2012 the PI and Co-PI National Science Council

Words from the Director I

his is the fourth year Prof. He is very energetic and of the third phase of our efficient. Under his leadership, the center. The center continues to physics division has already seen make good steady progress in all positive changes. aspects of the missions set by the Beginning 2012 the PI and Co-PI National Science Council. Both of Subproject I in Taipei are Pei-Min mathematics and theoretical Ho from the Physics Department physics divisions appreciate the of NTU and Jung-Kai Chen from allotted space in the new Science the Mathematics Department of Building III in the National NTU, respectively. The leadership of Chiao Tung University, which Subproject II in Tainan has remained was completed this summer. the same since 2011: Yan-Tien Lu To enhance the interaction from the Physics Department of between NCTS and NCTU, a National Cheng Kung University new research focus group on Computing Platform as PI and Ching-Hung Lam from the Mathematics for Strong Coupling Systems (in physics) is formed. Institute of Academia Sinica as co-PI. Moreover, the new focus program in Theoretical and NCTS has signed MOU's with several Computational Chemistry will start its operation international institutions, with which we keep close within the physics division beginning 2013. In interactions. We also strive to expand international addition to these, both divisions also restructured cooperation and collaboration. In 2012 Taiwan certain programs in response to last year's review. joined China, India, Japan, Korea, Singapore, and There have been important leadership changes Vietnam to become a member country of the Pan this year. After one year's leave, Wen-Ching Li has Asian Number Theory Conference, with Wen-Ching returned to NCTS to continue serving as the Director Li serving in the scientific committee led by John of NCTS. We are grateful to Sze-Bi Hsu of National Coates of Cambridge University. Three number Tsing Hua University who graciously served as the theorists from Taiwan gave invited talks in the PANT interim Director from August 2011 to April 2012. conference held in Pune, India, this July. In June, Thanks to his leadership and skills, the transition Xiao-Gang He signed a new MOU with the physicists has been seamless. Furthermore, he initiated new at Hue University in Vietnam. This December we interdisciplinary workshops between mathematicians expect to sign an MOU with mathematicians in and theoretical physicists on various topics, one Norway. per year, beginning December 2011. Ling-Fong Li Joint activities between mathematicians and completed his term as the head of the physics division theoretical physicists have increased noticeably as of December 31, 2011. We are deeply indebted to this year. The summer school in Taipei, run by his selfless service and devotion in the past two years. both divisions, on "The Physics and Mathematics It has been a pleasure to work with him. The new of Symmetry" was a big success. We aim to create division head of theoretical physics since Jan. 2012 more dialogs between both sides, hoping to lead to is Xiao-Gang He from National Taiwan University collaboration eventually. (NTU). A renowned expert in high energy physics,

1 ‹‹- Words from the Director In September the physics division went through a This has been a very fruitful year. We are proud thorough review by distinguished external experts, of what we have achieved this year and look forward who made valuable suggestions to NCTS and NSC. to a bright and exciting new year ahead. Next year the mathematics division will go through a I similar review.

Words from the Director ‹‹- 2 Mathematics Division A Report of the Division Head

his is the fourth year of the phase III Shou Lin. Another new venture is the "Seminar on T funding at NCTS. The Mathematics Modular Forms: Theory and Applications", jointly Division did very well this year. We continued organized by NCTS, TIMS and Academia Sinica. making good and steady progress towards the four This weekly seminar is simultaneously held at Taipei missions set by the NSC. The hiring in recent years (NTU) and Hsinchu (NCTS), connected via instant brought new blood and energy to many programs; the audio-visual transmission. This may become a new growth of younger programs is especially noticeable. mode of cooperative activity in the future. Kudos goes to the regional program in statistics in the To nurture young talents is our most important main project, which has improved a lot this year. mission. Young researchers, including Ph.D. students, The NCTS started the theme year in 2010. postdocs, and junior faculty members, are strongly After the special years in number theory (2010) encouraged to attend important conferences/programs and geometry (2011), the theme of 2012 is applied abroad or spend an extended period of time to work math. People in dynamical systems, mathematics with international experts. Renowned mathematicians biology, partial differential equations, and scientific like Ram Murty of Queens University were invited to computation combined their forces to organize several offer short courses in our center. Winter and summer inter-disciplinary and cross-area activities throughout schools on various topics were organized, in addition the year. It is a very fruitful and successful year in to the usual research seminars, student seminars, and applied math. To coordinate with this year's theme, special programs to prepare young researchers prior the NCTS-Postech joint workshop in 2012 is on to important conferences. Our efforts have proven Partial Differential Equations, instead of number extremely effective, as witnessed by the numerous theory as in the past three years. The highlight of papers appearing in the top journals in pure and this special year is our most prestigious Distinguish applied mathematics, and the many prestigious Lectures delivered by Fang-Hua Lin of New York awards won by our avid participants. Univ. Dec 17-19. There are two recipients of the NCTS 2011 Subproject I at NTU hosted the annual meeting Young Theorists Award in mathematics. They are of East Asia Society of Industrial and Applied Chieh-Yu Chang of National Tsing Hua University, Mathematics (EASIAM 2012) in June, attended specializing in number theory, and Je-Chiang Tsai by more than 100 people from abroad. During of National Chung Cheng University, specializing the meeting, the society of Taiwanese SIAM in differential equations and mathematical biology. was initiated. This is a giant step forward for the Jenn-Nan Wang of National Taiwan University Taiwanese mathematicians working in applied working in nonlinear partial differential equations mathematics. and Chiafu Yu of Academia Sinica in arithmetic This year NCTS launched a new "Meet with geometry and number theory are the two new holders Professor ..." series to devote one day to feature a of the Theoretical Sciences Honorary Researcher famous mathematician. Activities include lectures to award. The continuing recipients are Dong-Ho Tsai highlight his/her research achievements and a forum of National Tsing Hua University, and Yifan Yang discussion to show how he/she handled challenges and Ming-Chih Lai of National Chiao University. in mathematics. We have featured Sun-Yung Alice The recipients of these awards were selected from all Chang, Yum-Tong Siu, Ching-Li Chai, and Chang- applicants by the Executive Committee based on the

Report of the Rivision Head ‹‹- 4 rigorous evaluations by international experts. It is a great pleasure to see so many outstanding (young) mathematicians.

The theme of next year will be algebraic geometry A and representation theory. Moreover, the 6th International Congress of Chinese Mathematicians will be held in Taipei next July. We look forward to a very exciting and productive 2013.

5 ‹‹- Report of the Rivision Head AB Executive Committee Members

Committees Affiliation

Chiun-Chuan Chen National Taiwan University

Jung-Kai Chen National Taiwan University

Sze-Bi Hsu National Tsing-Hua University

Ming-Chih Lai National Chiao Tung University

Ching-Hung Lam Academia Sinica

Wen-Ching Winnie Li National Center for Theoretical Sciences

Shuenn-Jyi Sheu National Central University

Executive Commi ee Members ‹‹- 6 Academic Committee Members AC

Committees Affiliation

Gerard J. Chang National Taiwan University

Jung-Kai Chen National Taiwan University

Shun-Jen Cheng Academia Sinica

Yng-Ing Lee National Taiwan University

Tai-Chia Lin National Taiwan University

Shuenn-Jyi Sheu National Central University

Yuah-Chung Sheu National Chiao Tung University

Chih-Wen Shih National Chiao Tung University

Dong-Ho Tsai National Tsing Hua University

Wei-Cheng Wang National Tsing-Hua University

Zhu Eugene Xia National Cheng Kung University

Yifan Yang National Chiao Tung University

Chia-Fu Yu Academia Sinica

7 ‹‹- Academic Commi ee Members D Highlights of the Focus Programs

D.1 Algebraic Geometry

Coordinators: Jungkai Chen (National Taiwan University)

e have regular weekly seminar on the *: major member of the group of Algebraic W topics we proposed. We also have regular Geometry in TIMS. The program of TIMS focus on student seminar weekly as part of the project. These Gromov-Witten Theory, quantum cohomology and seminars are really the foundation of our current string theory, while the group of NCTS focus on project. During summer, we have many visitors birational geometry. We have discussion, dialogue visiting NCTS. Among them, some of them are our and cooperation and some members participate former students who are junior scholars or studying activities both sides actively. We always avoid to abroad now. doubly count the academic outputs of both sides. We are editing the conference proceeding of 4th conference“Algebraic Geometry in East Asia”held in NCTS/TPE in Nov. of 2011. The proceeding is going 1-2 Visitors Miles Reid (Warwick), Ching-Ray Lai (Utah/ to appear in the prestigious series “Advanced Studies Purdue), Chenyang Xu (Utah), Vincent Maillot in Pure Mathematics”. (CNRS/IMJ), Yukinobu Toda(IPMU, Tokyo), Yuri We are preparing the organization of “2013 Prohkorov (Moscow State), Zhi Jiang (Psris Sud). NCTS Special Program in Algebraic Geometry and Representation Theory”. The core of program in algebraic geometry will consists of several long- 2. Seminars term visitors, mini-course, and a workshop “Higher The regular joint seminar with TIMS was Dimensional Algebraic Geometry”in Mar. 25-29, organized by Jungkai Chen and Chin-Lung Wang. 2013. One of the main focuses of the seminar was on 1-1 Local Algebraic Geometry Group recent breakthrough in higher dimensional minimal Jungkai Chen (NTU), Jiun-Cheng Chen (NTHU), model program. The recent work of boundedness of *Chin-Lung Wang(NTU), *Hui-Wen Lin, (NTU), varieties of log general type by Hacon, McKernan Jeng-Daw Yu (NTU), Eugene Xia (NCKU), Wan- and Xu was the main theme of the seminar. Keng Cheong (NCKU), Hung-Jen Chiang-Hsieh The other main theme was on the recent work (CCU), *Wu-Yen Chuang (NTU), Chen-Yu Chi of Bridgeland on Stoke factors and wall crossing (NTU), Jheng-Jie Chen (NCTS postdoc), Tatsuki phenomena. The series of seminar was mainly Hayama (NTU postdoc), Hou-Yi Chen (AS postdoc), organized by Jeng-Daw Yu, Wu-Yen chuang and Chin-Yi Lin (NTU), Ph.D. student), Tsung-Ju Lee Chen-Yu Chi. (NTU, Ph.D student), Tian-Shun Feng (NTU, Ph.D student), *Sz-Sheng Wang (NTU, Ph.D student), There is also a regular student seminar organized and some other students in master program and by Jungkai Chen. The participants consist of NCTS undergraduate. research assistants and students from NTU and

Highlights of the Focus Programs ‹‹- 8 some faculty members. The main topic is on derived Birkar (Cambridge) and Hajime Tsuji (Tokyo Univ.), categories in birational geometry. the above mentioned results was extend to log pairs allowing klt singularities. In the recent joint wotk of Jungkai Chen with Olivier Debarre(Ecole Normale 3. Accomplishments Superieure, France) and Zhi Jiang (Paris Sud), further 1.Explicit Minimal Model Program in Dimension geometric properties of irregular varieties was D Three investigated. The recent work of Jungkai Chen on minimal model program in dimension three provide a detail and clearer picture of three-dimensional geometry. 4. Publications (year 2010, 2011- and By the series of work of Jungkai Chen and partly joint preprints) [1] J. A. Chen, M. Chen, Explicit birational with Christopher Hacon and Meng Chen, it’s now geometry of threefolds of general type, I, Ann. known that each birational map in dimension three Sci. École Norm. Sup (43) 2010, 365-394 (with at worst terminal singularities) can be factored into a composition of flops, blowup along a smooth [2] J. C. Chen* On Fano varieties with large curve in a smooth neighborhood, and divisorial pseudo-index, Proceeding of 2008 East-Asia contractions to a point with minimal discrepancies (or Conference in Algebraic Geometry, Advanced its inverse). This work reduces the study of birational Studies in Pure Mathematics, 60 (2010) maps in dimension three into very simple and [3] J. A. Chen, M. Chen, Explicit birational concrete ones. It is then possible to compare some geometry of threefolds of general type, II, more delicate invariants for threefolds. Jour. Diff. Geom, 86 (2010), 237-271 2.Stacky Method in Algebraic Geoemtry [4] J. A. Chen, C. D. Hacon, Factoring 3-fold flips and divisorial contractions to curves. Jour. The stacky method developed by Jiun-Cheng Reine Angew. Math., 657, (2011), 173-197 Chen (NTHU) find some more applications. In his article appeared in Advanced Studies in Pure Math., [5] J. J. Chen, J. A. Chen, M. Chen, On weighted it is prove that a variety with large pseudo-index complete intersections. J. Alg. Geom, 20, has Picard number one. There is also some result (2011), 239-262 on varieties with maximal length extremal rays. All [6] C.Y. Chi, C.L. Wang, S.S. Wang, Extensions these kind of varieties are closely related to projective of multiply twisted pluri-canonical forms, spaces and Fano varieties. In his joint work with Pure and Appl Math. Quarterly, 7 (2011). H.H. Tseng (Ohio State Univ.), he proved a version of [7] J. A. Chen, C. D. Hacon, Kodaira dimension Bogomolov-Miyaoka-Yau inequality from the method of irregular varieties, Invent. Math. 186, of Deligne-Mumford stack method. The important (2011), 481-500, arXiv 1008.2404 contribution is to provide a stacky point of view and [8] J.A, Chen, O. Debarre, Z. Jiang, Varieties with simple stacky interpretation of Bogomolov-Miyaoka- vanishing holomorphic Euler characteristic, Yau inequality. Jour. Reine Angew. Math., to appear arXiv 3.Iitaka’s Conjecture and Irregular Varieties 1105.3418 A variety with Kodaira dimension zero plays an [9] J.A. Chen, Factoring threefold divisorial important role in the classification theory of algebraic contractions to points, Ann. Scuola Norm. varieties. It is conjectured by Ueno that such varieties Sup. Pisa, to appear, arXiv 1106.1705 can be factored into abelian varieties and Calabi-Yau [10] J. C. Chen & H. H. Tseng. O n T he varieties according to the irregularity. In a joint work Bogomolov-Miyaoka-Yau inequality for with Christopher Hacon (Utah Univ.), the conjectured Deligne-Mumford surfaces, submitted. of Ueno’s was confirmed. As a consequence, Iitaka’s [11] J.A. Chen, Explicit Resolution of three conjecture Cnm was proved when base variety is of dimensional terminal singularities, preprints, maximal Albanese dimension. In the recent joint submitted. work in progress of Jungkai Chen with Caucher

9 ‹‹- Highlights of the Focus Programs [12] J.J. Chen, Finiteness of Calabi-Yau [15] J.A. Chen, Explicit Resolution of three quasismooth weighted complete intersections, dimensional terminal singularities, preprints, preprints, submitted. submitted. [13] J.A. Chen, M. Chen, Z. Jiang, On 6-canonical [16] J.J. Chen, Finiteness of Calabi-Yau D map of irregular threefolds of general type, quasismooth weighted complete intersections, preprints, submitted. preprints, submitted. [14] J.A. Chen, M. Chen, Y. Kawamata, J.H. [17] J.A. Chen, M. Chen, Z. Jiang, On 6-canonical Keum, Proceeding of “Algebraic Geometry map of irregular threefolds of general type, in East Asia-Taipei 2011”, Advanced Studies preprints, submitted. in Pure Mathematics, to appear.

D. 2 Discrete Mathematics

Coordinators: Gerard Jennhwa Chang (National Taiwan University) and Li-Da Tong (National Sun Yat Sen University).

iscrete mathematics is an active research and Combinatorics and Symposium for Young D area in Taiwan. In the program of discrete Combinatorialists, there is a three-day workshop mathematics supported by the NCTS, various on Combinatorics on August 10~12 of 2012 held at activities are organized to broaden the spectrum the Department of Applied Mathematics, National of research on discrete mathematics in Taiwan, to Sun Yat-sen University. It is now a tradition of promote international collaborations, and to provide the combinatorics community in Taiwan to hold training and opportunities for young scholars and a Symposium for Young Combinatorialists in students. The activities organized and related results the summer, to provide a platform for the Ph.D. are as follows. graduates and M.S. graduates of that year to report their research results, to communicate and discuss with each other. Also some senior professors are D.2.1 Regular weekly seminar invited to give lectures at the symposium. It is an There is a weekly seminar every Tuesday opportunity for discussion of mathematics, and also afternoon at National Taiwan University, and a an opportunity to meet friends and make the society weekly seminar every Thursday morning at National more like a big family. This event has been a tradition Sun Yat-sen University. They are platform for the for more than twenty years now and has become an center members, visitors, post doctoral fellows and important event in the community. The symposium students to share their research experiences. The for the year 2012 will be held in National Sun Yat- contents of the seminars could be talks on previous sen University from August 10 to 12. This year is results as well as current idea for a research topic. special, as one of the founders of the combinatorics community in Taiwan, Professor Gerard Jennhwa Chang, turns 60. Gerard has made tremendous D.2.2 Workshops contribution to the development of combinatorics in As part of the 2012 Workshop on Graph Theory Taiwan, through teaching and supervising students,

Highlights of the Focus Programs ‹‹- 10 doing administration work at university departments • Daphne Der-Fen Liu, California State University, U. and at National Science Council (NSC), and pursuing S. A., 2012/07/29 ~2012/08/17. research. To celebrate Gerard’s 60th birthday, • Jerrold Griggs, University of South Carolina, U. S. we expand the scale of this annual symposium, A., 2012/08/03~2012/08/25. by extending it to a 3 day workshop and inviting • Rangaswami Balakrishnan, Bharathidasan some scholars from abroad to this workshop. As D University, India, 2012/08/09~2012/08/11. before, this symposium will issue Excellent Thesis • Yuehua Bu, Zhejiang Normal University, China, awards at the end of the symposium to selected 2012/08/08~2012/08/14. theses. The selection will be done in June and July, by a committee. Students graduating this year are encouraged to submit thesis to the organizing D.2.4 Research results committee of the symposium. The conference is The results of this year are fruitful. We describe quit successful. It attracts many participants. The three most important results as follows. following is a list of invited speakers and their titles The first one is a short proof for Chen's Alternative of talks. Kneser Coloring Lemma, which leads to a short proof • Jerrold R. Griggs, Families of subsets with a of Johnson-Holroyd-Stahl's conjecture that Kneser forbidden subposet. graphs have their circular chromatic numbers equal • Rangaswami Balakrishnan, Cartesian product of to their chromatic numbers. In 1978, Lovasz proved oriented graphs with oriented hypercubes. the Kneser conjecture that the chromatic number of • Stephane Bessy, Enumerating the edge-colourings KG(n,k) is n-1k+2, by using a theorem in algebraic and total colourings of a regular graph. topology. This is one of the citations when Lovasz • Daphne Liu, From topological methods to received his Wolf Prize. Since then this method has combinatorial proofs for Kneser graphs. become an important tool with wide applications in combinatorics. Johnson, Holroyd and Stahl (1997) • Hong-Gwa Yeh, Diffusion on networks. first studied the circular chromatic number, which is a • Xuding Zhu, On-line list colouring of graphs. refinement of the chromatic number, of Kneser graphs • Sen-Peng Eu, Permutation patterns and ARM and conjectured that the circular chromatic numbers identities. is the same as the chromatic numbers. Partial results • David Kuo, The game L(d,1)-labeling problem of were established by Hajiabolhassan and Zhu (2003), graphs. Meunier (2005), Simonyi and Tardos (2006). It • Gerard Jennhwa Chang, First-fit chromatic numbers seemed not of much hope to apply their methods to of graphs. completely prove Johnson-Holroyd-Stahl's conjecture. However, recently Chen (2011) completely proved Johnson-Holroyd-Stahl's conjecture by using Fan's D.2.3 Hosting aboard visitors Lemma in an innovative way. A key step in Chen's The visitors from aboard of this year are listed as proof is to prove the Alternative Kneser Coloring follows. The visitors have close discussions with the Lemma. Chen's proof of the Lemma is rather Center members. Some join work is done during their complicated. This March we established a very short visiting, as will be described below. proof of the Alternative Kneser Coloring Lemma. It is • Daphne Der-Fen Liu, California State University, U. accepted by JCT in a very short time. The following S. A., 2012/02/05~2012/04/05. is the opinions of one referee: I feel that the note under consideration is significantly closer to a "book • Chun-Hung Liu, Georgia Institute of Technology, U proof" of this result than the original. The lemma .S. A., 2012/05/21~101/06/14. under consideration is very neat, and I agree with the • Mei Lu, Tsinghua University, China, 2012/07/20 authors that it "reveals a more delicate structure" on ~2012/08/20. optimal colorings of Kneser graphs. I anticipate that • Xuding Zhu, Zhejiang Normal University, China, this lemma will quickly become a well-discussed 2012/07/25~2012/08/20. result in the circle of ideas related to Kneser graphs,

11 ‹‹- Highlights of the Focus Programs and it would be good to have a clean, intuitive proof [4] G. J. Chang, C. Lu, J. Wu and R. Yu, Vertex- in the literature. coloring edge-weightings of graphs, Taiwnese J. The second one is a solution to a conjecture by Math. 15 (2011), 1807-1813. Chambers, Kinnersley, Prince and West on Roman [5] Y. Zhao and G. J. Chang, Consecutive edge- D domination. Domination is an important graph colorings of generalized θ-graphs, Graph parameter which has many applications in the Combin. 7033 (2011), 214-225. real world such as the location problems. Recent a [6] G. J. Chang, L.-H. Huang and H.-G. Yeh, A variation of domination called Roman domination has characterization of graphs with rank 4, Linear been extensively studied in the literature. Chambers, Algebra Appl. 434 (2011), 1793-1798. Kinnersley, Prince and West (2009) gave a challenge [7] G. J. Chang, S.-H. Cheng, Y. Qu, G. Wang and conjecture that the Roman domination number of a H. Zhang, On the number of subsequences with 2-connected graph of n vertices is upper bounded by a given sum in a finite abelian group, Elect. J. (2n+2)/3. We first disproved the conjecture by giving Combin. 18 (2011), #P13. an infinitely many counterexamples. We then proved a modified upper bound which is not too far from the [8] G. J. Chang, J. Hou and N. Roussel, Local original upper bound (see the published paper 1 of condition for planar graphs of maximum degree 2012 below). The method we employed is considering 7 to be 8-totally colorable, Discrete Appl. Math. three functions together, and then taking the average. 159 (2011), 760-768. This method is powerful and so leaded to other results (see paper 4 of 2012). Algorithmic results on 2012 strongly chordal graphs were also established (see [1] C.-H. Liu and G. J. Chang, Roman domination paper 15 of 2012). on 2-connected graphs, SIAM Disc. Math. 26 The concept of balanced decomposition (2012), 193-205. number f(G) of a graph G was introduced by Fujita [2] B.-J. Li and G. J. Chang, The competition and Nakamigawa (2008) in connection with a number of a graph with exactly two holes, J. simultaneous transfer problem. In their pioneer Combin. Optim. 23 (2012), 1-8. papers, the balanced decomposition numbers or [3] W.-H. Lin and G. J. Chang, Equitable colorings their upper bounds of complete graphs, trees, of Cartesian products of graphs, Discrete Appl. complete bipartite graphs, generalized theta-graphs, Math. 160 (2012), 239-247. subdivisions of complete graph of four vertices, and [4] C.-H. Liu and G. J. Chnag, Upper bounds on serial-parallel graphs were established. They also Roman domination numbers of graphs, Discrete proposed a challenge conjecture that the balanced Math. 312 (2012), 1386-1391. decomposition number of a 2-connected graph of n [5] G. J. Chang, P. Dorbec, M. Montassier and A. vertices is upper bounded by n/2. We recently proved Raspaud, Generalized power domination of this conjecture by a neat induction. Some other graphs, Discrete Appl. Math. 160 (2012), 1691- interesting results were also obtained. 1698. [6] G. J. Chang, T.-P. Chang and L.-D. Tong, The D.2.5 Publications Hamiltonian numbers of Mobius double loop 2011 networks, J. Combin. Optim. 23 (202), 462-470. [1] G. J. Chang and C. Lu, The L(2,1)-F-labeling [7] G. J. Chang and N. Roussel, (Δ+1)-total problem of graphs, Taiwanese J. Math. 15 (2011), choosability of planar graphs with no cycles of 1277-1285. length from 4 to k and without close triangles, Discrete Math. 312 (2012), 2126-2130. [2] G. J. Chang, Near automorphisms of paths, J. Graph Theory 68 (2011), 323-325. [8] G. J. Chang and H.-C. Hsu, First-fit chromatic numbers of d-degenerate graphs, Discrete Math. [3] W.-H. Lin and G. J. Chang, Resource-sharing 312 (2012), 2088-2090. systems and hypergraph colorings, J. Combin. Optim. 22 (2011), 499-508.

Highlights of the Focus Programs ‹‹- 12 [9] G. J. Chang, L.-H. Huang and H.-G. Yeh, A [17] G. J. Chang and N. Narayanan, Strong chromatic characterization of graphs with rank 5, Linear index of 2-degenerate graphs, J. Graph Theory, Algebra Appl. 436 (2012), 4241-4250. accepted. [10] H.-C. Hsu and G. J. Chang, Balanced [18] H.-C. Hsu and G. J. Chang, Parity and strong k-decompositions of graphs, Discrete Appl. parity edge-colorings of graphs, J. Combin. D Math. 160 (2012), 1639-1642. Optim., accepted. [11] G. J. Chang and D. D.-F. Liu, Strong edge- [19] G. J. Chang, B. S. Panda and D. Pradhan, coloring for cubic Halin graphs, Discrete Math. Complexity of distance paired-domination 312 (2012), 1468-1475. problem in graphs, Theor. Compt. Sci.-D, [12] A. Raspaud and L.-D. Tong*, Minimum accepted. identifying code graphs, Discrete Applied Math. [20] G. J. Chang, D. Liu and X. Zhu, A short poof for 160 (2012), 1385-1389. Chen's Alternative Kneser Colouring Lemma, J. [13] G. J. Chang, Algorithmic aspects of domination Combin. Theory, Series A, accepted. in graphs, Handbook of Combinatorial [21] H.-H. Lai, K.-W. Lih, C.-Y. Lin, and L.-D. Optimization, eds. Panos Pardalos, Ding-Zhu Du Tong, When is the direct product of generalized and Ronald Graham, Springer, to appear. Mycielski graphs a cover graph, Ars Combin., [14] C.-C. Lin, G.-H. Chen and G. J. Chang, An accepted. optimal algorithm for finding locally connected [22] T.-P. Chang and L.-D. Tong*, The hamiltonian spanning trees on circular-arc graphs, numbers of graphs, Ars Combin., accepted. Algoritmica, accepted. [23] Hsin-Hao Lai, K. W. Lih, C.-Y. Lin, and L.-D. [15] C.-H. Liu and G. J. Chang, Roman domination Tong, When is the direct product of generalized on strongly chordal graphs, J. Combin. Optim., Mycielski graphs a cover graph, Ars Combin., accepted. accepted. [16] B.-J. Li and G. J. Chang, Competition numbers of [24] T.-P. Chang and L.-D. Tong*, The Hamiltonian complete r-partite graphs, Discrete Appl. Math., numbers in digraphs, J. Combin. Optim., accepted. accepted.

13 ‹‹- Highlights of the Focus Programs D.3 Dynamical System

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

T he primary investigators of this focus seminars have been held at a weekly basis with talks program are Kuo-Chang Chen (NTHU), given by visiting scholars and local researchers. Ming-Chia Li (NCTU), Song-Sun Lin (NCTU), Summer schools in dynamical systems were Chih-Wen Shih (NCTU), Cheng-Hsiung Hsu (NCU) arranged with focus on specific topics. International conference or workshop is organized every year in Coordinators: Kuo-Chang Chen, Chih-Wen Shih May at NCTS. Some mini courses are arranged in the The other investigators include Jung-Chao Ban workshops. These activities broaden the spectrum of (NDHU), Chang-Yuan Cheng (NPUE), Yi-Chuan current research in Taiwan, promote the collaboration Chen (Academia Sinica), Wen-Chiao Cheng (CCUT), with international scholars, and enhance the training Shyan-Shiou Chen (NTNU), Bau-Sen Du (Academia of graduate students. Both individual and group Sinica), Jin-Long Li ((NHCTC), Ken Palmer (NTU), researchers have delivered significant works in the Jun-Hsiung Hsia (NTU), Chen-Chang Peng (NCU), past few years. We have started in 2012 spring a Shih-Feng Shieh (NTNU), Li-Chin Yeh (NHCTC), workshop for younger generations – the NCTS Young Je-Chiang Tsai (NCCU), Yalun Tsai (NTHU), Chi- Dynamics Day. Two of such workshops have been Ru Yang (NCTS), Ting-Hui Yang (Tamkang), Tzi- organized this year, and the third is under preparation. Sheng Yang (Tonghai), Suh-Yuh Yang (NCU) We expect to make it a biannual workshop held at the beginning of each semester. Such programs are intended to encourage young people to present and Dynamical System is one of the major and classical work on projects with ambition. We also have joint research areas in mathematics and mathematical activities with the topical programs of mathematical science. The discipline traces back to Newton, biology and scientific computation on some Poincare, and Birkhoff. Current interesting research applications and computational aspects of dynamical topics in the field contain the ones of classical origin: systems. The activities this year (2011.8.1-2012.7.31) celestial mechanics, Hamiltonian systems, the ones are listed below. developed since the sixties: chaotic dynamics and ergodic theory, and the ones that attract increasing attention: random dynamical systems. In addition D.3.1 Conference and Workshop: to the theoretical side, the application of dynamical 2012 NCTS Spring Young Dynamics Day system is closely linked to the nonlinear dynamics in 2012/02/18 Physics, both historically and contemporarily. The range of applications crosses from physics, biology, Introduction: The purpose of this mini workshop is information science, engineering, to economy to provide a forum for young generations within the and finance. There are more than twenty active dynamical systems community in Taiwan. researchers in dynamical systems in Taiwan. Their Speakers are encouraged to present their research research topics include n-body problem, homoclinic interests or projects with ambition, contents need orbits, entropy, delayed equation, chaotic saddle, not be finished works of their own. In this regard, synchronization, multi-dimensional perturbation, the workshop is a meeting for people to share their heterodimensional cycles, noisy oscillators, anti- "mathematical dreams", instead of limited to their integrable systems, geometric singular perturbation, research accomplishments. monotone dynamics, traveling waves, lattice Anyone interested in dynamical systems are dynamical systems, and chaotic attractors. Regular welcomed to participate, especially young scholars and graduate students.

Highlights of the Focus Programs ‹‹- 14 Organizers: 4.De-Jun Feng (The Chinese University of Hong 1.Kuo-Chang Chen (National Tsing-Hua University) Kong, Hong Kong) 2.Chih-Wen Shih (National Chiao-Tung University) 5.Wen-Guei Hu (National Chiao Tung University, Taiwan) Invited Speakers: 6.Chih-Wen Shih (National Chiao Tung University, 1.Jung-Chao Ban (National Dong Hwa University) Taiwan) D 2.Yi-Chiuan Chen (Academia Sinica) 7.Je-Chiang Tsai (National Chung Cheng University, 3.Cheng-Hsiung Hsu (National Central University) Taiwan) 4.Tsung-Lung Tsai (National Changhua University of Education) Poster Sessions: 1.Chih-Hung Chang, Feng Chia University, Taiwan 2012 NCTS Spring Young Dynamics Day 2.Te-Hsuan Chen, National Chiao Tung University, 2012/02/18 Taiwan 3.Kang-Ling Liao, National Chiao Tung University, Introduction: Dynamical Systems is a major and Taiwan active field of research in mathematical science. In 4.Ming-Jiea Lyu, National Chiao Tung University, this annual meeting on dynamical systems, we plan Taiwan to invite world leading experts to deliver lecture 5.Chi-Ru Yang, National Center for Theoretical series on active research subjects, and arrange Sciences, Taiwan several one-hour talks. Our aim is to broaden the spectrum of current research in Taiwan, to enhance the collaboration with international scholars, and D.3.2 Courses and Seminars: to lift up the academic standard of our graduate students. 2011 NCTS Summer Program on Dynamical Organizers: Systems 1.Jung-Chao Ban (National Dong-Hwa University) This summer course is intended for graduate 2.Kuo-Chang Chen (National Tsing-Hua University) students and advanced undergraduate students 3.Chih-Wen Shih (National Chiao-Tung University) who are interested in dynamical systems. Students are expected to have some basic knowledge about Invited Speakers: measure theory and differential equations. There Mini Courses Speakers: will be three topics on measure theoretic aspects of 1.Marty Golubitsky (MBI, Department of dynamical systems delivered by three instructors Mathematics, Ohio State University, US) working in related fields, plus a topic related to 2.Phil Holmes (Mechanical and Aerospace computational dynamics. Topics to be covered Engineering, Princeton University) include: 3.Hiroshi Kokubu (Department of Mathematics, Kyoto University) July 14 & 19 (Th & Tu) AM 10:30-12:00 & PM 1:30- 4.Barbara Gentz (University of Bielefeld, Germany) 3:00 5.Ka-Sing Lau (The Chinese University of Hong 陳國璋 教授 ( 清華大學數學系 ) Kong, Hong Kong) Introduction to twist maps 7/14 (R723, 7F), 7/19 (Lecture Room A, 4F) One Hour talks speakers: 1.Jung-Chao Ban (National Dong Hwa University, July 20 & 21 (W & Th) AM 10:30-12:00 & PM 1:30- Taiwan) 3:00 2.Chao-Nien Chen (National Changhua University of 陳賢修 教授 ( 臺灣師範大學數學系 ) Education, Taiwan) An Introduction to Hopf bifurcation 3.Hayato Chiba (Department of Mathematics, Lecture Room A Kyushu University, Japan)

15 ‹‹- Highlights of the Focus Programs July 26 & 28 (Tu & Th) AM 10:30-12:00 & PM Abstract for (3): 1:30-3:00 In the framework of the weak kam theory, a new 鄭文巧 教授 ( 中國文化大學應用數學系 ) kind of Lax-Oleinik type operators is introduced in An introduction to fractal geometry [Commun. Math. Phys. 309, 663 每 691 (2012)]. We Lecture Room A will introduce some important results on the new D Lax-Oleinik type operators. August 3 & 4 (W & Th) AM 10:30-12:00 & PM 1:30-3:00 (4) March 8 (Thu.), PM 1:30-3:30 班榮超 教授 ( 東華大學應用數學系 ) Rates of convergence of the Lax-Oleinik The sofic shifts and sofic measures semigroup and the new Lax-Oleinik type Lecture Room B operators

August 10 & 11 (W & Th) AM 10:30-12:00 & PM Abstract for (4): 1:30-3:00 How fast do the Lax-Oleinik semigroup and the 鄭昌源 教授 ( 屏東教育大學應用數學系 ) new Lax-Oleinik type operators converge? It is an Type-K monotone systems and the applications interesting question which is well worth discussing. Lecture Room B We believe that there is a deep relation between dynamical properties of the Aubry set (Mather set) Organizers: and the rates of convergence of the Lax-Oleinik 石至文 ( 交通大學應用數學系 ) semigroup (time independent case) and the new Lax- 李明佳 ( 交通大學應用數學系 ) Oleinik type operators. We would like to detail on 陳國璋 ( 清華大學數學系 ) available relative works in the literature.

2012 NCTS Mini Course in Dynamical Systems: Place: Weak KAM Theory and New Lax-Oleinik Type Operators (1)(2)(4), Lecture Room B , NCTS, 4th Floor, (3), R631, 6th Floor, The 3rd General Building, National Speaker: Prof. Kaizhi Wang 王楷植 (Jilin University, Tsing Hua Univ. China) (1) February 20 (Mon.), PM 1:30-3:30 2012 NCTS Summer Program on Dynamical A short introduction of the weak KAM theory I Systems

(2) February 23 (Thu.), PM 1:30-3:30 This summer course is intended for graduate A short introduction of the weak KAM theory II students and advanced undergraduate students who are interested in dynamical systems. Students Abstracts for (1) (2): are expected to have some basic knowledge about measure theory and differential equations. There will The weak kam theory introduced by Fathi makes be several topics on measure theoretic aspects of a bridge between the celebrated Mather theory and dynamical systems delivered by researchers in Taiwan the classical theory of viscosity solution of Hamilton- and China, plus some topics related to delayed Jacobi equations. This theory has been developing differential equations and bifurcation theory. rapidly for its potential applications. In this talk, We will recall some important definitions and results of July 10 & 12 (Tu & Th) PM 2:00-4:00 the weak kam theory. 班榮超 教授 ( 東華大學應用數學系 ) On the Multifractal Analysis of Gibbs and (3) (NCTS and NTHU Colloquium) Equilibrium Measures March 5 (Mon.), PM 4:00-5:00 New Lax-Oleinik type operators in the weak kam July 17 & 19 (Tu & Th) PM 2:00-4:00 theory 鄭昌源 教授 ( 屏東教育大學應用數學系 ) Applied Delayed Differential Equations

Highlights of the Focus Programs ‹‹- 16 July 24 & 26 (Tu & Th) PM 2:00-4:00 2012 NCTS Seminars on Dynamical Systems 陳賢修 教授 ( 臺灣師範大學數學系 ) Speaker: Mr. Jun-Shian Hsiao 蕭俊賢 Introduction to Bifurcation Theory (National Tsing Hua University) Time: PM 1:30-2:40, Fri., November 4, 2011 July 31 (Tu) PM 2:00-4:00 & Topic: Central Configuration (I): Introduction Aug. 7 (Tu) PM 4:00-6:00 D 鄭文巧 教授 ( 中國文化大學應用數學系 ) Speaker: Prof. Yi-Chiuan Chen 陳怡全 An Introduction to Measure-Theoretic Entropy (Academia Sinica) Time: AM 10:30, Fri., November 18, 2011 Aug. 7 & 9 (Tu & Th) PM 2:00-4:00 Topic: Abrupt Bifurcation in Chaotic Scatterings 趙云 教授 ( 蘇州大學數學系 ) Observable Measures and Applications Speaker: Mr. B. Y. Pan 潘柏宇 (National Tsing Hua University) Aug. 14 & 16 (Tu & Th) PM 2:00-4:00, Student Time: PM 1:30-2:40, Fri., November 18, 2011 Seminar Aug. 21 & 23 (Tu & Th) PM 2:00-4:00, Topic: Central Configuration (II): (1+N)-body Student Seminar Problem There will be several assignments for this Speaker: Mr. Jun-Shian Hsiao 蕭俊賢 summer courses. Students signed up for the classes (National Tsing Hua University) and supported by the CTS are required to present Time: PM 1:30-2:40, Fri., December 2, 2011 assigned materials or problems during the student Topic: Central Configuration (III): Symmetry of seminar. Details will be available during the first central configurations week of classes. Speaker: Mr. Jun-Shian Hsiao 蕭俊賢 Organizer : (National Tsing Hua University) 石至文教授 交大應數 [email protected] Time: PM 1:40-2:50, Fri., December 16, 2011 陳國璋教授 清大數學 [email protected] Topic: Central Configuration (IV): Number of central configurations Prerequisite: Real analysis, differential equations Speaker: Dr. Chi-Ru Yang 楊其儒 (NCTS) Time: PM 1:30-3:30, Fri., March 16, 2012 References: (more references will be provided during Topic: Nash-Moseriteration and KAM Theory (I) classes) 1.Y. Pesin and H. Weiss, A multifractal analysis of Speaker: Dr. Chi-Ru Yang 楊其儒 (NCTS) equilibrium measures for conformal expanding Time: PM 1:30-3:30, Fri., March 23, 2012 maps and Moran-like geometric constructions, J. Topic: Nash-Moseriteration and KAM Theory (II) Statist. Phys. 86 (1997), 233-175. 2.Y. Pesin and H. Weiss, The multifractal analysis Speaker: Dr. Chi-Ru Yang 楊其儒 (NCTS) of Gibbs measures: Motivation, mathematical Time: PM 1:30-3:30, Fri., March 30, 2012 foundation, and examples, Chaos, 7 (1997), 89-106. Topic: Nash-Moser Iteration and KAM Theory (III) 3.P. Walters, An Introduction to Ergodic theory, Cambridge University Press, 2000. Speaker: Dr. Chi-Ru Yang 楊其儒 (NCTS) Time: PM 1:30-3:30, Fri., April 13, 2012 Place: Topic: Nash-Moser Iteration and KAM Theory (IV) Lecture Room B, National Center for Theoretical Sciences (NCTS), 4th Floor, The 3rd General Speaker: Dr. Chi-Ru Yang 楊其儒 (NCTS) Building, Nat'l Tsing Hua University Time: PM 1:30-3:30, Fri., April 20, 2012 Topic: Nash-Moser Iteration and KAM Theory (V)

17 ‹‹- Highlights of the Focus Programs Speaker: Professor Chih-Wen Shih 石至文 cellular neural networks with distributive time (National Chiao Tung University) delays, Journal of Differential Equations, 251, Time: PM 12:30-1:30, Fri., April 27, 2012 630--650. Topic: Introduction to Networks of Coupled [6] Kang-Ling Liao, Chih-Wen Shih, Snapback Dynamical Systems with Symmetry Repellers and Homoclinic Orbits for Multi- D dimensional Maps, J. Math. Anal. Appl., 386 Speaker: Professor Shuh-Jye Chern 陳樹杰 (2011), 387-400. (National Tsing Hua University) [7] C.-W. Shih* and J.-P. Tseng, 2011, Global Time: PM 1:30-3:00, Fri., April 27, 2012 synchronization and asymptotic phases for a ring Topic: Introduction to Mechanical Models of Legged of identical cells with delayed coupling, SIAM J. Locomotion. Math. Anal., Vol. 43, 4, 1667-1697.

(Seminars on Analysis) 2012 Speaker: Dr. Chun-Yen Shen 沈俊嚴 [1] Jung -Chao Ban, Chih-Hung. Chang and Song- (Michigan State University) Sun Lin “On The Structure of Multi-Layer Time: PM 4:00-5:00, Thu., June 28, 2012 Cellular Neural Networks” J. Differential Topic: Recent Progresses on Some Topics in Equations (2012) vol. 252, no.8, 4563-4597. Additive Combinatorics [2] John M. Hong, Cheng-Hsiung Hsu, Bo-Chih Huang and Tzi-Sheng Yang, Geometric singular Speaker: Professor Lingmin Liao 廖靈敏 perturbation approach to the existence and (LAMA Universite Paris-Est Creteil Val de instability of stationary waves for viscous traffic Marne, France) flow models, Communications on Pure and Time: AM 10:30-12:00, Mon., July 23, 2012 Applied Analysis, (2012), accepted. Topic: Continued Fractions and Multifractal [3] John M. Hong, Cheng-Hsiung Hsu and Bo-Chih Analysis Huang, Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section, Journal D.3.3 The accomplished and the of Differential Equations 253, (2012), 1088--1110. [4] Shi-Liang Wu and Cheng-Hsiung Hsu, Entire anticipations solutions of nonlinear cellular neural networks with distributed delays, Nonlinearity, 25 (2012), 2011 [1] Jung-Chao Ban, Wen-Guei Hu, Song-Sun Lin 2785-2801. and Yin-Heng Lin (2011), Zeta functions for two- [5] Cheng-Hsiung Hsu, Chi-Ru Yang, Ting-Hui dimensional shifts of finite type, Memoirs of the Yang and Tzi-Sheng Yang, Existence of traveling Amer. Math. Soc., to appear. wave solutions for diffusive predator-prayer type [2] Jung-Chao Ban, Chih-Hung Chang and Song- model, Journal of Differential Equations 252, Sun Lin (2011), Diamond in multi-layer cellular (2012), 3040--3075. neural networks, International Journal of Circuit [6] L. Bunimovich, M.-C. Li and M.-J. Lyu, 2012, Theory and Applications, to appear. Covering relations for coupled map networks, [3] Jung-Chao Ban, Chih-Hung Chang, Ting- Journal of Mathematical Analysis and Ju Chen and Mei-Shao Lin, The Complexity Applications, 396, 189-198. of Permutive Cellular Automata, Journal of [7] K.-C. Chen*, J.S. Hsiao, Convex central Cellular Automata, 6(4-5): 385-397 (2011). configurations of the n-body problem which [4] J.-C. Ban and C.-H. Chang, Factor, Diamond and are not strictly convex. J. Dynam. Differential Density of Pressure, Proc. Amer. Math. Soc., Equations, 24, 119{128 (2012) K.-C. Chen*, T. Volume 139 (2011), 3985–3997. Ouyang, Z. Xia, Action-minimizing periodic and [5] Cheng-hsiung Hsu, Qin Jiang, Zhi-Xian Yu and quasi-periodic solutions in the n-body problem. Rong Yuan (2011), Traveling waves for nonlinear Math. Research Letters, 19, 483-497 (2012).

