There have C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi, been very few lattice calculations for the b-baryon E. Shintani and T. Yamazaki, "Search for the spectrum, and the parameters (quark mass, lattice IR fixed point in the twisted Polyakov loop volume, etc.) in our work are the closest to the scheme", arXiv:0910.4196 [hep-lat] (Lattice physical values. Figure 4 collects our results for 2009 proceedings). this spectrum calculation. It is shown that our [4] W. Detmold, C.-J.D. Lin and M. Wingate, results are largely compatible with experiments. "Bottom hadron mass splittings in the static This calculation has been published in Ref. [4]. limit from 2+1 flavour lattice QCD", Nucl. Phys.B818:17-27,2009. [5] S. Meinel, W. Detmold, C.-J.D. Lin and M. Wingate, "Bottom hadrons from lattice QCD with domain wall and NRQCD fermions", arXiv:0909.3837 [hep-lat] (Lattice 2009 proceedings).
We are also performing the same calculation using a different heavy-quark formulation. The result has been reported in Ref. [5]. At the same time, we are proceeding with calculations of various matrix elements. We have accumulated data for measuring the coupling amongst a vector B meson, a pseudoscalar B meson and a pion.
References [1] T. Appelquist, G. Fleming and E. Neil, "Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories", Phys.Rev. D79:076010,2009.
213 ‹‹- Research Activities of Individuals Research Activities on Spintronics
Hsiu-Hau Lin (Department of Physics, National Tsing Hua University; email: [email protected]) Center scientist, 2006/2/1~2010/1/31
n the past year (2008-2009), I have Appl. Phys. Lett 95, 082104 (2009) continued my research on low [C3] Jhih-Shih You, Wen-Min Huang and Hsiu- dimensional correlated systems (L) and Hau Lin spintronics (S) with publications listed below. Let Relativistic ferromagnetic magnon at the me briefly summarize our research results here zigzag edge of graphene and leave detail explanations for key findings in arXiv: 0901.4567 later paragraphs. Phys. Rev. B (Rapid Comm.) 78, 161404 On the low-dimensional correlated system (2008) side, we tried to address various physical [C4] Hsiu-Hau Lin, Toshiya Hikihara, Horng-Tay properties in low dimensional systems including Jeng, Bor-Luen Huang, Chung-You Mou the charge-density wave formation, conductance and Xiao Hu anomaly in carbon nanotubes and flat-band Ferromagnetism in armchair graphene freeomagnetism in armchair graphene nanoribbon. nanoribbon One of the most striking features we tried to arXiv: 0901.4177 investigate is symmetry restoration under Phys. Rev. B 79, 035405 (2009) renormalization group transformation. We devise [C5] J. E. Bunder and Hsiu-Hau Lin an elegant transformation to map the metallic Phase diagram of the metallic zigzag carbon zigzag carbon nanotube to a non-conventional nanotube two-leg ladder (without inter-leg hopping) and arXiv: 0803.3107 found an approximate SO(6) symmetry in the Phys. Rev. B 78, 035401 (2008) neutral sector. Pursuing the same direction, we [C6] J. E. Bunder and Hsiu-Hau Lin combine the techniques of the perturbative Generic short-range interactions in two-leg renormalization group and the non-perturbative ladders bosonization to obtain global phase diagram for arXiv: 0808.3297 zigzag carbon nanotube. As the interaction Phys. Rev. B 79, 045132 (2009) strength decreases into the weak-coupling regime, symmetry restoration emerges giving rise to [C7] Wen-Min Hunag and Hsiu-Hau Lin various non-trivial binding mechanism and also Identifying the pairing symmetry in sodium excitation degeneracy, which may help us to cobalt oxide by Andreev edge states: understand how non-conventional pairing arises in theoretical analysis strongly correlated systems in low dimensions. arXiv: 0901.4570 Phys. Rev. B 78, 224522 (2008) [C1] Wen-Min Huang, Jian-Ming Tang and Hsiu- [C8] Po-Yao Chang, Wen-Min Huang and Hsiu- Hau Lin Hau Lin Power-law singularity in the local density of Impurity-induced conductance anomaly in states due to the point defect in graphene zigzag carbon nanotubes arXiv: 0901.4141 J. Phys.: Conf. Ser. 150, 022007 (2009) Phys. Rev. B (Rapid Comm.) 80, 121404 (2009) [C2] Po-Yao Chang and Hsiu-Hau Lin [C9] Yen-Chen Lee and Hsiu-Hau Lin Conductance through a single impurity in Flat-band ferromagnetism in armchair the metallic zigzag carbon nanotube graphene nanoribbons