Highlights of the Focus Programs ‹‹- 18 [8] K.-L. Liao, C.-W. Shih* and J.-P. Tseng, 2012, [4] Shi-Liang Wu and Cheng-Hsiung Hsu, Entire Synchronized oscillations in a Mathematical solutions of non-quasi-monotone delayed model of segmentation in zebrafish, Nonlinearity reaction-diffusion equations with applications, 25, 869–904. submitted to Proceeding of the Royal Society of [9] K.-L. Liao, and C.-W. Shih*, 2012, A lattice Edinburg-A , (2012) model on somitogenesis of zebrafish, Discrete [5] Cheng-Hsiung Hsu and Jian-jhong Lin, Traveling D and Continuous Dynamical Systems –Series B, wave solutions for discrete-time model of 17 (8), 2789-2814. (SCI-Applied Math) delayed cellular neural networks, submitted to [10] A. Friedman, C.-Y. Kao, and C.-W. Shih*, International Journal of Bifurcation and Chaos, 2012, Asymptotic limit in a cell differentiation (2012). model with consideration of transcription, J. [6] John M. Hong, Cheng-Hsiung Hsu and Weishi Differential Equations 252, 5679-5711. Liu, Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a Preprints nozzle of varying area, submitted to Journal of Differential Equations, (2012). [1] Cheng-Hsiung Hsu and Tzi-Sheng Yang, [7] C.-W. Shih and J.-P. Tseng, Synchronizations in Existence, uniqueness, monotonicity and coupled systems, submitted 2012. asymptotic behavior of traveling waves for an [8] K.-L. Liao, C.-W. Shih and C.-J. Yu, Rigorous epidemic model, Nonlinearity, (2012), revised. numerical verification for snapback repellers and [2] Cheng-Hsiung Hsu, Tetu Makino, Song-Sun Lin homoclinic orbits, submitted 2012. 2. and Chi-Ru Yang, An application of Nash-Moser [9] C.H.Hsu, C.R. Yang, A Note on the Zeros of theorem to smooth solutions of one-dimensional Bessel Functions, submitted. compressible Euler equation with gravity, [10] C.R. Yang, T.H. Yang, Existence of traveling submitted to Archive for Rational Mechanics and wave solutions in a diffusive predator–prey Analysis, (2012). model with Holling’s type III Functional [3] Cheng-Hsiung Hsu, Jian-Jhong Lin and Tzi- Response, submitted. Sheng Yang, Traveling wave solutions for delayed [11] C.H.Hsu, C.R.Yang, T.S.Yang, Stability and lattice reaction-diffusion systems, submitted to Bifurcation Analysis of Neural Network Loop IMA Journal of Applied Mathematics, (2012). with distributed time delay, preprint.

D.4 Geometric Analysis and Differential Geometry

Coordinators: S.-C. Chang (NTU), Y.-I. Lee (NTU), J.-H Cheng (Academia Sinica), D.-M Nhieu (NCU), C.-J. Sung (NTHU), D.-H. Tsai (NTHU), R. Chiang (NCKU).

eometric Analysis and Differential progress in the past 25 years and yields important G Geometry (GADG) is a broad subject applications to geometry, topology, physics, nonlinear which is currently undergoing vast and rapid analysis, and so on. Of course, the most spectacular development. The newest feature in GADG is development is Hamilton's theory of Ricci flow and its probably “Geometric Flows”, which can be roughly application to three-manifold topology, including the stated as “non-linear parabolic/hyperbolic differential Hamilton-Perelman proof of the Poincaré conjecture. equations which describe the evolution of geometric The mathematicians in Taiwan whose researches structures”. Inspired by Hamilton's Ricci flow, are related to this category have a wide variety of the field of geometric flows has seen tremendous research topics and directions. During the past year,

19 ‹‹- Highlights of the Focus Programs we mainly focus on, but not limited to, the following D.4.1 Researcher in local focus group directions: Geometric Evolution Equations, Function and Map Theory, Geometric Structures, and General PI: Y.-I. Lee (NTU), S.-C. Chang (NTU), J.-H. Relativity. Cheng (Sinica), D.-M Nhieu (NCU), C.-J. Sung D Main research focus of GADG group at (NTHU), D.-H. Tsai (NTHU), River Chiang NCTS (NCKU). AI: S.-T. Yau (Harvard U, NTU), M.-D. Wang • Geometric Evolution Equations: (Columbia U, NTU), N.-K. Ho (NTHU), C.-S. Lin (NTU), C.-C. Chen (NTU), T.-C. Lin (NTU), (i) Mean curvature flow in higher co-dimension. J.-F. Hwang (Sinica), D.-C. Wu (Sinica), K.- (ii) The torsion flow and geometrization problem M. Hui (Sinica), T.-H. Chang (Sinica), Y.-K. Lu of contact 3-manifolds. (NTHU), K.-W. Lee (NTU), K.-L, Lin (NTU), (iii) The curvature flow of curves and hypersurfaces. J.-W. Chen (NTU), C.-J. Liu (NTU), C.-J. Tsai • Function and Map Theory: (NTU), T.-R. Guo (NTU), C.-C. Lin (NTNU), (i) Function theory on pseudohermitian J.-T. Chen (NTNU), J.-S. Guo (Tamkang U.), M.- manifolds. L. Yau (NCU), H.-L..Chiu (NCU), R.-T. Huang (NCU), D. Neuyen (NTU), C.-I. Ho (NCTS), (ii) Analysis on sub-manifold in a sub- L.-C. Chang (NTHU), S.-C. Chu (NCCU), C.- Riemannian manifold. C. Poon (NCCU), S.-Y. Hsu (NCCU), Y.-C. Lin (iii) Harmonic function theory, minimal (NCKU), R. Chen (NCKU), Y.-J. Hong (NCKU), submanifolds, harmonic forms on E. Z. Xia (NCKU), W.-K. Cheong (NCKU) H.-G. manifolds, heat flow of harmonic maps. Chan (NPUE), C.-T. Wu (NPUE). (iv) Analysis on sub-manifold in a sub- Riemannian manifold. • Geometric Structures: D.4.2 Visitors (i) Special Lagrangian and Hamiltonian Sun Yung Alice Chang (Princeton University), stationary sub-manifolds. Bo Guan (Ohio State University), Zhengchao Han (ii) Spherical CR structures in Cauchy-Riemann (Rutgers University), Xingwang Xu (National geometry and topology of contact manifolds. University of Singapore), Matthew J. Gursky • Other Topics: (University of Notre Dame), Hao Fang (University Motivated by Professor S. T. Yau from Harvard of Iowa), Emmanuel Hebey (Université de Cergy- University, the GADG research at Taipei also include Pontoise), Shihshu Walter Wei (University of General Relativity. Recently there has been some Oklahoma), Neil Trudinger (Australian National success in using the Geometric Flow method to University), Maria del Mar Gonzalez (Universitat solve problems in General Relativity. One significant Politecnica de Catalunya), Guofang Wei (University example is the Penrose Conjecture, which was solved of California Santa Barbara), Ray Yang (Courant by Huisken and Illmanen via the method of Inverse Institute of Mathematical Sciences), Yannick Sire Mean Curvature Flow. (Université Aix-Marseille -Paul Cézanne), Paul The GADG research at Tainan ranges from Yang (Princeton University), Wenxiong Chen symplectic geometry to algebraic geometry or (Yeshiva University), Ki-Ahm Lee (Seoul National geometric analysis. Research topics include: moduli University), Jeffrey Case (Princeton University), spaces of vector bundles, representation varieties, Xiaojun Huang (Rutgers University), Sai-Kee Yeung moment maps in various geometries, contact (Purdue University), Der-Chen Chang (Georgetown homology, Lagrangian submanifolds, orbifolds, University), Yum-Tong Siu (Harvard University), quantum cohomology, cohomological crepant Alexander Vasilev (University of Bergen), Irina resolutions, local positivity and syzygies of algebraic Markina (University of Bergen), Siye Wu (University varieties, geometric flows and harmonic maps. of Hong Kong) Steven Zucker (Tokyo Institute of

Highlights of the Focus Programs ‹‹- 20 Ki-Ahm Lee - Seoul National University , Korea Technology),Stanley Chang (Wellesley College), Kuo-Wei Lee - Academia Sinica, Taiwan Ginz Viktor L (University of California), Yoshikazu Yng-Ing Lee - National Taiwan University, Taiwan Yamagishi (Ryukoku University), David Spring (Glendon College, York University, Toronto, Canada), Chang-Shou Lin - National Taiwan University, Dan Pollock (University of Victoria), Tatiana Toro Taiwan (University of Washington). Yannick Sire - University of Marseille, France D Neil Trudinger - Australian National University, Australia D.4.3 Workshops, Course and Lecture Lihe Wang - University of Iowa, U.S.A. • NCTS Meet with Prof. Sun-Yung Alice Chang, Mu-Tao Wang - Columbia University, U.S.A. June 5, 2012 Guo-Fang Wei - Uuniversity of California Santa Invited Speakers: Barbara, U.S.A. Sun-Yung Alice Chang (Princeton University) Shihshu Walter Wei - University of Oklahoma, U.S.A. Guofang Wei (University of California Santa Barbar) Xingwang Xu - National University of Singapore, Singapore Chiung-Jue Anna Sung (National Tsing Hua University) Paul Yang - Princeton University, U.S.A. Yng-Ing Lee (National Taiwan Univesity) Ray Yang - Courant Institute of Mathematical Sciences, U.S.A. Organizers: • 2012 Workshop on Geometric Partial Differential Equations, June 7-13, 2012 Sun Yung Alice Chang The main topics of the conference include PDE (Princeton University,Princeton, USA) problems in conformal geometry and the study of Jih-Hsin Cheng (Academia Sinica, Taipei, Taiwan) fractional Laplacian operators and their applications. Chiung-Jue Sung (National Tsing-Hua University, The purpose of this conference is to bring together Hsinchu, Taiwan) active researchers to discuss recent development in the areas related to Geometric Analysis and Partial • NCTS Meet with Prof. Yum-Tong Siu, July 7, 2012 Differential Equations. Invited Speakers: Invited Speakers: Yum-Tong Siu (Harvard University) Jeffrey Case - Princeton University, U.S.A. Xiaojuan Huang (Rutgers University) Shu-Cheng Chang - National Taiwan University, Taiwan Sai-Kee Yeung (Purdue University) Chiun-Chuan Chen - National Taiwan University, Shun-Cheng Chang (National Taiwan University) Taiwan Wenxiong Chen - Yeshiva University, U.S.A. • NCTS Meet with Prof. Chang-Shou Lin, October Hao Fang - University of Iowa, U.S.A. 18, 2012 Maria del Mar González - Universitat Politècnica de Invited Speakers: Catalunya, Spain H.-Y. Huang (National SunYat-sen University) Bo Guan - Ohio State University, U.S.A. D.-H. Tsai (National Tsing Hua University) Matt Gursky - University of Notre Dame, U.S.A. C.-N. Chen (National Changhua University of Zheng-Chao Han - Rutgers University, U.S.A. Education) Emmanuel Hebey - Université de Cergy-Pontoise, T.-C. Lin (National Taiwan University) France Nan-Kuo Ho - National Tsing Hua University, Taiwan • 2012 NCTS & NCU The Workshop on CR Obata's Theorem, Nov. 29, 2012

21 ‹‹- Highlights of the Focus Programs Invited Speakers: the classification of isoparametric hypersurfaces with 吳進通 教授 ( 國立屏東教育大學 ) four principal curvatures and multiplicities 7, 7, 8, 8 in the 31-dimensional sphere. In the first part of the 陳瑞堂 教授 ( 國立台灣師範大學 ) lecture I will talk about the structure of homogeneous 邱鴻麟 教授 國立中央大學 ( ) isoparametric hypersurfaces in spheres and how D 題目 : they interact with certain representations, etc. In 1. The Introduction to CR Obata's Theorem the second part I will talk about the classification of 2. A Note on CR Obata's Theorem isoparametric hypersurfaces in spheres and have a look at the last unsettled case. 3. CR Obata's Theorem The Lecture will start with group action and homogenous spaces. • 2012 NCTS Mini-Course on Geometric Analysis (6/4、6/6) Organizer: Lecturer: Prof. Yng-Ing Lee (National Taiwan University) Prof. Gonzlez, Maria del Mar (Universitat Politecnica de Catalunya, Spain) • The Fifth Taiwan Geometry Symposium, Oct27, Prof. Guo-Fang Wei (University of California Santa 2012 Barbara) The purpose of the Taiwan Geometry Symposium • 2012 NCTS Summer Course on Fourier Analysis is to foster discussions and interactions within the and Its Applications to Several Complex geometry community in Taiwan. It hopes to meet Variables (6/28-7/10) regularly in the years to come, running on a Saturday Lecturer: Prof. Der-Chen Chang 張德健 (Georgetown from late morning to late afternoon, with 3 speakers, University) followed by dinner. The activity will rotate among • 2012 NCTS Mini-Course on Differential Taipei, Hsin-Chu and Tainan. We encourage everyone Geometry, July 10-11, 2012 that is interested in Geometry, and particularly Lecturer: Prof. Huai-Liang Chang 張 懷 良 (The students, postdoctoral fellows and young scholars to Hong Kong University of Science and participate in the Symposium. Technology) Speakers will include: • < Summer 2012 > NCTS Summer Course on Shu-Cheng Chang, National Taiwan University Introductory PDEs Wan-Keng Cheong, National Cheng Kung University Lecturer: Prof. Tsai, Dong-Ho 蔡 東 和 (National Hung-Lin Chiu, National Central University Tsing Hua University) Organizers: • NCTS/TPE 2012 Geometry Summer Course, Nan-Ko Ho, National Tsing Hua University June 25-July 8, 2012 Yng-Ing Lee, National Taiwan University Speaker: Eugene Zhu Xia, National Cheng Kung University Prof. Quo-Shin Chi Department of Mathematics, • The 4th Taiwan Geometry Symposium, May 19, Washington University in St. Louis, USA 2012 Title The purpose of the Taiwan Geometry Symposium The isoparametric story is to foster discussions and interactions within the Abstract: geometry community in Taiwan. It hopes to meet 94 years after Laura first investigated the kind regularly in the years to come, running on a Saturday of wave fronts, called isoparametric surfaces, in the from late morning to late afternoon, with 3 speakers, Euclidean 3-space, the classification of isoparametric followed by dinner. The activity will rotate among hypersurfaces in spheres is near the end; at this point Taipei, Hsin-Chu and Tainan. We encourage everyone there remains only one last case to tackle, namely, who is interested in Geometry, and particularly

Highlights of the Focus Programs ‹‹- 22 students, postdoctoral fellows and young scholars to Fujiie, Hiroshi Isozaki, Hiroya Ito, Hiroshi Ito, Mishio participate in the Symposium. Kawashita, Koji Kikuchi, Shiro Kubo, Takeshi Organizers: Mandai, Kiyoshi Mochizuki, Akira Morimoto, Sei Nagayasu, Hideo Nakazawa, Takashi Ohe, Hideo Prof. Nan Kuo Ho (Department of Mathematics, Soga, Hiroyuki Takamura, Hideki Takuwa, Tomio NTHU) Umeda, Michiyuki Watanabe, Hideshi Yamane. D Prof. Yng-Ing Lee (Department of Mathematics, Organizers: NTU) Ryuichi Ashino, Chiun-Chuan Chen, Mishio Prof. Eugene Zhu Xia (Department of Mathematics, Kawashita, Hideki Takuwa, Jenn-Nan Wang NCKU) Invited Speakers: Chen-Yu Chi (Department of Mathematics, Harvard D.4.4 Seminars and Student Seminars University & NTU) Shu-Yu Hsu (Department of Mathematics, NCCU) • 2012 NCTS Student Complex Geometry Seminar Chiung-Jue Sung (Department of Mathematics, NTHU) Organizer: Professor Jiun-Cheng Chen 陳俊成 (National Tsing Hua University) 陳志豪 同學 清華大學 • 2012 NCTS Taiwan-Japan Joint Conference on Speaker: ( ) PDE and Analysis, December 26- 28, 2012 游薪軒 同學 ( 國立清華大學 ) The 2011 Taiwan-Japan Joint Workshop on PDEs Topic include: Complex Manifolds: Definition and and Geometric Analysis will be held at the National Examples, Complex Manifolds: Examples, Divisors Center for Theoretical Sciences on December 19-21, and Line Bundles, Projective Spaces and Blow Up, 2011. The aim of this workshop is to bring together Differential Calculus on Complex Manifolds, Kahler Identity, Kahler Manifolds active researchers with different backgrounds to discuss recent and prospective advances related to Geometric Analysis and Partial Differential • 2012 NCTS Student Algebraic Geometry Equations. The workshop will contain lectures Seminar related to elliptic and sub-elliptic partial differential Speaker: Professor Jiun-Cheng Chen 陳俊成 equations, sub-Riemannian geometry and problems (National Tsing Hua University) related to mathematical physics. We hope to use this Topic include: Curves and Divisor on Algebraic opportunity to discuss possible joint projects between Varieties, Ample Line Bundles and Nef Line researchers in Taiwan and Japan. We also hope Bundles, Exceptional Loci of Birational Morphisms, to attract young scholars and Ph.D. students to do Mori's Bend and Break, Deformation Theory, Mod p research along these directions. During the workshop, Reduction and Rational Curves there will be discussion sessions every afternoon for postdocs and graduate students to promote the advances between Taiwan and Japan. This workshop • 2012 NCTS Geometry Learning Seminar is partially supported by the National Center for Organizer: Prof. Jyh-Haur Teh 鄭志豪 ( 清大 ) Theoretical Sciences (Taiwan Hsinchu) and the Japan Speaker: 李育浚、廖軒毅、官侑萱、鄭期佑、徐嘉隆、 Society for the Promotion of Science. 吳旻駿 Speakers will include: Topic include: Axiomatic Topological Quantum Chiun-Chuan Chen, I-Liang Chern, Jann-Long Field Theory, Preschemes, Topological K-theory, Chern, Jong-Shenq Guo, Meng-Kai Hong, Chun- Categories of TQFT, Theorems of Radon and Hsiung Hsia, Hsin-Yuan Huang, Jin-Cheng Jiang, Caratheodory, Nearest Point Map and Supporting Hung-Wen Kuo, Kuo-Ming Lee, Tai-Chia Lin, Chun- Hyperplanes, Hurewicz Isomorphism, TQFT formed Liang Lin, Ching-Lung Lin, Tu Nguyen, Jenn-Nan by finite CW-Complexes, Faces and Normal Cones, Wang, Fumioki Asakura, Ryuichi Ashino, Setsuro Homotopical Cohomology Groups, Brouwer Fixed

23 ‹‹- Highlights of the Focus Programs Point Theorem, Tropical Algebraic Geometry, Support and Lukasik) ll Function and Distance Function, Thom Isomorphism Mar27, 2012 Theorem, 2D TQFT, Lie Derivatives, Polar Bodies, Speaker: 李國瑋博士 (Academia Sinica) Brown Representability, Proof of the Stokes Title: Particlelike solutions of the Einstein-Yang-Mills Theorem, Polar Polytopes and Quotient Polytopes, equations (after Bartnik and McKinnon) D Serre-Swan Theorem, De Rham Cohomology, Finite Generation of Cones, Toric Varieties, Homotopy Apr10, 2012 Groups, Rational Homotopy Theory. Speaker: Prof. Lars Anderson(Albert-Einstein-Institut Golm, Potsdam, Germany) • 2012 NCTS Geometry Seminar Title: Hidden symmetries and conserved charges (I) Organizer: Prof. Jyh-Haur Teh 鄭志豪 ( 清大 ) Apr17, 2012 Speaker: Dr. 陳泰蔚 (NTHU), Dr. 何忠益 (NCTS) Speaker: 蔡忠潤博士 (National Taiwan University) Topic include: Generalized Complex Geometry, Bott- Title: On conformally Kahler, Einstein manifolds Chern Cohomology (after Chen,LeBrun and Weber) Apr24, 2012 • 2012 NCTS Geometry Learning Seminar Speaker: 王文才教授 ((National Taiwan University)) Organizer: Prof. Chiung-Jue Sung 宋瓊珠 ( 清大 ) Title: Connectedness of the space of positive scalar Speaker: Nguyen Thac Dung、陳義麟、王一珊、鄭期 curvature metrics 佑、徐嘉隆、吳旻駿 May08,2012 Topic include: On the Gradient Ricci Solitons, Speaker: 王業凱先生 (National Taiwan University) The Function Theory on Complete Smooth Metric Title: Page Metric (after D. Page) Measure Space, On Spaces of Harmonic Functions, May15, 2012 Volume Estimate on Gradient Ricci Soliton. Speaker: 黃信元教授 (National Taiwan University) Title: The Chenciner-Montgomery Figure-Eight Orbit • 2012 NCTS Analysis Seminar, June 28, 2012 May22, 2012 Speaker: Dr. Chun-Yen Shen 沈俊嚴 (Michigan State 洪培根先生 University) Speaker: (National Taiwan University) Topic: Recent Progresses on Some Topics in Additive Title: The existence of negatively Ricci curved Combinatorics metrics on three manifolds May29, 2012 • NTU & NCTS/TPE working seminar on Speaker: 李國瑋博士 (Academia Sinica) Riemannian Geometry and General Relativity Title: Gravitational instantons (after M. J. Perry) Feb21, 2012 Oct02, 2012 Speaker: 王業凱先生 (National Taiwan University) Speaker: 蘇瑋栢先生 (National Taiwan University) Title: Conformal Yano-Killing tensor for the Kerr Title: Heat kernel comparison and eigenvalue metric and conserved quantities(following estimate Jezierski and Lukasik) Oct09, 2012 Mar06, 2012 Speaker: 陳志偉博士 (National Taiwan University) 李國瑋博士 Speaker: (Academia Sinica) Title: Geometry of gradient Ricci solitons (I) ’ Title: Review Mu-Tao Wang s lectures on General Oct16, 2012 Relativity Speaker: 黃垣熊先生 (National Taiwan University) Mar13, 2012 Title: Existence of Heat Kernel in Riemannian 王業凱先生 Speaker: (National Taiwan University) Manifold Title: Conformal Yano-Killing tensor for the Kerr metric and conserved quantities(following Jezierski

Highlights of the Focus Programs ‹‹- 24 Oct23, 2012 • NCTS Student Reading Seminar on Geometry, Speaker: 黃垣熊先生 (National Taiwan University) May 21, 2012 Title: Existence of Heat Kernel in Riemannian Speaker: Mr. 康仕承 (Dept. of Math., NCKU) Manifold ll Topic: Fundamental Groups and Ribbon Graphs 1 Oct30, 2012 • NCTS Student Reading Seminar on Geometry, D Speaker: 陳志偉博士 (National Taiwan University) May 29, 2012 Title: Geometry of gradient Ricci solitons ll Speaker: Mr. 康仕承 (Dept. of Math., NCKU) Nov06, 2012 Topic: Fundamental Groups and Ribbon Graphs 2 Speaker: 黃書庭先生 (National Taiwan University) • NCTS Student Reading Seminar on Geometry, June 5, 2012 Title: Eigenvalues of the Laplacian on spheres Speaker: Mr. 康仕承 (Dept. of Math., NCKU) Nov13, 2012 Topic: Fundamental Groups and Ribbon Graphs 3 Speaker: 蘇瑋栢先生 (National Taiwan University) • NCTS Student Reading Seminar on Geometry, Title: Asymptotic Expansion of Heat Kernel June 12, 2012 Speaker: Mr. 康仕承 (Dept. of Math., NCKU) • NTU & NCTS/TPE Geometry Seminar Topic: De Rham Comology and Ribbon Graphs Mar20, 2012 • NCTS Seminar, July 19, 2012 Speaker: Prof. David Spring(Glendon College, York Speaker: Prof. Huai-Liang Chang 張 懷 良 University, Toronto, Canada) (Department of Mathematics, The Hong Kong Title: Convex Integration theory: past and present University of Science and Technology, Hong Kong) • NCTS Reading Seminar on Symplectic Geometry, Topic: Algebraic Geometric Construction of Seiberg- April 20, 2012 Witten Invariants Speaker: Prof. River Chiang 江孟蓉 (Dept. of Math., • NCTS Algebraic Geometry Learning Seminar, NCKU) September 26, 2012 Topic: Iterated translated points (after S. Sandon) Speaker: Mr. 宋政蒲 (Dept. of Math., NCKU) • NCTS Reading Seminar on Symplectic Topic: Excess Intersection (I) Geometry, April 27, 2012 • NCTS Algebraic Geometry Learning Seminar, Speaker: Prof. Rung-Tzung Huang 黃榮宗 (Dept. of October 3, 2012 Math., NCU) Speakers include: Mr. 許用 (Dept. of Math., NCKU)、 Topic: Signature quantization (after V. Guillemin, S. Mr. 宋政蒲 (Dept. of Math., NCKU) Sternberg & J. Weitsman) Topics include: Topology of algebraic varieties (II), • NCTS Student Reading Seminar on Geometry, Excess Intersection (II) May 8, 2012 • NCTS Algebraic Geometry Learning Seminar, Speaker: Mr. 康仕承 (Dept. of Math., NCKU) October 17, 2012 Topic: Ribbon Graphs Speakers include: Mr. 許用 (Dept. of Math., NCKU)、 • NCTS Reading Seminar on Symplectic Geometry, Mr. 宋政蒲 (Dept. of Math., NCKU) May 11, 2012 Topics include: On birational maps, Excess Speaker: Prof. River Chiang (Dept. of Math., NCKU) intersection (III) Topic: Iterated translated points II (after S. Sandon) • NCTS Algebraic Geometry Learning Seminar, • NCTS Reading Seminar on Symplectic Geometry, November 7, 2012 May 18, 2012 Speakers include: Mr. 許用 (Dept. of Math., NCKU)、 Speaker: Prof. Mei-Lin Yau (Dept. of Math., NCU) Mr. 宋政蒲 (Dept. of Math., NCKU) Topic: Weinstein structures III (after K. Cieliebak and Topics include: Elimination of indeterminacies, The Y. Eliashberg) moduli space of stable maps

25 ‹‹- Highlights of the Focus Programs D.4.5 Accomplishments 364, no. 11, 5735-5763, 2012. [12] Y.-C. Lin, D.-H. Tsai, Application of Andrews In below we list papers published (or accepted) in the and Green-Osher inequalities to nonlocal flow year 2012. of convex plane curves, Journal of Evolution Equations, published on-line, June 27, 2012. D [1] Y.-I. Lee, The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds [13] D.-C. Chang, W. Eby, E. Grinberg, of any dimension, Calc. Var. Partial Differential Deconvolution for the Pompeiu problem on the Equations, vol. 45 (2012), 231-251. Heisenberg group I, The mathematical Legacy of Leon Ehrenpreis, edited by D. Struppa and I. [2] J.-H Cheng, J.-F. Hwang, A. Malchiodi and P. Sabadini, Springer Proceedings in Mathematics, Yang, A Codazzi-like equation and the singular 2012, Volume 16, Part 2, 61-94. set for smooth surfaces in the Heisenberg group, to appear in Journal fur reine und angewandte [14] Jyh-Haur Teh, Families of algebraic varieties Mathematik, 2012. parametrized by topological spaces, to appear in Communications in algebra, 2012. [3] Y.-I. Lee and Y.-K. Lue, the stability of self- shrinkers of mean curvature flow in higher co- [15] T.-D. Nguyen, C.-J. Sung, Smooth metric dimension (2012), to appear in Trans. Amer. measure Space with weighted Poincare Math. Soc. inequality, to appear in Mathematische Zeitschrift, 2012. [4] C.-J. Tsai, L.-S. Tseng, and S.-T. Yau, Symplectic cohomologies on phase space, J. Math. Phys. 53, [16] T.-D. Nguyen, C.-J. Sung, Manifolds with a 095217 (2012). weighted Poincare Inequality, to appear in Proc. of the AMS, 2012. [5] Goldman, William M.; Xia, Eugene Z. Action of the Johnson-Torelli group on representation [17] Yongsheng Han, Ming-Yi Lee and Chin-Cheng varieties. Proceedings of The American Lin, Atomic Decomposition and Boundedness Mathematical Society 140 (2012), 1449-1457. of Operators on Weighted Hardy Spaces, Canad. Math. Bull. Vol. 55 (2), 303–314, 2012. [6] Xia, Eugene Z. Dehn twists and invariant classes. Proceedings of The American Mathematical [18] M. G. Molina, I. Markina: Sub-Riemann Society 140 (2012), 1173-1183. geodesics and heat operator on odd dimensional spheres, Analysis and Mathematical Physics [7] Xia, Eugene Z., Abelian and Non-Abelian June 2012, Volume 2, Issue 2, pp 123-147. Cohomology, Geometry, Topology And Dynamics Of Character Varieties, Lecture [19] Sakai, Hironori. The symplectic Deligne– notes series, institute of mathematical sciences, Mumford stack associated to a stacky polytope. national university of Singapore, 309-349, Vol. 23 Results in Mathematics, 2012. DOI: 10.1007/ (2012). s00025-012-0240-3. [8] S.-C. Chang and C.-T. Wu, The Diameter Estimate and Its Application to CR Obata's Theorem on Closed Pseudohermitian (2n+1)- Manifolds, Trans. Amer. Math. Soc. 364 (2012), 3349-3363. [9] Y.-C. Lin, D.-H. Tsai, Remarks on some isoperimetric properties of the k-1 flow, Pacific J of Math, 260 (2012). 197-214. [10] Jyh-Haur Teh, Semi-topological cycle theory I, Pacific J. Math., 259 (2012), 195-208. [11] Y.-C. Lin, C.-C. Poon, D.-H. Tsai, Contracting convex immersed closed plane curves with slow speed of curvature, Transactions of the AMS,

Highlights of the Focus Programs ‹‹- 26 D.5 Mathematical Biology

Coordinators: Sze-Bi Hsu (National Tsing-Hua University), Chih Wen Shih (Natinal Chiao-Tung University) D

T he purpose of the focus program in Schedule: Mathematical Biology is to promote the Mini-courses: interdisciplinary interaction between mathematicians, Friday (May 4, 11, 18): 2 - 5 PM biologists, physicists, statisticians and computer scientists on the new problems arising from biology. Saturday (May 5, 12, 19): 9 - 12 AM, and 2 - 5 PM In the past one year, we held one month program in Sunday (May 6, 13, 20): 9 -12 AM “Nonlinear Equations in Spatial Population Biology” International Workshop in May, 4-26,2012. The mini-courses were given May 24 (Thursday) - May 26 (Saturday) in the weekends of May (5/4-5/6,5/11-5/13,5/18- Mini-course Lecturers 5/21) by the visitors and local experts. We had a workshop in May 24-26. In addition to the mini- (1) Steve Cantrell (University of Miami, USA) courses and workshop, we held a weekly seminars Exploring the evolutionary advantages of quasi- in Mathematical Biology, a summer course in linear dispersal: A beginning Mathematical Models in Molecular Biology . We also (2) Chris Cosner (University of Miami, USA) invite several speakers to give talks in population Models for dispersal and its evolutionary Ecology: biology, uniformly persistence theory and traveling A Comparative approach waves. (3) Chuin-Chuan Chen (National Taiwan University) We state as follows: Traveling waves of three competing species Local Group: Jann-Long Chern (NCU), Sze-Bi (4) Yihong Du (University of New England, Australia) Hsu (NTHU), Chui-Ju Lin (NTHU), Chih-Wen Shih (NCTU), Yong-Li Tang(NCTS), Shin-Hwa Wang Concentration phenomena in a nonolocal quasi- (NTHU), Chih-Jiang Tsai (NCCU), Ting-Hui Yang linear problem modeling phytoplankton (Tamkang University), Lin-Feng Mei (NCTS) (5) Jong-Shenq Guo (Tamkang University) Travelling front for a Lattice Dynamical System in a mono-stable two-species competition system D.5.1 Mini-courses and Worshop in the program of “Nonlinear Equations (6) Sze-Bi Hsu (National Tsinghua University) in Spatial Population Biology” Mathematical analysis of the model for single phytoiplankton species growth with light and 2012 NCTS Program On Nonliear Equations In advection in a water column Spatial Population Biology (7) Wei-Ming Ni (ECNU, China, and University of The purpose of this one-month program is to Minnesota, USA) survey new developments in nonlinear equations Diffusion and spatial heterogeneity with applications to spatial population biology. This (8) Jzy-Chiang Tsai (National Chung-Cheng program consists of several mini-courses and various University) talks, scattered throughout the month of May, 2012, The buffering effect on travelling wave in buffered and an international workshop toward the end of FitzHugh-Nagumo model. May. In the mini-courses, we shall emphasize both new mathematical methods as well as modeling in (9) Kohei Yoshiyama (River Basin Research Center, spatial population biology. Gifu University, Japan)

27 ‹‹- Highlights of the Focus Programs Models of the vertical distributed of phytoplankton. 2.3 Noncoding Sequences (10) Xiaoqiang Zhao (Memorial University of 2.4 Protein-Coding Sequences Newfoundland, Canada) < July 20 (Friday), 2:00-5:00 pm > Basic reproduction ratios and Spreading speeds Phylogenetic Reconstruction D Workshop Speakers 3.1 Comparing Two Sequences --- The Basic Steve Cantrell (University of Miami, USA) Algorithm Chuin-Chuan Chen (National Taiwan University) 3.2 Database Search --- BLAST Chris Cosner (University of Miami, USA) 3.3 Phylogenetic Trees and Applications Yihong Du (University of New England, Australia) < July 27 (Friday), 2:00-5:00 pm > Robert Holt (University of Florida, USA) Gene Duplication and Diversification Tai-Chia Lin (National Taiwan University) 4.1 Gene duplication mechanism Salome Martinez (University of Chile, Chile) 4.2 Transcription factors --- the input function of a gene Jzy-Chiang Tsai (National Chung-Cheng University) 4.3 Functional diversification Chuin-Chang Lee (National Taiwan University) Feng-Bin Wang (Wu-Lin High School & NCTS) II. 2012 NCTS Focus Program in Mathematical Organizers Biology Sze-Bi Hsu (National Tsing-Hua University) Organizers: Wei-Ming Ni (East China Normal University and Professor Sze-Bi Hsu 許世壁 (NTHU) University of Minnesota) Professor Jann-Long Chern 陳建隆 (NCU) Professor Shin-Hwa Wang 王信華 (NTHU) D.5.2 Course & Seminars Professor Ting-Hui Yang 楊定輝 (Tamkang University) The weekly seminar (2/21/2011~5/9/2011) was held I. 2012 NCTS Summer Course in Mathematical every Monday, 2:00pm-4:00pm. In addition to invited Models in Molecular Biology talks, the post doctors and graduate students present Dates : 7/6-7/27, Every Friday(7/6, 7/13, 7/20, 7/27) 。 their own work or some important papers in PDE and Speaker: Dr.Tzeng Yun-Huei 曾雲輝 (China Medical Mathematical Biology. The topics are followings: University) 2011 NCTS Seminar on Mathematical Biology < July 6 (Friday), 2:00-5:00 pm > Invited talks Dynamics of Genes in Polulation (1) Speaker: Prof. Peter Chesson 1.1 Changes in Allele Frequencies (Dept of Ecology and Evolutionary Biology, 1.2 Natural Selection University of Arizona, USA) 1.3 Random Genetic Drift Time: PM 4:00-5:00, Wed., October 12, 2011 1.4 Effective Population Size Topic: Modeling the Effects of Environmental Variation in Community Ecology 1.5 Gene Substitution (2) Speaker: Professor Hamn-Ching Chen 陳漢卿 1.6 Genetic Polymorphism (Department of Civil Engineering, Texas A & M 1.7 The Fundamental Theorem of Natural Selection University) < July 13 (Friday), 2:00-5:00 pm > Time: PM 3:00-4:00, Wed., December 14, 2011 Estimating the Number of Nucleotide Substitutions Topic: Introduction to Finite Analytic Method for between Sequences Computational Fluid Dynamics and Some of Its 2.1 Nucleotide Substitution in a DNA Sequence Applications 2.2 Divergence Between DNA Sequences (3) Speaker: Prof. Yihong Du 杜一宏 (University of

Highlights of the Focus Programs ‹‹- 28 New England, Australia) (11) Speaker: Prof. James Cushing (University of Time: PM 2:00-4:00, December 5 &12 (Mon.), Arizona, USA) 2011 Time: 10:00am-11:00, Tue., August 7, 2012 Topic: Semi-waves in Homogeneous Media & Topic: Mathematical Models and Experimental periodic waves Nonlinear Population Dynamics D (4) Speaker: Professor Chiu-Yen Kao (Ohio State (12) Speaker: Prof. Kohei Yoshiyama (Gif u University) University, Japan) & Prof. Sze-Bi Hsu 許 世 壁 Time: PM 4:00-5:00, Thu., January 12, 2012 (NTHU) Topic: Principal Eigenvalue Minimization for Time: PM 2:00-4 :00, Thu., Aug. 9 & 16 & 23, an Elliptic Problem with Indefinite Weight and 2012 Robin Boundary Conditions Topic: Discussions and open problems in (5) Speaker: Prof. Xueying Wang (Texas A & M Phytoplankton Ecology University) (13) Speaker: Prof. James Cushing (University of Time: PM 4:00-5:00, Mon., December 19, 2011 Arizona, USA) Topic: Stochastic Trojan Y-chromosome Models Time: PM 3:00-4:00, Fri., August 10, 2012 for Eradication of an Invasive Fish Species Topic: Semelparity and a Dynamic Dichotomy (6) Speaker: Professor Leonid Hanin(Idaho State (14) Speaker: Prof. James Cushing (University of University and Georgia Institute of Technology, Arizona, USA) USA) Time: PM 3:00-4:00, Fri., August 17, 2012 Time: PM 3:00-4:00, Wed., February 29, 2012 Topic: Darwinian Matrix Models Topic: Spatial Periodicities in Chromosomeal (15) Speaker: Prof. Nie Hua 聶華 ( 陝西師大數學與 Gene Expression Revealed by Spectral Analysis 信息科學院 ) (7) Speaker: Professor Je-Chiang Tsai 蔡 志 強 Time: 14:00-16 :00, Tue., August 28, 2012 (National Chung Cheng University) Topic: Competition of Phytoplankton Species in Time: PM 1:00-3:00, Mon., March 5, 2012 a Water Column under the Excessive CO_2 Topic: Traveling Waves in a Simplified Model of Calcium Dynamics Student and post doctor Seminars (8) Speaker: Prof. Ariel Fernandez (Morgridge (1) Speaker: Dr. Yong-Li Tang 唐永立 (NCTS) Institute for Research, University of Wisconsin) Time: PM 2:00-4 :00, Mon., March 12, 2012 Time: PM 3:10-4:00, Fri., March 30, 2012 Topic: Existence and Uniqueness of Coexistence Topic: Nonadaptive Origins of Interactome States for a One-Dimensional Predator-Prey Complexity Model with Diffusion (9) Speaker: Prof. Yun-Huei Tzeng 曾雲輝 (Graduate (2) Speaker: Miss Chiu-Ju Lin 林秋如 (NTHU) Institute of Biostatistics, Chinese Medical Time: PM 2:00-4 :00, Mon., March 19, 2012 University) Topic: Single Phytoplankton Growth on Light: Time: PM 4:10-5:00, Fri., March 30, 2012 The Deep Water Column Case T o p i c : M a t h e m a t i c a l M o d e l s o f Subfunctionalization and Fitness in Gene (3) Speaker: Dr. Yong-Li Tang 唐永立 (NCTS) Duplication Time: PM 2:00-4 :00, Mon.,April 11 & April 23, 2012 (10) Speaker: Professor Polly Sy (University of Topic: Multiple Species Competition in a Water Philippine, Dilman) Column Time: PM 4:00-5 :00, Mon., April 23, 2012 Topic: On the Bifurcations and Multiple Endemic States of a Single Strain HIV Model

29 ‹‹- Highlights of the Focus Programs D.5.2 Accomplishments Threshold dynamics of an infective disease model with a fixed latent period and non-local infections, Journal of Mathematical Biology [1] Ariel Fernández, Yun-Huei Tzeng, and Sze-Bi (DOI 10.1007/s00285-011-0500-y), Published Hsu, Subfunctionalization reduces the fitness online. D cost of gene duplication in humans by buffering dosage imbalances, Genomics 2011, 12:604. [13] N. K. Vaidya, Feng-Bin Wang and Xinfu Zou, Avian influenza dynamics in wild birds with bird [2] Sze-Bi Hsu and Lih-Ing Wu Roeger, A Refuge- mobility and spatial heterogeneous environment, mediated Apparent Competition Model, to Discrete and Continuous Dynamical System appear in Canadian Applied Math. Quaterly. Series-B, in press. [3] Sze-Bi Hsu, Jifa Jiang and Feng-Bin Wang, [14] Tzy-Wei Hwang and Feng-Bin Wang, Dynamics Reaction–diffusion equations of two species of a dengue fever transmission model with competing for two complementary resources crowding effect in human population and spatial with internal storage, J. Diff. Eq. Vol. 251(2011), variation, Discrete and Continuous Dynamical 918-940. System Series-B, accepted. [4] James P. Grover, Sze-Bi Hsu and Feng-Bin [15] C.-W. Shih and J.-P. Tseng, Global Wang, Competition between microorganisms synchronization and asymptotic phases for a ring for a single limiting resource with cell quota of identical cells with delayed coupling, SIAM J. structure and spatial variation, J. Math. Biol. Math. Anal., Vol. 43, 4, (2011) 1667-1697. (2012), Vol 64 No.5, 713-743 [16] A. Friedman, C.-Y. Kao, and C.-W. Shih, [5] Sze-Bi Hsu, Feng-Bin Wang and Xiao-qiang Asymptotic limit in a cell differentiation model Zhao, Dynamics of a Periodically Pulsed Bio- with consideration of transcription, J. Differential Reactor Model with a Hydraulic Storage Zone, J. Equations 252, (2012) 5679-5711. Dyn. Diff. Eq. 23 (2011) no.4, 817-842 [17] K.-L. Liao, C.-W. Shih and J.-P. Tseng, [6] Sze-Bi Hsu and Xiao-qiang Zhao, A Lotka- Synchronized oscillations in a mathematical Volterra Competition model with season model of segmentation in zebrafish, Nonlinearity succession, J. Math. Biology, 64 (2012), 109-130. 25, (2012) 869–904. [7] Yu-Yun Chen and Sze-Bi Hsu, Synchronized [18] K.-L. Liao, C.-W. Shih, A lattice model on reproduction promotes species coexistence somitogenesis of zebrafish, Discrete and through reproductive facilitation, J. Theoretical Continuous Dynamical Systems –Series B, 17 Biology, Vol. 274 (2011), 136-144. (8), (2012) 2789-2814. [8] J.-C. Tsai and J. Sneyd, Traveling Waves in the Buffered FitzHugh-Nagumo Model, SIAM J. Appl. Math., (2011), pp. 1606--1636. [9] J.-C. Tsai, W. Zhang, V. Kirk, and J. Sneyd, Traveling waves in a simplified model of calcium dynamics, SIAM J. Appl. Dyn. Syst. (to appear). [10] Naveen K. Vaidya, Feng-Bin Wang, Xingfu Zou and Lindi Wahl, Transmission dynamics of the recently-identified BYD virus causing duck egg- drop syndrome in China, PLoS ONE (www. plosone.org), Vol. 7, April 2012, e35161. [11] Feng-Bin Wang, A Periodic Reaction-Diffusion Model with A Quiescent Stage, Discrete and Continuous Dynamical System Series-B, Vol. 17, No. 1 (2012), 283–295. [12] Zhiming Guo, Feng-Bin Wang and Xinfu Zou,

Highlights of the Focus Programs ‹‹- 30 D.6 Number Theory and Arithmetic Geometry

Coordinators: Wen-Ching Li (Penn State University and NCTS), Liang-Chung Hsia (National Normal University), Yifan Yang (National Chiao-Tung University), Chia-Fu Yu (Academia Sinica) D

he research topics in the number theory and NCTS), C.-F. Yu (AS), J.-D. Yu (NTU), Jing Yu T program at NCTS cover a wide spectrum (NTU), Y.-J. Yu (N. Cheng-Chi U). of number theory, including traditional algebraic number theory, arithmetic geometry and Diophantine geometry and arithmetic of algebraic function fields D.6.2 Visitors are also the main focus of number theory at NCTS. The scope of our number theory group is broadening, Hsinchu: several international cooperation programs have been Sheng-Chi Liu (Texas A&M University, established this year. The following is a list of the 2011.12.18~12.23), Hajime Kaneko (Nikon University, main research areas in number theory. 2.21~2.28), Shinichi Kobayashi (Tohoku University, 3.1~3.11), Yingnan Wang (Hongkong University, 5.14-5.14), Yuichiro Taguchi (Kyushu University, Main Research Focus of the working group 5.23-5.23), Jianqiang Zhao (Eckerd College, 5.30- Arithmetic and geometry of moduli spaces 5.31), Ram Murty (Queen’s University, 8.11~8.30), Diophantine geometry Fang-Ting Tu (Waseda University, 8.23~9.9), Takao Modular forms, modular curves, and Shimura curves Yamazaki (Tohoku University, 8.23~9.9), Kiichiro Automorphic Representations and zeta functions Hashimoto (Waseda Univsersity, 8.25~9.8), Takeshi Miura (Keio University, 8.26~9.1), Yoshinori Coding theory Mishiba (Kyushu University, 8.26~9.1), Tomoya Transcendence theory in positive characteristic Machide (Kinki University, 8.26~9.8), Kensaku Kinjo (The University of Tokyo, 8.26~9.8), Yasuo D.6.1 Local participating members Ohno (Kinki University, 8.26~9.4), Shu Kawaguchi (Kyoto University, 8.26~9.8), Tomatsu Ikeda (Kyoto University, 8.26~8.31), Eiichi Bannai (Shanghai Jiao C.-Y. Chang (NTHU and NCTS), Y.-M. J. Chen Tong University, 8.26~9.6), Yoichi Mieda (Kyoto (NCU), H.-J. Chen (AS, postdoc.), Y.-H. Chen University, 8.28~9.8), Masataka Chida (Kyoto (NCU, postdoc.), W.-C. Chi (NTNU), C.-Y. Chuang University, 8.28~9.5), Masanori Morishita (Kyushu (NTHU, Ph.D. student), Y.-L. Guan (NCU), L.-C. University, 9.2~9.8), Yasuhiro Goto (Hokkaido Hsia (NCU and NTNU), M.-L. Hsieh (NTU), P.-Y. University of Education, 9.4~9.9), Wen-Wei Li Huang (NCKU), P.-C. Hung (NCU, Ph.D. student), (Morningside Center of Mathematics, Chinese M.-C. Kang (NTU), M.-H. Kang (NCTU), C.-W. Academy of Sciences, 10-3-10.3). Kuo (NTHU, Ph.D. student), K.-F. Lai (NSYSU), M.- G. Leu (NCU), A. Li (Fu Jen U.), H.-C. Li (NTNU), W.-C. Li (NCTS), Y.-H. Lin (NCTU, student), C. Vistors (at Taipei): Nien (NCKU), S.-C. Shih (AS, research assistant), Akinari Hoshi (Rikkyo University, one week in K.-S. Tan (NTU), F.-T. Tu (NCTU, student), C.-J. 2012/8), Christian Kappen (Universitat Duisburg- Wang (NCU), J.-Y. Wang (AS), J.-H. Wang (NCU, Essen, one month in 2012/9), Kai-Wen Lan (University Ph.D. student), F.-T. Wei (NTHU, postdoc), J.-W. Xue of Minnesota, 5 weeks in 2012/7-8), Vincent Maillot (Academia Sinica, postdoc), W.-C. Yao (TMUE), (CNRS and Universite Paris 7, 2 weeks in 2012/9), T.-C. Yang (NTU, Ph.D student), Y. Yang (NCTU E. Puczylowski (University of Warsaw, 3 weeks in

31 ‹‹- Highlights of the Focus Programs 2012/9), Domian Roessler (Universite of Toulouse by Ram Murty of Queen’s University. The topic is III, 1.5 weeks in 2012/9), Fabien Trihan (Univ. of “Zeta and L-functions”. Abstract: We plan to give Nottingham, one week in 2012/5), Aiichi Yamasaki 5-6 lectures on the general theme of L-functions, (Kyoto University, one week in 2012/8), Ting-Yu Lee beginning with Artin L-series and the Chebotarev (Universite Paris 6). density theorem. We will also discuss special values D of these L-series with some emphasis on Stark's conjectures and the Siegel-Klingen theorem as D.6.3 International Conferences and generalized by Coates and Lichtenbaum. In the Workshops second half of the series of lectures, we will focus on automorphic L-functions and discuss, in this context, International Conferences/Workshops: the recent progress on the Sato-Tate conjecture. We In the area of number theory, this year there are explore several consequences of this work, namely to one international conference and several workshops. the study of maximal orders of Fourier coefficients of cusp forms, and Chebotarev-Sato-Tate type theorems. Hsinchu: 1. 2012 NCTS mini-workshop on number theory D.6.5 Seminars and Courses (organized by Y. Yang), March 7, featuring two speakers from Japan and two speakers from Hsinchu: Taiwan. There are several regular seminars and one 2. 2012 NCTS Japan-Taiwan joint conference on summer program on number theory for senior/junior number theory (organized by T. Yamazaki and undergraduate students and beginning graduate Y. Yang), held from August 27 to September 7 students. for two weeks. There were totally 28 speakers 1. Shimura curve seminar, organized by Y. Yang, 34 and more than 45 participants. The first week talks since September 2011. consisted of 25 talks in the usual format and the 2. Number theory seminar, organized by C.-Y. second week consisted of two lecture series by Chang, W.-C. Li, and Y. Yang, 18 talks since W.-C. Li and Morishita. Their topics were “zeta September 2011. functions in combinatorics and number theory” and “primes and knots – an introduction to 3. Student number theory seminar, organized by C.- arithmetic topology”, respectively. The purpose of Y. Chang and W.-C. Li, 18 talks since September the conference is to foster long-term collaboration 2011. between number theorists from the two sides. 4. Seminar on modular forms, joint with Academia Taipei: Sinica and TIMS, organized by C.-L. Chai, W.- C. Li, and C.-S. Lin and started on September 12, 1. One-day Workshop of Algebra (organized by M.- 2012. C. Kang), August. 16 and 20, 2012: 6 talks given by A. Hoshi, T.-Y. Lee, A. Yamsaki, M.-C. Kang. Each talk is 50 minutes. Taipei: 2. 2012 NCTS Arithmetic and Algebraic Geometry There is a regular seminar on arithmetic geometry Day (organized by C.-F. Yu), September 14, 2012: and representation theory at NCTS (Taipei). 5 speakers include J.-K. Chen, C. Kappen, V. Arithmetic geometry group at Taipei join the TIMS Maillot, D. Roessler and C.-F. Yu. Each speaker number theory seminar and also attend several gives a one-hour talk. international conferences and lecture series organized in Hsin-Chu. About 18 seminar talks scheduled in Taipei and two one-semester courses given. The D.6.4 Lecture Series purpose of these courses is aiming at training PhD students and generates some projects to work on. NCTS Short course on number theory given

Highlights of the Focus Programs ‹‹- 32 1. Seminar on arithmetic geometry and representation C.-L. Chai is a leading expert in Arithmetic theory, 18 talks in 2012. Geometry. He has sovled several fundamental 2. 2012 NCTS Spring Course on Abelian Varieties. problems: smooth compactification of Shimura This is the second half of one year topics course. varieties, Hecke orbits problem. Recently F. Oort and The purpose is to provide graduate students he showed that for g>3, there is no abelian varieties isogenous to a Jacobian under GRH; this was a D working knowledge on abelian varieties. We covered the context of the paper by G. Prasad folklore conjecture and their results are published in and Rapinchuk on the local-global principle Ann. Math. They also showed several irreducibility for embedding fields in simple algebras with results on leaves and Newton polygon strata in Siegel involutions, and we also made some detail moduli spaces; the results are published in Ann. discussion on the class numbers of definite Math. Joint with B. Conrad, they wrote a book for quaternion algebras. their several joint research projects on CM lifting, which contains several new ideas and techniques. 3. 2012 NCTS Course on Topics on Abelian Varieties. This is the continuation of the last year L.-C. Hsia, together with his collaborators, worked NCTS course. We plan to discuss class numbers on arithmetic dynamic systems. In particular, they and type numbers of quaternion algebras, Honda- determined the Julia set of cubic polynomials over Tate theory and counting points, isogeny classes non-Archimedean local fields. They also determined on Hilbert modular varieties, orbital integrals the preperiodic points for family of polynomial maps. and Satake isomorphisms, supersingular abelian M.-L. Hsieh follows up several important problems varieties, construction of QM abelian varieties. in the Main Conjecture of the Iwasawa Theory. His work on the computation of Eisenstein series, p-adic L-functions for CM fields, non-vanishing of certain D.6.6 Summer Programs for Students L-values and the Iwasawa main conjecture for CM fields have received international recognization as a A summer program in number theory was offered working expert in the field. at Hsinchu in July and August of this year. The W.-C. Li proved the unbounded denominator program, organized by C.-Y. Chang, M.-H. Kang, and conjecture (with Ling Long) for Y. Yang, gave an introduction to algebraic number noncongruence cusp forms when the space is theory. This program gave undergraduate students 1-dimensional and the modular curve is defined over and beginning graduate students some flavor about the field of rational numbers. She also obtained closed modern number theory. form zeta functions and zeta identities (with Yang Fang and Chian-Jen Wang) for finite quotients of the D.6.7 Important Results,Breakthroughs building associated to Sp(4) over a nonarchimedean local field F with a finite residue field. This There are many progresses. Here we mention only the zeta function provides topological and spectral following directions: information of the finite quotient, and is related to the spin L-function of GSp(4, F). In recent years, NCTS has become a worldwide center of research in arithmetic of function fields Y. Yang’s recent work on automorphic forms on in positive characteristic. In each year, many top Shimura curves provides the first known method to experts in this area visit the NCTS and collaborate determine Hecke eigenforms on Shimura curves. By with local number theorists. Especially in the area of interpreting hypergeometric functions as automorphic transcendence theory for functions fields in positive forms on Shimura curves, he and his student have characteristics, many important results have been proved many elegant identities for hypergeometric obtained in the last few years by J. Yu, C.-Y. Chang, functions, such as special values, Ramanujan- F.-T. Wei and their collaborators. All these results type formulas, and algebraic transformations of correspond to big unapproachable open problems in hypergeometric functions. classical theory.

33 ‹‹- Highlights of the Focus Programs C.-F. Yu, joint with F.-T. Wei, successfully [8] Yang Fang, Chian-Jen Wang, and Wen-Ching Li, completed the computation of the class numbers of the zeta functions of complexes from Sp(4), Int. arbitrary hereditary orders in definite central simple Mat. Res. Not, in press, doi:10.1093/imrn/rns007. algebra over global function field. The previous key [9] Shinji Fukuhara and Yifan Yang, a basis for results in this topic were obtained by M. Denert and representations of integers as D and J. Van Geel, and Gekeler around the late 1980's. sums of squares, Ramanujan J. 28 (2012), 25—43. They determined the cases for central simple algebra [10] Shinji Fukuhara and Yifan Yang, a basis with strong strict condition: either of Drinfeld type for , preprint. or of prime degree. He also described the explicit reciprocity law arising from the superspecial abelian [11] U. Görtz and Chia-Fu Yu, On the supersingular varieties. This enables him to give a new proof locus in Siegel modular varieties with Iwahori though not so short of the result of Katsura and level structure. Math. Ann. (2012). (NCTS/TPE Ibukiyama on the field of definitions for principally Technical Report 2008-013). polarized superspecial abelian varieties. This may be [12] Ki-Ichiro Hashimoto, Ling Long, and Yifan viewed as the arithmetic of abelian varieties. Finally, Yang, Jacobsthal identity for Q(sqrt(-2)), Forum he worked out the reduction modulo $p$ of moduli Math., in press. spaces of type D. He determined the possible Newton [13] Ming-Lun Hsieh, On the non-vanishing of Hecke polygons and prove an analogue of the Rapoport-Zink L-values modulo p. to appear in Amer. J. Math. conjecture for the flatness of local models. 2012 (NCTS/TPE Technical Report 2010-004). [14] Ming-Lun Hsieh, on the $\mu$-invariant of D.6.8 Accomplishments anticyclotomic $p$-adic $L$-functions for CM fields, to appear in J. Reine Angew. Math. 2012 (NCTS/TPE Technical Report 2010-005), 23 [1] A. Burungale and Ming-Lun Hsieh, the vanishing pages. of the μ-invariant of p-adic Hecke L-functions for CM fields, to appear in Int. Math. Res. Not. [15] Ming-Lun Hsieh, special values of anti- 2012 (DOI:10.1093/imrn/rns019). cyclotomic Rankin-Selberg L-functions. Preprint 2012, 40 pages. Submitted. [2] Chieh-Yu Chang, Special values of Drinfeld modular forms and algebraic independence, [16] Ming-Lun Hsieh Eisenstein congruence on Mathematische Annalen 352 (2012), 189-204. unitary groups and Iwasawa main conjectures for CM fields. 2012 modified version, 81 pp. [3] Chieh-Yu Chang, Transcendence of special values of quasi-modular forms, For u m [17] Hau-Wen Huang, two-lit trees for lit only sigma- Mathematicum 24 (2012), 539-551. game, to appear on Linear Algebra and its Applications. [4] Chieh-Yu Chang and M. A. Papanikolas, algebraic independence of periods and [18] Hau-Wen Huang, correction of a theorem on the logarithms of Drinfeld modules. With an symmetric group generated by transvections, to appendix by B. Conrad, J. Amer. Math. Soc. 25 appear on Quarterly Journal of Mathematics. (2012), 123-150. [19] Wen-Ching Li, the arithmetic of [5] Chieh-Yu Chang, linear independence of noncongruence modular forms. Proceedings monomials of multiple zeta values in positive of the Fifth International Congress of Chinese characteristic, submitted. Mathematicians, Beijing, China, 2010, Part I, AMS/IP Studies in Advanced Mathematics, vol. [6] Chieh-Yu Chang, on periods of the third kind 51 (2012), 253-268. for rank 2 Drinfeld modules, to appear in Mathematische Zeitschrift. [20] Wen-Ching Li and Ling Long, Fourier coefficients of noncongruence cuspforms, Bull. [7] Masataka Chida and Ming-Lun Hsieh, special London Math. Soc. vol. 44 (2012), 591-598. values of anticyclotomic L-functions for modular forms. Preprint 2012, 32 pages. Submitted. [21] Wen-Ching Li and Maosheng Xiong, statistics of zeros of families of L-functions over function

Highlights of the Focus Programs ‹‹- 34 fields: a survey, Proceedings of the conference [35] Chia-Fu Yu, Superspecial abelian varieties over on Number Theory and Related Topics, Hefei, finite prime fields. J. Pure and Appl. Algebra China, June 6-12, 2011, Higher Education Press 216 (2012), 1418—1427. (NCTS/TPE Technical and International Press, to appear. Report 2010-002). [22] Sheng-Chi Shih, Tse-Chung Yang and C.-F. Yu, [36] Chia-Fu Yu, on Hermitian forms over dyadic D Embeddings of fields in simple algebras over non-maximal local orders. To appear in Pure global fields. arXiv:1108.0830. 27 pp. Submitted. Appl. Math. Q. 2012. (NCTS/TPE Technical (NCTS/TPE Technical Report2011-002). Report 2010-003). [23] Fang-Ting Tu and Yifan Yang, algebraic [37] Chia-Fu Yu, characteristic polynomials of transformations of hypergeometric functions and central simple algebras. arXiv:1109.3851, 7 pp., automorphic forms on Shimura curves, accepted to appear in Taiwanese J. Math. 2012. (NCTS/ for publication, Trans. Amer. Math. Soc. TPE Technical Report 2011-003). [24] Fang-Ting Tu and Yifan Yang, lattice packing [38] Chia-Fu Yu, An explicit reciprocity law arising from quaternion algebras, accepted for from superspecial abelian varieties. Preprint, publication, RIMS Kokyuroku Bessatsu. 2011, 34 pp. [25] Fu-Tsun Wei, on metaplectic forms over function [39] Chia-Fu Yu, Endomorphism algebras of QM fields, Math Annalen, DOI 10.1007/s00208-012- abelian surfaces. NCTS/TPE-Math Technical 0785-1. Report 2011-004, 13 pp. Submitted. [26] Fu-Tsun Wei and C.-F. Yu, Mass formula of [40] Jeng-Daw Yu, on ordinary crystals with division algebras over global function fields. J. logarithmic poles. Preprint 2011. Number Theory. 132 (2012), 1170—1184. (NCTS/ [41] Jeng-Daw Yu, irregular Hodge filtration on twisted TPE Technical Report 2010-008). de Rham cohomology. Preprint (2012), 46 pp [27] Fu-Tsun Wei and Chia-Fu Yu, on class numbers of hereditary orders over global function fields. Preprint, February, 2012, 17 pp. (NCTS/TPE D.6.9 Exchange programs and Technical Report 2012-001). international cooperations [28] Fu-Tsun Wei and Chia-Fu Yu, Class numbers Listed below are the overseas visits by members of central simple algebras over global function in our focus group. fields. Preprint, August 2012, 37 pp. Submitted. (NCTS/TPE Technical Report 2012-003). Canada: In August 2011, J.-D. Yu was invited to [29] Fu-Tsun Wei and Jing Yu, on theta Series from give a lecture in the conference on Arithemetic and Quaternion Algebras over Function Fields, Geomtery of K3 surfaces and Calabi-Yau threefolds, preprint, 2011. held in the Fields Institute. In the spring of 2012, W.- [30] Yifan Yang, Schwarzian differential equation F. Wei visited three months at MaGill University in and automorphic forms on Shimura curves, Montreal, working with Henri Darmon. In March accepted for publication, Compositio Math. 2012, C.-F. Yu attended a workshop on Galois [31] Yifan Yang, modular forms of half-integral representations and Automorphic forms, held in the weights on SL(2,Z), submitted. Fields Institute. [32] Yifan Yang, computing modular equations for China: In August 2011, J. Yu was invited to give an Shimura curves, submitted. talk in the conference Pan Asian Number Theory Conference, held in Beijing. F.-T. Wei and C.-Y. [33] Yifan Yang, Ramanujan-type formulas for Chang gave talks at the first workshop on number Shimura curves, preprint. theory between two Tsing Hua Universities ( 兩 岸 [34] Chia-Fu Yu, Embeddings of fields into simple 清華首屆數 論合作 討 論班 ) in April. L.-C. Hsia, algebras: generalizations and applications. W.-C. Li, Y. Yang, and J. Yu will give talks in the J. Algebra. 368 (2012), 1—20. (NCTS/TPE conference on number theory held in Xi’an in the Technical Report 2012-002). coming October.

35 ‹‹- Highlights of the Focus Programs France: In May 2012, C.-F. Yu visited Institute de USA: W.-C. Li was a plenary speaker in the Rocky Mathematiques de Jussiue in Paris. C.-Y. Chang Mountain discrete math days, held in Laramie, on visited IHES in July. October 21, 2011, the Palmetto number theory series Germany: C.-F. Yu visited Universitaet Duisburg- held at the Clemson University in December 2011, Essen in this summer for cooperating with Ulrich and the 10th algorithmic number theory symposium D held in San Diego on July 10, 2012. She gave talks in Gortz. In July 2012, he gave an invited talk at the Oberwolfach Workshop on Reduction of Shimura the algebra seminar at the University of Pennsylvania varieties. J.-D. Yu spent 9 months in the academic in November 2011, the number theory of the Texas year 2011-12 visiting Universitaet Duisburg-Essen, A&M University on March 7, 2012, and the Boston working with Helene Esnault. In June 2012, he was College-MIT joint number theory seminar on invited to give a talk in the conference Char p and April 3. She also participated in the conference on p-adic geometry, held at the University Mainz. In automorphic form—in memory of Piatetskii-Shapiro August 2012, M.-L. Hsieh was invited to give a held at the Yale University in April. L.-C. Hsia lecture in the conference Iwasawa 2012 in Heidelberg. participated in the spring program of ICERM, Brown F.-T. Wei was invited to give talks in the Penn State— University on“complex and arithmetic dynamics”in Goettingen number theory conference. March and April, giving a talk in the first workshop on“complex and p-adic dynamics”and participating Hong Kong: In April, M.-H. Kang, J. Xue, and Y. in the second workshop on“global arithmetic Yang visited the Hong Kong University of Science dynamics”and the third workshop on“moduli spaces and Technology. C.-Y. Chang visited the same associated to dynamical systems”. He also visited university in May. Y. Yang was invited to give a talk the City University of New York and the University in the international conference on number theory held of Colorado during the period. H.-J. Chen visited in June. M.-H. Kang visited the Chinese University of the University of Arizona from March to May, Hong Kong in August. giving a talk in the number theory seminar. She also India:In July 2012, M.-L. Hsieh, W.-C. Li, and C.-F. participated in the Arizona winter school. Yu were invited to give talks in Pan Asian Number Theory Conference, held in IISER, Pune. W.-C. Li was one of the scientific committee members for the conference. She was also invited to give a colloquium lecture at the Indian Institute of Technology, Mumbai. Japan: In October 2011, M.-L. Hsieh and Y. Yang were invited to give a talk in the Workshop on Arithmetic Geometry, held in Okinawa. In April 2012, M.-L. Hsieh was invited to give a talk in the Mini-Workshop on Arithmetic Geometry and Related Topics. In October 2012, he will give a talk in the 15th Autumn Hakauba Workshop on Number Theory, held in Nagano. In February 2012, C.-F. Yu visited RIMS, Kyoto University. Y. Yang visited the Tohoku University in November 2011. He also visited the Tsuda College and the Waseda University in July and August 2012. Korea: F.-T. Wei attended the Postech winter school on the Birch and Swinnerton-Dyer conjecture from January 6 to 14. In July 2012 M.-L. Hsieh was invited to give a lecture series in the Summer School on Automorphic forms and Number Theory, held at Postech, Pohang.

Highlights of the Focus Programs ‹‹- 36 D.7 Partial Differential Equations

Coordinators: Chiun-Chuan Chen (National Taiwan University), Jong-Shenq Guo (Tamkang University), Tai-Chia Lin (National Taiwan University), Jenn-Nan Wang (National Taiwan University), Jann-Long Chern (National Central University), Yung-Fu Fang (National Cheng Kung University) D

1. Research Goals and Contents in which the stability becomes Lipschitz type as the frequency increases. Nonetheless, the constant increases exponentially in the frequency. Our next aim is to determine whether the exponential behavior he main topics are as follows. is the nature of the question. This problem is closely T I. Inverse problems related to the behavior of the wave equation energy II. Nonlinear Schrödinger equation/ Generalized Kdv with a variable sound speed. The most challenging equation/ Scattering problem question is when the rays are trapped. We hope to • Phase separation of nonlinear Schrodinger construct examples demonstrating the exponential (NLS) systems/ Bilinear estimates behavior of the constant. • Nonlinear Schrodinger equations with nonlocal We have been working on Carleman estimates, nonlinearity which can apply to geometric analysis, inverse • Generalized Kdv equation problems, controlability of PDE, etc. We have derived • Scattering problem several quantitative uniqueness estimates for elliptic III. Biological systems and quasilinear parabolic type./Navier-Stokes eq., and applied these estimates equations to solve the size estimate problem. The next project • Pattern formation and rotating spots is to extend some results to the parabolic type eq. • Free boundary problem and travelling waves Moreover, we plan to derive quantitative estimates for for competition systems the elliptic eq. with jump discontinuity coefficients. • Formation of singularities IV. Nonlinear elliptic problems Nonlinear Schrödinger equation/ Generalized Kdv • Inverse nodal problem for p-Laplacian operators equation/ Scattering problem • Existence and multiplicity of positive solutions (1) Phase separation of nonlinear Schrodinger • Cafarelli-Kohn-Nirenberg inequality and (NLS) systems: Continuing the works on NLS Hardy-Sobolev type equations systems, we study bound state solutions of • Chern-Simons-Higgs Model 2-component nonlinear systems with a large parameter tending to infinity. This parameter We highlight the motivations and goals of some of the study with more details. giving strong inter-component repulsion induces phase separation and forms segregated nodal domains divided by an interface. Such a problem Inverse problems may come from the physics of Bose-Einstein We study inverse boundary value problems (IBVP) condensate (BEC). The main goal is to learn the and quantitative behaviors of elliptic/parabolic eq. regularity theorem and study the interface called The stability property of IBVP is always interesting the domain wall of 2-component BEC. from the view point of numerical computation. It (2) NLS equations with nonlocal nonlinearity: is well known that the IBVP is highly ill-posed. In the past year, mathematicians (TC Lin ,TL But it was observed numerically that the stability is Horng) and physicists (CH Hsueh, WC Wu) have improved when one uses high frequency waves. In completed interdisciplinary joint works on a this project, we consider the IBVP for the acoustic trapped Rydberg-dressed BEC described by NLS equation. We have completed a preliminary result eq. with nonlocal nonlinearity. Ground state and

37 ‹‹- Highlights of the Focus Programs several bound state patterns including multiple (2) Inverse nodal problem: We focus on p-Laplacian peaks and ringlike structures can be obtained by operators. theoretical analysis and numerical computations. (3) Cafarelli-Kohn-Nirenberg inequality and The 1st paper has been published in PRA (2012). Hardy-Sobolev type equations: We study A new domestic focus group for the study of the minimizers of Cafarelli-Kohn-Nirenberg D supersolids is forming. inequality with singularity on the boundary. (3) Bilinear space-time estimate for homogeneous We are interested in how the geometry of equations and coupled nonlinear equations. boundary singularities affects the existence of (4) Generalized Kdv equations: Continuing the minimizers. This problem is related to the the works of Prof. Kamchatnov (Russian existence of a solution to an elliptic equation Math. Physicist), TC Lin and TL Horng involving the Sobolev critical term and the Hardy (Mathematicians), and SC Gou (Physicist), we critical terms with multiple singularities on the studied modulation theory for dispersive shock boundary. waves in the framework of the GKdv eq. The Chern-Simons-Higgs Model: We study (a) an elliptic motivation is to learn internal waves in deep system arising from the Chern-Simons model with water described by the GKdv eq. Using analysis 2 Higgs particles; (b) the solutions with prescribed and numerical computation, rich phenomena zeros and poles of the Einstein equations coupled were found. Our results have been published in with the sigma model and an Abelian gauge field; (c) PRE (2012). the elliptic equation that arises from a cosmic string (5) Scattering problem: We study the scattering model with the action of the Born-Infeld nonlinear problem for the Dirac-Klein-Gordon equations electromagnetism. in 1+1 dimensions. Also we consider a Dirichlet type scattering problem for the wave equation in 2. Research content some domain of the Minkowski space-time with Inverse Problem a 3 dim boundary surface. For the shallow shell eq., we have derived quantitative uniqueness estimates and applied them Biological systems and quasi-linear parabolic to the size estimate problem. Precisely, we use the equations three ball inequality to the size problem under the (1) Pattern formation/rotating spots: We study the fatness condition, which was removed by successfully existence/uniqueness of rotating spots in disks. deriving global doubling inequality. (2) Free boundary problem and travelling waves For the stationary Navier-Stokes equations, for competition systems: The 2-species we obtained the asymptotic behavior at infinity of diffusion-competition system with free boundary nontrivial velocity fields. We do not know if it is is studied, which is very important in invasion optimal for NS equations. On the other hand, when ecology. We consider the long time behavior and the velocity decays like |x|-1, we could get a stronger traveling wave solutions. asymptotic behavior for the velocity. (3) Formation of singularities: We study the non- In view of the equivalence of the 2D elasticity self-similar singularities of quasilinear equations. and the thin plate eq., we proved that the inverse For the locations of singularity, we investigate boundary value problems for both systems are in fact whether a zero of the potential can be a blow-up equivalent. Based on this result, we derived bounds point if the solution blows up in finite time. on the size of the inclusion embedded in the shallow shell. Nonlinear elliptic problems (1) Existence and multiplicity of positive solutions: Nonlinear Schrödinger equation/ Generalized Kdv We investigate these problems for nonlinear equation/ Scattering problem elliptic equations on unbounded domain or with critical exponent. We also consider multiple spike (1) Phase separation of nonlinear Schrodinger solutions for singularly perturbed systems. (NLS) systems: We prove the uniform Lipschitz

Highlights of the Focus Programs ‹‹- 38 continuity of bound state solutions when spatial the cases of 1+2 and 1+3 dim later. dim is 1. Also we show that the limiting nonlinear On the other hand, we consider a Dirichlet type elliptic system that arises has unbounded scattering problem: the solution of the wave equation solutions with symmetry and monotonicity. in a domain of the Minkowski space-time with a These unbounded solutions are useful to derive 3D boundary surface. The data is prescribed on rigorously the asymptotic expansion of the D the surface. Using Minkowski tensor and covariant minimizing energy. When spatial dim is two, we derivatives, we derive an integral representation of establish the De Giorgi type conjecture for the the solution in terms of unknown density function. blowup elliptic system under suitable conditions Then we relate it to the given data by taking the limit at infinity on bound state solutions. These results as the point in the domain approaches a point on naturally lead us to formulate De Giorgi type the boundary. By inverting the operator, the density conjectures for this system in higher dim. function is then determined. Thus we can substitute (2) NLS equations with nonlocal nonlinearity: In the formula back into the solution representation and 2d space, ground state solutions with multiple determine the solution by the data function. We also peaks were obtained by theoretical analysis and derive the corresponding far-field equation which numerical computation. Many fruitful bound contains the information of the curvature of the states like a hexagonal lattice of condensate surface, hence we can compare the data function with droplets, a bilayer lattice and a square lattice the far-field. were also observed due to the long range interaction. We expect to get other patterns in the Biological systems and quasi-linear parabolic near future. equations (3) Bilinear estimates for NLS: We derived a We have proved the existence and uniqueness bilinear scaling invariance space-time estimate of rotating spots in disks by the model proposed by for homogeneous Schrodinger equations. We Zykov. It is a joint work with H Ninomiya and CC proved a result for two coupled nonlinear Wu to be published in CPAA. We also proved the Schrodinger equations involving a non-constant existence of spirals in the plane (joint with YY Chen coupling coefficient. and H Ninomiya, to appear in Physica D). (4) Generalized Kdv equations: Using a reduced In a joint work with A Ducrot published in version of the finite-gap integration method we Nonlinearity (2012), we study a singular predator- derive the Gardner-Whitham modulation system prey system which gives either self-similar or non- in a Riemann invariant form and show that it self-similar quenching. For the dead-core problem, a can be mapped onto the well-known modulation joint work with Xinfu Chen and Bei Hu on the porous system for the Kdv equation. The resolution of medium eq. with strong absorption, we show the an initial discontinuity for the GKdv equation existence of self-similar dead-core rate. In contrast reveals rich solutions including nonlinear with the cases of semi-linear and fast diffusion, the trigonometric bores, solibores, rarefaction waves, dead-core rates are all non-self-similar. Also, a joint and combinations of the above structures. work with CS Lin and M Shimojo on the location of (5) Scattering problem: First we study the scattering blowing-up is to be published in Appl. Math. Letters problem for the Dirac-Klein-Gordon equations (2013). in 1+1 dimensions which are evolution equations. Extending the work of Yi-Hong Du on 1-species We use the stationary phase method to study scalar equation, we have done a work on 2-species the asymptotic behavior of the free solution for competition system with free boundary. This is a the Klein-Gordon equation and for the Dirac joint work with Chang-Hong Wu accepted by JDDE. equation. Also we use the method to analyze the In this work, the habitat is assumed to be the same quadratic terms of the system. We also discover for the 2 species which is quite restrict. Therefore, an interesting phenomenon of resonance when we are investigating the case that each species has its the masses of spinor field and scalar field satisfy own habitat. There is certain difficulty such as the a particular condition. We will also investigate intersection of two free boundaries to be overcome .

39 ‹‹- Highlights of the Focus Programs Nonlinear elliptic problems Yoshihisa Morita (Ryukoku University) We obtain the following results: Eiji Yanagida (Tokyo Institute of Technology) (1) Multiple spike solutions for singularly perturbed Shoji Yotsutani (Ryukoku University) elliptic systems. Nakamura Ken-Ichi (Kanazawa University) D (2) Existence/multiplicity for Schrodinger-Poisson eq. 石渡 哲哉 ( 芝浦工業大學 , Japan) and non-homogeneous problems in R^N. Nagayama Masaharu (Kanazawa University) (3) Nice properties of Nehari manifold for an Ryham Rolf (Fordham University) indefinite system involving critical exponent. Shu-ichi Kinoshita (Meiji University) (4) Existence and multiplicity of positive solutions for a class of nonlinear BV problems. Theodore Kolokolnikov (Dalhousie University) (5) Cafarelli-Kohn-Nirenberg inequality and related Plechac Petr (University of Delaware) Hardy-Sobolev type equations: We propose a Ou Miao-Jung Yvonne (University of Delaware) finer analysis of the geometry of a boundary Yu Shih-Hsien (National University of Singapore) singularity, which provides a systematic way to Sternberg Peter (Indiana University) analyze boundary singularity for many problems. Francois Hamel (Aix-Marseille University) (6) Chern-Simons-Higgs Model: We obtained the Minkyu Kwak (National Chonnam University) uniqueness of topological solutions and give a Hirokazu Ninomiya (Meiji University) complete study of the solutions, in particular, the existence of Non- topological solutions. Masayasu Mimura (Meiji University) Yoshihisa Morita (Ryukoku University) 3. Visitor Eiji Yanagida (Tokyo Institute of Technology) Sternberg Peter (Indiana University) Shoji Yotsutani (Ryukoku University) Francois Hamel (Aix-Marseille University) Nakamura Ken-Ichi (Kanazawa University) 石渡 哲哉 芝浦工業大學 Minkyu Kwak (National Chonnam University) ( , Japan) Hirokazu Ninomiya (Meiji University) Nagayama Masaharu (Kanazawa University) Masayasu Mimura (Meiji University) Ryham Rolf (Fordham University)

4. Conference and Workshop

Date Venue Title Participant Country

Taiwan, Korea, 2012/01/06-08 Tamkang University The 20th Annual Workshop on Diff. Eq. France,USA,Japan

National Taiwan The 3rd Taiwan-Japan Joint Workshop for 2012/02/27-28 Japan, Taiwan University Young Scholars in Applied Math.

Taiwan, Malaysia, National Taiwan The 8th East Asia Section of SIAM Singapore, Japan, Korea, 2012/06/25-27 University Conference (EASIAM 2012) China, USA, Macau, Hong Kong

National Tsing Hua NCTS-Postech joint Partial Diff. Equations 2012/11/08-09 Taiwan, Korea University Workshop

National Taiwan Taiwan-Japan Joint Conf. on PDE and 2012/12/26--28 Taiwan, Japan University Analysis

Highlights of the Focus Programs ‹‹- 40 5. Important Results, Breakthrough for the De Giorgi type conjecture. Inverse problems - NLS eq with nonlocal nonlinearity: We studied 1. C L Lin, G Nakamura, G. Uhlmann, and J N 2d ground and bound state solutions and found Wang, Quantitative Unique continuation for the several interesting patterns including a hexagonal Lame System with Less Regular Coefficients, lattice of condensate droplets, a bi-layer lattice and a nearly square lattice due to the long range D Methods and Applications of Analysis, 18 (2011), 85-92: We proved the strong unique continuation interaction. Until now, very few math results on property for the Lame system with rough such a kind of NLS eq have been done. Further coefficients. Precisely, we obtained the SUCP for works should be complete in the near future. the case where λ is essentially bounded and μ is - GKdv eq: After completing our works, we found Lipschitz. This is the most optimal assumption on that Prof. Grimshaw and El (UK Math Physicists) the coefficients for the SUCP to hold. Our method also have related results. Hence we combined is based on the Carleman estimate and the so- results of two groups together as a joint paper called optimal three ball inequalities. published in PRE (2012). This is a successful 2. S Nagayasu, G Uhlmann, and J N Wang, cooperation with foreign research groups. Increasing stability in an inverse problem for Biological systems and quasilinear parabolic the acoustic equation, preprint: We derived a equations stability estimate of the inverse boundary value 1. Jong-Shenq Guo and Chang-Hong Wu, problem for the acoustic equation. The stability we Traveling wave front for a two-component lattice derived depends on the wave number k. It turns dynamical system arising in competition models, out the stability changes from the logarithmic JDE, 252(2012), 4357-4391: We study traveling type to the Lipschitz type when k is large. Also, front solutions for a 2 component system on a 1-d we pointed out an interesting phenomenon that lattice, which arises from 2 species completion the constant depends exponentially on the wave model with diffusion. We consider both Lotka- number k. Whether the behavior of the constant is Volterra type and mono-stable case. We show that generic or not is yet to be explored. a traveling front exists iff its speed is above the • The stability estimates derived in this project min wave speed, and show the monotonicity of the explicitly show the dependence of the stability wave. Under some conditions, we also show the on the a priori data. These estimates give us uniqueness of the wave for a given wave speed. deeper understanding on the ill-posed nature Finally, we characterize the minwave speed by the of the inverse boundary value problem. The parameters in the system. phenomenon of increasing stability for the 2. A Ducrot and Jong-Shenq Guo, Quenching inverse problem or other related questions was behavior for a singular predator prey model, first studied by Isakov. Our result focuses on Nonlinearity, 25 (2012), 2059-2073: This paper the acoustic equation which is more difficult to studies quenching behavior for a system arising study for this phenomenon. As for the SUCP from spatio-temporal interaction of prey and for the Lame system, our condition on the predator populations in fragile environment. We coefficients is the weakest assumption for this provide sufficient conditions on the initial data kind of problem. for finite time quenching and classify the initial Nonlinear Schrödinger equation/Kdv equation data to distinguish type I and type II quenching, - Phase separation of NLS systems: Recently, by introducing a delicate energy functional. Also there are several scholars (including E Dancer, S we show the quenching set can be a singleton, the Terracini et al) have studied 2-component NLS whole domain, or a compact subset. systems with a large inter-component repulsion. 3. Jong-Shenq Guo and F Hamel, Propagation and However, only few results related to the interface blocking in periodically hostile environments, profile of 2-component NLS systems which may Arch. Rational Mech. Anal., 204 (2012), 945- describe the domain wall of 2-component BEC. 975: We study the persistence and propagation/ Here we develop math theorems to see the physical blocking for a species in periodically interface profile and also initiate a new direction environments. The problem is described by a

41 ‹‹- Highlights of the Focus Programs reaction–diffusion equation with the zero Dirichlet Nonlinear Schrödinger equations with nonlocal boundary condition. We obtain the existence of nonlinearity a min stationary solution and study the large- Find more bound state solutions with different time behavior of the initial boundary value patterns and study their dynamics. Develop the problem. Also we study approximated problems convergence theorem for bound state sol. of NLS D in the whole space with very negative growth eq with nonlocal nonlinearity. reaction outside the domain. By using the min Poisson-Boltzmann (PB) equations with nonlocal speeds of approximated problems, we provide a nonlinearity simple geometric condition for the blocking of propagation. Moreover, for the case of constant For multi-species ions, it is very interesting to diffusion matrix, we provide conditions for the study the PB eq with nonlocal nonlinearity. We limit of approx. min speeds to be positive. expect to get results different from our previous works published in Nonlinearity (2011). Nonlinear elliptic problems Wave patterns in biological systems and 1. Jann-Long Chern, ZY Chen and YL Tang, singularities of parabolic systems Uniqueness of Finite Total Curvature and Structure of Radial Solutions for Nonlinear 1. Pattern formation: meandering spirals Elliptic Equations, Trans AMS, 363(2011), 3211– 2. Formation of singularity: some parabolic system 3231: The correspondence between the initial and p-Laplace equation values of positive radial solutions of the curvature 3. Free boundary problem: curvature flow with equation and the associated finite total curvatures forcing term is derived. We also conduct the zeros of radial Nonlinear Elliptic Problems solutions in terms of the initial data under specific 1. Elliptic systems: Chern-Simons-Higgs Model; conditions. Furthermore, based on the Pohozaev Bennett and Hamiltonian-type systems. identity and openness for the regions of initial data corresponding to certain types of solutions, 2. Cafarelli-Kohn-Nirenberg inequality and Related we obtain the whole structure of radial solutions Hardy-Sobolev type equations depending on various situations. Scattering Problems Jann-Long Chern, ZY Chen and YL Tang, On We will start a new topic on the scattering the solutions to a Liouville-type system involving problems for wave equation in Minkowski space singularity, Cal.Var. and PDE,43(2012), 57- time with Dirichelet condition and for Dirac- 81: The paper studies a Liouville system with Klein-Gordon equations. singularity in the plane. The existence/uniqueness of solutions to the Dirichlet problem are proved. Also the structure of solutions in terms of the total 7. Publication curvature /total mass is obtained. ( 一 ) 以 NCTS 名義發表 2011 6. Research Topics in 2013 [1] Jong-Shenq Guo and Masahiko Shimojo, Blowing The study will focus on the following topics. up at zero points of potential for an initial Inverse problem boundary value problem, Communications on Pure and Applied Anal., 10 (2011), 161-177. 1. Pattern formation: meandering spirals 2. Formation of singularity: some parabolic system [2] C L Lin, G Nakamura, G Uhlmann, and J N and p-Laplace equation Wang, Quantitative strong unique continuation for the Lame system with less regular coefficients, 3. Quantitative estimates and the asymptotic Methods Appl. Anal., V 18 (2011), 85-92. behaviors of the velocity field for the time- dependent Navier-Stokes equations. [3] S Nagayasu, G Uhlmann and J N Wang, Reconstruction of penetrable obstacles in 4. Study of the behavior of the solution for the acoustic wave eq in high frequency regime. acoustic scattering, SIAM J. Math. Anal., Vol 43 (2011), 189-211. 5. Quantitative estimates for elliptic equations with discontinuous coefficients.