Research Activities of Individuals -›› 214 arXiv: 0901.4387 coupling mediated by itinerant carriers with J. Phys.: Conf. Ser. 150, 042110 (2009) different Fermi surfaces On the spintronics part, we applied the arXiv: 0901.4577 developed self-consistent Green’s function Phys. Rev. B 79, 045315 (2009) approach to nanoscale junctions and find the [S6] Hung-Ta Lin, Wei-Ji Huang, Shuo-Hong carrier-mediated exchange coupling strongly Wang, Hsiu-Hau Lin and Tsung-Shune Chin depends on the topology of the Fermi surface Carrier-mediated ferromagnetism in topology. We also collaborate with p-Si(100) by sequential ion-implantation of experimentalists to see whether the theoretical B and Mn predictions can be verified. In p-type Si film J. Phys.: Condensed Matter 20, 095004 implanted with B and Mn ions, the theoretical (2008) predictions are in qualitative agreement with the [S7] Wen-Min Huang, Hsin-Hua Lai, Cheng- experimental data. Furthermore, in a recent Hung Chang and Hsiu-Hau Lin collaboration, we were able to achieve Carrier-mediated exchange coupling and quantitative explanation of the magnetization Fermi surface topology (invited article) curve in amorphous Si film doped with Cr. It is Int. J. Mod. Phys. B 22, 88 (2008) rather remarkable that the quantitative agreement between the theory and the experiment can be Correlation effects of single-wall carbon achieved by only one fitting parameter! nanotubes in weak coupling Hsiu-Hau Lin [S1] Meng-Shian Lin, Hao-Cheng Hou, Yun- cond-mat/9709166 Chung Wu, Po-Hsiang Huang, Chih-Huang Phys. Rev. B 58, 4963 (1998) Lai, Hsiu-Hau Lin, Hong-Ji Lin and Fan- Hsiu Chang Effects of perpendicular interlayer coupling strength on canting angles of TbCo- sublattice magnetization Phys. Rev. B (Rapid Comm.) 79, 140412 (2009) [S2] S. Yeo, J. E. Bunder, Hsiu-Hau Lin, Myung- Hwa Jung and Sung-Ik Lee Concurrent magnetic and metal-insulator transitions in Eu1−xSmxB6 single crystals arXiv: 0901.4384 Appl. Phys. Lett. 94, 042509 (2009) [S3] Jia-Hsien Yao, Hsiu-Hau Lin and Tsung- Shune Chin Room Temperature Ferromagnetism in Cr-doped Hydrogenated Amorphous Si Films arXiv: 0901.4123 Appl. Phys. Lett. 92, 242501 (2008) [S4] J. E. Bunder and Hsiu-Hau Lin Ruderman-Kittel-Kasuya-Yosida interactions A spin liquid phase predicted in carbon on a bipartite lattice nanotubes more than a decade ago is recently arXiv: 0908.1432 spotted by experimental groups at Cal Tech and Phys. Rev. B 80, 153414 (2009) Columbia. Their experimental findings were [S5] Hsin-Hua Lai, Wen-Min Huang and Hsiu- published in Science 323, 106 (2009). Hau Lin Previous theoretical investigations show that Spatial trends of noncollinear exchange electronic interactions in carbon nanotubes at half
215 ‹‹- Research Activities of Individuals filling lead to gaps in charge and spin sectors near the edge of graphene. Meanwhile, it also without breaking the translational invariance. The indicates that the interplay between the electronic ground state is described by the so-called spin interactions and the open boundaries plays an liquid with various interesting properties. Using important role in relativistic systems. transport spectroscopy, an energy gap exisits in nominally metallic carbon nanotubes and also Ferromagnetism in armchair graphene occurs in addition to the band gap in small-band- nanoribbon gap nanotubes, indicating that carbon nanotubes Hsiu-Hau Lin, Toshiya Hikihara, Horng-Tay Jeng, Bor-Luen are never metallic. They also observed neutral Huang, Chung-You Mou and Xiao Hu arXiv: 0901.4177 excitations within the gap as predicted for this Phys. Rev. B 79, 035405 (2009) state. These experimental findings underline nanotubes' exceptional capabilities for use in studying correlated electron phenomena in one dimension. Relativistic ferromagnetic magnon at the zigzag edge of graphene Jhih-Shih You, Wen-Min Huang and Hsiu-Hau Lin arXiv: 0901.4567 Phys. Rev. B 78, 161404(R) (2008)
Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, there are exciting proposals to build spin qubits in graphene nanoribbons with armchair boundaries. However, the mutual interactions between electrons are neglected in most studies so far and thus motivate us to investigate the role of electronic correlations in armchair graphene nanoribbon by both analytical and numerical methods. Here we show that the inclusion of Relativity ensures every particle is mutual repulsions leads to drastic changes and the accompanied by its own anti-particle. Well, when ground state turns ferromagnetic in a range of arriving at the edge of the universe, we found that carrier concentrations. Our findings highlight the these relativistic twins may break apart. While it is crucial importance of the electron-electron tough to make such a long trip in our universe, it interaction and its subtle interplay with boundary is relatively easy to explore all sorts of relativistic topology in graphene nanoribbons. Furthermore, effects in graphene, a recently discovered material since the ferromagnetic properties sensitively made of single-layer graphite in your pencils. depends on the carrier concentration, it can be Interactions among electrons in graphene give rise manipulated at ease by electric gates. The to a particle named “magnon”, which describes resultant ferromagnetic state with metallic how spin disturbances propagate in the two- conductivity is not only surprising from an dimensional flatland. Remarkably, we spot a new academic viewpoint, but also has potential type of magnon near the edge of graphene with applications in spintronics at nanoscale. lower excitation energy compared with their cousins in the bulk. It is surprising that the edge Identifying the pairing symmetry in magnon does not have antiparticle while its sodium cobalt oxide by Andreev edge cousins in the bulk always appear in twin pairs as states: theoretical analysis predicted by relativity theory. This highlights the Wen-Min Hunag and Hsiu-Hau Lin importance to investigate the relativistic effects arXiv: 0901.4570 Phys. Rev. B 78, 224522 (2008)
Research Activities of Individuals -›› 216
We study the Andreev edge states with different pairing symmetries and boundary topologies on semi-infinite triangular lattice of sodium cobalt oxide. A general mapping from the two dimensional lattice to the one dimensional tight-binding model is developed. It is shown that the phase diagram of the Andreev edge states depends on the pairing symmetry and also the boundary topology. Surprisingly, the structure of the phase diagram crucially relies on the nodal points on the Fermi surface and can be explained by an elegant gauge argument. We compute the momentum-resolved local density of states near the edge and predict the hot spots which are measurable in Fourier-transformed scanning tunneling spectroscopy.
217 ‹‹- Research Activities of Individuals Research Activities on Relativistic Quantum Information
Shih-Yuin Lin (Department of Physics, National Cheng Kung University; email: [email protected]) Assistant research scholar, 2006/8/1~31, 2009/7/31
y research on relativistic quantum interference pattern of the relative degree of information (RQI) in 2009 is an extension entanglement (compared to those at spatial of my work in 2008 [1]. I study the detailed infinity) develops a parametric dependence on d. entanglement dynamics of atoms or Unruh-DeWitt The detectors separated at those d with a stronger (UD) detectors (quantum objects localized in relative degree of entanglement enjoy longer space with internal degrees of freedom such as disentanglement times. harmonic oscillators) moving in a relativistic Taking advantage of our exact, analytic quantum field. expressions of correlators, we can monitor the Our detector-field model is an open quantum behavior of the detectors from initial moment all system, in which properties of the environment the way to very late times. We find that the (the quantum field) will affect the dynamics of the detectors always disentangle at late times in the system (the detectors) via coupling, which could cases with weak coupling and large separation. depend on the position of the detectors. One of For sufficiently small d, on the other hand, the two those properties is the intrinsically relativistic detectors can have residual entanglement at late nature of the quantum field, in which physical times even if they were initially in a separable information propagates at a finite speed. Issues of state, while for d a little larger, there could be causality are unavoidably involved in our models. transient entanglement created by mutual influences. Such transient entanglement can have Since 2005 I have done a series of work on the a very long life-time which could not be handled detector-field system in collaboration with Prof. by