Highlights of the Focus Programs ‹‹- 42 [4] C L Lin, S Nagayasu, and J N Wang, Quantitative in R^{N}, Nonlinear Analysis: T.M.A. 75 (2012), uniqueness for the power of Laplacian with 5639-5652. singular coefficients, Ann. Sc. Norm. Super. Pisa [5] C. Y. Chen and T. F. Wu, The Nehari manifold Cl. Sci(5), Vol X (2011), 513-531. for a indefinite semilinear elliptic system [5] C. C. Lee, H. Lee, Y. Hyon, T. C. Lin* and C. involving critical exponent, Applied Math. and D Liu, New Poisson–Boltzmann type equations: Computation 218 (2012), 10817-10828. (SCI) one-dimensional solutions, Nonlinearity 24 (2011) [6] T. F. Wu, Two coupled nonlinear Schrödinger 431–458 equations involving a non-constant coupling [6] X. Chen, Y.H. Cheng and C.K. L a w coefficient, Nonlinear Analysis: T.M.A. 75 (2012), Reconstructing potentials from zeros of one 4766-4783. eigenfunction, Trans. AMS,363, (2011), 4831- [7] T. F. Wu, Existence and multiplicity of positive 4851. solutions for a class of nonlinear boundary vlaue [7] Yung-fu Fang, On a Bilinear Estimate of problems, Journal of Differential Equations 252, Schrödinger Waves, RIMS Kôkyûroku Bessatsu (2012), 3403-3435. B26: Harmonic Analysis and Nonlinear PDE, [8] C.K. Law and E. Yanagida , A solution to an May, 2011, p1-14. Ambarzumyan problem on trees, Kodai J. Math., [8] C-L Lin, G. Nakamura and J-N Wang, 35 (2012), 357-372. (SCI) Quantitative uniqueness for 2 order elliptic [9] X. Chen, Y.H. Cheng and C.K. Law, A Tikhonov operators with strongly singular coefficients. Rev. regularization for the inverse nodal problem for Math. Iberoamericana, 27, no 2 (2011), 475-491. p-Laplacian, J. Math. Anal. Appl., 395 (2012), 2012 230-240 [1] T Nguyen and JN Wang, Quantitative uniqueness Accepted papers estimate for the Maxwell system with Lipschitz [10] H Berestycki, TC Lin*, J Wei, C Zhao, Phase- anisotropic media, Proc AMS, Vol 140 (2012), separation model, Arch. Rational Mech. Anal. 595-605. [11] CH Chang, CC Chen, Traveling wave of a [2] CC Chen, LC Hung, M Mimura and D Ueyama, 2-species free boundary problem, CPAA. Exact traveling wave solutions of 3 species [12] CC Chen, T Kolokolnikov, Simple PDE model of competition-diffusion systems, DCDS -B, Vol 17, spot replica. in any dim., SIAM Math. Anal. No 8 (2012), 2653-2669 [13] WC Wang, TF Wu CH Liu, Multiple spike sol. [3] C.Z. Chen, C.K. Law, W.C. Lian and W.C. Wang, for singularly perturbed ellip. sys., DCDS-B. Optimal upper bounds for the eigen. ratios of 1-dim p-Laplacian, P. AMS (2012), http://dx.doi. [14] CY Chen, YC Kuo, TF Wu, Existence for org /10.1090/S0002-9939-2012-11365-6. Schrödinger-Poisson eq, Pro. Roy. S. Edinburgh [4] T. Li and T. F. Wu, Existence of multiple positive [15] CZ Chen, CK Law, WC Lian, WC Wang, Optim. solutions for nonhomogeneous elliptic problems eigen-ratios of 1-d p-Laplacian, Proc. AMS

( 二 ) 有 acknowledge NCTS

NO Journal 2011 2012 Else 1 Journal of Differential Equations 1 2 SIAM J. Appl. Math. 1 3 Phys. Rev. E 1 4 Phys. Rev. A 1 5 Discrete and Continuous Dynamical Systems - Series B 1 6 Nonlinear Analysis: Theory, Method & Applications 1 7 Quarterly of Applied Mathematics 1 註：.Else 係指論文投稿於期刊中、已接受未正式發表、已有初步成果整理成論文但尚未投稿等

43 ‹‹- Highlights of the Focus Programs 2011: 2. X Chen, JS Guo, Motion by curvature of planar 1. J-C Tsai-J Sneyd, Traveling waves in the buffered curves, Math. Annalen FH-N Model, SIAM Appl. Math. 3. JS Guo, CH Wu, Wave propagation for a 2012: 2-component lattice compet. model, JDE D 1. X Chen, J-S Guo, B Hu, Dead-core for porous 4. JL Chern, ZY Chen, YL Tang, Uniqueness of med. eq. with strong absorp., DCDS-B finite total curvature, Tran. AMS 2. Kamchatnov, Kuo, TC Lin, Horng, Gou, Clift, El, 5. JL Chern, CS Lin, J Shi, YL Tang, Existence of Grimshaw, Gardner eq., Phys. Rev. E. sublinear sys., P. Royal S. Edinburgh 3. CH Hsueh, TC Lin, TL Horng, WC Wu, Quantum 2012: crystals in BEC, Phys. Rev. A. 1. YY Chen, JS Guo and H Ninomiya, Rotating 4. CC Peng, WC Lien, Self-similar sol. of the Euler spiral waves, Physica D eq. with spherical Symmetry, Nonl. Anal. 2. A Ducrot and JS Guo, Quenching for a singular 5. E Crooks JC Tsai, Front-like entire solutions for predator prey model, Nonlinearity eq. with convection, JDE 3. JS Guo, F Hamel, Propagation/blocking in Accepted papers: periodically environ., Arch Rat Mech Anal 6. WC Lien, SY Ha, HC Huang, Stability of spherical 4. JS Guo and CH Wu, Traveling wave for lattice flows, Q. Appl. Math. competition models, JDE 5. JS Guo, N Kavallaris, Nonlocal parabolic problem in MEMS control, DCDS ( 三 ) 其他 6. JL Chern, ZY Chen, YL Tang, Liouville system 2011: involving singularity, Cal. Var. PDE 1. JS Guo, X Liang, Min speed of traveling fronts for LV comp. system, J Dyn. and DE

D.8 Probability Theory & Related Topics(2012)

Coordinators: Shuenn-Jyi Sheu(NCU) and Yuan-Chung Sheu (NCTU)

I. Research Goals and Contents On pricing and hedging in exponential L\’evy models. On stochastic analysis and applications. Exponential L\’evy models generalize the classical Black and Scholes model by allowing the stock prices to jump while preserving the independence and stationarity of returns. Motivated by problems n the past few years, Shuenn-Jyi of pricing perpetual American exotic options, Y.-C. Sheu has been working closely with Sheu and his Ph.D. students study optimal stopping I some international visitors on several problems under jump-diffusion models. research topics, including portfolio optimization in mathematical finance, problems motivated by Markov On Markov chains and mixing times. Chain Monte Carlo method, and the large time The project is two-fold. First, we focus on the asymptotics of the solution of the Hamilton-Jacobi- logarithmic Sobolev constants in one-dimensional Bellman equations. Riding on his past success, S.-J. case. The exact computation of the logarithmic Sheu works along a similar line to push his research Sobolev constant is important in bounding to a more challenging regime. the Lp-mixng times. Second, we establish the

Highlights of the Focus Programs ‹‹- 44 relationship between the lazy Markov chains and the II. Important Research Results and corresponding semigroups. The goal is to properly Achievements relate their cutoff phenomena and identify the cutoff time in total variation. There are many progresses. Here we mention the On conditional modeling in hierarchical models following directions: D and image applications. On stochastic analysis and optimal control. S.- Generative approach for modeling images is often J. Sheu and H. Hata study an optimal consumption of two steps, building a hierarchical prior distribution problem on infinite time horizon. They derive the on image interpretations and building a conditional HJB (Hamilton-Jacobi-Bellman) equation and prove distribution on the image given its interpretation. the existence of solution for HJB equation assuming In this year, we develop theoretical foundation of the equation has a pair of sub/supersolution. This attribute representations in the hierarchical prior work will appear in SIAM J. Control Optimization. distribution. The preliminary goal is to coherently Also another work with Hata on verification theorem represent any number of parts or subparts using will appear in SIAM J. Control Optimization. S.-J. the same tilting formulation so that we can obtain Sheu is also collaborating with Naoyuki Ichihara, H. the distributions automatically. In the meantime, Nagai and D. Hernendaz-Hernandez , respectively, we strive to establish a better data model resolving on HJB equations and related topics. S.-J. Sheu overlapping problems based on our conditional collaborates with F.Branke on the study of the modeling technique. Then, we can generalize the limiting behavior of a family of diffusion processes parts model in Chang (2011) in order to compute with growing drift. The related studies in literature more complicate hierarchical models with huge are in general two dimensional. Here they consider number of states. We also study foveal limit to diffusion process on arbitrary dimension. compare the generalized model with Gods model On L\’evy processes with applications in finance. via ROC analysis and deviation theorem. The big The work of Y.-C.Sheu with M.-Y.Tsai on optimal goal is always to narrow down the ROC gap between stopping problems for jump-diffusion processes has biological and machine vision performance. been published in Journal of Applied Probability 2012. On importance sampling estimation for joint Also work of Sheu with M.-C.Chang on free boundary lower tail probability problems and perpetual American strangles has been In credit risk modeling, Gaussian and Student's t submitted to Quantitative Finance for publication variates arise primarily from the copula method to consideration and now is in revision. Based on retain certain correlation structures among defaultable free boundary problem approach, Sheu and Chang assets. We propose efficient importance sampling consider problems of pricing perpetual American algorithms to estimate lower tail probabilities exotic options under jump-diffusion models. The work of these two variates in any finite dimension. along this line is now being written up. Variances of importance sampling estimators are On Markov chain and mixing times. The joint shown asymptotically optimal by means of the work by G.-Y. Chen, Y.-J. Fang and Y.-C. Sheu on large deviation theory and a truncation argument. the cutoff phenomenon for Ehrenfest chains has Moreover, the flexibility of these algorithms can be been accepted and appeared in Stochastic Processes seen from two applications, including (1) probability and Their Applications (2012). On the project of estimation for the nth-to-default, i.e., the nth order computing the spectra of finite birth and death statistic, given a large credit portfolio (2) portfolio chains, C.-Y.Chen and L. Saloff-Coste successfully optimization problems. The latter application builds extend their method on the spectral gap to any up a new connection between importance sampling, specified eigenvalue. For the mixing time of finite entropy, and optimization. We plan to investigate Markov chains, the comparison of mixing time in deeper on this new direction. total variation between the lazy walks and continuous semigroups is finished and the result holds in a very general setting and includes a precise comparison of the cutoff phenomenon, the cutoff time and the

45 ‹‹- Highlights of the Focus Programs window size. For birth and death chains, they obtain 者 有 :Andreas Kyprianou (Bath, UK), Jun Sekine the exact order of the total variation mixing time in (Osaka University, Japan), Ning Cai (The Hong Kong continuous time case, which is formulated by the University of Science and Technology), Svetlana birth and death rates and is closely related to the Boyarchenko (University of Texas, Austin, USA), expected hitting time. The above results are collected Yoshio Miyahara (Nagoya City University), Hideo D in the following drifts, which are submitted for Nagai (Osaka University, Japan), Budhi Arta Surya publication. (Bandung Institute of Technology, Indonesia) 國內學 [1] Guan-Yu Chen and Laurent Saloff-Coste, Spectral 者有姜祖恕，韓傳祥，張洛賓，Hsuan-Ku Liu，Ming- computation for birth and death chains. Chi Chang，透過這個活動國內的機率學者有機會 與國外學者相互做學術交流。 [2] Guan-Yu Chen and Laurent Saloff-Coste, On the mixing time and spectral gap for birth and death chains. (B) Seminar/Short Course [3] Guan-Yu Chen and Laurent Saloff-Coste, (a) 在中央大學在每週星期三舉行定期的機率及其 Comparison of cutoffs between lazy walks and 應用研討會，主要參加人員有數學系同仁趙一 Markovian semigroups. 峰，許玉生，于振華，饒瑞彬， 陳韋達，楊如琛， On conditional modeling in hierarchical models 統計所的同仁有傅承德，鄧惠文，中央研究院數 and image applications. L.-B.Chang is collaborating 學研究所同仁有謝仲，藉由這個活動大家有機 with Stuart Geman on empirical scaling laws and 會聚會討論。今年的演講者有幾位是國外學者， the aggregation of non-stationary data. Remarkably Toshio Mikami (Hiroshima University), Jun Sekine precise empirical evidence for the alpha-scaling of (Osaka University), Kenjiro Yanagi (Yamaguchi returns, provided from many articles is not consistent University), N. Ichihara(Hiroshima University), with modern finance models. Chang and Geman Yoshio Miyahara (Nagoya City University), demonstrated analytically that empirical evidence Yuhong Yang(University of Minnesota)，董昭 ( 北 for scaling can be explained as an effect of the 京中科院 )。我們也請其他學校同仁來演講，有許 aggregation of large amounts of data generated by a 元春 ( 交通大學 )，吳慶堂 ( 交通大學 )，韓傳祥 non-stationary random-walk process. This is the first ( 清華大學 )，須上苑 ( 中研院 )，王家禮 ( 東華大 article mathematically arguing that that empirical 學 )，吳順益 ( 成功大學 )，這個研討會讓我們增 scaling is asymptotically consistent with this class 加與其他學校的學術互動。其中 Toshio Mikami of models, and in fact can be viewed as support for (Hiroshima University) 給 系 列 演 講 (3 次 ):A rather than evidence against this class of models. Short Course on Optimal Transportation Process. Chang’s other works are as follows. 1. ( with Zhidong Kenjiro Yanagi (Yamaguchi University) 給系列演 Bai, Su-Yun Huang, Chii-Ruey Hwang) Asymptotic 講 (4 次 ): Short Course on Quantum Information Error Bounds for Kernel-based Nystrom Low-Rank Theory. Approximation Matrix, submitted. 2. (with Stuart (b) 於每周星期五在中央大學舉行書報討論會，讓學 Geman, Fushing Hsieh, Chii-Ruey Hwang) On the 生有機會學習機率論專題，我們有兩個課題，分 invariance of waiting times between large returns 別於隔周舉行，一個課題為 Stochastic Calculus， (drift), in preparation. 一個課題為 Stochastic Control in Insurance，前者 為機率論的一個重要而基礎的課程，後者為機率 論的一個應用課程，因此未來可以延續而變成一 III. Seminars/Courses/Workshops/ 個研究題材，Stochastic Calculus 的報告人主要 Visitors 有楊如琛，須上苑，許順吉，Stochastic Control in Insurance 的報告人主要有吳政訓，許順吉，另外 (A) Workshop 許順吉給了一個系列演講，簡介控制理論。書報 Workshop on Stochastic Processes and Applications 討論會參加成員有學生：張凱君，林柏佐；助理： 該會議由黃啟瑞、許順吉、許元春籌畫，由新竹 陳韋達，研究助理楊如琛；博士後研究人員：須 理論中心、中央研究院數學研究所、中央大學資 上苑，吳政訓；同仁有趙一峰，許玉生，謝仲，另 助，邀 請 的國內及 國外 機 率 學者 演 講，國外 學 外姜祖恕，吳慶堂，韓傳祥，傅承德有時參與。

Highlights of the Focus Programs ‹‹- 46 (c) Professor Stuart Geman visited Taiwan for a (D) 國外訪問學者 Short/Long term visitors month in the fall semester of 2011 to continue the Stuart Geman (Brown University), Andreas research with Lo-Bin Chang and gave two lectures Kyprianou (Bath, UK), Zhen-Qing Chen (University as follows in National Chiao Tung University:(1) of Washington) ,Svetlana Boyarchenko (University On the Peculiar Statistics of Natural Images. (2) of Texas, Austin), Budhi Arta Surya (Bandung Conditional Modeling and the Construction of a D Institute of Technology, Indonesia), Ning Cai (The Computer Vision System. Hong Kong University of Science and Technology), (d)Summer Courses in Probability Theory and Hideo Nagai (Osaka University), Jun Sekine (Osaka Applications University), Yusuke Watanabe (Osaka University), Speakers: Shuenn-Jyi Sheu , Shang-Yuan Shiu, Naoyuki Ichihara, Toshio Mikami (Hiroshima Chuan-Hsiang (Sean) Han University), Yoshio Miyahara (Osaka City University), Hiroaki Hata (Shizuoka University)., Topics: Random Walk (I-IV) , Stochastic Partial Sergei Kucherenko(Imperial College) Differential Equation (I- IV) , Monte Carlo Simulation with Applications in Finance (I-IV) IV. Accomplishments (C) 國外訪問 Shuenn-Jyi Sheu visited Japan in 2012, Jan. 6-13. (A) 已被雜誌接受刊登 In this trip he visits Osaka University to disicuss [1] Chen, Lung-Chi Asymptotic behavior for a with Hideo Nagai, Jun Sekine, Hidehiro Kaise and version of directed percolation on a square Yusuke Watanabe. He visits Hiroshima University lattice. Phys. A 390 (2011), no. 3, 419–426. to attend a workshop: Probability and PDE 2012. [2] Wang, H., Lu, H. H.-S., Chueh, T.-H., He also visits Arturo Kohatsu-Higa and probability "Constructing Biological Pathways by a Two- group at Ritsumeikan University and gives a seminar Step Counting Approach." , PLoS ONE 6(6): talk. In 2012, July 15-22, he visits Bejing Normal e20074.(SCI), 2011 University to attend a workshop organized by Mu- [3] Deng, L.-Y. , Shiau, J.-J. H., and Lu, H. H.-S., Fa Chen: Workshop on Stochastic Processes and "Large-order multiple recursive generators with Applications. During the trip, He also visits with Jin modulus $2^{31}-1$" , INFORMS Journal on Feng (University of Kansas) to Nanjing University Computing, Published online before print (SCI), and Nanjing Normal University and gives talks. 2011 Guan-Yu Chen visited Cornell University(started [4] Yuan-Chung Sheu and Ming-Yao Tsai, at Dec. 16, 2011 and ended at Jun. 15, 2012) for On optimal stopping problems for matrix- continuing his research with Professor Laurent exponential L\'{e}vy processes, Journal of Saloff-Coste (Member, American Academy of Applied Probability, 49, 531-548(2012). Arts and Sciences; Department Chair). During the [5] Guan-Yu Chen , Yang-Jen Fang and Yuan- academic visit, they considered birth and death Chung Sheu, The cutoff phenomenon for chains and focus on the spectral computation and the Ehrenfest chains, Stochastic Processes and Their estimation of total variation mixing time. The results Applications 122 (2012) 2830-2853. have been collected in two papers and submitted for publications. [6] Deng, L.-Y. , Shiau, J.-J. H., and Lu, H. H.- S., "Efficient computer search of large-order Lo-Bin Chang visited Brown University in the multiple recursive" , Journal of Computational whole summer of 2012 for continuing his research and Applied Mathematics, 236, 3228–3237, (SCI), with Professor Stuart Geman(Member, National 2012 Academy of Sciences) and their pattern theory research group. During the summer, Lo-Bin also [7] Chueh, T.-H., and Lu, H. H.-S., "Inference of visited some other research groups in the United Biological Pathway from Gene Expression States and attended their summer workshops. Profiles by Time Delay Boolean Networks" , PLoS ONE 7(8): e42095, 2012. (SCI), 2012

47 ‹‹- Highlights of the Focus Programs [8] Yu-Ting Chen and Jean-Francois Delmas, [2] H. Hata, H. Nagai and S.J.Sheu, An optimal Smaller population size at the MRCA time for consumption problem for general factor model. stationary branching processes, Ann. Probab. 40, [3] D. Hernendaz-Hernandez and S.J.Sheu, Solution 2034-2068(2012) of HJB equations involved in indifference D [9] Guan-Yu Chen , Yang-Jen Fang and Yuan- pricing Chung Sheu, The cutoff phenomenon for [4] Lo-Bin Chang, Stuart Geman, Fushing Hsieh, Ehrenfest chains, Stochastic Processes and Their Chii-Ruey Hwang, On the invariance of waiting Applications 122 (2012) 2830-2853. times between large returns(drift), in preparation. [10] H. Hata and S.J.Sheu, On the Hamilton-Jacobi- [5] Lo-Bin Chang, Stuart Geman, Empirical Scaling Bellman equation for an optimal consumption Laws and the Aggregation of Non-stationary problem: I. Existence of solution. To appear in Data (drift), in preparation. SIAM J. Control Optimization. [6] Ming-Chi Chang and Yuan-Chung Sheu, Two- [11] H. Hata and S.J.Sheu, On the Hamilton-Jacobi- sided optimal stopping problems and perpetual Bellman equation for an optimal consumption American exotic options. problem: II. Verification Theorem. To appear in [7] Ming-Chi Chang, Yuan-Chung Sheu and Ming- SIAM J. Control Optimization. Yao Tsai, Pricing perpetual American compound options under a jump-diffusion model. (B) Submitted [1] Naoyuki Ichihara and S.J.Sheu, Large time behavior of solutions of Hamilton-Jacobi- Bellman equations with quadratic nonlinearity in gradients, submitted. [2] Zhidong Bai, Lo-Bin Chang, Su-Yun Huang, Chii-Ruey Hwang, Asymptotic Error Bounds for Kernel-based Nystrom Low-Rank Approximation Matrix, submitted. [3] Ming-Chi Chang and Yuan-Chung Sheu, Free boundary problems and perpetual American strangles, Submitted (2012) [4] Yu-Ting Chen, Ming-Chi Chang and Yuan- Chung Sheu, A note on Gerber-Shiu function for hyper-exponential jump-diffusion processes . Submitted (2012) [5] Guan-Yu Chen and Laurent Saloff-Coste, Spectral computation for birth and death chains. [6] Guan-Yu Chen and Laurent Saloff-Coste, On the mixing time and spectral gap for birth and death chains. [7] Guan-Yu Chen and Laurent Saloff-Coste, Comparison of cutoffs between lazy walks and Markovian semigroups.

(C) In preparation [1] B. Franke and S.J.Sheu, Homogenization of a diffusion driven by a large incompressible drift.

Highlights of the Focus Programs ‹‹- 48 D.9 Representation Theory

Coordinators: Shun-Jen Cheng (Academia Sinica), Ching Hung Lam (Academia Sinica), Wen Fong Ke (National Cheng Kung University) D

his research group investigates the by the Istituto Nazionale di Alta Matematica ``F. T representation theory of groups, Lie Severi'', and held in “La Sapienza”, Rome, Italy. (2) algebra, Lie superalgebras and vertex operator Nien was invited to the following conferences: ESI algebras. Research topics include the representation Programme on Automorphic Forms: Arithmetic and theory of finite groups and p-adic groups, the Geometry, Jan and February, Erwin Schrodinger investigations of the relationship between the Institute, Vienna, Austria, and Workshop on Lie representation theories of classical Lie algebras and group representations and automorphic forms in July, Lie superalgebras and the structure theory of vertex MCM, Beijing, China. (3) N. Lam was an invited operator algebras and their relationship with certain speaker for the conference on Cross-straits Workshop sporadic simple groups. in Xiamen, July 2011 (4) Yang was invited to visit Investigators: Shun-Jen Cheng (Academia Tsinghua University, Beijing and Zhejiang University, Sinica), Po Yi Huang (NCKU), Shih-Chang Huang Hangzhou during May 2012, where he gives some (NCKU), Wen Fong Ke (NCKU), Ching Hung Lam lectures on his study on cluster algebra of finite type. (Academia Sinica), Ngau Lam (NCKU), Chu-Feng He also attended the 5th Mathematical Society of Nien (NCKU), Shih-Wei Yang (NCKU). Japan Seasonal Institute, 2012 International summer Visitors: Weiqiang Wang (Virginia, USA), school and conference on Schubert calculus in July. Hiroshi Yamauchi (Tokyo, Japan), Tomoyuki In September, he visited Prof. Giovanni Cerulli Irelli Arakawa (Nara, Japan), Hiromichi Yamada (Tokyo, to discuss a joint project on symmetric functions; Japan), Hiroki Shimakura (Aichi, Japan), Johannes while in October, he was invited to attend a MSRI Meyer (Bloemfontein, South Africa), Yu Cai Su workshop on Cluster Algebras in Combinatorics, (Shanghai Tongji University), Edmund Puczylowski Algebra, and Geometry. (5) C.H. Lam was an (Warsaw, Poland), Nan Hua Xi (Academy of Science, invited speaker for the conference on vertex operator China), Ruibin Zhang (Sydney University) . algebras, finite groups in Tokyo, Feb 2012 and Most of the members of this group made visits the Symposium on Algebraic combinatorics in to foreign institutes and attended many conferences. Hirosaki, Japan, June 2012. He was also invited to (1) S.-J. Cheng visited the University of Virginia in speak in the 29th International symposium on group April 2012 and was invited to attend the Third ECNU theoretical methods in Physics held in China, Aug Summer School and Workshop in Representation 2012 and a conference on vertex operator algebras Theory held in the East China Normal University in in Shanghai, Aug 2012. In addition, he also attended Shanghai in June 2012, where he gave a talk in the the conference on finite groups, vertex operator workshop. In August he was invited to attend the algebras and related topics in Tsukuba, Sep 2010. (6) 29th International Colloquium on Group-Theoretical W.-F. Ke visited University Tartu in April and was Physics held in the Chern Institute in Nankai, invited to give an invited talk in the “Algebra and its China, where he gave an invited talk in the session applications Workshop”. Also he were in Johannes quantum algebra. He was invited to attend the TWAS Kepler University Linz in February and September annual conference and general meeing in Tianjin in to conducted joint researches with Professor Guenter September. The event is organized by the Academy of Pilz, Dr. Gerhard Wendt of the Department of Sciences for the Developing World, and S.-J. Cheng Algebra. This visit also had Dr. Hubert Kiechle from delivered an invited talk during this annual event. In Hamburg University involved, who also came to Linz December he is scheduled to give an invited talk in to Linz during the time. the INdAM Workshop in Lie superalgebras organized An international conference on vertex operator

49 ‹‹- Highlights of the Focus Programs algebras, finite groups and related was held in classical types (SU(p;q); SU(p), SU(q)), (Sp(2n);U(n)) Academia Sinica from Dec 13-18, 2011. There were and (SO(2n);U(n)). We also give a first conceptual over 15 foreign speakers from 5 different countries. explanation for the resemblance of Enright’s A Spring Algebra Workshop was held in National u-cohomology formulas and Kostant’s u-cohomology D Taitung University from April 1 to 3 that brought formulas. together mathematicians from three different C.H. Lam and H. Shimakura have completed their universities to exchange the results of their active program on classification of holomorphic framed researches. vertex operator algebras of central charge 24. They The second Cross-straits Workshop has been showed that there are exactly 56 such vertex operator planned and scheduled to take place in NCKU from algebras and they are uniquely determined by the Lie December 1 to 5. This will bring together about 30 algebras of their weight one subspaces. In addition, mathematicians from China, and 25 algebraists from C.H. Lam (joint with T. Arakawa and H. Yamauchi) Taiwan. Graduate students will be encouraged to made a new breakthrough in the study of parafermion participate or attend the workshop. vertex operator algebras. In particular, they showed parafermion vertex operator algebras associated to any finite dimensional simple Lie algebras are C2 Important Results, Breakthrough cofinite, which confirmed a very famous conjecture. In addition, we also discovered a new level-rank S. J. Cheng, N. Lam and W. Wang formulate and duality among parafermion vertex operator algebras establish a super duality which connects parabolic of type A. categories O between the ortho-symplectic Lie S. C. Huang and F. Himstedt have completed superalgebras and classical Lie algebras of B, C, D their program on the decomposition numbers of types. More precisely, we show that certain parabolic 3 n Steinberg’s triality groups D4(2 ). They determined BGG categories over the ortho-symplectic Lie the l-modular decomposition matrices of this family superalgebras and classical Lie algebras of B, C, for all primes l not equal to 2 except for some entries D types are equivalent. This provides a complete in the unipotent characters. As an application, and conceptual solution of the irreducible character they use the decomposition matrices to classify all problem for the ortho-symplectic Lie superalgebras 3 n absolutely irreducible representations of D4(2 ) in in a parabolic category O, which includes all finite- non-defining characteristic up to a certain degree, dimensional irreducible modules, in terms of classical solving a problem proposed by P. H. Tiep and A. E. Kazhdan-Lusztig polynomials. S. J. Cheng, N. Lam Zalesskii. and W. Wang also prove the Brundan’s conjecture In “Combinatorial expressions for F-polynomials in the new preprint. In particular, they obtained the in classical types”, (published in Journal of irreducible character of all modules with integral Combinatorial Theory, Series A_119 (2012), Issue 3, weights over the general linear superalgebra. N. Lam 747—764), Yang gives combinatorial formulas for show that the u-cohomology groups with coefficients F-polynomials in cluster algebras of classical types in infinite dimensional irreducible unitarizable in terms of the weighted paths in certain directed highest weight modules are introduced for the general graphs. As a consequence he proved the positivity of linear superalgebra. The corresponding cohomology F-polynomials in cluster algebras of classical types. groups associated with a large class of infinite dimensional irreducible unitarizable representations Nien found a way to work out Jacquets’ conjecture known as the oscillator representationsare computed on local converse theorem for twisted gamma factor explicitly. P. Y. Huang, N. Lam and T. M. To obtain in the finite field case. This is the first evidence that the u-homology formulas for unitarizable modules Jacquets’ conjecture holds and the finite field result at negative levels over classical Lie algebras of shed some light on crash the problem on p-adic case. infinite rank of types gl(n), sp(2n) and so(2n) are P.-Y. Huang and W.-F. Ke, together with G. F. obtained. As a consequence, we recover the Enright’s Pilz of University of Linz, solved a conjecture on the formulas for three Hermitian symmetric pairs of cardinality of some symmetric differences, which

Highlights of the Focus Programs ‹‹- 50 originated from a study on coding theory. Huang [2] Chebotar, Mikhail A.; Ke, Wen-Fong; Lee, also worked with N. Lam and T.-M To applying Pjek-Hwee; Puczylowski, Edmund R. A linear combinatorics to algebraic structure. In the paper algebra approach to Koethe's problem and related “Super dua1ity and homology of unitarizable questions. Linear and Multilinear Algebra, to modules of Lie algebras”, they successfully apply appear (online 18 Jul 2012) combinatorial technique (similar to dual of partitions) [3] G. Hohn, C.H. Lam, H. Yamauchi, McKay's E7 D to prove a duality problem in Lie groups. Finally, observation on the Babymonster, International Huang also worked with T.-L. Wong and X. Zu and Mathematics Research Notices (2012) Vol. 2012, solve some chromatic number problem in graph 166-212; doi: 10.1093/imrn/rnr009. theory using algebraic method (combinatorial [4] Robert L. Griess Jr. and C.H. Lam, Diagonal Nullstelensatz). lattices and rootless EE8 pairs, Journal of Pure and Applied Algebra, Volume 216, Issue 1, With Kiechle, Pilz, and Wendt, W.-F. Ke January 2012, Pages 154-169. just finished a characterization of topological [5] G. Hohn, C.H. Lam, H. Yamauchi, McKay's planar nearrings on Euclidean plane. In the work, E6 observation on the Fischer group Fi24, isomorphism theorems were established for general Communications in Mathematical Physics, planar nearring and applied to planar nearrings on Volume 310, Issue 2 (2012), Page 329-365 Euclidean plane.. [6] C.H. Lam and H. Shimakura, Quadratic spaces and holomorphic framed vertex operator algebras Accomplishments of central charge 24, Proceedings of London Mathematical Society 104 (2012), no. 3, 540- 576(doi: 10.1112/plms/pdr041). 2011: [7] P.-Y. Huang, N. Lam and T.-M. To, Super duality [1] N. Lam and R. B. Zhang, u-cohomology formula and homology of unitarizable modules of Lie for unitarizable modules over general linear algebras, Publ. Res. Inst. Math. Sci. 48 (2012) algebras, J. Algebra 327 (2011), 50-70. 45-63. [2] Nien, Chufeng; Jiang Dihua; Qin, Yujun. [8] Robert L. Griess Jr. and C.H. Lam, A new Generalized Shalika models of p-adic SO4n and existence proof of the Monster by VOA theory, functoriality. Accepted for publication by Israel Michigan Mathematical J. 61 (2012), 555–573. Journal of Mathematics (2011) [3] Robert L. Griess Jr. and C.H. Lam, A moonshine path for 5A and associated lattices of ranks 8 and Submitted articles and Preprints 16, Journal of Algebra 331 (2011), 338-361. [1] T. Arakawa, C.H. Lam, and H. Yamada, Zhu's [4] C. H. Lam, On the constructions of holomorphic algebras, C2-algebras and C2-co_niteness of vertex operator algebras of central charge 24, parafermion vertex operator algebras, preprint Communications in Mathematical Physics, Vol (arXiv:1207.3909). 305,No. 1, 2011, pp 158-193. [2] Robert L. Griess Jr. and C.H. Lam, Moonshine [5] R. L. Griess Jr. and C.H. Lam, A moonshine paths for 3A and 6A nodes of the extended E8- path from E8 to the Monster, Journal of Pure and diagram, preprint . Applied Algebra, 215(2011), 927-948. [3] H.Y. Chen and C.H. Lam, Coset construction of [6] S.-J. Cheng, N. Lam and W. Wang, Super duality the Z3 orbifold vertex operator algebra , and irreducible characters of ortho-symplectic preprint . Lie superalgebras, Invent. Math. 183 (2011), [4] C.H. Lam and C.S. Su, Griess algebras generated 189-224. by 3 Ising vectors of central 2A-type, preprint. [5] C.H. Lam and H. Shimakura, Classification of 2012: holomorphic framed vertex operator algebras of central charge 24, preprint. [1] Ke, Wen-Fong; Meyer, Johan Matrix near-rings and 0-primitivity. Monatshefte fur Mathematik, [6] S.-J. Cheng, N. Lam and W. Wang, Brundan- 165 (2012), 353--363. Kazhdan-Lusztig conjecture for general linear Lie superalgebras, preprint.

51 ‹‹- Highlights of the Focus Programs D.10 Scientific Computation at NCTS

Coordinators: Chien-Cheng Chang (NTU), I-Liang Chern (NTU and NCTU), Ming-Chih Lai (NCTU), Wen-Wei Lin (NCTU), Tony W. H. Sheu(NTU), Wei-Cheng Wang (NTHU), Wei- D Chung Wang (NTU), Soon-Yi Wu (NCKU)

he aim of this focus program include In this three day conference, two plenary T speakers, five invited speakers, 87 contributed talks and three students prize awards constitute the prime i. Promote quality research on Scientific event for the Applied Math community on East Computation and related topics in Taiwan. Asia. With over 180 participants from East Asia and ii. Enhance international visibility of local around the world, the meeting has greatly enhanced reseacher groups. international visibility of NCTS and local Applied iii. Cultivate junior researchers and students in mathematicians, as well as abundant opportunity for Scientific Computation. academic collaboration in the future. Details of the iv. Promote interdisplinary research collaboration. conference can be found in http://www.math.ntu.edu. For these purposes, we have coordinated a series tw/~easiam2012 of academic activities (see below for details) in order 2. International Conference on Optimization and to support local researchers and to bring in frontiers Engineering Systems (NCKU, June 27-30, 2012). of international resarch trends. The purpose of the interdisciplinary workshop Based on the PIs’ expertise, our proposed research is trying to bridge mathematical methods in focus and potential topics include: optimization and engineering systems such as the (1) Numerical Linear Algebra and Applications total energy of a ferroelectric system, Kac-Ising model in quantum mechanics, wireless network (2) Numerical PDE and Applications services, public transportation and so forth. (3) Optimization and Numerical Computation Engineering systems are usually large and complex (4) Multiscale Analysis and Computation and they often require mathematical analysis in their (5) Medical and Industrial Applications models to help optimize a preset goal subject to We now report the activities of SC group in this year: resources and capacity constraints. The main focus is frontier and recent development in optimization D.10.1 Activities theory and methods, including linear/nonlinear programming, conic optimization, semi-definite Year 2012 is NCTS special year on Applied Math. relaxation, variation inequality, combinatorial In addition to regular seminars and short courses, we optimization, complex system modeling an Chaird have to organize several major activities to achieve analysis, optimal control. the above stated goals. In addition to international conferences and workshops, we have also organized We have managed to invite many distinguished local workshop and short courses to provide a speakers from overseas to participate in this event, presentation platform for junior scholars to and to including Shu-Cherng Fang (Walter Clark Chair broaden academic views for graduate students with Professor and Alumni Graduate Distinguished diverse topics in applied Math. Professor, NCSU), Jong-Shi Pang (Head and Caterpillar Professor, University of Illinois at Urbana- Champaign), Kok-Lay Teo (Head and Chair Professor, D.10.1.1 Conference and Workshop: Curtin University of Technology, Australia) Jie Sun 1. 2012 East Asia Section of SIAM annual meeting (Provost’s Chair Professor, National University of (NTU, June 25-27, 2012. Co-organized with Singapore) David Yang Gao (Alexander M. Rubinov related focus programs)

Highlights of the Focus Programs ‹‹- 52 Chair Professor, University of Ballarat, Australia) Elliott (University of Warwick, UK), Irene Fonseca Wenxun Xing (Beijing Tsinghua University, China), (Carnegie Mellon University, USA), Yoshikazu Giga Zhenbo Wang (Beijing Tsinghua University, China), (The University of Tokyo, Japan), Chun-Hsiung Hsia Yong Xia (Beihang University, China), and Che-Lin (NTU, Taiwan), Hideo Kozono (Tohoku University, Su (The University of Chicago). Japan), Chi-Kun Lin (NCTU, Taiwan), Fang Hua Lin (NYU, USA), Tai-Chia Lin (NTU, Taiwan), Benoit D In addition, there were more than 40 local participants who joined the conference and gave a Perthame (UPMC (Paris 6), France), Edriss S. Titi talk, including National Tsing Hua University Chair (UC, Irvine) and Tai-Peng Tsai (Univ. of British Professor Wang, Hsiao Fan, Chung-Yuan Christian Columbia, Canada) University Chair Professor Lai, Hang Chin, and 4. 2012 South Taiwan Workshop on Scientific many other post doctors and graduate students. Computing and Applications (NSYSU, Feb 18, Those leading experts from the world contribute 2012). Details available on http://www.ncts.ncku. and integrate the newest research results, as well as edu.tw/math/workshop/120218/poster.pdf promote the development of operations research and optimization in National Cheng-Kung University. D.10.1.2 Schools, regular courses, and The conference is also dedicated to Prof. Shu-Cherng short courses: Fang on the occasion of his 60th birthday to honor his long term contribution to the area of optimization 1. NCTS Short Course on Introduction of Numerical and engineering systems. Analysis for Partial Differential Equations (Feb 13- The participants include graduate students and 17, 2012) postdocs from mathematical sciences and from Speakers : Prof. Yuusuke Iso (Kyoto University), Engineering and Management Sciences. This Prof. Hiroshi Fujiwara (Kyoto University), Prof. conference has provided a great opportunity for the Hitshi Imai (University of Tokushima). participants from different disciplinary to exchange 2. Summer School on Optimization and its Recent ideas and to enhance mutual understanding. Development (Jul 9 – Aug 23, 2012) Moreover, we held a forum to review the development Speakers : Prof. Zhen-Bo Wang (Beijing Tsinghua), of Operations Research and Optimization in Taiwan Prof. Xia Yong (Beihang University, Beijing), for the past twenty years and discuss the future Prof. Yu-Chen Shu (NCKU). opportunity of OR both in academic and industrial 3. NCTS Summer Course on Scientific Computation perspectives. We hope that this would provide an (Aug 20 – 22, 2012) overall view for junior researchers to have a much Speakers : Prof. Shingyu Leung (Hong Kong better picture in their future careers. In addition, a University of Science and Technology) follow up summer school on Optimization and its 4. NCTS Short Course on Introduction to Numerical recent development was held in July 9 - Aug 23 2012. Methods for Control Systems (Sep 3 – 11, 2012). 3. NCTS workshop on Theoretical and Numerical Challenges in PDE (NTHU, December 13-15, 2012. Co-organized with related focus programs) This international workshop is aimed to bring world experts on theoretical analysis and computational methods for different PDEs that arise from nature and applications. The ultimate goal is to introduce frontier research directions to the local community and to initiate some potential research collaborations. Confirmed speakers include Dongho Chae (Chung-Ang University, Korea), Chi- Hin Chan (NCTU, Taiwan), I-Kun Chen (NCTU, Taiwan), Ching-Hsiao Cheng (NCU, Taiwan), Peter Constantin (Princeton University, USA), Charlie

53 ‹‹- Highlights of the Focus Programs D.10.2 Visiting Scientists Name Affiliation Duration Goong Chen Texas A&M University 2011/12/11~2012/01/11 Rolf Ryham Fordham University 2011/12/30~2012/01/11 D Eric K - W Chu Monash University, Australia 2012/01/15~2012/01/20 Michiel Hochstenbach Eindhoven University of Technology 2012/02/24~2012/03/05 Toshiyuki Ogawa Meiji University 2012/02/26~2012/02/29 Nobuhiro Suematsu Meiji University 2012/02/26~2012/02/29 Junta Matsukidaira Ryukoku University 2012/02/26~2012/02/29 Mr. Yuumi Nakamura Meiji University 2012/02/26~2012/02/29 Richard Tsai University of Texas at Austin 2012/05/17~2012/06/01 Petr Plechac University of Tennessee 2012/05/21~2012/06/14 Xuejun Xu Chinese Academy of Science 2012/06/22~2012/06/29 Zhenning Cai Beijing University 2012/06/22~2012/06/29 Seonjeong Lee Seoul National University 2012/06/22~2012/06/29 Linda Petzold University of California 2012/06/23~2012/06/28 Weiqing Ren National University of Singapore 2012/06/24~2012/06/26 Hyung-Chun Lee Ajou University 2012/06/24~2012/06/28 Dongwoo Sheen Seoul National University 2012/06/24~2012/06/28 Yalchin Efendiev Texas A&M University 2012/06/25~2012/06/28 David Yang Gao University of Ballarat, Australia 2012/06/26~2012/07/03 Jie Sun National University of Singapore 2012/06/26~2012/07/03 Kok Lay Teo Curtin University of Technology, Australia 2012/06/26~2012/07/03 Houde Han Tsinghua University, Beijing 2012/07/21~2012/07/23 Zhongyi Huang Tsinghua University, Beijing 2012/07/21~2012/07/23 Yimin Wei Fudan University, Shanghai 2012/07/31~2012/08/04 Wenjun Ying Shanghai Jiao Tong University 2012/07/26~2012/08/19 Xuding Zhu Zhejiang Normal University 2012/08/02~2012/08/03 Aiichi Yamasaki Kyoto University 2012/08/12~2012/08/31 Shunsuke Hayashi Kyoto University, Japan 2012/08/30~2012/09/24 De-Kang Mao Shanghai University 2012/10/14~2012/10/21 D.10.3 Important Results, Breakthrough: (a) The matrix equation X + A^{T}X^{-1}A = Q arises in Green's function Calculations in nano With inspiration from the academic activities and research, where A is a real square matrix and close collaboration with international visitors, we Q is a real symmetric matrix dependent on a have successfully promoted quality researches on parameter and is usually indefinite. In practice Scientific Computation and related topics in Taiwan. one is mainly interested in those values of the We have published 17 SCI papers in 2012, many parameter for which the matrix equation has of them are published or accepted for publication no stabilizing solutions. The solution of interest on high-ranking research journals such as the in this case is a special weakly stabilizing SIAM series, Journal of Computational Physics, complex symmetric solution X_{*}, which is Computational Optimization and Application, Journal the limit of the unique stabilizing solution X of Global Optimization, etc. The publication details of the perturbed equation X + A^{T}X^{-1} can be found in the end of this report. A = Q + i \eta I, as \eta approaches to 0^{+}. It has been shown that a doubling algorithm can be used to compute X efficiently even for The research highlight in 2012 include: very small values of \eta, thus providing good (1) Numerical Linear Algebra and Applications: approximations to X_{*}. It has been observed

Highlights of the Focus Programs ‹‹- 54 by nano scientists that a modified fixed- potential applications to study the dynamics of point method can sometimes be quite useful, a compound vesicle and is less investigated in particularly for computing X for many different literature. We show the spreading operator of values of the parameter. We provide arigorous the tension and the surface divergence operator analysis of this modified fixed-point method of the velocity are skew-adjoint mathematically. and its variant, and of their generalizations. This skew-adjoint property is also preserved D We also show that the imaginary part X_{I} in the discrete form which makes the resultant of the matrix X_{*} is positive semi-definite linear system to be symmetric. A fractional and determine the rank of X_{I} in terms of step method that exploits fast Poisson solvers the number of unimodular eigenvalues of the can be efficiently applied to solve the linear quadratic pencil \lambda^2 A^{T} - \lambda system. Unlike our previous work using penalty Q + A. Finally we present a new structure- approach, we are able to estimate the local error preserving algorithm that is applied directly on of inextensibility for two successive time steps the equation X + A^{T}X^{-1}A = Q. In doing in the present work. In addition, there are no so, we work with real arithmetic most of the penalty parameters introduced, so the time step time. size can be significantly increased. We present (b) Computing Spectrum Boundary Eigenvalues numerical results of the tank-treading to for Three-dimensional Photonic Crystals: We tumbling motions for an inextensible interface consider the eigenvalue problems corresponding enclosing a solid particle with different filling to wave vectors that are close to the center fractions under shear flow. We have found of the Brillouin zone of a three dimensional, that by the increase of the filling fraction, the simple cubic photonic. On the theoretical side, interface tends to transit from tank-treading to the structures of the null spaces are analyzed tumbling. We also compute the critical filling to explicitly determine the number of zero fractions for different reduced areas and the eigenvalues of the target eigenvalue problems. results are qualitatively consistent with the ones On the computational side, the Krylov- in literature. Schur and Jacobi-Davidson methods are used (b) Hamiltonian-preserving solver for shallow to compute the smallest, positive, interior water equation. Our aim is to develop a long eigenvalues that are of interest. This article is term accurate solution solver for the Camassa- accepted by Journal of Scientific Computing. Holm (CH) equation. The adopted strategy to (c) Matrix Representation of the Double-Curl achieve the goal is the application of symplectic Operator for Simulating Three Dimensional Runge-Kutta time integration method. To Photonic Crystals: Three dimensional photonic improve the dispersive accuracy, we have crystals can be modeled by the Maxwell optimized the numerical wavenumber for the equations as an generalized eigenvalue first-order spatial derivative term. The ongoing problem (GEVP). From a viewpoint of matrix work is to explore the link between structure of computation, we derive explicit matrix CH equation with the Painleve’ transcendents representation of the double-curl operator existing possibly between the solution and the associated with the photonic crystal with fastly oscillatory solution regions. Also, DP FCC lattice. The explicit matrix leads to equation is under current investigation. an eigendecomposition of the degenerate (c) Preservation of dispersion solution equation for coefficient matrix and then a fast eigenvalue the Maxwell’s equations. Our aim is to develop solver. This article is accepted by Mathematical a long distance accurate electromagnetic wave and Computer Modelling. prediction. To achieve this goal, we optimize (2) Numerical PDE and Applications: the numerical dispersion equation (DRE) for the Maxwell’s equations. Our current (a) We develop a linearly semi-implicit scheme for ongoing work is to extend the DRE scheme for the model of Stokes flow with an inextensible the non-dispersive medium to its dispersive interface enclosing a solid particle which has

55 ‹‹- Highlights of the Focus Programs counterparts. (DNLS) equations that model rotating Bose– (3) Optimization and Numerical Computation: Einstein Condensates (BEC) both analytically and numerically. We propose a quotient Prof. Soon-Yi Wu has the collaborative paper transformation invariant continuation method with Prof. Shunsuke Hayashi,. They prove that to circumvent this obstacle. We also analyze there are very good convergence rate on the D the bifurcation properties of the primal stalk semi-infinite programming (SIP) problems solution curve corresponding to the DNLS with second-order cone constraints. Besides, equations for an isotropic trap. In numerical the implement results for this algorithm we get computation, the existence of a bistable region is better than all other exiting algorithms for corresponding to the bound states with a 0- SIP. This is a breakthrough in the implement of or 1-vortex is shown. This finding not only infinite programming and it is very important. agrees with the physics of the experimental In addition, Prof. Soon-Yi Wu also has two joint phenomena, but also explains why a 0- or papers with Prof. Guanglu Zhou. One entitled 1-vortex may be observed within a certain “Nonnegative polynomial optimization over unit region that has an angular velocity. Numerical spheres and convex programming relaxations” has evidence shows that trap potentials have little been published in SIAM Journal on Optimization effect on the width of the bistable regions. In and the other entitled “Efficient algorithms for contrast, intra-component scattering length computing the largest eigenvalue of a nonnegative significantly affects the bistable region. tensor” has been accepted by Numerical Linear Algebra with Applications. (b) We investigate the dynamic phase transition of a binary system in a cylindrical geometry. Two (4) Multiscale Modeling, Analysis and Computation. types of phase transitions (the continuous type (a) We developed a pseudo-arclength continuation and the jump type) are determined explicitly method (PACM) to study the spin-1 Bose- in terms of relevant physical and geometric Einstein condensates. We reveal that the parameters. We also propose a phase field component separation and population transfer model for surfactant in a binary system. It is between the different hyperfine states can a combination of Cahn-Hilliard model (for only occur in excited states due to the spin- binary system) and Fokker-Planck model (for exchange interactions. In additional to the surfactant). In this new model, entropy term numerical study, we also investigated the for surfactant is included. The structure of existence and non-existence of ground states the interface and the effect of surfactant were for spin-1 BEC with/without trapped potential studied. We also developed a pseudo-spectral in one dimension. We further characterize method to simulation this equation in both two the possible ground states of spin-1 BEC. and three dimensions. We develop a mathematical technique called (5) Medical and Industrial Applications: kinetic-energy decreasing mass-redistribution technique. Using this technique, we are able (a) We study lung registration problem. We use to show that the only ground states are so- mass transport method to match lung branch called single mode approximation (SMA) for points with almost 100% correct rate. Each ferromagnetic systems, and two-component unlabeled point set consists of about 1500 BEC for anti-ferromagnetic systems. We study points. The promising result indicates that long-time behaviors of damped Schrodinger the proposed distance is a suitable biological system, modeled by Schrodinger-Langevine metric for lung deformations. The registration equation. We showed that the damping effect results can be used to estimate the deformation will overwhelm the quantum fluctuation at structure of lungs. large time and the solution approaches to a (b) We propose a string-average expectation diffusion wave time-asymptotically. We also maximization (SA-EM) algorithm to solve study the discrete nonlinear Schrödinger the image reconstruction problem in positron

Highlights of the Focus Programs ‹‹- 56 emission tomography (PET). The method [7] X. J. Tong, C. Ling, S. Y. Wu and L. Qi (2012), borrows ideas of block iteration projection Semi-infinite Programming Method for Optimal algorithm from optimization theory and the EM Power Flow with Transient Stability and algorithm in statistics and reaches a reasonable Variable Clearing Time of Faults, to appear in result for PET reconstruction. Journal of Global Optimization. [8] L. P. Zhang, S. C. Fang, and S. Y. Wu (2012), D (c) Optimizing Latin Hypercube Designs by Particle Swarm: The large number of feasible An Entropy-Based Central Cutting Plane designs makes the search for optimal Latin Algorithm for Convex Min-Max Semi-Infinite Programming Problems, to appear in SCIENCE hypercube designs LHDs a difficult discrete CHINA Mathematics. optimization problem. We propose a new population-based algorithm named LaPSO that [9] M. C. Lai, W. F. Hu and W. W. Lin, A Fractional is adapted from the standard particle swarm Step Immersed Boundary Method for Stokes Flow with an Inextensible Interface Enclosing optimization (PSO) and customized for LHD. a Solid Particle, SIAM Sci. Comp., 2012, to We further accelerate LaPSO via a graphic appear processing unit (GPU). [10] M. A. Solovchuk, Tony W. H. Sheu, W. L. Lin, I. Kuo, M. Thiriet (2012) , Simulation study D.10.4 Publications on acoustic streaming and convective cooling in blood vessel during a high-intensity focused [1] C.-H. Teng, I.-L. Chern and M.-C. Lai, ultrasound thermal ablation, International J. of Heat and Mass transfer, Vol. 55(4), 1261-1270 Simulating binary fluid-surfactant dynamics by a phase field model, Discrete and Continuous [11] Tony W. H. Sheu, C. H. Yu (2012), Numerical Dynamical Systems - Series B , Vol 17, No 4, simulation of free surface by an area- 1289-1307 (2012) preserving level set method, Communications in [2] X. J. Tong, L. Qi, and S. Y. Wu (2012), A Computational Physics, Vol. 11(4), 1347-1371 Smoothing SQP Method for Nonlinear Programs [12] Tony W. H. Sheu, K. C. Lin, J. H. Li (2012), with Stability Constraints Arising from Power Development of a convection-diffusion-reaction Systems, Computational Optimization and model for solving Maxwell’s equations in Applications, Vol. 51, 175-197. frequency domain, International Journal for [3] T. J. Shiu and S.Y. Wu (2012), Relaxed Cutting Numerical Methods in Fluids, Vol. 69, 430-441 Plane Method with Convexification for Solving [13] Ching-Long Huang, Tony W. H. Sheu (2012), Nonlinear Semi-Infinite Programming Problems, Development of a moving and stationary mixed Computational Optimization and Applications, particle method for solving the incompressible Vol. 53, 91-113. Navier-Stokes equations at high Reynolds [4] Y. H. Xiao, S. Y. Wu, and D. H. Li (2012), numbers, Numerical Heat Transfer, Part B : Fundamentals, Vol. 62, 71-85 Splitting and Linearizing Augmented Lagrangian Algorithm for Subspace Recovery from [14] Tony W. H. Sheu, S. H. Kuo, R. K. Lin Corrupted Observations, to appear in Advances (2012), Prediction of temperature-dependent in Computational Mathematics. electroosmotically driven microchannel flows [5] Y. H. Xiao, H. Zhu, and S. Y. Wu (2012), Primal with the Joule heating effect, International Journal of Numerical Methods for Heat & Fluid and Dual Alternating Direction Algorithm Flow, Vol 22(15), 554-575 for ℓ1–ℓ1–Norm Minimization Problems in Compressive Sensing, to appear in [15] CY Chiang, EKW Chu, WW Lin, On the Computational Optimization and Applications. w-Sylvester equation AX ± Xw Bw = C, Applied [6] K. F. C. Yiu, M. J. Gao, T. J. Shiu, and S. Y. Mathematics and Computation (2012) Wu, T. Tran and I. Claesson (2012),An Fast [16] CH Guo, YC Kuo, WW Lin, On a nonlinear Algorithm for the Optimal Design of High matrix equation arising in nano research, SIAM Accuracy Windows in Signal Processing, to Journal on Matrix Analysis and Applications 33 appear in Optimization Methods and Software. (1), 235-262 (2012)

57 ‹‹- Highlights of the Focus Programs [17] CH Guo, YC Kuo, WW Lin, Numerical [27] Liren Lin and I-Liang Chern, “Characterization solution of nonlinear matrix equations arising of ground states of spin-1 Bose-Einstein from Green’s function calculations in nano condensates,” preprint, (2012). research, Journal of Computational and Applied [28] Yair Censor , Tai-Been Chen, I-Liang Chern, Mathematics (2012) Alvaro Rodolfo De Pierro, Elias Salomao Helou, D [18] T Li, EKW Chu, WW Lin, PCY Weng, Solving Ming Jiang and Henry Horng-Shing Lu, “String- large-scale continuous-time algebraic Riccati average expectation-maximization for maximum equations by doubling, Journal of Computational liklihood estimation in emission tomography,” and Applied Mathematics (2012) preprint, (2012). [19] PCY Weng, EKW Chu, YC Kuo, WW Lin, [29] P. Chen, C. Lin and I. Chern, “A Perfect Match Solving large-scale nonlinear matrix equations Condition for Point-Set matching Problems via by doubling, Linear Algebra and its Applications Optimal Mass Transport Approach,” preprint, (2012) (2012). [20] Y. Kim, Y. Seol, M.-C. Lai and C. S. Peskin, The [30] Chern, I-Liang and Hai-Liang Li, “Long-time immersed boundary method for two-dimensional behavior of the nonlinear SchrÖdinger Langevin foam with topological changes, Communications equations,” preprint, (2012). in Computational Physics , Vol 12, No 2, 479- [31] Shunsuke Hayashi and Soon-Yi Wu, “On finite 493 (2012) convergence of an explicit exchange method for [21] Tsung-Ming Huang, Han-En Hsieh, Wen- convex semi-infinite programming problems Wei Lin, and Weichung Wang (2012). “Matrix with second-order cone constraints”, preprint, Representation of the Double-Curl Operator (2012) for Simulating Three Dimensional Photonic [32] Tony W.H. Sheu, R.Y. Chang, Y.W. Chung, J.H. Crystals.”Mathematical and Computer Li, “Study of the effect of defect layer on the Modelling. Accepted. unmagnetized plasma photonic crystals using the [22] Weichung Wang, Tsung-fang Wu, and Chien- optimized numerical group velocity scheme”, Hsiang Liu (2012). "On the Multiple Spike preprint, (2012) Solutions for Singularly Perturbed Elliptic [33] Wei-Cheng Wang and Wenjun Ying, “A kernel- Systems.” Discrete and Continuous Dynamical free boundary integral method for the Stokes Systems-Series B. Accepted. system”, preprint, (2012) [23] Yueh-Cheng Kuo, Shih-Feng Shieh, and [34] Wenjun Ying and Wei-Cheng Wang, “An Weichung Wang* (2012)."Rotational overlapping surface decomposition based kernel- Quotient Procedure: a Tracking Control free boundary integral method”, preprint (2012) Continuation Method for PDEs on Radially Symmetric Domains.”Computer Physics Communications.183(4):998-1001. [24] G. L. Zhou, L. Caccetta, K. L. Teo, and S. Y. Wu (2012), Nonnegative Polynomial Optimization over Unit Spheres and Convex Programming Relaxations, SIAM Journal on Optimization, Vol. 22, 987-1008. [25] G. L. Zhou, L. Qi, and S. Y. Wu (2012), Efficient Algorithms for Computing the Largest Eigenvalue of a Nonnegative Tensor, to appear in Numerical Linear Algebra with Applications [26] Tsung-Ming Huang, Yueh-Cheng Kuo and Weichung Wang, Computing Extremal Eigenvalues for Three-Dimensional Photonic Crystals with Wave Vectors Near the Brillouin Zone Center. To appear in Journal of Scientific Computing

Highlights of the Focus Programs ‹‹- 58 Highlights of the Regional Programs E

E.1 Regional Programs on Statistics at Hsinchu

Coordinators: H. Wang (National Chiao-Tung University), N.-J. Hsu (National Tsing-Hua University), S.-T. Tseng (National Tsing-Hua University)

his is the fourth year of this statistics The field of industrial statistics is broad, both in T program and we have a significant progress theory and in application. In this workshop, we had on developing the research group. First of all, we invited 12 outstanding researchers (including Prof. had run a very successful summer NCTS workshop Berry Arnold, S. B. Kim, Yili Hung, Ying Hung, on Industrial Statistics and its Applications on June Dennis Lin, Regina Liu, W. Q. Meeker, K-B Wang, 26-27. The main goal of this workshop is to share Arthur Yeh and others) of various fields and focus interesting research topics and exchange research on frontier research topics of data mining, DOE, experience with colleagues in the industrial statistics reliability, and SPC. The main goal of this workshop research group (ISRG) at NCTS. It also stimulated is to share interesting research topics and exchange some interesting researching topic for international research experience with colleagues in the ISRG at collaborations. Regarding the research group, the NCTS. This workshop has about 70 participants and ISRG operated by S.-T. Tseng is well developed and it also stimulated some interesting researching topic functioned in this year. The primary goal of ISRG for international collaborations. is to promote frontier research of statistical methods that can be efficiently applied to improve the quality (A2) Classification and Regression Trees NCTS and productivity of high-tech industry. In this year, Workshop (July 03-18, 2012) ISRG had held monthly seminars and discussions to generate interactions between academic researchers Speaker: Prof. Wei-Yin Loh and industrial engineers. It usually takes time for collaborations among multi-disciplines. We (Department of Statistics, University of Wisconsin– satisfy the current accomplishment and we are very Madison, USA) confident on the enhancement and improvement of Classification or regression tree model is an the program in the future. The activities held by the important tool in data analysis, where the data and statistics program this year are listed below and more sample space are split into two or more partitions information can be found at the website: and a simple statistical model is fitted to each of them. The resulting model is intuitive to interpret http://stat.web.nthu.edu.tw/files/11-1017-428.php. because the partitions can be displayed as decision tree. The best algorithms can produce models with Workshop and Courses prediction accuracy at least as good as that of linear discriminant analysis and linear regression. This (A1) NCTS Workshop on Industrial Statistics and course reviews the major algorithms, including C4.5, its Applications (June 26-27, 2012) CART, CHAID, CRUISE, GUIDE, M5, QUEST, and RPART. Furthermore, we will also emphasize

59 ‹‹- Highlights of the Regional Programs the prediction accuracy and interpretability over We run a one-day regular ISRG seminar inside statistical inference. NCTS monthly. This year we invited 8 speakers to introduce contemporary research topics in industrial (A3) Recent Advances in Statistical Process statistics (such as run to run process control, Bayesian Control (July 6, 2012) inference in screening experiment, degradation E modeling and inference, profile monitoring, fault detection and classification and etc). Except for Speaker: Prof. Fugee Tsung running a regular seminar, we also have a subgroup (Department of Industrial Engineering, HKUST, meeting that allows all participants to exchange their Hong Kong) research experience. We hope that it can promote As quality and Six Sigma excellence has become useful, collaborated research works in the near future. a decisive factor in global market competition, The seminar activities are listed below: quality control techniques are becoming popular in (1) Speaker: Prof. Shui-Pin Lee 李水彬 (Ching Yun industries. With advances in information, sensing, University) and data capture technology, large volumes of data are being routinely collected and shared over Title: Diagnose the Faulty Tools of Profile multiple-stage processes, which has a growing impact Monitoring by Using LASSO Selection on the existing methods. Moreover, with the shift in Time: Nov. 18, 2011 economic focus from manufacturing to service, we (2) Spearker: Prof. Lirong Cui 崔 利 榮 (Beijing have to apply industrial statistics to increase quality Institute of Technology) and efficiency of service practices as well. This Title: Aggregated Stochastic Processes and seminar will give an overview of statistical quality Maintenance Models techniques, and discuss several technical challenges and recent extensions in both manufacturing and Time: Nov. 18, 2011 service Industries. (3) Spearker: Prof. Jionghua (Judy) Jin 金 炯 華 (University of Michigan, Ann Arbor)

(A4) Computer Search for Large Order Multiple Title: Overview of Data Fusion for Quality Recursive Generators (Dec 16~30, 2011) Improvements in Complex Systems Time: Nov. 25, 2011 Speaker: Professor Lih-Yuan Deng (4) Spearker: Prof. Jionghua (Judy) Jin 金 炯 華 (Department of Mathematical Sciences, University (University of Michigan, Ann Arbor) of Memphis, USA) Title: Engineering-Driven Wavelet Analysis Multiple Recursive Generators (MRGs) have for Feature Extraction and Diagnosis of Cyclic become the most popular random number generators Waveform Signals recently. They compute the next value iteratively from Time: Nov. 25, 2011 the previous k values using a k-th order recurrence (5) Spearker: Prof. Jye-Chyi Lu 盧 捷 琦 (Georgia equation which, in turn, corresponds to a k-th degree Institute of Technology, Atlanta, USA) primitive polynomial under a prime modulus p. Title: A Review of Statistical Methods for Quality In general, when k and p are large, checking if a Improvement and Control in Nanotechnology k-th degree polynomial is primitive under a prime modulus p is known to be a hard problem. In this Time: Dec, 23, 2011 talk, we discuss the major bottlenecks and recently (6) Spearker: Prof. Jye-Chyi Lu 盧 捷 琦 (Georgia proposed solutions for the computer search for large Institute of Technology, Atlanta, USA) order multiple recursive generators. Title: Experimental Design and Modeling Issues for Nano-manufacturing Regular Seminars Industrial Statistics Research Time: Dec, 23, 2011 Group (ISRG) (7) Spearker: Prof. Changliang Zou (Nankai University, China)

Highlights of the Regional Programs ‹‹- 60 Title: On-line Monitoring of High-dimensional Journal of X-ray Science and Technology, 20, Data Streams 339-349. Time: Dec, 29, 2011 [2] Chueh, T.-H., Lu, H. H.-S. (2012). “Inference (8) Spearker: Prof. Changliang Zou (Nankai of Biological Pathway from Gene Expression University, China) Profiles by Time Delay Boolean Networks.” E PLoS ONE 7(8): e42095. Title: Directional Cont rol Schemes for Multivariate Categorical Processes [3] Deng, L.-Y. , Shiau, J.-J. H., Lu, H. H.-S. (2012). “Efficient computer search of large- Time: Dec, 29, 2011 order multiple recursive pseudo-random number (9) Spearker: Prof. Changliang Zou (Nankai generators.” Journal of Computational and University, China) Applied Mathematics, 236, 3228– 3237. Title: Spatial-signs Based High-dimensional Tests [4] Fan, T. H. and Hsu, T. M. (2012). “Accelerated for Sphericity Life Tests of a Series System With Masked Time: Dec. 30, 2011 Interval Data Under Exponential Lifetime (10) Spearker: Prof. Changliang Zou (Nankai Distributions.” IEEE Transactions on Reliability, University, China) Vol. 61, pp. 798-808. Title: A Multivariate Sign Chart for Monitoring [5] Hsu, N. J., Chang, Y. M., and Huang, H. Process Shape Parameters C. (2012). “A group lasso approach for Time: Dec. 30, 2011 nonstationary spatial-temporal covariance estimation.” Environmetrics, 23, 12-23. (11) Spearker: Prof. Frederick K. H. Phoa 潘 建 興 (Academia Sinica, Taiwan) [6] Jou, B. Y., Chan, Y. T. and Tseng, S. T. (2012). “Designing a variable EWMA controller for Title: A Brief Retrospect to Recent Development the process disturbance subject to linear drift in Nonregular Designs and step changes.” IEEE Transactions on Time: Mar. 30, 2012 Semiconductor Manufacturing, 25(4), 614-622. 潘 建 興 (12) Spearker: Prof. Frederick K. H. Phoa [7] Tsai, C. C., Tseng, S. T. and Balakrishnan, (Academia Sinica, Taiwan) N. (2012), “Optimal design for degradation Title: Recent Development in Quaternary-code tests based on gamma processes with random Designs effects.” IEEE Transactions on Reliability, 61(2), Time: Mar. 30, 2012 604-613. (13) Spearker: Prof. Tzong-Ru Tsai 蔡宗儒 (Tamkang [8] Wang, H. and Hung, S. L. (2012). Phylogenetic University) Tree Selection by the Adjusted K-means Title: SPC for Monitoring Nonlinear Profiles: A Approach. Journal of Applied Statistics, 39, 643- Six Sigma Project on Curing Process 655. Time: Apr. 27, 2012 [9] Wang, W. L. and Fan, T. H. (2012). “Bayesian Analysis of Multivariate t Linear Mixed Models (14) Spearker: Christine Chen 陳美玲 (TSMC) Using the IBF-Gibbs Sampler.” J. of Multivariate Title: Some Statistical Practice Problems in Analysis, 105, 300-310. Semiconductor Manufacturing [10] Yang, S. F. Cheng, T. C., Hung, Y. C. and Time: Apr. 27, 2012 Cheng, S. W. (2012). “A New Chart for Monitoring Service Process Mean.” Quality and Publications Reliability Engineering International, 28(4), 377- [1] Chen, T.-B, Chen, J.-C., Lu, H. H.-S. (2012). 386. “Segmentation of 3D microPET Images of the [11] Lin, C. T., Chou, C. C. and Huang, Y. L. (2012). Rat Brain via the Hybrid Gaussian Mixture “Inference for the Weibull distribution with Method with Kernel Density Estimation.” progressive hybrid censoring.” Computational

61 ‹‹- Highlights of the Regional Programs Statistics and Data Analysis, 56(3), 451-467. [12] Yen, C. L., Shiau, J.-J. H. and Yeh, A. B. (2012). “Effective Control Charts for Monitoring Multivariate Process Dispersion.” Quality and E Reliability Engineering International, 28(4), 409-426.

Accepted papers [1] Cheng, T. C., Hsieh, P. H. and Yang, S. F. (2012). “Process control for the vector autoregressive model.” To appear in Quality and Reliability Engineering International. [2] Fan, T. H. and Yu, C. H. (2012). “Statistical Inference on Constant Stress Accelerated Life Tests Under Generalized Gamma Lifetime Distribution.” To appear in Quality and Reliability Engineering International. [3] Lin, C. H., Tseng, S. T. and Wang, H. F. (2012), “Modified EWMA controller subject to metrology delay.” To appear in IIE Transactions (Focus on Quality and Reliability Engineering). [4] Lu, I.L. and Wang, H. (2012). “Protein-specific Scoring Method for Ligand Discovery.” To appear in Journal of Computational Biology. [5] Peng, C. Y. and Tseng, S. T. (12012). “Statistical Lifetime Inference with Skew-Wiener Linear Degradation Models.” To appear in IEEE Transactions on Reliability. [6] Wang, Yi-Hua Tina and Huwang, Longcheen (2012). “On the monitoring of simple linear Berkson profiles.” To appear in Quality and Reliability Engineering International. [7] Wang, H. (2012). “Confidence Intervals for A Bounded Mean in Exponential Families.” To appear in Statistics. [8] Yang, S. F. (2012). “Using a Single Average Loss Control Chart to Monitor Process Mean and Variability.” To appear in Communications in Statistics-Simulation and Computation.

Highlights of the Regional Programs ‹‹- 62 E.2 Regional Programs on Statistics at Tainan Coordinators: Tiee-Jian Wu (National Cheng-Kung University) E

K Lee, U. Rochester gave:”Spatial Bayesian var. selection models on fMRI time series data” on W he state our activities in several different 3/29 at NCKU. 中研院統計所袁新盛 & 鄭宏文 focus areas (I-III below): gave:”Protein co-evolutionary diverg. as a new I. Probability & Statistical Methods. Coordinator: feature in protein-protein interaction prediction“ Wen-Jang Huang & Tiee-Jian Wu & ”Multistep prediction errors in integrated AR proc’s with polynomial time trends” on 3/15 & 3/16, Seminar S-J Wu of N-C State U. gave a respectively, at NCKU. 牛維方 (交大Inst. Bioinf. & talk:”Large deviations for a randomly indexed System Biology) gave:”Networking Stock Market“ branch i ng proc. wit h appl. i n f i nance”on on 3/8 at NCKU & 5/16 at NUK. 4/5 at NC K U.中央大 統計所曾 議寬g ave:”A Semiparametric extended hazard model with Visitor K. Shedden, Dept. Stat., U. Michigan, ” longitudinal covariates” on 4/12 at NCKU. visited 8/6-8/19, gave a talk: Statist. issues in the analysis of high content images” at NSYSU & Visitor P-Y Chen, Dept. Math., Syracuse U. visited on 6/22-7/18 & gave a talk:“Depth Based discussed research topics in bioinfo. with M-N. Lo. Nonpar. multivariate Selection” at NCKU. He discussed research topics with T-J Wu. S. Lee, Dept. Research Results: Statist., Seoul Nat. U. visited on 2/20-2/26 & gave a From Jan.-Sep./2012: (1) our program has invited talk:”Entropy based goodness of fit test” at NSYSU 5 visiting scholars, hold 10 seminar talks and 1 and discussed research topics with M-H Guo. workshop in Industrial statistics, (2) 17 papers (8 published and 9 submitted) have acknowledged the II. Industrial Statistics Coordinator: S.-L. Jeng support of NCTS (South), (3) program coordinator T.-J. Wu has given a plenary talk in The 2012 Seminar 中研院統計所張源俊 gave a talk“: Item 5th International Conference on Management calibration using seq. method and two-stage adaptive Engineering & Technology of Statistics (sponsored design method” on 3/1 at NCKU. by IEEE Beijing Section, etc.). Visitor & Workshop董潤楨 (Dept. Indust. & With only 250,000 NT dollars annual budget for Systems Eng., Nat. U. Singapore) &蔣煒 (Dept. the whole program, we have achieved a lot! Operations Management, 上海交大) visited NCTS (South) on 6/21-6/22 and gave lectures in “2012 Workshop in Industrial Statistics” by NCTS (South) Publications: and discussed research ideas with faculties at NCKU. [1] R-B Chen, Jian-Zhong Weng and Chi- 董gave the talk:”Plann. & inf. of accelerated life Hsiang Chu (2012). Screening Procedure for testing” & 蔣:”Likelihood-based EWMA charts for Supersaturated Designs Using a Bayesian monitoring Poisson count data with time-varying n“. Variable Selection Method. Quality and Reliability Engineering International. DOI: III. Financial Statist., Time Series, Bio-statist. & 10.1002/qre.1299 SCI Bioinformatics Coordinator: Mei-Hui Guo & [2] R-B Chen, D-N Haieh, W Wang, Y Hung (2012). Tiee-Jian Wu Optimizing Latin Hypercube Designs by Particle Seminar 暨南大國企胡毓彬gave a talk:”Principal Swarm. Statistics & Computing (in press) SCI volatility comp.’s with Appl’s”on 3/29 at NCKU. [3] S Lee and M-H Guo, (2012). Test for Dispersion

63 ‹‹- Highlights of the Regional Programs Constancy in SDE Models. Applied Stochastic [6] R-B Chen, Y-W Shu, Y Hung and W Models in Business & Industry. DOI: 10.1002/ Wang*(2012). Central Composite Discrepancy asmb.908. SCI Based Uniform Designs for Irregular [4] C-K Wen, G-M Pan, K-K Wong, M-H Guo, J-C Experimental Regions. Technometrics E Chen (2012). A Deterministic Equivalent for the (Submitted). Analysis of Non-Gaussian Correlated MIMO [7] W Wang, R-B Chen*, C-C Huang and W K Multiple Access Channels. IEEE Transactions on Wong (2012). Particle Swarm Optimization Information Theory (in press). SCI Techniques for Finding Optimal Designs for [5] S.-C. Chen, L-A Li, S. Li and J. He (2012). Mixture Models. Biometrics (Submitted). Influence of choices of statistical models on [8] S Lee and M-H Guo (2012). Monitoring Change neural spike trend. J. of Data Science, 10, 619- Point for Diffusion Parameter Based on Discretely 651 Observed Sample from SDE Models (Submitted). [6] W-J Huang, N-C Su, A. K. Gupta (2012). A [9] C-Y Hsu and T.-J. Wu (2012). Eff icient study of generalized skew-normal distribution. Estimation of the Mode of Continuous Statistics: A Journal of Theoretical & Applied Multivariate Data. Comp. Statist. & Data Statistics, DOI:10.1080/02331888.2012.697164 Analysis (Submitted) SCI [7] T-J Wu, P. Chen, Y. Yan. (2012). The weighted average information criterion for multivariate regression model selection. Signal Processing. 92 DOI: 10.1016/j.bbr.2011.03.031 SCI [8] S.-C. Chen and B. Lindsay (2012). Improving mixture tree construction using better EM algorithms. Comp. Statist. & Data Analysis (in press). SCI

Preprints submitted [1] R-B Chen, M-H Guo, Wolfgang K. Hardle, and S-F Huang (2012). COPICA - Independent Component Analysis via Copula Techniques. Statistics and Computing (Under revision). [2] R-B Chen, Y-C Hung, W Wang, S-W Yen (2012). Contour Estimation via Two Fidelity Computer Simulators under Limited Resources. Computational Statistics (Under revision). [3] L-C Lin, S Lee and M-H Guo (2012). Goodness- of-fit Test for Stochastic Volatility Models (Under revision). [4] T-J Wu, C-Y Hsu, H-Y Chen, H-C Yu (2012). Root n estimates of integrated squared density partial derivatives Ann. Inst. Statist. Math. (Under revision) [5] R-B Chen, Ying Chen, Woflgang K. Hardle (2012). TVICA-Time varying indep. component analysis & its appl. to financial data. J Business & Economic Statistics (Submitted).

Highlights of the Regional Programs ‹‹- 64 65 ‹‹- Highlights of the Regional Programs F Activities of Onsite Scientists

Title Name Field Period Kuo-Chang Chen Dynamical Systems 2009/08/01-2012/07/31 (Chern Fellow) Jann-Long Chern Nonlinear PDE 2011/08/01-2012/07/31

Sze-Bi Hsu Mathematical Biology 2010/08/01-2013/07/31 Center Scientists Wen-Ching Winnie Li Number Theory 2009/05/14-2012/07/31

Shuenn-Jyi Sheu Probability 2010/08/01-2013/07/31

Chih-Wen Shih Dynamical Systems 2009/08/01-2013/07/31

Ming-Chih Lai Scientific Computation 2012/01/01-2013/12/31

Honorary Fellowship Dong-Ho Tsai Differential Geometry 2011/01/01-2012/12/31 Yi-Fan Yang Number Theory 2011/01/01-2012/12/31 (Center Scientists) Chieh-Yu Chang Number Theory 2012/01/01-2014/12/31 Young Theory Award Je-Chiang Tsai Mathematical Biology 2012/01/01-2013/12/31

Huei-Jeng Chen Number Theory 2011/08/01-2012/07/31

Chung-I Ho Differential Geometry 2011/08/01-2013/07/31

Postdoctoral Fellow Yong-Li Tang Mathematical Biology 2011/08/01-2013/07/31

Jiangwei Xue Number Theory 2010/08/01-2012/07/31

Chi-Ru Yang Dynamical System 2011/08/01-2013/07/31

Activities of Onsite Scientists ‹‹- 66 (2) Nash-Moser iteration and KAM theory, March 16-April 20, 2012. .1 Center Scientists F Speaker: Chi-Ru Yang (NCTS) 5. Organized several NCTS dynamical systems I. CHEN, KUO-CHANG seminar. F National Tsing Hua University, Professor 6. NCTS Summer Course on Dynamical Systems, July–August, 2012. (co-organizer) Invited Conference Talks 1. Symposium on Celestial Mechanics, September 1-2, Other Events 2011. The Consortium of Applied Mathematicians, June 29, Osaka University, Osaka, Japan. (1 hour talk) 2012. 2. Cross-Strait Conference on Integrable Systems and Tsing Hua University, Beijing, China. (short Related Topics, October 5-7, 2011. (1 hour talk) presentation on behalf of NCTS) 3. International Conference on Variational Methods, May 21-25, 2012. Recent Publications Chern Institute of Mathematics, Nankai 1. Variational constructions for some satellite orbits University, Tianjin, China. (1 hour talk) in periodic gravitational force fields. Amer. J. 4. Workshop on Variational methods in N-body and Math., 132, 681-709 (2010). Vortex Dynamics, June 4-8, 2012. 2. On the barycenter of the tent map (with Xun Dipartimento di Matematicae Fisica, Lecce, Italy. Dong). Proc. Amer. Math. Soc., 138, 4025-4035 (1 hour talk) (2010). 3. Action-minimizing periodic and quasi-periodic Invited Visits solutions in the n-body problem (with T. Ouyang and Z. Xia). Math. Research Letters, 19, 483–497 1. Nanjing University, Nanjing, China, August 21-28, (2012). 2011. 4. Convex central configurations of the n-body 2. Tsing Hua University, Beijing, China, February problem which are not strictly convex (with 24-March 5, 2012. J.S.Hsiao). J. Dynam. Differential Equations, 24, 3. IMCCE, Paris, France, May 27-June 3, 2012. 119–128 (2012). 4. Chinese Academy of Sciences, and Capital Normal University, Beijing, China, July 2012. II. Chern, Jann-Long National Central University, Professor NCTS Activities 1. NCTS Summer Course on Dynamical Systems, Conferences, Workshops and NCTS Activities July–August, 2011. (speaker and co-organizers) 1. The 3rd Taiwan-Japan Joint Workshop for Young 2. NCTS Workshop on Dynamical Systems, National Scholars in Applied Mathematics Time: February Tsing Hua Univeristy, Hsinchu, Taiwan, May 16- 27-28, 2012 (One of Organizer) 19, 2012. (co-organizer) 2. 2012 NCTS (Taiwan)-POSTECH (Korea) Joint 3. NCTS Spring Young Dynamics Day, February 18, Workshop on Partial Differential Equations (One 2012 (co-organizer) of Organizers and Speaker) 4. Organized mini courses on dynamical systems: 3. Application of Partial Differential Equations to (1) Weak KAM theory in Dynamical Systems, Mathematical Biology (Organizers with with Prof. February 20 - March 8, 2012. Sze-Bi Hsu) Speaker: Kai-Zhi Wang (Jilin University) 4. NCTS & NCU Joint Seminar on Mathematics and

67 ‹‹- Activities of Onsite Scientists Theoretical Physics (Organizer) 4. Chinese Mathematical Society 理監事 5. NCTS Summer Program on Maximal Principle, (2012/01~2015/12)、Program Commit- Moving Plane Method and Applications (Speaker) tee(2012/01-2015/12) 5. Distinguished Professorship of National Central University, Taiwan, 2010/01~2012/12. F Invited Talks and Visits Resarching Works (2010-2011) 1. Organizer of Section SS38 and Invited Speaker of Section SS33 of the 9th AIMS Conference on 1. Jann-Long Chern*, Z.-Y. Chen and Y.-L. Tang, Dynamical Systems, Differential Equations and Uniqueness of Finite Total Curvature and Applications, Orlando, Florida, USA, July 1-5, Structure of Radial Solutions for Nonlinear 2012. Elliptic Equations, Transactions of the American Mathematical Society, 363 (2011), 3211–3231. 2. Summer Seminar on PDE in 2011 夏の偏微分方 程 式セミナー 2011{ 田邊先生を囲む偏微分方程 2. Jann-Long Chern, C.-S. Lin, J. Shi and Y.-L. Tang, 式研究集会}, Japan, August 1-8, 2011 (Invited Existence, uniqueness and stability of positive Two Lectures Talks: 90 Minutes) solution to sublinear elliptic systems, Proc. Royal Society of Edinburgh, 141A, 45-64, 2011. 3. June 28, 2011, Tokyo Institute of Technology, Japan.: (i) Structural Analysis of Solutions to Some 3. Jann-Long Chern and C.-S. Lin, Minimizers of Nonlinear Elliptic Systems (ii) On the Minimizers Cafarelli-Kohn-Nirenberg inequality with the of (CKN)’s Inequality with the Singularity on the singularity on the boundary, Archive for Rational Boundary. (Invited 90 Minutes Lecture Talks) Mechanics and Analysis 197 (2010), 401-432 4. Minimizers of Caffarelli-Kohn-Nirenberg 4. Jann-Long Chern*, Z.-Y. Chen and C.-S. Lin, inequality and Related Sobolev-Hardy Partial Uniqueness of Topological Solutions and Differential Equations, 2011 Annual Meeting of The Structure of Solutions for the Chern- Math. Society, Dec. 4-6, 2011. (Invited Speaker: Simons Equations with Two Higgs Particles, 50 minutes) Communications in Mathematical Physics. 296, 323–351 (2010). 5. Uniqueness of solution to a coupled coorperative system, 19th Workshop on Differential Equations 5. Jann-Long Chern*, Z.-Y. Chen, Y.-L. Tang and and its Applications, Taiwan, Jan. 14-17, 2011. Z.-H. Chen, On the Classifications of Standing (Invited Lecture Talk: 50 minutes) Wave Solutions for the Schrodinger Equation, Communications in Partial Differential Equations 6. Minimizers of Cafarelli-Kohn-Nirenberg 35 (2010), 275-301. inequality with the singularity on the boundary, in 2010 NCTS Workshop on Calculus of Variations 6. Jann-Long Chern*, Z.-Y. Chen, J.. Shi and Y.- and Related Topic. (Invited Talk: 50 minutes) L. Tang, On the Uniqueness and Structure of Solutions to a Coupled Elliptic System, Journal of Differential Equations, 249 (2010), 3419-3442. Academic and Researching Services 7. Z.-Y. Chen, Jann-Long Chern and Y.-L.Tang*, 1. Referee’s Committee of National Science Council Erratum to "On the Classification of Standing of Taiwan, 2012/01~2013/12. ( 國科會審議委員 , Wave Solutions for the Schrodinger Equation", 2012/01~2013/12) Communications in Partial Differential Equations 2. Chair of Mathematical Division for Center of 35 (2010), 1920-1921. Mathematics and Theoretical Physics, National 8. Jann-Long Chern* and S.-G. Yang, The Non- Central University, Taiwan, 2012-2015. Topological Fluxes Of A Two-Particle System 3. Center Scientist of National Center for Theoretical In The Chern-Simons Theory, submitted for Sciences, Taiwan, 2011/08~2012/07. publication in Communications in Mathematical Program Committee and Execute Committee Physics, 2011. of National Center for Theoretical Sciences, 9. Jann-Long Chern* and S.-G. Yang, A 2011/08~2012/07. Classification of Semilocal Vortices in a Chern-

Activities of Onsite Scientists ‹‹- 68 Simons Theory, submitted online and is presently Colloquium / Seminar Talks being given full consideration for publication in 1. USA Annales de l'Institut Henri Poincare/Analyse non Talk given at MBI, Ohio State University, July lineaire, 2011. 19, 2012 , title: Lotka-Volterra two species competition with season succession. F III. Sze-Bi Hsu A talk was given at Department of Mathematics, National Tsing Hua University, Professor University of Texas at Arlington, June 28, NCTS Center Scientist 2012. The title is “ Single species growth of phytoplankton for light with advection in a water column”. Activities Organized Participate the AIM 9th conference on Dynamical 1. I organized a weekly student and post doctor systems and Differential Equations and its seminar titled "Seminar in Mathematical Biology", application, at Orlando, Florida, July 1-5, 2012. from fall 2011 to spring 2012. Two talks were given in the conference. The title 2. I hosted the visit by Prof. James Cushing, of the first one is “ Refugee-mediated Apparent University of Arizona,University, Aug.1-Aug. 21 competition ” and the second one is “ Single ,2012. We worked together on structure population species growth of phytoplankton for light and models. nutrient in a water column” 3. I host the visit by Professor Xiaqiang Zhao, 2. China Memorial University of Newfoundland, Canada, Two talks given at Tongi University and University for the period, May 1-May 31, 2012. of Science and Technology of China at Sept.11 4. I hosted the visit by Professor Bernold Fiedler, Free and 13, 2012 . The title is “Competition between Berlin University, Germany for one week in Nov. microorganisms for a single limiting resource with 18-25, 2011. cell quota structure and spatial variation" 5. I host the visit of Professor Yihong Du, University 3. Taiwan of New England, Australia In 12/05-12/12, 2011. Invited speaker, 20th Annual DE workshop. Title 6. I organize a summer course“ Mathematical Models : A mathematical model arising from condensed in Molecular Biology” given by Dr. Tzeng Yun- matter. Jan. 2012. Huei in the month of July, 2012.

Publications Conferences / Workshops NCTS affiliated 1. I organized with Prof. Wei-Ming Ni, University 1."Subfunctionalization reduces the fitness cost of of Minnesota, for NCTS Program on Nonlinear gene duplication in humans by buffering dosage Equations in Spatial Population Biology , May imbalances " (with Ariel Fernández, Yun-Huei 4-26, 2012, . The workshop was held in 5/24- Tzeng), Genomics 2011, 12:604. 5/26. The mini-courses were held in 5/4-5/6,5/11- 5/13,5/18-5/20. 2. "Reaction–diffusion equations of two species competing for two complementary resources with 2. NCTS (Taiwan)-Postech (Korea) Joint workshop in internal storage" (with Jifa Jiang and Feng-Bin Partial Differential Equations, Nov 7-8, 2012. Wang), J. Diff. Eq. Vol. 251(2011), p 918-940. 3. Organize 2012 NCTS Distinguished Lectures in 3. "Dynamics of a Periodically Pulsed Bio-Reactor Applied Mathematics, Dec. 17-19. Model with a Hydraulic Storage Zone" (with Feng- 4. Initiate 2012 and 2011 Interdisciplinary workshop Bin Wang and Xiao-qiang Zhao) J Dyn. Diff. Eq. between Mathematics and Theoretical Physics. 23 (2011) no.4, pp817-842 4. "Synchronized reproduction promotes species coexistence through reproductive facilitation"(with

69 ‹‹- Activities of Onsite Scientists Yu-Yun Chen), J. Theoretical Biology 274(2011), p Conferences / Workshop talks 136-144. - India - 5. "Competition between microorganisms for a 1. Pan Asian number Theory Workshop, invited single limiting resource with cell quota structure speaker, ISSER, Pune, India, July 23, 2012, "The F and spatial variation" (with James P. Grover and impact of computing to noncongruence modular Feng-Bin Wang) J. Math. Biol.(2012),Vol 64 No.5, forms". pp.713-743 - Taiwan - 6. "A Lotka-Volterra Competition model with season 1. National Chung Cheng University, Algebra succession" (with Xiaoqiang Zhao), J. Math. Conference, June 29, 2012, "Novel applications of Biology, 64(2012), p.109-130. number theory" (2 hour lecture). - United States - IV. Wen-Ching Winnie Li 1. Keynote Speaker, Rocky Mountain Discrete Math Director, National center for Theoretical Sciences Days, Laramie, Wyoming, Oct. 21, 2011, "Various I returned to Penn State Aug 1, 2011-May 9, 2012, aspects of Ramanujan graphs" and came back to NCTS on May 10, 2012. 2. Plenary Speaker, Palmetto Number Theory Series (PANTS), Clemson University, Dec 3-4, 2011, Activities Organized "Zeta functions in combinatorics and number 1. I organized the 2011 NCTS "Distinguished Lecture theory" Series" by Prof. Gerhard Huisken, Director, 3. Plenary speaker, 10th Algorithmic Number Theory Max Planck Institute for Gravitational Physics, Symposium (ANTS-X), San Diego, July 10, 2012, Germany, Oct. 24-26, 2011. "The impact of computing on noncongruence 2. I launched the new "Meet with Professor..." series modular forms". in 2012. The purpose is to devote one day to feature one master who has made ground breaking Colloquium / Seminar Talks contributions to mathematics. The scientific - India - activities include a talk by the master him/herself 1. Indian Institute of Technology, Math. Colloquium, as well as several talks by well-known experts Mumbai, India, July 30, 2012, "Zeta functions in who work in areas related to the master's. There is combinatorics and number theory" also a forum for the audience to ask questions on how to deal with challenges in mathematics. We - Taiwan - have featured Sun-Yung Alice Chang of Princeton 1. Tamkang University, Taiwan, Lecture Series by University on June 2, Yum-Tong Siu of Harvard Masters, May 29, 2012, "Novel applications of University on July 7, 2012. number theory". 3. I organized 2012 NCTS Interdisciplinary Seminar - United States - between Mathematics and Theoretical Physics, 1. University of Pennsylvania, Algebra Seminar, June 19, 2012, speakers are Mu-Tao Wang of Nov 21, 2011, "Modularity of low degree Scholl Columbia University (Math) and Pei-Ming Ho of representations" National Taiwan University (theoretical physics). 2. Texas A & M, Number Theory Seminar, March 4. I served on the organization committee of the 6th 7, 2012, "The arithmetic of modular forms for ICCM, to be held July 14-19, 2013. noncongruence subgroups" 5. I also organized regular lectures in arithmetic 3. MIT, BC-MIT joint Number Theory Seminar, geometry, combinatorics and number theory by April 3, 2012, "Recent progress on noncongruence postdoctoral fellows and research associates at modular forms" NCTS. The goal is to learn background materials leading to future research projects. Publications

Activities of Onsite Scientists ‹‹- 70 1. (with J. C. Lagarias) The Lerch zeta function I. An introduction of stochastic control (Shuenn-Jyi Functional equations, Forum Mathematicum, vol. Sheu) 24 (2012), issue 1, 1-48. An introduction of stochastic partial differential 2. (with J. C. Lagarias) The Lerch zeta function II. equation ( Shang-Yuan Shiu) Analytic continuation, Forum Mathematicum, vol. An introduction of backward stochastic F 24 (2012), issue 1, 49-84. differential equation ( 林柏佐 ) 3. (with Ling Long) Fourier coe_cients of The participants include students, research noncongruence cuspforms, Bull. London Math. assistants, post docs and colleagues from Soc. 44 (2012), 591-598. Academia Sinica, National Central University and 4. The arithmetic of noncongruence modular also National Tsing Hua University. forms. Fifth International Congress of Chinese I gave several lectures on the theory of random Mathematicians (ICCM 2010), Part I, AMS/IP walk at NCTS as a part of summer program on Studies in Advanced Mathematics, vol. 51 (2012), probability theory. In the next coming year I plan 253-268. to run a reading seminar at NCU on the subject 5. (joint with Yang Fang and Chian-Jen Wang) The which also covers theory of Levy process. zeta functions of complexes from Sp(4), Int. Math. 2. Two lecture series given by visitors Res. Not. IMRN 2012, doi: 10.1093/imrn/rns007. Toshio Mikami (Hiroshima University) 6. (joint with Maosheng Xiong) Statistics of zeros A Short Course on Optimal Transportation of families of L-functions over function fields: Problem a survey, Proceedings of the conference on Number Theory and Related Topics, Hefei, China, Kenjiro Yanagi (Yamaguchi University) June 6-12, 2011, Higher Education Press and Short course on Quantum Information Theory International Press, to appear. 3. Organize a workshop on 2012, March 8-9 at NCTS jointly with Chii-Ruey Hwang (Sinica) and Yuan- V. Shuenn-Jyi Sheu Chung Sheu (Chiao Tung University) National Central University Workshop on Stochastic Processes and Applications Academia Sinica The invited speakers include foreign guests: Hideo National Center for Theoretic Sciences, Center Scientist Nagai, Jun Sekine, Yoshio Miyahara, Andreas Kyprianou, Svetlana Boyarchenko, Budhi Arta Surya, Ning Cai, and our colleagues in Taiwan 姜 Activities Organized 祖恕 , 韓傳祥 , 張洛賓 , Hsuan-Ku Liu, Ming-Chi 1. Organize two series of study seminars. Chang. This provides a chance for our colleagues Stochastic Control in Insurance to meet with probabilists from other country. Advanced Stochastic Calculus For the first topic, we want to learn basic Visitors from other countries: knowledge of insurance and some interesting Hideo Nagai (Osaka University), Jun Sekine mathematical problems from insurance. We (Osaka University), Yusuke Watanabe (Osaka also learn the applications of stochastic control University), Naoyuki Ichihara, Toshio Mikami to insurance. This is a research area with many (Hiroshima University), Yoshio Miyahara chances for mathematician. (Osaka City University), Hiroaki Hata (Shizuoka For the second topic, we learn theory of stochastic University). calculus. The topic is important and has broad applications. Conference / Invited talk / Organizer Series of lectures on the following topics are also 1. Mathematical Society Annual Meeting, Dec 9-10 given. (plenary speaker)