conventional numerical calculations. Bei-Lok Hu at University of Maryland and Prof. Chung-Hsien Chou at National Cheng Kung In [2] we see no evidence of entanglement University. To see the dependence on positions of creation for initially separable states before each the detectors and the effect of retarded mutual detector started to establish causal connection influences mediated by the quantum field, we with the other, while there have been some authors applied our well developed techniques to the cases [3] claimed that quantum entanglement between with two Unruh-DeWitt detectors at rest, without two causally disconnected atoms can be created. any direct interaction, and separated at a distance These are not contradictory claims because the d [2]. This simple model when analyzed properly setups of the problem are not exactly the same. To in quantum field theory shows many interesting definitely answer whether there is entanglement facets and helps to dispel some misunderstandings creation between two causally disconnected of entanglement dynamics. We find that there is objects, we further study the entanglement spatial dependence of quantum entanglement in dynamics of two uniformly accelerated Unruh- the stable regime due to the phase difference of DeWitt detectors moving back-to-back in the field vacuum fluctuations the two detectors experience, vacuum [4]. In this setup each detector never together with the interference of the mutual enters the other's light cone, so they cannot influences from the back-reaction of one detector exchange classical information and energy. For on the other. When two initially entangled two detectors moving in this way, our exact results detectors are still outside each other's light cone, show that quantum entanglement between the the entanglement oscillates in time with amplitude detectors can be created by the quantum field dependent on spatial separation d. When the two under some specific circumstances. Prior result detectors begin to have causal contact, an derived using the time-dependent perturbation
Research Activities of Individuals -›› 218 theory with extended integration domain is shown to be a limiting case of our exact solutions at some References specific moment. We find that the created [1] S.-Y. Lin, C.-H. Chou and B. L. Hu 2008, entanglement lasts only a finite duration, and Disentanglement of two harmonic oscillators always disappears at late times in this setup. In the in relativistic motion, Phys. Rev. D 78, weak coupling limit, this entanglement creation 125025 [arXiv:0803.3995] (selected for the can occur only if the initial moment is placed January 2009 issue of Virtual Journal of early enough and the proper acceleration of the Quantum Information). detectors is not too large or too small compared to [2] S.-Y. Lin and B. L. Hu 2009, Temporal and the natural frequency of the detectors. The spatial dependence of quantum entanglement entanglement dynamics here depend on the from a field theory perspective, Phys. Rev. D fiducial time, so they are intrinsically non- 79, 085020 [arXiv:0812.4391] (selected for Markovian. In the strong coupling and high the May 2009 issue of Virtual Journal of acceleration regime, vacuum fluctuations Quantum Information). experienced by each detector locally always dominate over the cross correlations between the [3] B. Reznik 2003, Found. Phys. 33, 167; J. D. detectors, so entanglement between the detectors Franson 2008, J. Mod. Opt. 55, 2117. will never be generated. [4] S.-Y. Lin and B. L. Hu 2009, Entanglement creation between two causally disconnected Based on these findings, we propose a objects, submitted to Phys. Rev. D. conjecture on the entanglement creation time, i.e., that quantum entanglement between two spacelike separated localized objects interacting only through a common quantum field cannot be created any earlier than the earliest possible moment for a third localized object (a spectator) begins to establish causal contact with both detectors. Currently I am considering some more general cases, including those with the quantum field initially in a thermal state at finite temperature, and the detectors initially in a separable Gaussian mixed state and/or moving in time-varying accelerations. Besides, I am also looking at the dynamics of entanglement in cosmological particle production and in parametric oscillators.
219 ‹‹- Research Activities of Individuals Research Activities on Strings
Dan Tomino (email: [email protected]) Assistant research scholar, 2008/8/1~present
n 2008 my research activities in NTCS spacetime with one compactified direction when are following: 1-loop calculation is available. Our calculation produced a consistent result with such 1. Study of membrane theory with Lie observation. 3-bracket structure And I proposed a new reduced model with Lie There are five-kind of superstring theories 3-bracket structure with Dr. Kazuyuki Furuuchi of formulated in ten dimensional spacetime which NTCS [2]. These models have a fermionic have been known. Nowadays it is widely believed symmetry. Combining this symmetry with other that all of them are different aspects of an guage symmetry and translational symmetry of unknown theory, this is the unified theory of this model, they can form supersymmetry which superstring. It is also well known that if this target space is 2+2 dimensional flat space. Indeed, conjecture is true then this unified theory should when dimension of Lie 3-albgebra is infinite, one have descriptions not only by string in ten can see that this model is classically equivalent to dimensional spacetime but also by membrane in the Green-Schwarz supermembrane in 2+2 eleven dimensional spacetime. From this reason dimensional flat space. Thus our reduced model finding suitable membrane theory has been can be a regularization of continues membrane by interesting problem, because we have known little Lie 3-algebra. Carry out path integral of this about whole picture of the unified theory of super reduced model would give the quantized string. Recently Bagger and Lambert proposed an membranes. To develop the technique in order to action (BL model) which describes low energy carry out the path integral will be a future subject dynamics of multiple membranes. In several of investigation. points of view, their action is remarkable. There have been no actions for multiple membranes, 2. Classical solution of a torsion gravity which is interacting and has local gauge and super from large N matrix model conformal symmetry until their proposal. Crucial It is well known that 2-dimensional quantum point of their proposal is introducing new gravity can be described by large N matrix model mathematical structure: Lie 3-algebra which is a through its critical phenomena. There is a similar generalization of Lie algebra. attempt to reformulate superstring theory We can consider several test whether this including quantum gravity by large N Yang-Mills proposal correctly gives the dynamics of multiple (YM) type matrix model. This matrix model is membranes in eleven dimension or not. I much more complicated than so-called “old examined the BL model in this view point with matrix model” which describes 2-dimensional Dr. Takayuki Hirayama of NCTS [1]. Our strategy gravity, because there are many numbers of was to calculate 1-loop potential between two matrices coupled each other. Therefore how to membranes with relative motion. If distance describe gravity in the large N YM matrix model between two membranes are large and relative was long standing problem. Recently it is found velocity is small, the one loop potential can be that large N matrix formally can describe curved interpreted as the Newton potential. The exponent space covariant derivative, and using this of the Newton potential tells us about dimension prescription one can obtain Einstein equation with of transverse space. Different study suggested that infinitely many higher spin fields from YM matrix BL theory would describe membranes in equation of motion. Except for the infinitely many
Research Activities of Individuals -›› 220 fields there are degrees of freedom which describe torsion. This is because torsion free condition, usually imposed in Einstein gravity, is not included in YM matrix model. Now I and Dr. Hiroshi Isono of NTU study the classical gravity equation with torsion originated from YM matrix model [3]. We are investigating on how this torsion changes large/short distance behavior of solutions of Einstein equation in vacuum.
References [1] “Membrane scattering from Bagger-Lambert theory”, Takayuki Hirayama, Dan Tomino, JHEP08(2009)071, arXiv:0812.1866. [2] “Super symmetric reduced models with a symmetry based on Filippov algebra”, Kazuyuki Furuuchi, Dan Tomino, JHEP 0905070,2009. arXiv: 0902.2041. [3] Hiroshi Isono, Dan Tomino, in preparation.