71 ‹‹- Activities of Onsite Scientists 2. Probability and PDE, January 10-12, 2012, • 2012 NCTS Workshop on Dynamical Systems, Higashi-Hiroshima. (invited speaker) Hsinchu, May, 2012 3. 8th Workshop on Markov Processes and • Seminar talk in UBC PDE/math biology joint Related Topics, July 16-18, 2012, Bejing Normal seminar, Feb. 14, 2012 F University.(invited speaker) • Department of Mathematics UBC (Professor Yue- 4. 第 八 屆 海 峽 兩 岸 機 率 統 計 研 討 會，2012 年 8 月 Xian Li), Canada, Jan-Feb., 2012 15、16 日，大 陸 哈 爾 濱 . ( 邀請演講 ) NCTS Activities Publications - 2012 NCTS Workshop on Dynamical Systems, 1. (with H. Hata) On the Hamilton-Jacobi-Bellman May, 2012 (organizer) equation for an optimal consumption problem: I. This workshop includes several minicourses, Existence of solution, to appear in SIAM J. Control poster session, and a rather appealing public Optimization. lecture by Phil Holmes (Princeton University) 2. (with H. Hata) On the Hamilton-Jacobi-Bellman - Tutorial talk for 2012 NCTS Workshop on equation for an optimal consumption problem: Dynamical Systems, May, 2012 II. Verification Theorem, to appear in SIAM J. - Dynamics Systems summer school, July-Aug. Control Optimization. 2012 (organizer) 3. (with Naoyuki Ichihara) Large time behavior of solutions of Hamilton- Jacobi- Bellman equations with quadratic nonlinearity in gradients, Research works submitted. A. Friedman, C.-Y. Kao, and C.-W. Shih*, 2012, 4. (with B. Franke) Homogenization of a diffusion “Asymptotic limit in a cell differentiation model driven by a large incompressible drift, in with consideration of transcription”, J. Differential preparation. Equations 252, 5679-5711. (SCI-Math). 5. (with H. Hata, H. Nagai) An optimal consumption K.-L. Liao, C.-W. Shih* and J.-P. Tseng, 2012, problem for general factor model, in preparation. “Synchronized oscillations in a mathematical model of segmentation in zebrafish”, Nonlinearity 6. (with D. Hernendaz-Hernandez) Solution of HJB 25, 869–904. (SCI-Applied Math) equations involved in indifference pricing, in preparation. K.-L. Liao, and C.-W. Shih*, 2012, “A lattice model on somitogenesis of zebrafish”, Discrete and Continuous Dynamical Systems –Series B, 17 (8), VI. Chih-Wen Shih 2789-2814. (SCI-Applied Math) Department of Applied Mathematics, National C.-W. Shih* and J.-P. Tseng, 2012, “Synchronization Chiao-Tung University for coupled systems”, submitted. National Center for Theoretic Sciences, Center Scientist Others:

Conferences and Visiting The quality of PhD students in NCTU Department of Applied Mathematics (also in other mathematics • Modeling and Analysis of PDE Models of departments I believe) has been dropping substantially Biological Processes, Beijing, Oct. 2011 in the past few years. In addition to the shrinking job • Workshop on Mathematical Models of Electrolytes market due to low birth rate and decreasing student with Application to Molecular Biology, Taipei, Jan. population in universities and colleges in Taiwan, the 6, 2012 PhD students in Taiwan seem to be in lack of right • 20th Annual Workshop on Differential Equations, perception about PhD discipline. It is obvious that Taipei, Jan. 7, 2012 some of our colleagues did not educate students under their guidance with the right idea incorporated with

Activities of Onsite Scientists ‹‹- 72 positive action toward successful PhD training. University, Kyoto, Japan, September 24-28, 2012 There are good talks given in NCTS, but some • Biological Complex Fluids, 2012 Cargese summer PhD students in the same field do not go the talks. school (invited lecturer), Corsica Island, France, The organizer or coordinator not only has to work June 25th-July 7th, 2012. on inviting speakers and other arrangements, • Workshop on Nonlinear Partial Differential F but also worry about the attendance. It is even Equations: Analysis, Computation and Applications worse if the workshop or minicourse is arranged (invited speaker), IMS Singapore, March 7 - 10, in weekends. Since the number of good graduate 2012 students is decreasing, which is reasonable because of • The 4th Intl. Conference on Scientific Computing decaying job market, we may need to rethink about and Partial Differential Equations (invited speaker), the organization of activities in NCTS. We should Hong Kong Baptist University, December 5-9, 2011. get those who already have positions in universities • International Conference on Frontiers of Numerical involved in NCTS activities. In the past year, I PDEs (invited speaker, 35 mins talk) Guangzhou, organized a number of seminars with some young China, August 2-4, 2011 researchers. They teach in universities spreading from the south to the north of Taiwan. We did not announce the talks, nor applied funding from NCTS, NCTS Activities since it is restrictive. Some of them do not have NSC 1. Co-organized NCTS Workshop on “Theoretical grants and so have to pay for their own traveling, and Computational Challenges in PDEs”, will be although they continue to research and publish held at NCTS, Hsinchu, in December 13-15, 2012 papers. We finally realize that Taiwan is small and 2. Organized NCTS 2012 Summer Course has limited university positions. For now, it would be on Scientific Computation, August 20-22, better to encourage young researchers more, rather 10:00am-1:30pm, Title: Level set method and than neglecting or criticizing them. Otherwise, the its applications, Invited Lecture: Prof. Shingyu research community will be further shrinking. Leung (Hong Kong University of Science and Technology) F.2 Honorary Fellowship 3. Co-chaired 2012 SIAM East Asia Section Conference (EASIAM 2012, supported by NCTS I. Ming-Chih Lai Taipei branch) held in National Taiwan University, Center Scientist and Honorable Research Fellow of Taipei June 25-27, 2012 NCTS 4. Organized joint workshop with CMMSC of Department of Applied Mathematics, National Chiao NCTU on Mathematical and Computational Tung University, Professor Neuroscience, June 22, 2012 5. Organized joint seminars on PDEs and Scientific Computing with CMMSC of NCTU frequently. International Societies and Editorial Boards The details can be found in both NCTS and 1. Elected to the President of SIAM East Asia Section CMMSC websites (EASIAM) for the 2-year term of 2013-2014 2. Served as an additional Editorial Board of SCI Recent Publications 2011-2012 journal; Communications in Computational Physics (SCI, 5year IF=1.704) since 2012 1. C.-T. Wu, Z. Li and M.-C. Lai, Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method Invited Conferences and Workshops , International Journal of Numerical Analysis and • Annual Meeting of Taiwan Mathematical Society Modeling, Vol 8, No 3, 466-483 (2011). (plenary speaker), NCTU, December 7-9, 2012 2. M.-C. Lai, C.-Y. Huang and Y.-M. Huang, • Kinetic Theory and Related Fields: Theoretical and Simulating the axisymmetric interfacial flows with Numerical Approaches (invited speaker), Kyoto insoluble surfactant by immered boundary method

73 ‹‹- Activities of Onsite Scientists , International Journal of Numerical Analysis and (Korea) Joint Workshop on Partial Differential Modeling, Vol 8, No 1, 105-117, (2011). Equations, November 8-9, 2012, Hsinchu, Taiwan. 3. Z. Li and M.-C. Lai, New finite difference methods based on IIM for inextensible interfaces Publications during the year 2012: in incompressible flows , East Asian Journal of F • Y.-C. Lin, C.-C. Poon, D.-H. Tsai (2012) Contracting Applied Mathematics, Vol 1, No 2, 155-171 (2011). convex immersed closed plane curves with slow 4. K.-Y. Chen, K.-A. Feng, Y. Kim and M.-C. Lai, A speed of curvature, Transactions of the AMS, 364, note on pressure accuracy in immersed boundary no. 11, 5735-5763, 2012. method for Stokes flow, Journal of Computational • Y.-C. Lin, D.-H. Tsai (2012) Application of Andrews Physics, vol 230, 4377-4383 (2011). and Green-Osher inequalities to nonlocal flow 5. P. Constantin, M.-C. Lai, R. Sharma, Y.-H. Tseng of convex plane curves, Journal of Evolution and J. Wu, New Numerical Results for the Surface Equations, no. 4, 360-377, 2012. Quasi-Geostrophic Equation, Journal of Scientific • Y.-C. Lin, D.-H. Tsai (2012) Remarks on some Computing, Vol 50, Issue 1, 1-28 (2012). isoperimetric properties of the k-1 flow, to appear in 6. Y. Kim, Y. Seol, M.-C. Lai and C. S. Peskin, The Pacific J of Math, 2012. immersed boundary method for two-dimensional • D.-H. Tsai (2012) On a general linear nonlocal foam with topologica changes, Communications curvature flow of convex plane curves, submitted. in Computational Physics, Vol 12, No 2, 479-493 (2012). • D.-H. Tsai (2012) On some interesting examples of non-parabolic curve flows in the plane, submitted. 7. C.-H. Teng, I.-L. Chern and M.-C. Lai, Simulating binary fluid-surfactant dynamics by a phase • Y.-C. Lin, D.-H. Tsai (2012) Comparing intrinsic field model, Discrete and Continuous Dynamical and extrinsic distances of simple closed curves, Systems - Series B , Vol 17, No 4, 1289-1307 (2012). submitted. 8. M.-C. Lai, W.-F. Hu, and W.-W. Lin, A fractional step immersed boundary method for Stokes flow II. Yifan Yang with an inextensible interface enclosing a solid National Chiao Tung University, Professor particle, SIAM J. Sci. Comput., in press 2012. National Center for Theoretic Sciences, Center Scientist II. Dong-Ho Tsai National Tsing Hua University, Professor Conference talks (2011—2012) 1. Schwarzian differential equations and automor- Visit during the year 2012: phic forms on Shimura curves, International • Department of Mathematics, East China Normal conference on Galois representations, automor- University, August 13-26, 2012. phic forms, and Shimura varieties, NCTS, June • (invited speaker) Hokkaido University, February 20—23, 2011. 13-20, 2012, Sapporo, Japan. 2. Schwarzian differential equations and automor- • (invited speaker) University of Wollongong, phic forms on Shimura curves, NCTS, Taiwan – Wollongong, Australia, December 1-8, 2012. PMI, Korea workshop – number theory, Postech, July 24—26, 2011. 3. Schwarzian differential equations and automor- NCTS activities during the year 2012: phic forms on Shimura curves, workshop on • NCTS various seminars, workshops, and arithmetic geometry, Okinawa, Japan, October conferences. 10—13, 2011. • (invited speaker) NCTS Meet with Professor Chang- 4. Schwarzian differential equations and automor- Shou Lin, October 18, 2012, Hsinchu, Taiwan. phic forms on Shimura curves, International • (invited speaker) NCTS (Taiwan) - POSTECH conference on number theory, University of Hong Kong, June 18—22, 2012.

Activities of Onsite Scientists ‹‹- 74 5. Hypergeometric functions as automorphic and automorphic forms on Shimura curves, forms on Shimura curves, 6th number theory Compositio Math., in press. conference, Northwest University, Xi’an, China, 8. **Fang-Ting Tu and Yifan Yang, algebraic October 19—22, 2012. transformations of hypergeometric functions and automorphic forms on Shimura curves, Trans. F Visits (2011—2012) Amer. Math. Soc., to appear. 1. Waseda University, Japan, visit Ki-Ichiro 9. **Yifan Yang, modular forms of half-integral Hashimoto from June 29 to July 21, 2011. weights on SL(2,Z), submitted. 2. Tohoku University, visit Takao Yamazaki from 10. **Yifan Yang, computing modular equations for November 6 to 13, 2011. Shimura curves, submitted. 3. Hong Kong University of Science and Technology, 11. **Shinji Fukuhara and Yifan Yang, a basis for visit Maosheng Xiong from April 16 to April 22, , submitted. 2012. 打 ** 為以 NCTS 名義發表 4. Tsuda College, Japan, visit Shinji Fukuhara from July 20 to August 3, 2012. Summary of research works 5. Waseda University, Japan, visit Ki-Ichiro Yang is a specialist in the theory of modular forms Hashimoto from August 3 to August 13, 2012. and modular curves. In a series of joint works with Fukuhara (References [5,11] above), Yang studied NCTS Activities the periods of cusp forms. By combining Rankin’s methods, obtained bases for the space of modular 1. NCTS number theory seminar. forms on congruence subgroups of level 4 in terms 2. NCTS Shimura curve seminar (organizer). of Eisenstein series. As applications, they found new 3. 2012 NCTS Japan-Taiwan joint conference on formulas for the number of ways to write a positive number theory (co-organizer). integer as sums of squares and new methods to determine the special values of L-function of cusp Research Works (2011—2012) forms twisted by Dirichlet characters. 1. **Yifan Yang, congruences of the partition In [3], using the theories of Hecke characters, CM function, Int. Math. Res. Not., 2011, 3261—3288. modular forms, Galois representations, and algebraic curves, Yang and his coauthors obtained an beautiful 2. **Heng Huat Chan, Ling Long, and Yifan Yang, analogue of the classical Jacobsthal identity for a cubic analogue of the Jacobsthal identity, Amer. the case Q(sqrt(-2)). A simpler version for the case Math. Monthly 118:4 (2011), 316—326. Q(sqrt(-3)) was treated in a separate paper [2], which 3. **Ki-Ichiro Hashimoto, Ling Long, and Yifan involves only elementary properties of the Legendre Yang, Jacobsthal identity for Q(sqrt(-2)), Forum symbols and Jacobi sums. Math., in press. Yang [1] also worked on the classical problem 4. **Heng Huat Chan, Yoshio Tanigawa, Yifan of congruences for the partition function. He Yang, and Wadim Zudilin, new analogues of demonstrated that it is possible to obtain new Clausen’s identities arising from the theory of congruences for the partition function using only modular forms, Adv. Math 228 (2011), 1294-1314. modular forms of half-integral weights without 5. **Shinji Fukuhara and Yifan Yang, a basis for the use of the Shimura correspondence and Galois and representations of integers as sums of representations, which were key ingredients in squares, Ramanujan J. 28 (2012), 25—43. Ken Ono’s treatment of the problem. While he was 6. **Fang-Ting Tu and Yifan Yang, lattice working on this problem, he also discovered an packing from quaternion algebras, accepted for explicit Shimura correspondence between modular publication, RIMS Kokyuroku Bessatsu. forms of half-integral weights on SL(2,Z) and certain 7. **Yifan Yang, Schwarzian differential equation newform subspace of cusp forms of level 6. A paper [9] has been submitted for publication.

75 ‹‹- Activities of Onsite Scientists Finally, in recent months, he focused his research algebraic independence, Math. Ann. 352 (2012), on automorphic forms on Shimura curves. He [7] 189-204. showed that if a Shimura curve has genus zero, then 5. Transcendence of special values of quasi-modular automorphic forms on it can be expressed in terms of forms, Forum Math. 24 (2012), 539-551. solutions of the Schwarzian differential equations. He 6. (with M. Papanikolas and J. Yu) Frobenius F then devised a method to compute Hecke operators difference equations and algebraic independence of on these functions. By interpreting hypergeometric special zeta values in positive equal characteristic, functions as automorphic forms on Shimura curves, Algebra & Number Theory 5 (2011), 111-129. he and F.-T. Tu [8] established some elegant identities 7. (with M. Papanikolas) On algebraic relations among hypergeometric functions. among periods and logarithms of rank 2 Drinfeld modules, Amer. J. Math. 133 (2011), 359-391. F.3 Young Theory Award II. Je-Chiang Tsai I. Chieh-Yu Chang National Chung Cheng University, Professor National Tsing Hua University, Assistant Professor Conferences (invited speaker) Conferences (invited speaker) 1. Mathematical Conference and Annual Meeting 1. Mini Workshop on Number Theory between Two of the Taiwan Mathematical Society, Hsinchu, Tsing Hua, Beijing, China, April 19 2012. Taiwan, Dec 7-9, 2012. 2. Algebraic Number Theory and Related Topics, Kyoto, Japan, December 3-7 2012. Visits 1. University of Leicester, UK. Visit Prof. Sergei Visits Petrovskii from 1 Sep. 2012 to 9 Sep. 2012. 1. Hong Kong University of Science and Technology, 2. Max Planck Institute for Dynamics and Self- May 11-14 2012. Organization, Gottingen, Germany. Visit Prof. 2. Institut des Hautes Études Scientifiques, June 30- Vladimir Zykov from 10 Sep. 2012 to 16 Sep. July 23 2012. 2012.

NCTS Activities NCTS Activities (invited speaker) 1. NCTS Seminar on Number Theory. 1. NCTS Workshop on Dynamical Systems, Hsinchu, Taiwan, May 16-19, 2012. 2. Organizing NCTS Students’ Seminar on Number Theory. 2. NCTS Program on Nonlinear Equations in Spatial Population Biology: Mini-course, Hsinchu, Taiwan, May 19, 2012. Research Works 3. NCTS Workshop on Nonlinear Equations in 1. Linear independence of monomials of multizeta Spatial Population Biology, Hsinchu, Taiwan, May values in positive characteristic, submitted 2012. 24-26, 2012. 2. On periods of the third kind for rank 2 Drinfeld 4. NCTS (Taiwan)-POSTECH (Korea) Joint modules, to appear in Math. Z. Workshop on Partial Differential Equations, 3. (with M. Papanikolas) Algebraic independence of Hsinchu, Taiwan, Nov 8-9, 2012 periods and logarithms of Drinfeld modules. With an appendix by Brian Conrad, J. Amer. Amer. Research Works Soc. 25 (2012), 123-150. 1. (Joint with Bernard Brighi) Similarity solutions 4. Special values of Drinfeld modular forms and for a model arising from high frequency excitation

Activities of Onsite Scientists ‹‹- 76 of liquid metal in an antisymmetric magnetic field, Also they determined the range of the convergence IMA J. Appl. Math. 77 (2012), 157-195. of these functions in the case of Drinfeld modules of 2. (Joint with Elaine Crooks) Front-like entire rank 2. making use of the detailed description of their solutions for equations with convection, J. coefficients. Next we want to investigate the range Differential Equations. 253 (2012), 1206-1249. of the convergence of these functions in the case of Drinfeld modules of arbitrary rank by using El-Guindy F 3. (Joint with Wenjun Zhang, Vivien Kirk, and James and Papanikolas method and some combinatorial tools. Sneyd) Traveling waves in a simplified model of calcium dynamics, SIAM J. Appl. Dyn. Syst. 11 (2012), 1149-1199. Seminar/Workshop /Conference: 1. Six National Number theory conference (Oct 19th – nd F.4 Report of Post Doctors Oct 22 ). Place: North West University, Xian, China I. Huei Jeng Chen Day: Oct 21st National Center for Theoretical Sciences Title: Diophantine approximation and Hausdorff dimension in positive characteristic. Abstract: For any positive integer n and real Research: numberλ ≧ 1, let Kn (λ) be the set of all real numbers 1. Diophantine approximation on formal power θ such that for any λ’<λ, there exist infinitely many series over finite fields. algebraic numbersαwith degree at most n satisfying In the classical Diophantine approximation theory, |θ-α| < H(α)-(n+1)λ’. Moreover we let Kn ‘(λ) be the we are concerned with how well an irrational real subset of Kn (λ) consisting of all θ not in Kn (λ’) number can be approximated by rational numbers. In for anyλ’<λ. Baker and Schmidt proved that the 1955, Roth proved that for any irrational real algebraic Hausdorff dimensions of Kn (λ) and Kn ‘(λ) are number α and for andε>0, there exist only finitely both 1/λ. We will give similar results of Baker and many rational numbers p/q satisfying the inequality Schmidt in function field version. |α-p/q| < 1/ q(2+ε)|. Studying Diophantine approximation can help 2. Number theory seminar on Shimura Curves (2011 us solve solutions of Diophantine equations and Sep - present ) transcendence questions. But Roth’s theorem fails in Place: National Center for Theoretical Sciences the case of function field in positive characteristic. I am th th st interested in studying how the exponents distributes Day: Dec 7 , Dec 14 , and Dec 21 , 2011 when these algebraic elements vary. In [1] I describe Title: Arithmetic triangle groups a asymptotic distribution of exponents of elements in Abstract: Let π : SL2 (R) Aut( H ) be the Class IA. On the other hand, we want to find a way to homomorphism from special linear group to analytic derive or estimate an exponent of a given element . My automorphisms on upper half plane such that research [3] is try to calculate the exponents of some π((a b), (c d))(z) = az+b/cz+d. special families of algebraic elements, which come A discrete subgroup Γ of SL (R) such that the volume from Carlitz torsion of small degree. 2 of H/ π( Γ ) is finite is called the Fuchsian group of the 1st kind. It follows from a theorem which shows 2. Exponential and logarithmic functions for that it can be generated by 2g hyperbolic elements, Drinfeld modules. s elliptic elements and r parabolic elements. Γ is a We are interested in determining explicit formulas triangle group if g= 0, r+s =3, and we say Γ is of type for exponential functions, loga-rithms, and periods (e1 e2 e3 ). of Drinfeld modules. El-Guindy and Papanikolas Our first goal is to determine all the triangle groups gave a explicit formula of these functions defined by of given type (e1 e2 e3 ). Drinfeld modules of arbitrary rank by developing a Next we want to determine what kind of Γ ( or combinatorial framework of shadowed partitions.

77 ‹‹- Activities of Onsite Scientists what kind of (e1 e2 e3 ) ) is arithmetic, ( means it and Koksma’s classification of real numbers are is commensurable with one Γ (A, O) ). We will list equivalent by studying the relation between the all arithmetic types by using several lemmas and exponent of algebraic approximation and polynomial theorems. approximation. So we can also estimate the

Hausdorff dimension of some special set Mn (λ) F obtained from polynomial approximations. But Visiting: in the case of field of formal power series in finite 2012/3/1 – 2012/5/8 Visit University of Arizona, USA. characteristic, the relations were not clear yet. So Host: Professor Dinesh S. Thakur. We are interested in studying the relation between Mahler’s and Koksma’s classification and try to give

Publications and Preprints: an estimate of dim Mn (λ). [1] Distribution of Diophantine approximation exponents for algebraic quantities in finite II. Chung-I Ho characteristic (Submitted and revising) National Center for Theoretical Sciences [2] Diophantine approximation and Hausdorff dimension in finite characteristic (in preparation) Research: [3] Diophantine approximation and torsion elements 1. Geometric automorphism groups of symplectic of Carlitz modules. (in preparation ) 4-manifolds: My researches in the last year focus mainly on the Future plans: diffeomorphism groups of symplectic 4-manifolds. The classical results of Wall and Friedman-Morgan 1. Multiple zeta values for Fq [t] The multiple zeta values were introduced give a concrete description of the geometric originally by Euler and we were interested to know automorphisms groups of quadratic forms of rational what kind of a multiple zeta value (zeta values) is surfaces induced by diffeomorphisms. We extended Eulerian, i.e. it is a (rational or algebraic) multiple of the result to any symplectic 4-manifolds. Specifically, a power of the period , where the power depends on we prove the transitivity property of isotropic the weight of the multiple zeta values (zeta value). As subspaces with given conditions. Then we use the an analogue of classical case, we also have the same invariance of symplectic cone and Seiberg-Witten question of multiple zeta values (zeta vlues) for F basic class to show that the geometric automorphism q groups have infinite index for most of symplectic [t]. Professor Jing Yu proved that a zeta value for Fq [t] is not Eulerian if q-1 does not divide the weight. 4-manifolds. The next topic we want to study is the conditions of Eulerian property of double zeta values. 2. Lagrangian Klein-bottle in 4-manifolds: Another program is the continuation of my 2. Mahler’s and Koksma’s classification in the thesis. In the earlier work ([1]), we show that the field of formal power series over finite fields. Luttinger surgery along Lagrangian tori preserves In my previous project, we studied the Hausdorff the symplectic Kodaira dimension of symplectic dimensions of Kn (λ), which are related to Koksma’ 4-manifolds. Comparing with the classification of classification of transcendental numbers. Mahler also symplectic 4-manifolds, we provide constraints on gave a way to distinguish transcendental numbers the existence of Lagrangian subtorus. There is a by considering polynomial approximation: For a version of Luttinger surgery for Lagrangian Kelin real number θ and a natural number n, we want bottles. But we have to consider the -homology to see how small the exponent w can be such that group now. The computations can be achieved by there exist infinitely many integral polynomials either Rokhlin and Viro indices or monodromy of P(x) with degree at most n such that |P( θ )| < 1/ Lefschetz fibrations. This is in progress. H(P)^w. It follows from a theorem that Mahler’s

Activities of Onsite Scientists ‹‹- 78 3. Cohomology theory in generalized complex III. Yong-Li Tang geometry: National Center for Theoretical Sciences This is a joint work with Tai-Wei Chen and Jyh-Haur Teh. There are two part in this project. Research: First, we want to build Bott-Chern and Aeppli cohomology theory in generalized complex geometry. Under the supervision of Prof. Sze-Bi Hsu and F In particular, we want to understand the jumping collaborating with Dr. Linfeng Mei, the researches phenomenon of these cohomology in deformation. which I mainly focus on in this year include the Then we hope to find a mixed Hodge structure study of biological models arising from single inherited from complex geometry. phytoplankton in a water column with following situations: (i) two complementary nutrients; (ii) single nutrient and light; or (iii) two substitutable nutrients. Invited talks at Seminar/Workshop /Conference: Our goal is to establish the existence, uniqueness, 1. 2011 Mathematical Conference and Annual stability of steady states, and even dynamics of Meeting of the Taiwan Mathematical Society, Dec. the models. In (i), due to the growth rate function 9-11, 2011. following the minimum principle, it is not easy to 2. NCTS & NTHU Joint Geometry and Topology apply the bifurcation theory directly to deal with the Seminar, Oct.-Nov. 2011. steady states which involves the indifferentiability of 3. Colloquium at Dept. of Math., National Tsing Hua the nonlinearity. Fortunately, by using method related Univ., April 2012. to the eigenvalue problem and monotone scheme, the uniqueness of the coexistence steady states for 4. Colloquium at Dept. of Math., National Central situation (i) has been derived. Besides, a structure Univ., April 2012. of steady states in terms of initial values of nutrient I also attend the following conferences outside NCTS: densities, which is classified by the characterization 2012 Workshop and Conference on Holomorphic of nutrient limitedness, is also obtained. Although Curves and Low dimensional Topology at Stanford some observations have been attained, it is still not University(U.S.) July 30-August 11, 2012. complete for situations (ii) and (iii). We will keep working on the issues for problems (i)-(ii) mentioned Visiting: above. 2012 August 12-19 Visit University of Minnesota for In the meanwhile, I also revised a paper [2], a one week. Host: Prof. Tian-Jun Li joint work with Prof. Jann-Long Chern and Dr. Zhi- You Chen, which is part of my Ph.D. dissertation. It has been accepted for publication in Discrete and Publication and Preprint: Continuous Dynamical Systems- Series A. 1. Chung-I, Tian-Jun Li “Luttinger surgery and Kodaira dimension”, Asian Journal of Math., Vol Workshop /Conference: 16, No.2(2012), pp 299-318. 1. Invited Speaker in The 3rd Taiwan-Japan Joint 2. Bo Dai, Chung-I Ho, Tian-Jun Li, “Geometric Workshop for Young Scholars in Applied Automorphism Groups of Symplectic 4-manifolds” Mathematics, National Taiwan University, Taiwan, (2012) submitted. February 27-28, 2012 3. Chung-I Ho “Algebraic properties of -lemma”, [Title: On a model arising from single species (2012) preprint. consuming two complementary nutrients in a 4. Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh, “Bott- water column] Chern and Aeppli cohomology in generalized 2. Invited Speaker in The 9th AIMS International complex geometry. in preparation. Conference on Dynamical Systems, Differential Equations and Applications, Orlando, USA, July 1-5, 2012

79 ‹‹- Activities of Onsite Scientists [Title: Structural analysis of solutions to nonlinear Endomorphism algebra of certain superelliptic systems of elliptic partial differential equations] Jacobians, Japan-Taiwan joint conference on number theory, NCTS, Aug 27, 2012. Publication and Preprint: Etale Cohomology, NCTS number theory seminar, F 1. Sze-Bi Hsu, Linfeng Mei and Yong-Li Tang, “On June - August, 2012. a model arising from single species consuming two complementary nutrients in a water column”, Visiting: Notes, 2012. Hong Kong University of Science and Technology, 2. Jann-Long Chern, Zhi-You Chen and Yong- Apr 14-20, 2012. Li Tang, “Structure of solutions to a singular Liouville system arising from modeling dissipative V. Chi-Ru Yang stationary plasmas”, accepted for publication in Discrete and Continuous Dynamical Systems- National Center for Theoretical Sciences Series A [DCDS-A Vol.33 No.6 #4 June 2013 Research: issue]. 1. Mathematic Biology IV. Jiangwei Xue In [2], we consider the existence of traveling National Center for Theoretical Sciences wave fronts solution of diffusive predator-prey system with Holling-type III functional response. The Wazewski method works in this model through Research: high dimensional phase space analysis and shooting I classified the endomorphism algebra of the method. In [3], we extend the result for more general Jacobian variety of the superelliptic curves of the nonlinear functional response with some monotonic q form y =f(x), where f(x) is a degree 3 polynomial condition. However, there are many biology- with no multiple roots. This result generalizes the meaningful functional responses not under our well known results of elliptic curves that their consideration, such as Holling-type IV functional endomorphism algebra is either the rational numbers response. In the Holling-type IV case, we lose too or an imaginary quadratic field. The techniques used many monotonic properties to do the phase space involve complex multiplication theory, number theory analysis readily. To overcome this difficulty , we need and a very original proof of combinatory results. more powerful tool. Because of the non-monotonicity With some further work done in this fall, this work in functional response, there is no suitable tool in is in a satisfactory state and will be submitted in Dec Monotonic Dynamical System but Wazewski method 2012. works. That is what support me continuing this study. Furthermore, I am interesting in some questions Seminar / Workshop / Conference: about spreading speed and dealing with the reaction Endomorphism algebra of certain superelliptic diffusion equation without considering traveling Jacobians, inWorkshop on algebra and geometry, wave. National Cheng Kung University, Apr 28, 2012. Shimura curves as moduli spaces, NCTS, May 2, 2. Nash-Moser iteration 2012. There are several approaches to study the Shimura curves as moduli spaces II, NCTS, May 9, existence of periodic solutions of nonlinear wave 2012. equations. Rabinowitz and Berti used variational Canonical Models of Shimura curves, NCTS, May methods to prove the existence of periodic 30, 2012. solution with some appropriate assumptions on the nonlinearity. However, the restriction of his result Canonical Models of Shimura curves II, NCTS, is the periodic solution with a rational multiple of pi June 6, 2012. time period and the techniques fails in the existence Canonical Models of Shimura curves III, NCTS, of quasi-periodic solution. June 13, 2012.

Activities of Onsite Scientists ‹‹- 80 Nash-Moser iteration is the other approach. In spirit, the iteration is the Newton method adding a smoothing process. Craig[5] extended the Lyapunov- Schmidt method to the infinite dimensional problem without bounded inverse. Many authors have used the similar method. Fokam considered this approach F to a nonlinear wave equation with forced vibration term. Bourgain and Berti dealt with the nonlinear wave equation in high dimension. Recently, S.S.Lin , C.H.Hsu , T. Makino and me [1] were interested in the periodic solutions of a Compressible Euler Equation with Gravity. We hope this iteration leads to more understanding for the existence of periodic solution of this nonlinear equation.

Workshop / Conference: 1. 6th European Congress of Mathematics, Krakow, Polish, July 2-7, 2012 2. International Conference on Mathematical Methods and Models in Biosciences, Sofia, Bulgaria, June 17-22, 2012. 3. 2012 NCTS Workshop on Dynamical Systems, National Tsing-Hua University, Taiwan, May 16- 18, 2012. 4. The 3rd Taiwan-Japan Joint Workshop for Young Scholars in Applied Mathematics, National Taiwan University, Taiwan, February 27-28, 2012.

Publication and Preprint: 1. An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity (with C.H. Hsu, S.S. Lin, T. Makino), submitted. 2. Existence of traveling wave solutions in a diffusive predator–prey model with Holling’s type III Functional Response (with T.H. Yang), submitted. 3. Existence of traveling wave solutions for diffusive predator–prey type systems (with C.H. Hsu, T.S. Yang, T.H. Yang). J. Differential Equations 252, 3040-3075 (2012).

81 ‹‹- Activities of Onsite Scientists G Preprints

Series I Title and Author

Weighted Local Orlicz-Hardy Spaces on Domains and Their Applications 2012-1-01 in Inhomogeneous Dirichlet and Neumann Problems Jun Cao, Der-Chen Chang, Dachun Yang and Sibei Yang Boundedness of Generalized Riesz Transforms on Orlicz-Hardy Spaces 2012-1-02 Associated to Operators Jun Cao, Der-Chen Chang, Dachun Yang and Sibei Yang

Perturbation Analysis of The Stochastic Algebraic Riccati Equation 2012-1-03 Matthew M. Lin, Chun-Yueh Chiang, Hsin-An Chen, and Hung-Yuan Fan

A Large-Scale Nonsymmetric Algebraic Riccati Equation from 2012-1-04 Transport Theory Peter Chang-Yi Weng, Hung-Yuan Fan, Eric King-wah Chu Distribution of Diophantine Approximation Exponents for Algebraic 2012-1-05 Quantities Infnite Characteristic Huei Jeng Chen Eigendecomposition of The Discrete Double-Curl Operator with Application 2012-1-06 to Fast Eigensolver for Three Dimensional Photonic Crystals Tsung-Ming Huang, Han-En Hsieh, Wen-Wei Lin, and Weichung Wang Matrix Representation of the Double-Curl Operator for Simulating Three 2012-1-07 Dimensional Photonic Crystals Tsung-Ming Huang, Han-En Hsieh, Wen-Wei Lin, Weichung Wang Solving Large-Scale Continuous-Time Algebraic Riccati Equations by 2012-1-08 Doubling Tiexiang Li, Eric King-wah Chu, Wen-Wei Lin, Peter Chang-Yi Weng Solving Large-Scale Discrete-Time Algebraic Riccati Equations by Doubling 2012-1-09 Tiexiang Li, Eric King-wah Chu, Wen-Wei Lin Numerical Solution of Nonlinear Matrix Equations Arising from Green's 2012-1-10 Function Calculations in Nano Research* Chun-Hua Guo, Yueh-Cheng Kuo, and Wen-Wei lin Solving Large-Scale Nonsymmetric Algebraic Riccati Equations by 2012-1-11 Doubling Chang-Yi Weng, Tiexiang Li , Eric King-wah Chu, Wen-Wei Lin

Preprints ‹‹- 82 Series I Title and Author

Solving Large-Scale Stein and Lyapunov Equations by Doubling 2012-1-12 Tiexiang Li, Chang-Yi Weng, Eric King-wah Chu, Wen-Wei Lin G Numerical Studies on Structure-Preserving Algorithms for Surface 2012-1-13 Acoustic Wave Simulations Tsung-Ming Huang, Chin-Tien Wu, Tiexiang Li The Eigenvalue Shift Technique and Its Eigenstructure Analysis of a Matrix 2012-1-14 Chun-Yueh Chiang, Matthew M. Lin The Shift Techniques for a Nonsymmetric Algebraic Riccati Equation 2012-1-15 Chun-Yueh Chiang and Matthew M. Lin On the Inexact Structure-Preserving Arnoldi Methods for Hermitian and 2012-1-16 Skew-Hermitian Eigenvalue Problems Ching-Sung Liu and Che-Rung Lee An Inexact Inverse Iteration for Computing The Smallest Eigenvalue of An 2012-1-17 Irreducible M-Matrix* Michiel E. Hochstenbach, Wen-Wei Lin, and Ching-Sung Liu Linear Independence of Monomials of Multizeta Values in Positive 2012-1-18 Characteristic Chieh-Yu Chang Genus Two Lifts of Q-Curves Which Are of Type With Multiplication 2012-1-19 Ki-Ichiro Hashimoto and Fang-Ting Tu An Explicit Reciprocity Law Arising From Superspecial Abelian Varieties 2012-1-20 And Trace Formulas Chia-Fu Yu On the T-Stein matrix equation 2012-1-21 Matthew M. Lin, Chun-Yueh Chiang On the Dynamics of Two-consumers-one-resource Competing Systems with 2012-1-22 Beddington-DeAngelis Functional Response Sze-Bi Hsu, Shigui Ruan, and Ting-Hui Yang Global dynamics of zooplankton and harmful algae in flowing habitats 2012-1-23 where the algal toxin contains little limiting nutrient Sze-Bi Hsu, Feng-Bin Wang, and Xiao-Qiang Zhao Dynamics of phytoplankton community under photoinhibition 2012-1-24 Sze-Bi Hsu, Chiu-Ju Lin, Chih-Hao Hsieh, Kohei Yoshiyama On A Theorem of Swan 2012-1-25 Chia-Fu Yu Geometric Analysis on Ornstein-Uhlenbeck Operators with Quadratic Potentials 2012-1-26 Der-Chen Chang and Sheng-Ya Feng

83 ‹‹- Preprints Series I Title and Author Ergodic Optimization for a Sequence of Continuous Functions 2012-1-27 G Chen Yangyang and Zhao Yun Large-Scale Discrete-Time Algebraic Riccati Equations — Numerically 2012-1-28 Low-Ranked Solution, SDA and Error Analysis.* Tiexiang Li, Yueh-Cheng Kuo, Eric King-wah Chu, Wen-Wei Lin

Series II Title and Author

On class numbers of hereditary orders over global function fields 2012-2-01 Fu-Tsun Wei , Chia-Fu Yu

Embeddings of fields into simple algebras: generalizations and applications 2012-2-02 Chia-Fu Yu

Class numbers of central simple algebras over global function fields 2012-2-03 Fu-Tsun Wei , Chia-Fu Yu

The linear guessing number of undirected graphs 2012-2-04 Mei Lu, Gerard Jenn-hwa Chang, Liang-Hao Huang

Report on my stay at the NCTS Math Division (Taipei office), 2012-2-05 from September 31st to October 2nd Christian Kappen

Series III Title and Author

Action of the Johnson-Torelli group on representation varieties 2012-3-01 William M. Goldman and Eugene Z. Xia

Matrix near-rings and 0-primitivity 2012-3-02 Wen-Fong Ke and Johan Meyer

Contracting convex immersed closed plane curves with slow speed of 2012-3-03 curvature Yu-Chu Lin, Chi-Cheung Poon and Dong-Ho Tsai

Semi-infinite programming method for optimal power flow with transient 2012-3-04 stability and variable clearing time of faults X. J. Tong, C. Ling, S. Y. Wu and L. Qi

Dehn twists and invariant classes 2012-3-05 Eugene Z. Xia

Preprints ‹‹- 84 Series III Title and Author

Abelian and non-Abelian Cohomology, Geometry, Topology And Dynamics 2012-3-06 Of Character Varieties Eugene Z. Xia G

Quadratic spaces and holomorphic framed vertex operator algebras of 2012-3-07 central charge 24 C. H. Lam and H. Shimakura

McKay’s E6 observation on the Fischer group Fi24 2012-3-08 G. Hohn, C. H. Lam and H. Yamauchi

McKay’s E7 observation on the Babymonster 2012-3-09 G. Hohn, C. H. Lam and H. Yamauchi

Super duality and homology of unitarizable modules of Lie algebras 2012-3-10 P.-Y. Huang, N. Lam and T.-M. To

Diagonal lattices and rootless EE8 pairs 2012-3-11 Robert L. Griess Jr. and C.H. Lam

Test for dispersion constancy in stochastic differential equation model 2012-3-12 S Lee and M-H Guo

85 ‹‹- Preprints Appendix I. Visiting Mathematicians 2012

Appendix I Name Field Duration LU Zhong Xue (Xuzhou Normal University of PDE 2011-12-03~2012-02-01 mathematical Sciences) Goong Chen Applied Mathematics 2011-12-11~2012-01-11 (Texas A&M University) Yuan nan Young (New Jersey Institute of Complex Fluid Dynamics 2011-12-28~2012-01-12 Technology, USA) Partial differential equations, Rolf Ryham scientific computing and geometric 2011-12-30~2012-01-11 (Fordham University) measure theory. Hau-Tieng Wu Adaptive analysis for complex data 2012-01-01~2012-01-31 (Princeton University) Siye Wu Geometry 2012-01-03~2012-01-06 (University of Hong Kong) Tzyy Leng Horng Numerical Analysis and Scientific 2012-01-04~2012-01-08 (Feng Chia University) Computing Partial Differential Equation, Minkyu Kwak Ordinatry Differential Equation, 2012-01-05~2012-01-09 (Chonnam University, Korea) Dynamical System Eiji Yanagida Nonlinear Mathematical Analysis , (Tokyo Institute of 2012-01-05~2012-01-09 Differential Equation Technology) Hirokazu Ninomiya Structure of solutions of nonlinear 2012-01-05~2012-01-10 (Meiji University) partial differential equations Masayasu Mimura PDE 2012-01-05~2012-01-10 (Meiji University) General mathematics (includes Shoji Yotsutani probability theorystatistical 2012-01-05~2012-01-11 (Ryukoku University) mathematics) ,Global analysis Yu Jiang (Shanghai University of Applied Mathematics 2012-01-07~2012-01-15 Finance and Economics) Steven Zucker geometry 2012-01-07~2012-01-21 (Johns Hopkins University)

Appendix I ‹‹- 86 Name Field Duration Nakamura Gen Applied Mathematics 2012-01-08~2012-01-12 (Hokkaido University) Stanley Chang Appendix I (Department of Mathematics, Geometric Topology 2012-01-09~2012-01-10 Wellesley College) Viktor Ginzburg Geometry 2012-01-14~2012-02-10 (UC Santa Cruz) Eric Kingwah Chu Applied Mathematics 2012-01-15~2012-01-20 (Monash University) Ginz Viktor L. symplectic topology 2012-01-31~2012-01-31 (University of California) Daphne Liu coloring parameters of distance (College of Natural and 2012-02-05~2012-04-05 graphs Social Sciences) Sergei Kucherenko (Centre for Process Systems Probability Theory and Statistics 2012-02-06~2012-02-10 Engineering Imperial College London Kaizhi Wang Dynamical System 2012-02-15~2012-03-15 (Jilin University) Sangyeol Lee Statistics 2012-02-20~2012-02-26 (Seoul national University) Otto van Koert Geometry 2012-02-20~2012-02-28 (Seoul national University) Number Theory, Algebra, Hajime Kaneko Representation Theory and Related 2012-02-21~2012-02-28 (NIHON University) Topics Michiel Hochstenbach (Eindhoven University of Scientific Computation 2012-02-24~2012-03-05 Technology) Kota Ikeda Reactiondiffusion equation 2012-02-25~2012-02-29 (Meiji University) Junta Matsukidaira Applied mathematics 2012-02-26~2012-02-29 (Ryukoku University) Toshiyuki Ogawa Dynamical Systems Nonlinear PDE 2012-02-26~2012-02-29 (Meiji University) Scientific Computations Topology Hirokazu Ninomiya Reaction Diffusion Systems Pattern 2012-02-26~2012-02-29 (Meiji University) Formation Blowup Problems

87 ‹‹- Appendix I Name Field Duration Kazuyuki Nakamura Statistical modeling and analysis for 2012-02-26~2012-02-29 (Meiji University) spatiotemporal data Appendix I Nobuhiro Suematsu Applied mathematics 2012-02-26~2012-02-29 (Meiji University) Jamming Phenomena in Traffic Flow Akiyasu Tomoeda Illusion Phenomena in Perception of 2012-02-26~2012-02-29 (Meiji University) Drivers Yoshikazu Yamagishi Geometry 2012-02-26~2012-02-29 (Ryukoku University) Yuumi Nakamura Applied mathematics 2012-02-26~2012-02-29 (Meiji University) Jia-zhen Liu (National Chung Cheng Applied mathematics 2012-02-27~2012-02-28 University) Pattern formation in dissipative systems, Mathematical understanding of the complex pattern formation, Daishin Ueyama Controllability of the pattern 2012-02-27~2012-02-29 (Meiji University) formation processes (effect of the inhomogeneity etc.), Parallel computing for the 3D simulation, Effective visualization Number Theory, Algebra, Shinichi Kobayashi Representation Theory and Related 2012-03-01~2012-03-11 Tohoku University) Topics Andreas Kyprianou Probability Theory 2012-03-04~2012-03-11 (University of Bath) Yoshio Miyahara Probability Theory 2012-03-06~2012-03-10 (Nagoya City University) Budhi Arta Surya Applied Mathematics, Probability (Bandung INstitue of 2012-03-06~2012-03-11 Theory Technology Indonesia) Ning Cai (Hong Kong University of Probability Theory 2012-03-07~2012-03-10 Science and Technology) Hideo Nagai Probability Theory 2012-03-07~2012-03-10 (Osaka University) Jun Sekine Probability Theory 2012-03-07~2012-03-14 (Osaka University)

Appendix I ‹‹- 88 Name Field Duration Svetlana Boyarchenko Applied Mathematics, Probability 2012-03-07~2012-03-17 (University of Texas) Theory Appendix I King-Fai Lai Automorphic Form, Algebra 2012-03-11~2012-03-27 (University of Sydney)

David Spring (Glendon College, York Differential Topolog. 2012-03-19~2012-03-20 University, Toronto, Canada)

Ngo Viet Trung Commutative Algebra and (Vietnam Academy of Interactions to Algebraic Geometry 2012-03-19~2012-03-24 Science and Technology) and Combinatorics

Damian Rossler Arithmetic Algebraic Geometry 2012-04-13~2012-04-13 (Universite de Toulouse III)

Kenichi Namikawa Number Theory 2012-04-13~2012-04-27 (Osaka University)

Zhi Jiang Algebra 2012-04-15~2012-05-15 (Universit e ParisSud 11)

Choe Jaigyoung (Korea Institute for Advanced Differential Geometry 2012-04-29~2012-05-03 Study)

Fabien Trihan Number Theory 2012-04-29~2012-05-04 (University of Nottingham)

Chih-Kang Chu (National Dong Hwa Statistics 2012-04-30~2012-05-04 University Statistics)

Xiaoqiang Zhao Dynamical System Mathematical (Memorial University of 2012-05-02~2012-06-01 Biology Nonlinear PDE Newfoundland)

Kohei Yoshiyama (River Basin Research Center Mathematical Biology 2012-05-04~2012-05-07 Gifu University)

Nino Hirokazu (Meiji PDE 2012-05-05~2012-05-09 University)

W.M. Ni (Center for PDE ECNU & Nonlinear PDE 2012-05-07~2012-06-03 University of Minnesota)

Tzyy Leng Horng Numerical Analysis and Scientific 2012-05-09~2012-05-10 (Feng Chia University) Computing

89 ‹‹- Appendix I Name Field Duration Yucai Su Algebra 2012-05-10~2012-05-19 (Tong ji University)

Appendix I Peter Sternberg (Department of Mathematics, PDE 2012-05-13~2012-05-18 Indiana University, Bloomington)

Martin Golubitsky Dynamical System 2012-05-14~2012-05-20 (Ohio State University)

DeJun Feng (The Chinese University of Dynamical System 2012-05-15~2012-05-19 Hong Kong)

KaSing Lau (The Chinese University of Dynamical System 2012-05-15~2012-05-19 Hong Kong)

Barbara Gentz Dynamical System Probability 2012-05-15~2012-05-20 (University of Bielefeld) Theory and Statistics

Hiroshi Kokubu Dynamical System 2012-05-15~2012-05-20 (Kyoto University)

Hayato Chiba Dynamical System 2012-05-15~2012-05-21 (Kyushu University)

Philip John Holmes Dynamical System Mathematical 2012-05-15~2012-05-21 (Princeton University) Biology

Chris Cosner Mathematical Biology 2012-05-16~2012-05-27 (University of Miami)

Steve Cantrell Mathematical Biology 2012-05-16~2012-05-27 (University of Miami)

Multiscale problems, modeling, and the related numerical methods; Richard Tsai Inverse source problems and (University of Texas at 2012-05-17~2012-06-01 optimization involving visibility; High Austin) frequency wave propagation; Level set methods and their applications

Dynamical System Yihong Du Mathematical Biology 2012-05-18~2012-05-27 (University of New England) Nonlinear PDE

Salomé Martínez Mathematical Biology 2012-05-18~2012-05-27 (University of Chile)

Appendix I ‹‹- 90 Name Field Duration Adrian Lam Mathematical Biology 2012-05-18~2012-05-27 (Ohio State University) Nonlinear PDE Appendix I Toda Yukinobu Geometry 2012-05-21~2012-05-25 (The University of Tokyo) Chun-Hung Liu (School of Mathematics, Graph theory and combinatorics 2012-05-21~2012-06-14 Georgia Institute of Technology) Applied stochastic analysis, Monte Carlo methods and sampling algorithms, Multiscale computations and coarsegraining algorithms, Numerical analysis and computational methods for solving Petr Plechac PDEs, Multiresolution analysis and 2012-05-21~2012-06-14 (University of Tennessee) numerical algorithms, numerical methods for highdimensional problems computational methods in materials science, quantum chemistry, complex fluids and polymers parallel computing Dehomogenization for composite materials Timereversal for elastic MiaoJung Yvonne Ou composites, Mathematical biology for (University of Delaware, trabecular bones, Wave propagation 2012-05-21~2012-06-14 USA) in composite materials, Multiwavelet methods for definite and indefinte Helmholtz equations Robert D. Holt Mathematical Biology 2012-05-23~2012-05-26 (University of Florida) Shinichi Ohta Comparison geometry involving (Department of Mathematics, various kinds of curvature, and its 2012-06-03~2012-06-05 Kyoto University) applications Sano Taro Algebraic geometry: deformation (Mathematics Institute, theory, Fano varieties, CalabiYau 2012-06-03~2012-06-06 University of Warwick) varieties. Maria del Mar Gonzalez Differential Geometry and Geometric (Universitat Politecnica de 2012-06-04~2012-06-09 Analysis Catalunya) Guofang Wei Differential Geometry and Geometric (University of California 2012-06-04~2012-06-09 Analysis Santa Barbara)

91 ‹‹- Appendix I Name Field Duration Neil Trudinger Differential Geometry and Geometric (Australian National Analysis, Nonlinear PDE, Scientific 2012-06-05~2012-06-09

Appendix I University) Computation Yu ShihHsie Shock Wave theory, Boltzmann (National University of 2012-06-05~2012-06-08 Equation Singapore) Emmanuel Hebey Differential Geometry and Geometric 2012-06-06~2012-06-08 (Université de CergyPontoise) Analysis, Nonlinear PDE Bo Guan Differential Geometry and Geometric 2012-06-06~2012-06-09 (Ohio State University) Analysis Zhengchao Han Differential Geometry and Geometric 2012-06-06~2012-06-09 (Rutgers University) Analysis Xingwang Xu Differential Geometry and Geometric (National University of 2012-06-06~2012-06-09 Analysis Singapore) Matthew J. Gursky Differential Geometry and Geometric 2012-06-06~2012-06-09 (University of Notre Dame) Analysis Hao Fang Differential Geometry and Geometric 2012-06-06~2012-06-09 (University of Iowa) Analysis Shihshu Walter Wei Differential Geometry and Geometric 2012-06-06~2012-06-09 (University of Oklahoma) Analysis Wenxiong Chen Differential Geometry and Geometric 2012-06-06~2012-06-09 (Yeshiva University) Analysis KiAhm Lee Differential Geometry and Geometric 2012-06-06~2012-06-09 (Seoul National University) Analysis Jeffrey Case Differential Geometry and Geometric 2012-06-06~2012-06-09 (Princeton University) Analysis Paul Yang Differential Geometry and Geometric 2012-06-07~2012-06-09 (Princeton University) Analysis Ray Yang Differential Geometry and Geometric (Courant Institute of 2012-06-08~2012-06-09 Analysis Mathematical Sciences) Yan nick Sire Differential Geometry and Geometric (Université AixMarseille 2012-06-08~2012-06-09 Analysis Ⅲ Paul Cézanne) Hau-Tieng Wu Harmonic analysis, differential 2012-06-11~2012-07-14 (Princeton University) geometry, PDE

Appendix I ‹‹- 92 Name Field Duration

Ching-Jui Lai (Department of Mathematics, Algebraic Geometry 2012-06-13~2012-07-21

University of Utah) Appendix I Wei Jiang (Shanghai Jiaotong Statistics 2012-06-21~2012-06-22 University) Tang Loon Ching (National University of Statistics 2012-06-21~2012-06-22 Singapore) Quo-Shin Chi Differential Geometry 2012-06-21~2012-07-08 (Washington University) Pinyuen Chen Statistics 2012-06-22~2012-07-18 (Syracuse University) Victor Didenko Functional Analysis, Operator (Universiti Brunei Theory, Wavelets, Approximation of 2012-06-22~2012-06-29 Darussalam, Brunei PseudoDifferential Operators. Darussalam) Xuejun Xu Numerical analysis for PDEs by finite (Chinese Academy of 2012-06-22~2012-06-29 element methods Sciences) Computational fluid dynamics; Professor Weizhu Bao BoseEinstein condensation; (National University of Multiscale simulation; Problems 2012-06-22~2012-06-29 Singapore) in unbounded domain; Numerical analysisScientific computing XiaoQing Jin Scientific computing, numerical linear 2012-06-22~2012-06-29 (University of Macau) algebra Rafael P. Saldana Mathematical Modeling and (Ateneo de Manila 2012-06-22~2012-06-29 Computer Simulation University, The Philippines) Mohd Omar Industrial Optimisation And Control (University of Malaya, (Production planning, vendorbuyer, 2012-06-23~2012-06-27 Malaysia) optimal policy) Computational science and engineering; simulation, sensitivity Linda Petzold analysis, design optimization, (University of California, optimal control and problem solving 2012-06-23~2012-06-28 Santa Barbara, USA) environments for systems described by differentialalgebraic equations and partial differential equations.

93 ‹‹- Appendix I Name Field Duration Numerical Linear Algebra, Numerical Haiwei Sun PDEs, Control Theory, Computational 2012-06-24~2012-06-30 (University of Macau)

Appendix I Finance Yalchin Efendiev Numerical analysis, multiscale finite 2012-06-25~2012-06-28 (Texas A&M University) element method, flow in porous media Barry C. Arnold (University of California, Statistics 2012-06-26~2012-06-26 Riverside) Kaibo Wang Statistics 2012-06-26~2012-06-26 (Tsinghua University) Yi Li Hong Statistics 2012-06-26~2012-06-27 (Virginia Tech) Seoung Bum Kim Statistics 2012-06-26~2012-06-27 (Korea University) Dennis K. J. Lin Statistics 2012-06-26~2012-06-27 (Penn State University) Regina Liu Statistics 2012-06-26~2012-06-27 (Rutgers University) William Q. Meeker Statistics 2012-06-26~2012-06-27 (Iowa State University) Arthur B. Yeh (Bowling Green State Statistics 2012-06-26~2012-06-27 University) Ying Hung Statistics 2012-06-26~2012-06-27 (Rutgers University) Lingmin Liao Dynamical System 2012-06-26~2012-07-24 (Université ParisEst) David Yang Gao Applied Mathematics 2012-06-26~2012-07-03 (University of Ballarat) Kok Lay Teo (Curtin University of Applied Mathematics 2012-06-26~2012-07-03 Technology) Jie Sun (National University of Statistics 2012-06-26~2012-07-03 Singapore) Tsung-fang Wu (Department of Applied Partial Differentiation Equations, 2012-06-26~2012-06-27 Mathematics, National Analysis University of Kaohsiung)

Appendix I ‹‹- 94 Name Field Duration

ChunYen Shen Dynamical System 2012-06-27~2012-06-29 (McMaster University) Appendix I Yong Yu Partial Di fferential Equation, (The Chinese University of 2012-06-27~2012-06-29 Mathematical Physics Hong Kong) Kai-Wen Lan Arithmetic Geometry 2012-06-28~2012-07-15 (Princeton University) WeiYin Loh (University of Statistics 2012-07-01~2012-07-23 WisconsinMadison) Hülya İNCEBOZ GÜNAYDIN Algebra 2012-07-01~2012-07-29 (Adnan Menderes University) Juntao Sun (Shandong University of Applied Mathematics 2012-07-02~2012-07-23 Technology) Chi-Kwong Li (College of William and Linear Algebra, Operator Algebra 2012-07-05~2012-07-06 Mary)

Xiaojun Huang Differential Geometry and Geometric 2012-07-06~2012-07-08 (Rutgers University) Analysis

SaiKee Yeung Differential Geometry and Geometric 2012-07-06~2012-07-08 (Purdue University) Analysis

Algebraic Geometry YumTong Siu Differential Geometry and Geometric 2012-07-07~2012-07-07 (Harvard University) Analysis Douglas G. Simpson (University of Illinois at Applied and computational statistics 2012-07-08~2012-07-17 UrbanaChampaign) DerChen Chang Differential Geometry and Geometric 2012-07-15~2012-07-27 (Georgetown University) Analysis Traveling waves of chemotaxis and applications, Multiscale modeling of chemotactic movement, Modeling Zhi-An Wang and analysis of chemotaxis with cell (Hong Kong Polytechnic 2012-07-20~2012-07-28 population interactions, Modeling and University) analysis of cell movement in tissue, Regularization and sigunlarity of chemotaxis models

95 ‹‹- Appendix I Name Field Duration

Toshio Honda Statistics, Econometrics 2012-07-22~2012-07-28 (Hitotsubashi University) Appendix I Tong Yang (City University of Hong Conservation laws 2012-07-23~2012-07-28 Kong)

Mei Lu (Department of Mathematical Graph Theory, Uncertain 2012-07-23~2012-08-18 Sciences, Tsinghua Programming University, Beijing)

Daphne Liu coloring parameters of distance (College of Natural and 2012-07-29~2012-08-17 graphs Social Sciences)

Wenjun Ying (Shanghai Jiao Tong Scientific Computation 2012-07-31~2012-08-16 University)

Yimin Wei Applied Mathematics 2012-07-31~2012-08-04 (Fudan University)

J. M. Cushing Mathematical Biology 2012-08-01~2012-08-21 (University of Arizona)

Zhao Yun Dynamical System 2012-08-01~2012-08-31 (University of Suzhou)

Xuding Zhu Combinatorics, Computer Science 2012-08-02~2012-08-03 (Zhejiang Normal University)

Jerrold Griggs combinatorics, extremal set theory, (University of South 2012-08-03~2012-08-09 extremal graph theory Carolina)

Kerby Shedden Statistics 2012-08-06~2012-08-19 (The University of Michigan)

Kai-Wen Lan Arithmetic Geometry 2012-08-07~2012-08-13 (Princeton University)

Number Theory, Algebra, Ram Murty Representation Theory and Related 2012-08-11~2012-08-30 (Queen's University) Topics

Jerrold Griggs combinatorics, extremal set theory, (University of South 2012-08-12~2012-08-25 extremal graph theory Carolina)

Appendix I ‹‹- 96 Name Field Duration Rationality problem under finite group actions, Family of Thue

equations, Constructive aspects of Appendix I Akinari Hoshi the inverse Galois problem, Field (Department of Mathematics, 2012-08-12~2012-08-31 isomorphism problem of generic Rikkyo University) polynomials, Multiplicative quadratic forms on algebraic varieties, Gaussian period polynomials for finite fields. Aiichi Yamasaki Number theory, computerbased (Department of Mathematics, 2012-08-12~2012-08-31 numerical computation Kyoto University) Shingyu Leung (The Hong Kong University Scientific Computation 2012-08-13~2012-08-26 of Science and Technology) Number Theory, Algebra, Takao Yamazaki Representation Theory and Related 2012-08-23~2012-09-09 (Tohoku University) Topics Number Theory, Algebra, FangTing Tu Representation Theory and Related 2012-08-23~2012-09-09 (Waseda University) Topics Number Theory, Algebra, Kiichiro Hashimoto Representation Theory and Related 2012-08-25~2012-09-08 (Waseda University) Topics Number Theory, Algebra, Tamotsu Ikeda Representation Theory and Related 2012-08-26~2012-08-31 (Kyoto University) Topics Number Theory, Algebra, Yoshinori Mishiba Representation Theory and Related 2012-08-26~2012-09-01 (Kyushu University) Topics Number Theory, Algebra, Takashi Miura Representation Theory and Related 2012-08-26~2012-09-01 (Keio University) Topics Number Theory, Algebra, Yasuo Ohno Representation Theory and Related 2012-08-26~2012-09-04 (Kinki University) Topics Eiichi Bannai Number Theory, Algebra, (Shanghai Jiao Tong Representation Theory and Related 2012-08-26~2012-09-06 University) Topics Number Theory, Algebra, Kensaku Kinjo Representation Theory and Related 2012-08-26~2012-09-08 (The University of Tokyo) Topics

97 ‹‹- Appendix I Name Field Duration

Number Theory, Algebra, Tomoya Machide Representation Theory and Related 2012-08-26~2012-09-08 (Kinki University) Appendix I Topics

Number Theory, Algebra, Shu Kawaguchi Representation Theory and Related 2012-08-26~2012-09-08 (Kyoto University) Topics

Number Theory, Algebra, Masataka Chida Representation Theory and Related 2012-08-28~2012-09-05 (Kyoto University) Topics

Number Theory, Algebra, Yoichi Mieda Representation Theory and Related 2012-08-28~2012-09-08 (Kyoto University) Topics

Edmund Puczyłowski Ring Theory 2012-08-28~2012-09-21 (University of Warsaw)

Shunsuke Hayashi Applied Mathematics 2012-08-30~2012-09-24 (Kyoto University)

Vincent Maillot Algebraic Geometry 2012-08-31~2012-09-16 (Univerite Paris VI)

Number Theory, Algebra, Masanori Morishita Representation Theory and Related 2012-09-02~2012-09-08 (Kyushu University) Topics

Christian Kappen (Inst.Exp.Math.Universitat Arithmetic Geometry 2012-09-02~2012-10-02 DuisburgEssen)

Yasuhiro Goto Number Theory, Algebra, (Hokkaido University of Representation Theory and Related 2012-09-04~2012-09-09 Education) Topics

Damian Rossler Arithmetic Algebraic Geometry 2012-09-09~2012-09-17 (Universite de Toulouse III)

Shunsuke Hayashi Mathematical programming 2012-09-12~2012-09-12 (Kyoto University)

Edmund Puczylowski Algebra 2012-09-15~2012-09-19 (University of Warsaw)

King Fai Lai (Department of Applied Automorphic Form 2012-09-20~2012-09-21 Mathematics, national Sun Yat-sen Universit y)

Appendix I ‹‹- 98 Name Field Duration Boris Kunyavskii Algebraic Groups,Algebraic 2012-09-20~2012-10-18 (BarIlan University) Geometry Appendix I LU Zhong Xue (Xuzhou Normal University PDE 2012-09-24~2012-11-15 of mathematical Sciences) Atsushi Mochizuki (RIKEN Advanced Science Mathematical Biology 2012-09-26~2012-10-03 Institute) Bernold Fiedler Dynamical System 2012-09-26~2012-10-03 (Free University Berlin) King Fai Lai (Department of Applied Automorphic Form 2012-10-04~2012-10-05 Mathematics, national Sun Yat-sen Universit y) DeKang Mao Numerical Partial Differential 2012-10-14~2012-10-21 (Shanghai University) Equations Arnaud Ducrot (University Victor Segalen PDE 2012-10-23~2012-11-04 Bordeaux II) Mounir Hajli (University Pierre et Marie Arakelov Geometry 2012-10-23~2012-11-18 Curie) King Fai Lai (Department of Applied Automorphic Form 2012-10-25~2012-10-26 Mathematics, national Sun Yat-sen Universit y) Zhou Feng (East china Normal PDE 2012-11-02~2012-11-11 University,China) Number Theory, Algebra, Masanobu Kaneko Representation Theory and Related 2012-11-05~2012-11-08 (Kyushu University) Topics Seunghyu Kim Nonlinear PDE 2012-11-06~2012-11-10 (POSTECH) Seunghyuk Kim Nonlinear PDE 2012-11-07~2012-11-10 (POSTECH) Yonggeun Cho (Chonbuk National Nonlinear PDE 2012-11-07~2012-11-10 University)

99 ‹‹- Appendix I Name Field Duration

Bongsuk Kwon Nonlinear PDE 2012-11-07~2012-11-10 (Bongsuk Kwon) Appendix I Jaewoo Jung Nonlinear PDE 2012-11-07~2012-11-10 (POSTECH)

Dynamical System Hyung Ju Hwang Mathematical Biology 2012-11-07~2012-11-10 (POSTECH) Others

Jaeyoung Byeon Dynamical System, Nonlinear PDE 2012-11-07~2012-11-10 (POSTECH)

Namkwon Kim Nonlinear PDE, Others 2012-11-07~2012-11-10 (Chosun University)

Myoungjean Bae Nonlinear PDE 2012-11-07~2012-11-10 (POSTECH)

King Fai Lai (Department of Applied Automorphic Form 2012-11-08~2012-11-09 Mathematics, national Sun Yat-sen Universit y)

Johannes Meyer Algebra 2012-11-11~2012-11-25 (University of the Free State)

King Fai Lai (Department of Applied Automorphic Form 2012-11-15~2012-11-16 Mathematics, national Sun Yat-sen University)

Victor Isakov Inverse Problems and related subjects 2012-11-16~2012-11-24 (Wichita State University)

Mihran Papikian Number Theory, Algebra, (Pennsylvania State Representation Theory and Related 2012-11-18~2012-11-23 University) Topics

King Fai Lai (Department of Applied Automorphic Form 2012-11-22~2012-11-23 Mathematics, national Sun Yat-sen University)

Muddappa Seetharama Gowda Applied Analysis Optimization 2012-11-23~2012-12-02 (University of Maryland)

Jerry L. Bona (University of Illinois PDE 2012-11-27~2012-12-04 Chicago)

Appendix I ‹‹- 100 Name Field Duration Nan Chen (National University of Statistics 2012-12-06~ 2012-12-13

Singapore) Appendix I King Fai Lai (Department of Applied Automorphic Form 2012-12-06~2012-12-07 Mathematics, national Sun Yat-sen Universit y) Der Chen Chang Differential Geometry and Geometric 2012-12-08~2013-01-16 (Georgetown University) Analysis Irene Fonseca Nonlinear PDE 2012-12-09~ 2012-12-16 (Carnegie Mellon University) Scientific Computation Jin-Ting Zhang (National University Of Functional data analysis 2012-12-11~2012-12-17 Singapore) TaiPeng Tsai (University of British Nonlinear PDE 2012-12-12~2012-12-16 Columbia Canada) Edriss S. Titi Nonlinear PDE (University of California 2012-12-12~2012-12-16 Scientific Computation Irvine) Dongho Chae Nonlinear PDE (ChungAng University 2012-12-12~2012-12-16 Scientific Computation Korea) Yi-Li Hong Statistics 2012-12-12~2012-12-19 (Virginia Tech) ZhouPing Xin Nonlinear PDE (The Chinese University of 2012-12-12~2012-12-20 Scientific Computation Hong Kong) Yong Yu Nonlinear PDE (The Chinese University of 2012-12-12~2012-12-20 Scientific Computation Hong Kong) Benoit Perthame Nonlinear PDE 2012-12-13~2012-12-15 (UPMC (Paris 6) France) Scientific Computation

Andrew Belmonte Nonlinear PDE (Pennsylvania State 2012-12-13~2012-12-16 Scientific Computation University)

Fang Hua Lin Nonlinear PDE 2012-12-13~2012-12-16 (New York University) Scientific Computation

101 ‹‹- Appendix I Name Field Duration

King Fai Lai (national Sun Yat-sen Automorphic Form 2012-12-13~2012-12-14 Appendix I University)

Lim Johan Large scale multivariate statistical 2012-12-14~2012-12-20 (Seoul National University) problems

Edriss S. Titi (University of fluid mechanics.PDE 2012-12-15~2012-12-19 CaliforniaIrvine)

Siye Wu Differential Geometry and Geometric 2012-12-15~2012-12-23 (University of Hong Kong) Analysis

Regina Liu Statistics 2012-12-17~2012-12-29 (Rutgers University)

Differential Geometry and Geometric Irina Markina Analysis 2012-12-20~2013-01-10 (University of Bergen) Others Harmonic Analysis

Alexander Vasilev Differential Geometry and Geometric 2012-12-20~2014-01-10 (University of Bergen) Analysis

Michial NG Data Mining, Operational Research, (Hong Kong Baptist Image Processing and Scientific 2012-12-21~2012-12-25 University) Computing

Chia-Jung Chang Statistics 2012-12-22~2013-01-04 (Penn State University)

Siye Wu Geometry 2012-12-22~2013-01-05 (University of Hong Kong)

Dan Pollock Geometric Analysis and Differential 2012-12-23~2013-01-04 (University of Victoria) Geometry

Tatiana Toro Mathematical Analysis Geometry 2012-12-23~2013-01-04 (University of Washington)

Chun Liu Partial Differential Equations 2012-12-24~2012-12-28 (Penn. State University)

Naisyin Wang Statistics 2012-12-24~2013-01-09 (University of Michigan)

Appendix I ‹‹- 102 Name Field Duration Suk Joo Bae Statistics 2012-12-26~2012-12-30 (Hanyang University) Appendix I King Fai Lai (National Sun Yat-sen Automorphic Form 2012-12-27~2012-12-28 University)

Chun Liu Partial Differential Equations 2012-12-30~2013-01-08 (The Penn State University)

103 ‹‹- Appendix I NCTS 2012 Conference, Workshop & School, Special Lecture

Appendix II Conference & Workshop Time Place School & Special Lecture

The 20th Annual Workshop on Differential S104, Liu-hsien Equations Memorial Science January 6-8, 2012 Organizers： Whei-Ching C.Chan, Chuan-Jen Chyan, Jong-Shenq Guo, Hall, Danshui Chung-Tsun Shieh, Ting-Hui Yang Campus

Short Course on Introduction of Numerical Analysis for Partial Differential Equations Speakers R204, 2F, NCTS, February 13-17, Yuusuke Iso (Kyoto University) National Cheng 2012 Hiroshi Fujiwara (Kyoto University) Hitoshi Imai (University of Tokushima) Kung University Organizer: Chern-Shuh Wang (National Cheng Kung University)

2012 NCTS Spring Young Dynamics Day NCTS, Organizers: February 18, 2012 National Tsing Hua Kuo-Chang Chen (National Tsing Hwa University) Chih-Wen Shih (National Chiao Tung University) Univ.

2012 South Taiwan Workshop on Scientific Computing and Applications Speakers Zi-Cai Li (National Sun Yat-sen University) Min-Hung Chen (National Cheng Kung University) Li-Ming Yeh (National Chiao Tung University) Yung-Ta Li (National Chiao Tung University Chun-Yueh Chiang (National Formosa University) Room 4009-1, Min-Hsiung Lin (National Chung Cheng University) Faculty of Science, February 18, 2012 Chung Chien Hong (National Pingtung University of National Sun Yat- Science and Technology) sen University Yin-Liang Huang (National University of Tainan) Tsung-fang Wu (National University of Kaohsiung) Yueh-Cheng Kuo (National University of Kaohsiung) Jiunn-Shyan Lee (National Kaohsiung Normal University) Organizer: Tzon-Tzer Lu (National Sun Yat-sen University) Tsung-Lin Lee (National Sun Yat-sen University)

NCTS Mini Course in Dynamical Systems NCTS, February 20- Instructor: National Tsing Hua March 8, 2012 Kaizhi Wang (Jilin University, China) Univ.

Appendix II ‹‹- 104 Conference & Workshop Time Place School & Special Lecture

The 3rd Taiwan-Japan Joint Workshop for Young Appendix II Scholars in Applied Mathematics Organizers: Room 202, Astro- Chiun-Chuan Chen (National Taiwan University) February 27-28, Math. Building, Jann-Long Chern (National Central University) 2012 National Taiwan Jong-Shenq Guo (Tamkang University) University Chun-Hsiung Hsia (National Taiwan University) Shu-ichi Kinoshita (Meiji University) Yoshihisa Morita (Ryukoku University) Hirokazu Ninomiya (Meiji Universiyu)

2012 NCTS Mini-Workshop on Number Theory NCTS, March 7, 2012 Organizer: National Tsing Hua Yifan Yang (National Chiao Tung University) Univ.

Workshop on Stochastic Processes and Applications NCTS, Organizers: March 8 - 9, 2012 National Tsing Hua Chii-Ruey Hwang (Academia Sinica) Univ. Shuenn-Jyi Sheu (National Central University) Yuan-Chung Sheu (National Chiao Tung University)

2012 年東台灣暨理論中心 ( 南區 ) 春季代數組合研 討會 ( 第四屆東台灣數學研討會 ) Speakers Po-Yi Huang (National Cheng Kung University) Yiao-Tzu Chang (I-Shou University) Yuwen Cheng (National Taitung University) Shih-Wei Yang (National Cheng Kung University) Wan-Keng Cheong (National Cheng Kung University) T407, 4F, Academic Peng-An Cheng (National Taitung University) Building, National April 1-3, 2012 Eugene Zhu Xia (National Cheng Kung University) Taitung University Ching Hung Lam (National Cheng Kung University / Academia Sinica) Shih-Chang Huang (National Cheng Kung University) Wen-Fong Ke (National Cheng Kung University) Chufeng Nien (National Cheng Kung University) Feng-Kuo Huang (National Taitung University) Organizer: Wen-Fong Ke (National Cheng Kung University)

2012 NCTS & NCU Short Course on Quantum Information Theory National Central April 5-12, 2012 Instructor: University Kenjiro Yanagi (Yamaguchi University, Japan)

105 ‹‹- Appendix II Conference & Workshop Time Place School & Special Lecture

The 2012 Taipei International Statistics Workshop Appendix II Organizers: Room 440 Shu-Hui Chang (National Taiwan University) Astrophysics May 1- 3, 2012 Ming-Yen Cheng (National Taiwan University) and Mathematics Chih-Kang Chu (National Dong Hwa University) Building, National Byeong U. Park (Seoul National University) Taiwan University Masanobu Taniguchi (Waseda University)

2012 NCTS Program on Nonlinear Equations in Spatial Population Biology (Courses) NCTS, Organizers: May 4-26, 2012 National Tsing Hua Sze-Bi Hsu (National Tsing-Hua University) Univ. Wei-Ming Ni (East China Normal University and University of Minnesota)

2012 NCTS Workshop on Dynamical Systems Organizers: NCTS, May 16-19, 2012 Jung-Chao Ban (National Dong Hwa University) National Tsing Hua Kuo-Chang Chen (National Tsing-Hua University) Univ. Chih-Wen Shih (National Chiao-Tung University)

NCTS Math. & Phys. Popular Science Lecture NCTS, Lecture May 17, 2012 National Tsing Hua Speaker: Univ. Philip Holmes (Princeton University, USA)

The 4th Taiwan Geometry Symposium Speakers Chen-Yu Chi (Harvard University & National Taiwan University ) R204, 2F, NCTS, Shu-Yu Hsu (National Chung Cheng University) May 19, 2012 National Cheng Chiung-Jue Sung (National Tsing Hua University) Kung University Organizers: Nan Kuo Ho (National Tsing Hua University) Yng-Ing Lee (National Taiwan University) Eugene Zhu Xia (National Cheng Kung University)

NCTS Math. & Bionomics Popular Science NCTS, Lecture May 24, 2012 National Tsing Hua Speaker: Univ. Robert D. Holt (University of Florida, USA)

2012 NCTS Workshop on Nonlinear Equations in Spatial Population Biology NCTS, Organizers: May 24-26, 2012 National Tsing Hua Sze-Bi Hsu (National Tsing-Hua University) Univ. Wei-Ming Ni (East China Normal University and University of Minnesota)

Appendix II ‹‹- 106 Conference & Workshop Time Place School & Special Lecture Appendix II

2012 NCTS Mini-Course on Geometric Analysis Instructors: NCTS, June 4-6, 2012 Gonzalez, Maria del Mar (Universitat Politecnica de National Tsing Hua Catalunya, Spain) Univ. Guo-Fang Wei (University of California Santa Barbara)

NCTS Meet with Prof. Sun-Yung Alice Chang NCTS, June 5, 2012 Organizer: National Tsing Hua Wen-Ching Winnie Li (NCTS) Univ.

2012 Workshop on Geometric Partial Differential NCTS, Equations National Tsing Hua Organizers: June 7-13, 2012 Univ. Sun Yung Alice Chang (Princeton University, USA) and Jih-Hsin Cheng (Academia Sinica) Academia Sinica Chiung-Jue Sung (National Tsing-Hua University)

2012 Workshop in Industrial Statistics Audio-visual Room Speakers 62331, 3F, Dept. of Wei Jiang (Shanghai Jiaotong University) June 22, 2012 Statistics, National Loon Ching Tang (National University of Singapore) Cheng Kung Organizer: University Tiee-Jian Wu (National Cheng Kung University)

The 8th East Asia SIAM Conference (EASIAM 2012) Organizers: I-Liang Chern (National Taiwan University) Astrophysics and June 25-27, 2012 Ming-Chih Lai (National Chiao Tung University) Mathematics Jyh-Hao Lee (Academia Sinica) Building, National Keh-Ming Shyue (National Taiwan University) Taiwan University Jenn-Nan Wang (National Taiwan University) Weichung Wang (National Taiwan University)

NCTS Workshop on Industrial Statistics and Its Applications NCTS, June 26-27, 2012 Organizers: National Tsing Hua Sheng-Tsaing Tseng (National Tsing Hua University) Univ. Shuen-Lin Jeng (National Cheng-Kung University)

107 ‹‹- Appendix II Conference & Workshop Time Place School & Special Lecture

Appendix II 2012 International Workshop on Optimization and Engineering Systems Speakers Shu-Cherng Fang (North Carolina State University) David Yang Gao (University of Ballarat) Hang-Chin Lai (Chung Yuan Christian University) Jong-Shi Pang (University of Illinois at Urbana- Champaign) Che-Lin Su (University of Chicago) Jie Sun (National University of Singapore) Kok Lay Teo (Curtin University) Hsiao-Fan Wang (National Tsing Hua University) Zhen-Bo Wang (Tsinghua University) Cheng Kung Hall, June 27-30, 2012 Yong Xia (Beihang University) National Cheng Wen-Xun Xing (Tsinghua University) Kung University Nan-Jay Chiu (Yuanta Financial) Cheng-Feng Hu (I-Shou University) Chung-Cheng Huang (Southern Taiwan University) David Ta-Wei Hung (Shih Chien University) Jen-Yen Lin (National Chiayi University) Hsing Luh (National Chengchi University) Ruey-Lin Sheu (National Cheng Kung University) I-Lin Wang (National Cheng Kung University) Pei-Tsang Wu (I-Shou University) Ming-Jong Yao (National Chiao Tung University) Organizer: Ruey-Lin Sheu (National Cheng Kung University)

NCTS Summer Program on Number Theory Instructors: NCTS, June 27- Chieh-Yu Chang (National Tsing Hua University) National Tsing Hua August 6, 2012 Ming Hsuan Kang (National Chiao Tung University) Univ. Yifan Yang (National Chiao Tung University)

2012 NCTS Summer Course on Fourier Analysis NCTS, June 28-July 10, and Its Applications to Several Complex Variables National Tsing Hua 2012 Instructor: Der-Chen Chang (Georgetown University) Univ.

2012 NCTS Summer Course on Statistics NCTS, July 3-18, 2012 Instructor: National Tsing Hua Wei-Yin Loh (University of Wisconsin, USA) Univ.

NCTS Summer Course in Mathematical Biology NCTS, July 6-27, 2012 Instructor: National Tsing Hua Yun-Huei Tzeng ( Chinese Medical University) Univ.

Appendix II ‹‹- 108 Conference & Workshop Time Place School & Special Lecture

Room 519, Astro- Appendix II NCTS/TPE 2012 Geometry Summer Course Math. Building, July 6, 2012 Organizers: Yng-Ing Lee (National Taiwan University) National Taiwan University

NCTS Meet with Prof. Yum-Tong Siu NCTS, Organizers: July 7, 2012 National Tsing Hua Der-Chen Chang (Georgetown University, USA) Wen-Ching Winnie Li (NCTS) Univ.

NCTS Summer Course on An Introduction to NCTS, Fluid-Dynamics July 9-20, 2012 National Tsing Hua Instructor: Univ. Ching-Hsiao Cheng (National Central University)

2012 NCTS Mini-Course on Differential Geometry NCTS, July 10-11, 2012 Instructor: National Tsing Hua Huai-Liang Chang (The Hong Kong University of Science Univ. and Technology, HK)

NCTS Summer Course on Dynamical Systems Instructors: Jung Chao Ban (National Dong Hwa University) NCTS, July 10- Changyuan Cheng (National Pingtung University) National Tsing Hua August 23, 2012 Shyan Shiou Chen (National Taiwan Normal University) Univ. Wen-Chiao Cheng (Chinese Culture University) Yun Zhao (Soochow University, China)

NCTS Summer Courses in Probability Theory and Applications NCTS, July 11-August 3, Instructors: National Tsing Hua 2012 Shuenn-Jyi Sheu (National Central University) Univ. Shang-Yuan Shiu (Academia Sinica) Chuan-Hsiang (Sean) Han (National Tsing Hua Univ.)

NCTS Summer Course on Introductory PDEs NCTS, August 6-8, 2012 Instructor: National Tsing Hua Tsai, Dong-Ho (National Tsing Hua University) Univ.

「對稱的物理與數學」暑期研習營 Room 202, Astro- August 06-10, Organizers: Math. Building, 2012 Jung-Kai Chen (National Taiwan University) National Taiwan Pei-Ming Ho(National Taiwan University) University

109 ‹‹- Appendix II Conference & Workshop Time Place School & Special Lecture

Appendix II 2012 Workshop on Graph Theory and Combinatorics & 2012 Symposium for Young Combiantorialists Organizers: Sen-Peng Eu (National University of Kaohsiung) Da Jih Guan (National Sun Yat-sen University) National Sun Yat- August 10-12, David Kuo (National Dong Hwa University) sen University, 2012 Ko-Wei Lih (Academia Sinica) Kaohsiung, Taiwan Li-Da Tong (National Sun Yat-sen University) Tsai-Lien Wong (National Sun Yat-sen University) Hong-Gwa Yeh (National Central University) Xuding Zhu (National Sun Yat-sen University) NCTS Short Course on Number Theory NCTS, August 13-24, Instructor: National Tsing Hua 2012 Ram Murty (Queen's Research Chair & Head, Department Univ. of Mathematics & Statistics, Queen's University, Canada)

Room 440, Astro- One-day Workshop of Algebra August 16,2012 Math. Building, Organizers: August 20,2012 National Taiwan Ming-chang Kang (National Taiwan University) University

2012 NCTS Popular Science Lecture-- How Google works NCTS, Speaker: August 17, 2012 National Tsing Hua M. Ram Murty (Queen's Research Chair & Head, Univ. Department of Mathematics & Statistics, Queen's University, Canada)

NCTS Summer Course on Scientific Computation NCTS, August 20-22, Instructor: National Tsing Hua 2012 Shingyu Leung (Hong Kong University of Science and Univ. Technology, HK)

2012 NCTS Japan-Taiwan Joint Conference on August 27- Number Theory NCTS, September 7, Organizers: National Tsing Hua 2012 Takao Yamazaki (Tohoku University, Japan) Univ. Yifan Yang (National Chiao Tung University)

NCTS Short Course on Introduction to Numerical Methods for Control Systems NCTS, September 3-11, Instructors: National Tsing Hua 2012 Chern-Shuh Wang (National Cheng Kung University) Univ. Yung-Ta Li (Fu Jen Catholic University) Chun-Yueh Chiang (National Formosa University)

Appendix II ‹‹- 110 Conference & Workshop Time Place School & Special Lecture Appendix II NCTS Meet with Prof. Ching-Li Chai NCTS, September 12, Organizer: National Tsing Hua 2012 Wen-Ching Winnie Li (NCTS) Univ. 2012 NCU & NCTS Autumn Young Dynamics Day September 14, Organizers: National Central 2012 Cheng-Hsiung Hsu (National Central University) University Kuo-Chang Chen (National Tsing Hwa University) 2012 NCTS Arithmetic and Algebraic Geometry Day Room 440 Speaker: Astrophysics September 14, Jungkai Chen (National Taiwan University) and Mathematics 2012 Christian Kappen (University of Duisburg-Essen) Building, National Vincent Maillot (CNRS and Inst. Math. Jussieu) Taiwan University Domian Roessler (University of Toulouse III) Chia-Fu Yu (Academia Sinica) 6th Floor, Astro- September 14-15, Representation Theory Math. Building, 2012~ January 11, Instructor: National Taiwan 2013 Shun-Jen Cheng (National Taiwan University) University 2012 NCTS Short Course on Dynamical Systems NCTS, October 5- Instructor: National Tsing Hua December 7, 2012 Ya-Lun Tsai (National Tsing Hua University) Univ. First Annual Southern Taiwan Workshop on Differential Equations Speakers Yi-Hsin Cheng (National University of Kaohsiung) Jong-Shenq Guo (Tamkang University) Sze-Bi Hsu (National TsingHua University) Hsin-Yuan Huang (National Sun Yat-sen University) R204, 2F, NCTS, Jiann-Sheng Jiang (TungFang Design University) October 13,2012 National Cheng Yu-Yu Liu (National Cheng Kung University) Kung University Je -Chiang Tsai (National Chung Cheng University) Guan-Xiang Wang (National Chung Cheng University) Organizers: Yung-Fu Fang (National Cheng Kung University) Tzy-Wei Hwang (National Chung Cheng University) Chun-Kong Law (National Sun Yat-sen University) Tsung-Fang Wu (National University of Kaohsiung)

NCTS Meet with Prof. Chang-Shou Lin NCTS, October 18, 2012 Organizer: National Tsing Hua Wen-Ching Winnie Li (NCTS) Univ.

111 ‹‹- Appendix II Conference & Workshop Time Place School & Special Lecture Appendix II

The Fifth Taiwan Geometry Symposium Room 440 Speakers: Astrophysics October 27, 2012 Shu-Cheng Chang(National Taiwan University) and Mathematics Wan-Keng Cheong (National Cheng Kung University) Building, National Hung-Lin Chiu (National Central University) Taiwan University 2012 NCTS (Taiwan)-POSTECH (Korea) Joint Workshop on Partial Differential Equations Organizers: NCTS, November 8-9, Sze-Bi Hsu (National Tsing-Hua University) National Tsing Hua 2012 Chiun-Chuan Chen (National Taiwan University) Univ. Jann-Long Chern (National Central University) Jaeyoung Byeon (POSTECH, Korea) 2012 NCTS & NCU The Workshop on CR Obata's Theorem November 29, National Central Organizers: 2012 Univ. Hung-Lin Chiu (National Central University) Jann-Long Chern (National Central University)

The Second Cross Strait Workshop in Algebra Speakers Ching-Li Chai (Academia Sinica) Jung-Kai Chen (National Taiwan University) Meng-Kiat Chuah (National Tsing Hua University) Jun Hu (Beijing Institute of Technology) Ching Hung Lam (Academia Sinica) Ngau Lam (National Cheng Kung University) Shu-Yen Pan (National Tsing Hua University) Liangang Peng (Sichuan University) Hebing Rui (East China Normal University) Xiao Tao Sun (Chinese Academy of Sciences) Jianpan Wang (East China Normal University) R204, 2F, NCTS, December 1-5, Quanshui Wu (Fudan University) National Cheng 2012 Jie Xiao (Tsinghua University) Kung University Jeng-Daw Yu (National Taiwan University) Jiping Zhang (Peking University, China) Organizers: Shun-Jen Cheng (Academia Sinica) Shih-Chang Huang (National Cheng Kung University) Ming-Chang Kang (National Taiwan University) Ching Hung Lam (Academia Sinica) Ngau Lam (National Cheng Kung University) Yanan Lin (Xiamen University) Shaobin Tan (Xiamen University) Nanhua Xi (Chinese Academy of Sciences) Jiping Zhang (Peking University)

Appendix II ‹‹- 112 Conference & Workshop Time Place School & Special Lecture Appendix II

NCTS Workshop on Theoretical and Computational Challenges on PDEs Organizers: NCTS, December 13-15, Chiun-Chuan Chen (National Taiwan University) National Tsing Hua 2012 I-Liang Chern (National Taiwan University) Univ. Ming-Chih Lai (National Chiao Tung University) Tai-Chia Lin (National Taiwan University) Wei-Cheng Wang (National Tsing Hua University)

2012 NCTS Distinguished Lectures Series in Applied Math. NCTS, December 17-19, Speaker: National Tsing Hua 2012 Fanghua Lin Univ. (Courant Institute of Mathematical Sciences, New York University)

2012 NCTS & NCU The Workshop of Some December 20, Challenge Problems on PDEs National Central 2012 Organizer: Univ. Jann-Long Chern (National Central University)

2012 NCU & NCTS PDE Day Organizers: December 21, Jann-Long Chern(National Central University) National Central 2012 Cheng-Hsiung Hsu(National Central University) Univ. Meng-Kai Hong (National Central University) Ching-Hsiao Cheng (National Central University)

2012 NCTS Joint Workshop on Complex Systems (Interdisciplinary Workshop between Math. and NCTS, December 21-22, Theoretical Phys.) National Tsing Hua 2012 Organizers: Univ. Hsuan-Yi Chen (National Central University) Kuo-Chang Chen (National Tsing Hua University)

2012 NCTS Mini-course on Integralbe Systems and sub-Riemannian Geometry NCTS, December 24 & Instructor: National Tsing Hua 27, 2012 Alexander Vasiliev (University of Bergen, Norway) Univ. Irina Markina (University of Bergen, Norway)

2012 NCTS Lectures on PDE and Its Application NCTS, December 25-27, Speaker: National Tsing Hua 2012 Chun Liu (The Penn State University) Univ.