221 ‹‹- Research Activities of Individuals Research Activities on Particle Physics
Chih-Wei Wang (email: [email protected]) Postdoctoral researcher, 2008/4/1~present
n 2009, my research in NCTS has been one-to-one correspondence between the split flow focused on the detail studying of the trees and the components of well-defined microstate geometries that corresponding to some supergravity solutions. We have been studied supersymmertry black holes. The concept of more details of the supergravity solutions and try microstate geometries is based on Mathur's to understand that how this correspondence can be fuzzball proposal [1]. Roughly speaking, the true and how this correspondence explicitly work. proposal state that a classical black hole should be The initial result seems to suggest that one can thought of as some ensemble of many horizon- divide the components of the solution space of the free fuzzball states. In stronger version of the bubble equations into three subsets. One of them proposal, the majority of fuzzball states can be contains CTC's and should be regarded as realized as the solutions of supergravity. These unphysical (let's called it the bad subset). The solutions are natually can be considered as remaining two are corresponding to the split flow microstate geometries of a black hole. In 2005, a trees and the scaling solutions. While there are the family of horizon-free solutions of supergravity conjecture to ensure that the subset corresponding was discovered [2,3]. These solutions, the to the split flow trees is free of CTC's, so far there so-called bubbled geometries, are potential is no systematic way to distinguish the scaling and candidates of microstate geometries and was bad subset. However, by clarifying the relation studied in the following development [4,5,6]. In between the solutions belong to the split flow tree these papers, several examples are identified as subset and the split flow trees in the modulus microstate geometries of big black hole. However, space [9], at least one can identify a particular generally, bubbled geometries have serious subset of the solutions which is well-behaved if pathology called CTC's (closed-time-like curves). one believe the conjecture. Or one can also use To avoid the appearance of CTC's and therefore this relation to check the conjecture. the violation of the causality, one need to check if the solutions satisfy a series of the so-called bubble equations. So far, a systematic method to References study the solution space of bubble equations is [1] S. D. Mathur, The fuzzball proposal for black still lacking. Furthermore, the bubble equations holes: An elementary review, [arXiv:hep- are only the necessary conditions but not th/0502050]. sufficient. The sufficient conditions are non-local [2] I. Bena and N. P. Warner, Bubbling supertubes and require one to check every points in space. and foaming black holes, [arXiv:hep- These difficulties impede a more general search/ th/0505166]. analysis of these microstate geometries. [3] P. Berglund, E.~G. Gimon and T. S. Levi, On the other hand, in 2007, F. Denef and G. W. Supergravity microstates for BPS black holes Moore introduce the concept of the split flow trees and black rings, [arXiv:hep-th/0505167]. [7] which they use to investigate OSV conjecture [4] I. Bena, C. W. Wang and N. P. Warner, The [8]. The phenomena of the split flows was found foaming three-charge black hole, [arXiv:hep- in the splitting behavior of the attractor flow in th/0604110]. modulus space when one study the system with multiple centers of black holes. Furthermore, they [5] I. Bena, C. W. Wang and N. P. Warner, propose the split flow conjecture that state there is Mergers and Typical Black Hole Microstates, [arXiv:hep-th/0608217].
Research Activities of Individuals -›› 222 [6] I. Bena, C. W. Wang and N. P. Warner, Plumbing the Abyss: Black Ring Microstates, [arXiv:0706.3786 [hep-th]]. [7] F. Denef and G. W. Moore, "Split states, entropy enigmas, holes and halos," [arXiv:hep-th/0702146]. [8] H. Ooguri, A. Strominger and C. Vafa, "Black hole attractors and the topological string," [arXiv:hep-th/0405146]. [9] C. W. Wang, in preparation.Phys. Lett. B.
223 ‹‹- Research Activities of Individuals Research Activities on String Theory
Yi Yang (Department of Electrophysics, National Chiao Tung University; email: [email protected]) Center scientist, 2008/8/1~1009/7/31
uring the year 2008/8/1~1009/7/31, I conformal theory (CFT) on the boundary of AdS have been working mainly on the two space-time. Compatifying a space dimension on a projects. One of them is to study the relationship circle to break all supersymmetries, and adding between the high energy behavior of string flavor D-branes, the boundary field theory is scattering amplitudes and the hidden symmetry in conjectured to dual to QCD. We proposed a string theory. The other is to study the low energy model, Dp-Dq system, to study the low energy QCD by using the AdS/CFT duality. phenomenology of QCD. We investigate light For the first topic, we continue our previous scalar mesons and glueballs in Dp-Dq hard-wall studies. During the last a couple of years, most of models, including D3-Dq, D4-Dq, and D6-Dq our studies were focus on the scattering systems. It is found that only in the D4-D6 and amplitudes in the high energy limit with a fixed D4-D8 hard wall models, the predicted mass of scattered angle. We call it Gross regime. In this the scalar meson f_0, scalar glueball are consistent regime, we found that the string scattering with their experimental or lattice results. This amplitudes in the same mass level are linear indicates that D4-D6 and D4-D8 hard wall models related each other. In addition, we are able to are favorite candidates of the realistic holographic compute all the ratios between the string QCD model [3]. scattering amplitudes for arbitrary fixed mass During the last year, I have attended the annual level by using the saddle-point approximation. conference of Strings2009 in Roma, Italy. I have These linear relations reveal that there is a hidden also visited Institute of High Energy Physics symmetry in the string theory. We believe that it is (IHEP). I would like to thank CTS to support me this hidden symmetry that guarantees the high attending the international activities. energy behavior of the string scattering amplitudes is exponential fall-off in Gross regime. The exponential fall-off behavior makes string theory a References UV finite theory and it provides a way to quantize gravity. To understand this hidden symmetry, we [1] S.L. Ko, J.C. Leee, Y.Y., Kummer function started to study the string scattering amplitudes in and High Energy String Scatterings, arXiv: the high energy limit with a small angle, i.e. 0811.4502. Regge regime, during the last year. We found that [2] S.L. Ko, J.C. Lee, Y.Y., Patterns of high there are many more general string states in the energy massive string scatterings in the Regge Regge regime are calculatable than those in the Gross regime. Furthermore, the string scattering regime, arXiv: 0812.4190. amplitudes are able to be obtained analytically in [3] C. Wang, S. He, M. Huang, Q.S. Yan and Y.Y., the Regge regime instead of using the saddle-point Scalar Mesons and glueballs in Dp-Dq hard- approximation. We found under some certain wall models, arXiv: 0902.0864. limits, the results obtained in the Regge regime reduces to the linear relations obtained in the Gross regime. This shed a light to understand the hidden symmetry in string theory beyond the linear relations [1,2]. The second topic I have studied during the last year is the so called AdS/QCD duality. This is a realistic version of the original AdS/CFT duality in string theory. In AdS/CFT duality, the type IIB string theory in an Anti-de-Sitter (AdS) space- time is conjectured to dual to an N=4 supersymmetry Yang-Mills field theory, which is a
Research Activities of Individuals -›› 224 Introducing New Members
Dr. Chun-Chung Chen
Assistant research scholar (Ph.D., University of Washington, USA) email: [email protected]
y research field consists of statistical and For the large number of neurons and synapses computational studies of non-equilibrium in an entire brain coupling with the daunting critical phenomena, self-organized criticality, disparity between the time scales of neural reversible polymer systems, and, currently, plastic activities (in milliseconds) and synaptic plasticity neural networks. (in days), we can not hope to reproduce or represent the brain dynamics through computer Advances in neurobiology has bettered our modeling of neural and synaptic dynamics under understanding of the fundamental working of the state of current technology. However, there are nervous systems, starting from the dynamic cultured networks consisting of hundreds of principle of neuronal electro-physiology of neurons that can still exhibit interesting dynamics. membrane potential, biochemistry of various The studies of these networks in vitro are serving chemicals involved in synaptic transmission, and as an important steppingstone towards the recently, to synaptic plasticity driven by neural understanding of more complicated networks. activities such as spike-timing. With these And, the dynamics of these cultured network are fundamental building blocks gradually in place, on a scale very much accessible to neural network here come the questions of what implications modeling such as that I am currently engaged in. these microscopic understandings of the neural The success of such modeling will not only help systems have on the macroscopic scale such as the to elucidate the observed behaviors of these dynamics of central nervous system or even cultured networks, such as, synchronization, animal behavior. My current research interest is in bursting, reverberation, etc. as well as their onset resolving such a relationship through the means of and maturation, but will also help to uncover computer simulations and statistical physics that possible missing pieces in the fundamental have been proven fruitful in the studies of working of neural and synaptic dynamics. condensed matter systems, which have faced similar challenges in bridging the microscopic understanding of matters with macroscopic phenomena.
225 ‹‹- Introducing New Members Dr. Pei-Jen Fareh Lin
Postdoctoral researcher (Ph.D., National Chiao Tung University, Taiwan) email: [email protected], [email protected]
uring Winter of 2008, I started my The relation between response and input signal is postdoctoral position at the physical division of not a simple linear relation. In addition, I have NCTS after graduating under the supervision of made a necessary improvement of TDGL to Prof. B. Rosenstein at NCTU. accommodate fast response, since the usual phase transition theory is based on equilibrium I have a broad interest in Physics in general. conditions and its eventual time-dependent What fascinates me the most is the deep versions apply only to asymptotically slow consequences of statistical physics. In particular, I changes. Making use of these modifications to the am interested in the behaviour of macroscopic standard theory, I studied far infrared magneto- collective modes, solitons, predominantly the transmission for frequencies near but below the physical properties of a strongly correlated optical gap. I compare my result with recent system, rather than the microscopic nature of a experimental data on NbN from 2009. In material. Currently, I am focusing on the measurement made using light of short pulses, the dynamical properties of systems with effects of higher electric fields become comparatively fast response. measurable. I plan to extend my study in the Quantised magnetic flux in type-II vortex solid state to more interesting states visible superconductors is referred to as vortex matter. in high-temperature superconductors such as Since the interaction within this vortex matter liquid, glass and Bragg glass. depends on parameters which may be controlled Furthermore, I plan to initiate a study of other by external magnetic field and temperature, vortex systems with second-order phase transitions; such matter provides an excellent opportunity for study. systems rapidly change their physical properties Thermal excitation, pinning (from a without release of latent heat or dramatic changes background), and internal coupling are some of of their volumes. In fact, many of these systems the phenomena contributing to the intricate H-T are interesting from an applied-technology point phase diagram of vortex matter. Probing such a of view in practical devices. Perhaps the most system with an external oscillating force, the familiar device using some of this technology is response can be observed. In performing such the LCD screen, based on phase transitions in measurements, the choice of frequency of the liquid crystals. oscillating field determines the time scale under study. I have obtained a response function for a system with driving force based on the Time- Dependent Ginzburg-Landau model analytically.
Introducing New Members -›› 226 Dr. Eibun Senaha
Postdoctoral researcher (Ph.D., the Graduate University for Advanced Studies , Japan) email: [email protected]
received my Ph.D in physics at the scales such as the Grand Unified Theory or the Graduate University for Advanced seesaw model. The other is the so-called the Studies in Japan in 2005. After being a electroweak baryogenesis, which exclusively postdoctral fellow at National Central University relies on physics at scales that we can reach by the in Taiwan for three years, I moved on to NCTS in collider experiments. At the LHC/ILC era, the August, 2009 as a postoctral fellow. latter scenario can be completely tested, and thus the theoretical calculations are more urgent. So My principal research interest is far, I have been working on electroweak phenomenology of particle physics, especially, baryogenesis in the minimal supersymmetric Higgs physics, CP violation and their standard model and beyond. The reduction of the cosmological implication. Currently, I am tackling errors in the calculation of the electroweak phase an issue of the Baryon Asymmetry of the Universe transition and sphaleron decoupling condition (BAU). Unfortunately, the standard model (SM), using the two-loop effective potential are in which is a most successful theory in particle progress. The technique which we are developing physics, failed to explain the BAU due to the can be applied to any other beyond the SM. smallness of CP violation in the Cabibbo- Kobayashi-Maskawa matrix and the lack of strong first order phase transition. In general, two approaches can exist to explain the BAU. One scenario is based on physics at the high-energy
227 ‹‹- Introducing New Members I. Words from the Director ----- 1
II. Mathematics Division ------3 Report of the Division Head ------4 Executive Committee Members ------6 Academic Committee Members ------7 Highlights of the Focus Programs ------8 Highlights of the Regional Programs ------56 Activities of Onsite Scientists ------77 Preprints ------90 Appendix ------100 I. Visiting Mathematicians ------100 II. Conference, Workshop, School & Special Lecture ------120
III. Physics Division ------129
Report of the Division Head ------130 Highlights of Programs ------134 Focus Group & Working Group Complex Systems and Soft Matter ------134 Condensed Matter Physics ------142 Particles and Fields ------153 Interdisciplinary Fields ------171 Topic Program ------182 Initiative ------186 Research Activities of Individuals ------196 Introducing New Members ------225
Annual Report Publisher: Editors: National Center for Theoretical Sciences Wen-Ching Winnie L Mandy Chen(Mathematics Division) December 2009 Sherry Pang(Physics Division) Annual Report
National Center for Theoretical Sciences
December 2009 Annual Report December 2009 Annual Report
National Center for Theoretical Sciences
National Center for Theoretical Sciences
No. 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013 Mathematics Division Physics Division Tel: 886-3-5728263/5745253~5 Tel: 886-3-5734969 Fax: 886-3-5728161 Fax: 886-3-5735086 e-mail: [email protected] e-mail: [email protected] http://www.math.cts.nthu.edu.twl http://phys.cts.nthu.edu.tw December 2009