113 ‹‹- Appendix II Conference & Workshop Time Place School & Special Lecture Appendix II Taiwan-Japan Joint Conference on PDE and Analysis Speakers: Chiun-Chuan Chen, I-Liang Chern, Jann-Long Chern, Jong-Shenq Guo, Meng-Kai Hong, Chun-Hsiung Hsia, Hsin-Yuan Huang, Jin-Cheng Jiang, Hung-Wen Kuo, Room 937 Astro- Kuo-Ming Lee, Tai-Chia Lin, Chun-Liang Lin, December 26-28, Math. Building, Ching-Lung Lin, Tu Nguyen, Jenn-Nan Wang, 2012 National Taiwan Fumioki Asakura, Ryuichi Ashino, Setsuro Fujiie, University Hiroshi Isozaki, Hiroya Ito, Hiroshi Ito, Mishio Kawashita, Koji Kikuchi, Shiro Kubo, Takeshi Mandai, Kiyoshi Mochizuki, Akira Morimoto Sei Nagayasu, Hideo Nakazawa, Takashi Ohe, Hideo Soga, Hiroyuki Takamura, Hideki Takuwa, Tomio Umeda, Michiyuki Watanabe, Hideshi Yamane,

Appendix II ‹‹- 114 Physics Division Report of the Division Head

e are now in the 4th year of the fourth staffs. They helped us to identify problems and to phase of NCTS Physics Division give recommendations to improve the center to operation ending at the end of 2014. The another level of excellence. We thank our ISAB headquarter is located at the National Tsing Hua members. The report of recommendations by the University (NTHU), jointly hosted by NTHU, ISAB is attached at the end of this introduction. National Chiao Tung University (NCTU) and To implement the recommendations, we need to National Central University (NCU), with sub- have the whole theoretical community to work projects I and II located at National Taiwan together. We are working on more details on how University (NTU) and National Cheng Kung to implement recommendations by ISAB. By the University (NCKU), respectively. Professor Ling- end of the year, we will have more to report. Fong Li served as the division head for the last two years and completed his term at the end of 2011. Professor Xiao-Gang He of NTU (on leave for two years at NTHU) became the head at the beginning of this year. Professors Pei-Ming Ho and Yan-Ten Lu are the PIs for Sub-I and Sub-II, respectively. In 2012, the division operated in a similar fashion as previous years, that is, to have activities carried out by the center research staffs, and by the associated focus groups (FG) with emphasis on consolidating the operation of the center and on enhancing interactions between Physics and International Scientific Advisory Board members at the review meeting from Sep 26-28, 2012. From left to right: Profs. Yue- Mathematics Divisions, main and sub-projects, Liang Wu, Tian-Lun Ho, Naoto Nagaosa, Peter Fulde, Yu-Kao and also FGs. In the following we report some of Chen (Natural Science Division, NSC), Shih-I Chu, Terry Hwa, the highlights. More information about the center Xiao-Gang He (Physics Division head) can be found at: http://www.phys.cts.nthu.edu.tw/ main.php. New Committee Members To consolidate the effective running of the Understand Ourselves Better division, a new ISAB, a new Executive Committee (EC) and a new Program Committee Where are we and where are we going (PC) have been (re)-formed. They are as the concerns some people care about NCTS. To make follows. further improvement, we need understand better the status of NCTS and have visions for the The ISAB members: Professors Shih-I Chu future. For this purpose, the division conducted a (NTU, Taiwan), Da-Hsuan Feng (NTHU, Taiwan), review by our International Scientific Advisory Peter Fulde (Max Planck and APCTP, Korea), Board (ISAB) members in September from 26 to Jason Ho (Ohio State U., USA), Terry Hwa 28. During these 3 days, the ISAB members (UCSD, USA), Bruce McKellar (Melbourne U., worked very diligently and efficiently. They Australia), Naoto Nagaosa (Tokyo U., Japan), and listened reports from the head, the sub-I and II Yue-Lian Wu (KITPC, China). PIs, FG coordinators and some center scientific The EC members: Professors Chong-Saar Chu

Report of the Division Head -›› III-2 (NCTU), Pei-Ming Ho (NTU), Yan-Yen Lu To encourage scientists to engage more with (NCKU), Chung-Yu Mou (NTHU), Chien-Hua center for research and activities, we have newly Pao (NCCU) and Sungkit Yip (Academis Sinica/ implemented an Affiliate Scientist program AS). allowing maximal interaction of the NCTS with university faculties in Taiwan and also abroad. The PC members: Chia-Liang Cheng Affiliate Scientists can come to the center to use (NDHU), Hai-Yang Cheng (AS), Kingman the facilities and suggest activities. Currently Cheung (NTHU), His-Sheng Goan (NTU), more than 30 faculties have joined this program. Choon-Lin Ho (TKU), Hsien-Chung Kao (NTNU), Pik-Yin Lai (NCU), Sy-Sang Liaw This year the center has 12 focus groups (NCHU), Guey-Lin Lin (NCTU), Wei-Min Zhang covering a wide range of research programs. The (NCKU). Focus Groups and The Coordinators this year are: B1-1. Critical Phenomena and Complex Systems, Ming-Chia Wu (NCU and AS) Scientific Staffs and Associates: Old and B1-2. Complexity and Life, Chi-Lun Lee (NCU) New and Chun-Chung Chen (NCTS) The scientific staffs involved with NCTS B2-1. Mesoscopic Physics and Strongly operations are in the following categories. Correlated Systems, Chung-Hou Chung Center Scientists: Professors Hsuan-Yi Chen (NCTU and NCTS), Ming-Chiang Chung (NCU), bio-physics; Cheng-Wei Chiang (NCU), (NCTS) particle physics; Chung-Hsien Chou (NCKU, at B2-2. Numerical Methods for Strongly Correlated sub-II), quantum information science; Chao- Physics, Hong-Yi Chen (NTNU), Qiang Geng (NTHU), particle physics; Daw-Wei Po-Chung Chen (NTHU and NCTS) Wang (NTHU), condensed matter physics. B2-3. Computational Material Research, Chih- Professors Po-Chung Chen (NTHU), Chung-Hou Kai Yang (NCCU/National Chengchi Chung (NCTU) and Yoshiaki Teranishi (NCTU) University) joined the center as center scientists from August B3-1. Cosmology and Particle Astrophysics, this year. Chao-Qiang Geng (NTHU and NCTS) Assistant Research Scholars: Drs. Chun- B3-2. Gravitation, HingTong Cho (TKU/ Chung Chen (bio-physics), Ming-Chiang Chung Tamkang University) (condensed matter physics), Yu-Kuo Hsiao B3-3. Lattice QCD and Hadron Physics, Chung- (particle physics), Jackson Wu (particle physics). Wen Kao (CYCU/Chung Yuan Christian Dr. Chian-Shu Chen (particle physics) has University) recently been promoted to be an Assistant B3-4. LHC Physics, Chuan-Hung Chen (NCKU) Research Scholar. B3-5. String, Yi Yang (NCTU) Drs. Shu-Lin Sun and Yong Tang continues B4-1. Atomic Molecular Optical Physics, Daw- their Postdoc fellow position at the center. Drs. Wei Wang (NTHU and NCTS) Sung-Po Chao from UC Riverside (condensed matter physics), Shih-Hao Ho from MIT (particle B4-2. Quantum Information Science, Alec physics) and Chi-Hsien Yeh from NTU (string Maassen van den Brink (AS), Chung-Hsien and fields) have just joined the Center as new Chou (NCKU) postdocs from fall. Several research staffs left NCTS this year. New Groups They are: Drs. Kazuyuki Furuuchi, Hiroshi Yokoya, Wen-Ming Huang, and Hirotaka Irie. Dr. NCTS obtained some spaces in the new Ming-Chiang Chung will leave us early next year Science Building III completed this year for st to join NCHU as a faculty. activities in NCTU. On Nov. 1 , the office will be

III-3 ‹‹- Report of the Division Head officially inaugurated. This provides a new opportunity to enhance the interaction between NCTS and NCTU. To make maximal use of the precious space available, we have started a new research focus group on Computing Platform for Strong Coupling Systems. Professors Shun-Jen Cheng (NCTU) and Yoshiaki Teranishi (NCTU and NCTS) will act as the coordinators for this working group.

Prof. Wen-Yu Wen presents his awarding talk at the ROC Physical Society annual meeting in Feb 2012.

This year the division also established a new award: Best Research Paper for Postdoctoral Fellows. Postdocs research is one of the main forms of research. Their efforts should be recognized and encouraged. The 2012 selection for this award has completed. Two papers were selected among 11 applications received. The awards were given to Drs. Bailey Hsu (NCTU) and Debaprasad Maity (NTU). NCTU new office opening ceremory on November 1, 2012. From left to right: NSC vice chair of NSC Department of Natural Science I- Fan Ho, NCTU vice president Han-Ping Shieh and NCTS director Wen-Ching Li.

Another new addition to the division is a new FG in theoretical chemistry: Theoretical and Computational Chemistry. Theoretical chemistry is an active branch of sciences in Taiwan. The subjects studied there are closely related to the NCTS research areas. The Natural Science Division of NSC had the vision to expand the NCTS to include such activities. This FG will start its operation next year. The coordinator is Dr. Debaprasad Maity presents 2012 NCTS Physics Division Best Research Paper for Postdoctoral Fellows awarding talk at Professor Cherri Hsu from Institute of Chemistry division Colloquium on Sep 21, 2012. in AS.

International Relations Award Programs The division currently has memorandum of The division puts much emphasis on fostering understandings (MOU) with APCTP, KIAS young scientists. Each year we have an (Korea), KEK (Japan, renewed this year) and Outstanding Young Researcher Award to young Chong-Qing PCU (China). In June and November, faculties in Taiwan. Last year the award was given we signed new MOUs with the College of to Professor Wen-Yu Wen of CYCU. The selection Education of Hue University in Vietnam and the for 2012 will start soon. School of Physics of Peking University in China, respectively. These international links help to

Report of the Division Head -›› III-4 promote our center, and also to contribute to the Activities progresses in theoretical sciences worldwide. This year, we continued many of our previous successful activities through the center and also the FGs. The center has organized more than 300 NCTS seminars at various places through out Taiwan and also about 60 short courses, schools and workshops. We have 3 long term and more than 100 short term international visitors from abroad to give lectures and collaboration on research projects. We highlight some of the activities in the following.

Signing of MOU with College of Education, Hue University, Vietnam in June, 2012.

To make the MOUs enforced effectively, we have appointed some domestic scientists as contact persons for activities. Professors Cheng- Wei Chiang (NCU and NCTS), Kingman Cheung (NTHU), Chao-Qiang Geng (NTHU and NCTS) and Chia-Chu Chen (NCKU) are our contact persons for Korea, Japan, China and Vietnam, respectively. These arrangements allow us to have programs conducted in a more continuous fashion Visit to NCTS by 1997 Nobel Prize in physics laurate Professor to have more significant impact. For example, the Claude Cohen-Tannoudji in May, 2012 collaboration with KEK has been very substantial. Cross Disciplinary Activities by the Each year send 4 postdocs or faculties to KEK for one month. Jointly organizing activities. 4 Division postdocs visited KEP this year. Prof. Hagiwara We have many FGs involving people working from KEK with LHC focus group organized in different fields. Interactions between scientists Madgraph school on Taiwan in May 2012. Also working in different disciplines are important. To each year send 4 postodocs or faculties to KIAS achieve this, the division has now established a and joint activities. We will continue to explore monthly colloquium series to enhance interaction new international working relations with other between scientists working in different fields at institutions. the center. We also started several annual events to have different FGs to come together to learn from each other. On Jun. 2nd, we had an one day mini- workshop: Trends in Theoretical Physics, to provide a platform for discussing progresses in different fields. On Sept. 7th, we had an one day mini-workshop to discuss how FGs conduct research activities. To enhance interactions between Physics and Mathematics Divisions, we have also made efforts to have joint activities. In the summer from 6 to 10 of Aug., sub-I had a joint summer school on Symmetries in Mathematics and Physics. In Dec. from 21 to 22, we will have a Signing of MOU with the School of Physics of Peking joint Mathematics and Physics workshop on University in China in November, 2012. Complexity. Through interactions between scientists working in different fields, we hope to enhance the ability for the center to conduct interdisciplinary research projects.

III-5 ‹‹- Report of the Division Head Conference, Workshops and Schools example, we have sent students and postdocs to: Conferences and workshops are some of the Yongpyong Winter school, Korea in Feb.; effective ways to know the latest research Singapore on Particle and Field in Feb.; CTEQ developments and to know researchers to have school, USA in Jun.; Japan AEPSHEP2012 in new collaborations. Through these meetings, we Oct.; Beyond Standard Model meeting in Vietnam also get chances to invite well known scholars to in Dec.. We already planned to send students next visit Taiwan for collaborations. Among the about year in Feb. to APCTP for a gravity meeting. We 60 meetings 13 of them are international are working on more possibilities to send students conferences. Some of the examples are: The 2012 to some schools in the USA and Europe. Taiwan Int’l Workshop on Ultracold atoms and We have also held 18 schools and courses in molecules in May; The 2nd Workshop on Taiwan to train our students and postdocs. Nanoscience: Carbon Related Systems and Different types of schools are organized to serve Nanomaterials in Jul.; The 7th international different purposes. Some of them are small ones conference on nonlinear science (DDAP7); Int’l on some particular topics. And some of them are workshop on Quantum Condensation 2012 joint bigger ones organized by several countries, (QC’12) in Aug.; Int’l workshop on Correlations such as the Summer Institute on Phenomenology and Entanglement in Many-body Systems Out of of Elementary Particles and Cosmology in August. Equilibrium in Sept.; The 15th Asian Workshop on This is an international summer school running in First-Principles Electronic Structure Calculations; Japan, Korea and Taiwan, originated in Japan 14 9 th Symposium on Cosmology and Particle years ago. Young postdocs and senior PhD Astrophysics in Nov.; Mesoscopic and spin students have chances to give talks along with physics workshop; the 5th Taiwan School on String well know scholar giving review talks. This year and Fields; and 3rd Int’l Conf. on Dark Matter, there were about 130 participants with 70 of them Dark Energy and Matter-antimatter Asymmetry in from Japan, about 10 from Korea, and 1 from Dec.. Some of the smaller domestic ones serve the India. purpose to have rapid response to new developments, for example the Madgraph school Scientific out puts held in May was aimed to train researchers to The center is a research center. Therefore quickly learn new tools for LHC related carrying out research and producing high quality researches. results are expected. Our activities are aimed at providing better platform for this purpose. In 2012, so far, 72 papers with NCTS as one of the affiliations were published and 84 papers with acknowledgement to NCTS. Most of the papers are published in high impact journals in respective fields. For example, the research work by one of our postdoc, Dr. Shu-Lin Sun as the first author, on Gradient-index met-surfaces as a bridge linking propagating waves and surface waves was published in Nature Materials (11, 426(2012)). Many interesting research results have been obtained by center scientific staffs and members Visit to NCTS by Physics Today editor Dr. Toni Feder in June, in FGs. In this annual report, we have collected 2012. research highlights for center scientific staffs and Students and Postdocs Trainings FGs. We will not repeat them here, but The division pays much emphasis on guiding recommend the readers to find more descriptions and training our students and postdocs to conduct of the exciting achievements by reading reports competitive researches by supporting some of following this introduction. them to attend international schools and Xiao-Gang He conferences. We have supported/partial supported November 2012 42 students and postdocs for such purpose. For

Report of the Division Head -›› III-6 Report of the International Scientific Advisory Board of the Physics Division of the National Center for Theoretical Sciences

he International Scientific Advisory I. Some basic remarks Board consisting of: The rapid progress in theoretical physics has • Shih-I Chu (National Taiwan University) affected the style of research done in this field. • Peter Fulde (Asia Pacific Center, Korea), There has always been and will be the brilliant Chairman new idea of an individual scientist. Yet, the majority of researchers are more and more • Tin-Lun Ho (University of Ohio, USA) forming teams. In them each individual • Terence Hwa (University of California, San contributes with his/her very special expertise in Diego, USA) order to solve together a given problem in • Naoto Nagaosa (University of Tokyo and theoretical physics and to contribute this way to RIKEN, Japan) the progress of the field. These cooperations have • Yue-Liang Wu (Chinese Academy of Science, proven to be very effective when the right partners China) find each other. For that reason a number of Centers have been founded worldwide in order to evaluated the Physics Division of the National serve the regional physics community. They have Center for Theoretical Sciences at National Tsing gained worldwide in importance and serve as Hua University and National Chiao Tung catalysts by organizing conferences, workshops University in Hsinchu on September 26-28, 2012. and symposia. In most cases they have also a The committee member Prof. Bruce McKellar special program of support for especially talented (University of Melbourne) was unable to attend young scientists. This way they contribute the meeting because of illness and so was Prof. Da significantly securing the development of the Hsuan Feng because of other commitments. scientific leaders of the next generation. In Asia The Committee had all information available, Pacific regions like Japan, Korea, Mainland which it needed. It got all administrative help and China, Hong Kong and Singapore, Centers of this support, which it requested. Not only the kind have been founded. They play a significant executive board members of the NCTS but also a role in their respective region. Also in the US as number of scientists supported by the Center were well as in Europe they are an integral part of the available for discussions and questions. physics communities and have high priority as regard funding. Taiwan with a relatively large I. Some basic remarks number of small and medium sized Universities II. Structure of the NCTS and its effect on definitely needs a Center of this type, because the research organization number of local researchers is often too small to III. Research program and perspectives for the reach a critical size which is required to keep pace future with the rapidly changing field. Therefore joining IV. Summary forces and forming groups with strong interactions is their only chance of making respectable Appendix: Evaluation of the focus groups contributions to physics. Otherwise they are in a disadvantageous position as compared with their colleagues in other parts of the Asia Pacific region, not to mention the worldwide competition.

III-7 ‹‹- Report of the Division Head All these developments were clearly foreseen attract a fair portion of the most talented young when nearly 15 years ago the National Center for people in a country or a larger region. Building up Theoretical Sciences was founded. Yet, after a a high reputation takes a considerable time, good start its development stagnated after 2002 destroying it can go rather fast. A strongly for various reasons and even turned negative fluctuating support of a field like physics is during the last few years. The numerous changes inefficient hence uneconomical. in the directorship were certainly one of the In the following we evaluate the Physics sources of this unfortunate development. A much Division of the NCTS and make recommendation too small collaboration with experimentalists is for its operation under improved external another reason. Fortunately this period seems to conditions. have ended with the appointment of Prof. Xiao- Gang He. He is showing a strong leadership and is firmly determined to achieve a turn around. Yet, the fact is that after a number of years with II. Structure of the NCTS and its effect considerable budgets cuts the Center is by now on the research organization strongly underfinanced and cannot operate the When the NCTS was founded nearly 15 years way it should. To state it more clearly, it can ago, it was intended that it is located at the neither fulfil properly its purpose nor can it die. National Tsing Hua University and National Chiao This is an unhealthy situation, and also Tung University. It also was decided to divide it uneconomical. The rapid changes in theoretical into two branches, i.e., in one mathematical and sciences require frequent contacts and exchanges one theoretical physics branch. The total funding with the latest ideas and developments in order to was divided too into two equal parts, i.e., the two stay close to the forefront. It is very difficult to get branches obtained equal support each. This has back to the frontier once contact with it is lost. remained so until now. The two branches work With the reduction of support over the last several and operate in parallel, with virtually no cross years, NCTS is increasing its distance to the front connection between them. Attempts which were line year after years. Either the theorists at the made to change this by organizing common different academic institutions in Taiwan have fair seminars seem to have not been successful, yet conditions in comparison with their colleagues in will be repeated. All following remarks and Asia Pacific in the competition for scientific comments refer to the Physics Division of the progress, or Taiwan being among the technology NCTS only. oriented regions in Asia Pacific decides to give up to have a respectable theoretical physics In 2004 it was decided to add two sub-projects community. This decision is a political one, yet it with different locations, i.e., at the NTU and the should be made one way or another. We estimate NCKU sites, to the Center. Since then, the Physics that for an overall satisfactory operation of the Division is physically separated into three Physics Division of the NCTS, a budget increase locations with scientific activities conducted over of 50 % is minimum. Additional increase would 12 focus groups. To them two more new groups be needed to promote it to a state that make will be added in the coming year. bridges to the diverse experimental and The International Scientific Advisory Board engineering communities in Taiwan and enhance noticed that the NCTS Director and the Physics these disciplines. Division Head have changed too frequently in the There is another important aspect we want to last 10 years. This has had a negative effect on the draw attention to. Basic science needs a reliable NCTS. Therefore it makes the following and stable support over a long period of time. Any Recommendation: Extend the term of the support which is given must be such that it can be Division Head to three years with the possibility sustained for a long time. Otherwise it is of a renewal for a second term. The package for impossible to build up any reasonable degree of recruiting the NCTS Director and Division Heads quality in a field like theoretical physics. A high should be made strong enough, in order to make reputation is required of a field which wants to the position more attractive.

Report of the Division Head -›› III-8 The International Scientific Advisory Board The committee also noticed that the finds that the separation into three branches administrative work of the scientists is reduces the unity of this Center making its considerable beyond what is considered headquarter ambiguous to some degree. reasonable at other places. It should also be Considering these situations, it suggests the viewed under the aspect of the rather small following enhancement of centralization. budget. In total, the NCTS has seven administration staff members, i.e., 4 in the Recommendation: It is a general experience that headquarter, two in subproject I (NTU site) and 1 the organization of a good and strong center is in subproject II (NCKU site). Part of the large usually centralized to one place instead of being work originates from the splitting of the Center split into several fractions. The unity of the NCTS into three locations. Also the rapid changes of the and its international visibility will be improved by Heads of Physics Division have amplified the putting the headquarter at one institute/university administrative demands. Therefore the following instead of being split into three branches. External changes are suggested. advisory committee meetings should be held at least bi-annually to determine most important Recommendation: Free the administrative issues on the direction and organization of the demands from unnecessary ballast, i.e., from center. regulations not required by law. In a first step change the annually provided report of the Center The focus group structure has been effective in into a bi-annual report. maintaining the network of theorists in different subject areas. However, the narrowly defined focus of these groups (e.g., 5 in the closely related areas of condensed matter and cold atom physics) III. Research program and perspectives needlessly compartmentalizes the related for the future disciplines and impedes cross-fertilization. The research supported by the NCTS is carried on hand by scientists directly hired by the NCTS Recommendation: We recommend that the focus and on the other by the theoretical physicists in groups be restructured into 6 thematic areas, Taiwan, who are participating via the focus group whose directions should be reevaluated at a 2-year to its success. Currently the Physics Division interval. The streamlined group structure will consists of the Division Head, 9 center scientists, encourage collaboration, reduce paper work, and 5 assistant research fellows and 4 postdocs. In the put limited resources into more effective use. focus groups almost all theoretical physicists in Under the new organization, each thematic Taiwan are involved. This reemphasizes the area would inherit the current activity budget importance the NCTS has for the physics allocated to the corresponding focus groups so community in Taiwan. that there is no net change in the operational An evaluation of the program of the 12 focus budget during the transition. Each thematic area groups is given in the Appendix. The overall can be represented by 1-2 coordinators, along with impression has been that the scientists are highly an executive committee, nominated by the faculty motivated, that they are struggling hard to keep up members in the area. The coordinator(s) will with the fast development of theoretical physics decide on the use of activity budget in and that they are making the best out of the consultation with the executive committee as is limited resources they have. Despite these the current practice. In addition, the coordinator(s) disadvantages in a few areas some impressive together with the Head of the Physics Division contributions to the respective fields could be and the two sub-project leaders will form a made. divisional executive board, and make decision on the distribution of additional resources described Here we want to concentrate on two issues of below in consultation with an international research, which require rethinking – The first one advisory board. concerns the collaborations with experimentalists.

III-9 ‹‹- Report of the Division Head They are much too small and need considerable internationalization of theoretical sciences in expansions. The International Scientific Advisory Taiwan. This is of great importance because the Board found out that the low interaction with competent group of theorists that the government experimental physicists is a major reason that the has hired over the past decade need to be renewed NCTS budget has decreased so much over the last and reconnected with advances at the cutting edge few years. The NCTS should not expect a at a regular interval, or else the effectiveness of significant increase in its budget before these researchers will be permanently improvements of the collaborations with marginalized. The additional programs, which we experimental groups become visible. The NSC is propose should not be financed from the already apparently not willing to invest more money in the very limited theme-areas (previously focus NCTS, if it does not have the feeling that the groups) activities. physics community of Taiwan as a whole, i.e., including experimentalists will profit from a Recommendation: A small number of annual budget increase of the NCTS. We therefore high-profile symposia should be initiated. suggest. Every year 2-3 high profile symposia in selected theme areas should be held, with Recommendation: The NCTS should make a sufficient support to attract the participation of a major effort in order to increase the interaction number of world-leading experts in the selected with the experimentalists. fields, and their possible follow-up visits to The second issue is that of competition within selected member campuses. These symposia will the NCTS. Until now the small budget is increase the access of local students and faculties distributed rather evenly among the twelve focus to the latest development across the spectrum in groups, and hence each focus group is running physics. The symposia topics (together with with very tiny money compared with the world international organizers and key participants) will standard. An increase in the budget should be used be proposed by the theme areas and selected by to introduce competition to the NCTS. Additional international reviewers. The selection will be resources should be distributed to the proposed based on the quality and timeliness of the science themes of research as well as conferences/ and its key participants including their likeliness workshops on a competitive basis. The hiring of to participate), and the potential to foster the post-docs is better determined not by the development of new research activities in Taiwan individual focus groups but by the headquarter (including making new bridges between theory through a competition among the candidates. and experiments). At least for the first several years, it is recommended that these symposia be Recommendation: Budget increases should be held in the NCTS headquarter to boost the used to build up and strengthen competition based international recognition of the NCTS brand on quality among different research areas. name. Plans for the future depend to a large extent on Recommendation: Distinguished visiting faculty the proposed increase of the budget. Without an should be invited. increase activities will remain at the present level and eventually stagnate. The following New Funds should be used to support recommendations are based on increased intermediate- to long- term visits (e.g., weeks to resources. months) by leading experts to give lecture series and help chart the growth of new research To keep up with the very rapid development of directions (but not to support on-going theoretical physics worldwide, and to maintain the collaborations). Named lecture series may be competitiveness of theoretical physics in Taiwan established to boost the prestige of such at a level on par with other blossoming efforts in visitorship. Proposals from the theme areas will be the Asia Pacific region, the International Advisory decided by the NCTS board, in consultation with a Board recommends the following expansion of board of international advisors. programs and activities to enhance the

Report of the Division Head -›› III-10 Recommendation: Create a new form of Post- Recommendation: In order to secure the future of doctoral fellowship. the NCTS, an increase in funding should be used to extend the present program by strongly A number of named post-doc fellowships focusing on internationalization, i.e., by coupling should be established to make Taiwan competitive the physics community in Taiwan more strongly in attracting quality post-docs with respect to the to the international one. rest of the Asian-Pacific region. A centralized pool of applicants will be distributed to the thematic areas for initial review. Those selected by each thematic area will be considered by the NCTS IV. Summary executive board, in consultation with the international advisors, based on the quality of the The International Scientific Advisory Board is applicants and programmatic balance. These fully convinced that Taiwan needs definitely a fellowships are in addition to the post-doc Center like the NCTS. Only with a well- allocation from the current NCTS budget and functioning Center the theoretical physicists in expands upon the scope of the current research Taiwan have a chance to compete scientifically fellow program. The board will decide on the with their colleagues in the Asia-Pacific regions. appropriate level of support such that the desired At present, the Center is considerably candidates are not lost due to salary limitation or underfinanced and a budget increase by at least the term/level of the appointment. These post-doc 50% is necessary to make it well-function. A fellows will have the freedom to decide on where political decision is required whether or not and with whom to work in any of the thematic Taiwan with a technology-oriented economy areas. wants to have a theoretical physics community of a quality like that in the Asia-Pacific region. If this Recommendation: Student and post-doc training is the case, the Center has to be better financed. should be considerably enlarged. Weaknesses of the present structure are pointed out and recommendations to overcome them are Funds will be provided to support the made. The enthusiasm of the scientists is participation of local students and post-docs in admirable and so is the way they cope with the advanced international schools and workshops, as very small resources they have available. The well as to send them for longer-term visits at leadership of Prof. Xiao-gang He is remarkable collaborators’ home institutions, to learn new and guarantees for a good future of the Center topics and approaches, and establish network with provided the budget problem can be resolved. new theoretical communities. Requests will be made by each thematic area, and funding decisions will be made by the divisional executive board of NCTS to reward efforts to open new Appendix: Evaluation of the research of frontiers and transition into new fields. the focus groups. The advisory board believes that the In the following the scientific work and results competition for centralized resources supporting of the twelve focus groups are discussed in detail. the above programs/activities will help to Atomic, Molecular, and Optical (AMO) Physics stimulate the growth of new research activities within and between the thematic areas, while This Focus Group (FG) is aiming at research creating name recognition for NCTS on some of the recent frontiers in AMO physics, internationally. Despite the centralized decision- including strongly correlated effects in cold atoms making process, this system aims to channel and molecules, dynamical properties of weakly resources (e.g., post-docs and visitors) directly to interacting Bose gases, atom-light interaction and the individual thematic area and universities manipulation, and atomic structure theory and (compared to the current system, which has, e.g., spectroscopy. The committee is impressed by the post-docs centralized at one or two locations.) quality of the works, particularly in the study of strongly interacting cold atoms and polar

III-11 ‹‹- Report of the Division Head molecules, BEC dynamics, EIT and slow light optics in US, this focus group may want to physics. They have organized an international consider building connections to the US centers workshop on ultracold atoms/molecules, and the should the funding situation improve in the future. 9th annual AMO summer school in 2012, both LHC Physics were running successfully. The summer school is useful for training the graduate students on some The Focus Group mainly focuses on the topics: forefront AMO physics. There has been some investigation of physics of electroweak fruitful collaboration between international phenomena; physics beyond the SM; flavor visitors (including both theorists and physics and CP violation; exploration on the experimentalists) and the active AMO members in nature of dark matter. The Focus Group has this FG. But the research outcome can be still organized weekly seminars and journal clubs, the strengthened. schools and workshops, and reached its main goals, such as: training the students and young The AMO FG currently consists of about 30 postdocs to do the creative works, establishing the faculty members, including both theorists and local and international collaborations and experimentalists, 5 postdocs, and around 100 increasing the international visibility, especially students. The total size of the FG is less than ½ of responsing to the newly measured experimental the Taiwan AMO community. The AMO physics results and hot topics. The LHCb experiment has in Taiwan has another major and very active firstly measured an unexpected large CP violation research community in the study of highly in D-meson decays, and confirmed by CDF. To nonlinear multiphoton processes in intense make a better understanding, the group members ultrashort (femtosecond and attosecond) laser have analyzed in detail the phenomenon in the SM fields. This field has not yet been included into the and concluded that the SM cannot solve the NCTS research scope so far and should be anomaly. Then they have studied the contributions considered for the future. Also the quantum from colored scalar bosons and provided a computing/information research in general can be possible explanation. also categorized into the AMO physics domain. Cosmology and Particle Astrophysics Quantum Information The Focus Group has concentrated on the The Quantum Information focus group consists studies of dark energy, dark matter, neutrino of 11 theorists, focusing on four topics: Quantum physics. Investigating the nature of dark matter Decoherence, Quantum Entanglement, Quantum and dark energy is one of the biggest challenges Control, and Relativistic Quantum Information. today in the fields of cosmology and particle The networking of this group is very good. With physics. Some interesting progresses have been the little amount of funding received, this focus made, including: the construction of so-called group was able to find other sources to “Teleparallel Dark Energy” model, by introducing supplement their activities to run a large number a canonical scalar field and allowing for a non- of mini-workshop and schools organized. These minimal coupling with gravity, to explain the activities are highly beneficial, training lots of present accelerating universe. A new neutrino students and leading to successful collaborations mixing pattern was proposed to reproduce the between different members in the group as well as experimentally favored neutrino mixing angles with scientists aboard. and masses. The Group has paid attention to the The areas being studied by the focus group are training of graduate students and postdocs through major topics in quantum information theory. The advanced courses, international cooperation and area of relativistic quantum information science is exchange programs, the attendance of a new recent development. Because of limited international schools and visits to foreign research funding, the workshops and school are on a small institutes. They have also tried to increase the scale, and there are relatively few visitors and visibility by organizing various activities collaborators from the United States. Because of including seminars, working groups, workshops, the large number of world leaders in quantum jointing meeting and retreats.

Report of the Division Head -›› III-12 String Theory analytical methods. The special attention is paid to quantum chromodynamics(QCD), which include The String Theory Group has greatly been lattice QCD methods, effective field theories, strengthened through the support of NCTS. Now gravity/gauge duality approach or AdS/CFT. the Group committee consists of 14 faculty These approaches have well been applied to the members. The research goal is quite unique, by studies on the properties of hadrons, such as making the string theory as a realistic unified hadronic matrix elements, transition form factors, theory of four basic forces of nature, and the the fragmentation functions, the phase structure of string theory method to be applicable to other quark-gluon plasma. The regular activities of the fields, such as: hadronic physics and condensed Focus Group are seminar series, mini-workshops matter physics. The major activities of the Focus and schools, international visiting and Group include: regular seminar series, schools collaborations. The highlighted researches include series, journal clubs, study groups, mini- the first lattice computation of heavy hadron axial workshops. These activities create a good current matrix elements, the study on the IR atmosphere for discussions and collaborations, behavior of running coupling constant in SU(3) especially between students and young postdocs. gauge theory with 12 flavors, hadronic two body Some interesting progresses include: the Group decays of B-meson with hard-pion chiral members attempted to write down the action of perturbation theory, simulation for strong Yukawa M5-brane and D-brane in R-R field background, couplings with Higgs. Some of research directions which is crucial to understand the M theory. They and activities overlap with the LHC group and have also applied the Gravity/Gauge duality to the string theory group. strongly correlated system, such as holographic QCD, superconductor, topological insulator, Computational Material Research dipole coupling effect, Hall viscosity, The committee evaluates the activities of this entanglement entropy. FG with this limited budget of the program. This Gravitation field is now becoming more and more important in condensed matter physics, and the incubation of Quantization of gravity and gravitational wave the young researchers is an urgent demand. In this detection are the hard task in the gravitation study. respect, it is important that they had organized 3 The main research directions of the Focus Group courses for the educational purpose in 2012. As are canonical gravity, quantum field fluctuations, for the researches, even though they succeeded in gravitational wave and Black Hole physics. The some international collaborations which resulted major activities of the Focus Group include the in ,e.g., a Nature Physics paper in 2012, the annual Asia-Pacific School/Workshop on number of publications (29 in 2011, 9 in 2012) is Cosmology and Gravitation initiated by the Focus not satisfactory considering the members involved Group 5 years ago, the mini-workshop series, PhD (29 faculty and 10 PDs). This program will be student seminars, international visiting programs more efficient by promoting the collaborations and collaborations. The main progress made by within FG and with the foreign groups including the group members was the realization of a new the experimental people. formalism of the Horava gravity through 3D diffeomorphism invariance, which may be helpful Numerical methods for Strongly Correlated to formulate a consistent theory of quantum Physics gravity. The group remains too small to create the This FG is aiming at developing the numerical visibility, it may combine with the string theory methods to reveal the many-body problems in group and cosmology group to enhance its condensed matter physics. The committee activities. recognizes their continued efforts both in the Lattice QCD and Hadron Physics researches and education. However, the Taiwan community of this field is not yet large enough to The Focus Group concentrates on the be visible worldwide, although there are several investigation of the nonperturbative aspect of remarkable achievements such as the magnetic gauge field theories with numerical and/or monopole in quantum spin ice (Nature

III-13 ‹‹- Report of the Division Head Communications). The scope of this FG has some Such symptoms are not uncommon during the overlap with that of Computational Material initial phase of many statistical physicists who Research FG, and their collaborations will be have moved successfully to biological physics in beneficial. the past decade. However, too long of an Strongly Correlated Electron Systems and exploratory phase would undoubtedly dampen the Mesoscopic Physics momentum. Some tips may be useful: The complex phenomena in biology are often richer This FG is aiming at the focused research on and more interesting than what one could initially most of the recent frontiers in condensed matter imagine. Thus, instead of searching for a subtopic theory, i.e., quantum entanglement, quantum of biology that would suit some expertise in phase transition, strong electron correlation, statistical physics, it may be more profitable to topological phases, spintronics, and follow an interesting phenomenon and let it lead unconventional superconductors. The committee one to different topics in statistical physics. If it is recognizes their efforts on the researches and also possible to connect to local biologists open education in spite of the small budget. They have minded about physicists’ line of enquiry, then take several collaboration projects with the prominent full advantage of the connections. If not, then it foreign researchers, but only a few of the FG may be useful to go to conferences/workshops at members are involved in them. Since the topics the interface of physics and biology, since the are diverse in this field, it would be better that biological topics discussed there have often been they increase the collaboration within the pre-selected to be more amendable to physicists’ domestic people also to strengthen the Taiwan approach, and the biologists there are self-selected community of this field. It is also desirable to to be physics-friendly. [Examples of such increase the number of publications, e.g., 2-3 per conferences include the annual q-bio conferences each active members/year to improve the visibility (summer and winter series), GRC on stochastic of this FG and the center. physics and biology, annual biology-related “Critical Phenomena & Complex Systems” and program at KITP Santa Barbara.] As connection to “Complexity & Life” frontier problems in biology is the driving force for success in this endeavor, it is recommended These two focus groups share similar topics that the NCTS fund be used to support meetings/ (nonlinear dynamics, biophysics, and complex conferences with leading experimentalists systems), have significant overlap in the (biologists and biological physicists) to explore participating faculty and in the sponsored and evaluate new fields and establish connections, activities (the most significant event last year and to support sending students/post-doc to the being “Dynamic Days Asia Pacific 7”). labs of collaborators for joint studies. FG Differences appear to lie in style: The Critical members are also advised to look into exploring Phenomena group tends to emphasize more opportunities at KITPC in Beijing, to bring long formal results (exact solution and results, programs in biological physics into the region universality, large-size limit, finite size correction, (with KITPC bearing the major program cost). etc.) while the Complexity group tends to be more Such programs are usually quite competitive phenomenological, and strives to be closer to during the summer months, but not so much in the experimental studies. Both groups, comprised of spring and fall. The latter may be good time to run researchers well trained in statistical mechanics these programs for researchers based in Taiwan. and soft-matter physics, are struggling to make bridges to biology and complexity. The publication record is a testament of the dedicated For the International Scientific Advisory Board efforts made by quite a number of researchers in

various directions during this trial period. It is however quite clear that the two focus groups have yet to find a solid bridge that would couple Prof. Dr. Peter Fulde them tightly to a flourishing subject among the vast subfields of biology and complexity.

Report of the Division Head -›› III-14 NCTSPHYS ISAB MEETING Sep 26~28, 2012 @ meeting room P512

TIME SPEAKERS (All slots include both talk and question times)

Sep 26 09:00-09:10 ISAB meeting 09:10-10:20 Xiao-Gang He: NCTS Physics Division 10:20-10:40 Coffee 10:40-11:30 Pei-Ming Ho: subprojects I at NTU 11:30-12:20 Yan-Tian Lu: subprojects II at NCKU 12:20-14:00 Lunch 14:00-14:25 LHC Physics, Coordinator: Chuan-Hung Chen (NCKU) 14:25-14:50 Gravitation, Coordinator: Hing-Tong Cho (TKU) 14:50-15:15 Cosmology and Particle Asrophysics, Coordinator: Chao-Qiang Geng (NTHU & NCTS) 15:15-15:40 String, Coordinator: Yi Yang (NCTU) 15:40-16:00 Coffee 16:00-16:25 Critical Phenomena and Complex Systems, Coordinator: Ming-Chya Wu (NCU & AS) 16:25-16:50 Quantum Information Science, Coordinator: Chung-Hsien Chou (NCKU) 16:50-17:15 Computational Material Research, Coordinator: Chih-Kai Yang (NCCU) 17:15-17:40 Numerical Methods for Strongly Correlated Physics, Coordinators: Po-Chung Chen (NTHU & NCTS) 18:00 Leave for Dinner at Pong-Yuan Restaurant Sep 27 08:30-09:30 ISAB meeting 09:30-10:30 Meet with Chaif of Department of Natural Science, NSC 10:30-10:50 Coffee 10:50-11:15 Atomic Molecular Optical Physics, Coordinator: Daw-Wei Wang (NTHU & NCTS) 11:15-11:40 Mesoscopic Physics and Strongly Correlated Systems, Coordinator: Chung-Hou Chung (NCTU & NCTS) 11:40-12:05 Lattice QCD and Hadron Physics, Coordinator: Chung-Wen Kao (CYCU) 12:05-12:30 Complexity and Life, Coordinator: Chung-Chun Chen (NCTS) 12:30-13:30 Lunch 13:30-13:55 Hsuan-Yi Chen (Center scientist: NCU & NCTS) 13:55-14:20 Cheng-Wei Chiang (Center scientist: NCU & NCTS) 14:20-14:45 Ming-Chiang Chang (Assistant research scholar) 14:45-15:10 Yu-Kuo Hsiao (Assistant research scholar) 15:10-15:30 Coffee 15:30-17:20 ISAB meeting 17:20-18:20 ISAB meets NCTS main, subs heads to ask questions and clarifications 18:30 Dinner in NTHU Restaurant Sep 28 08:30-12:30 ISAB meeting, to finalize recommendations and outline report 12:30-13:30 Lunch 13:30-14:30 ISAB meeting, to finalize recommendations and outline report ISAB meets main, subs heads, FG coordinators, center scientist, scientific staffs to present review 14:30-15:00 recommendations 15:00-16:00 Meet with NTHU President 16:00-17:00 ISAB visit NCTSPHYS office at NCTU 18:30 Dinner with NTHU & NCTU presidents at Pong-Yuan Restaurant

2008 2009 2010 2011 2012 2013

National Center for Theoretical Sciences. Physics Division III-15 ‹‹- Report of the Division Head Highlights of Programs Complex System

Focus Group on Critical Phenomena and Complex Systems

Coordinator: Ming-Chya Wu (National Central University/Academia Sinica; email: [email protected])

I. Brief Description II. Activities As the distribution of the host institutes of our group members is distant in Taiwan, the academic activities of this focus group have been designed he main goal of Critical Phenomena and to enhance the interactions and communication Complex Systems focus group is to work among group members, and to train students. Four on various model systems to gain a better types of activities have been organized to achieve understanding of critical phenomena and then this purpose: apply the methods and concepts from such studies International conference: scale of 100 or 200 to interdisciplinary problems, especially the participants, 1/year (sponsorship: NSC, IPAS, complex systems. The topics under study include: NCTS, APCTP, Host Institutes). 1. lattice models of critical systems (such as Ising, • Potts, dimer models, etc), Broad topics in statistical physics, biophysics, and complex systems 2. self-organized critical systems (such as sandpile • model), Plenary lectures / invited talks / contributed papers 3. structure and properties of biological • macromolecules (such as DNA, RNA, and For people interested in the meeting protein), International workshop: about 25 participants, 4/year (sponsorship: IPAS/NCTS). 4. biochemical networks and molecular biological evolution models, and • Specified topics closely related to our focus group 5. models for biomedical, economic and social systems. • Invited talks / work reports The members are grouped together for their • For people interested in the meetings common research interest in the topics mentioned Local workshop: about 25 participants, 2+/year above. In September of 2012, there are 37 (sponsorship: NCTS, Host Institutes). members, including 19 faculties, 2 visiting scholars, 3 postdoctoral fellows, and 13 students • Specified topics of our focus group (see NCTS website for details). The coordinator of • Work reports / Student reports this focus group in 2012 is Dr. Ming-Chya Wu, who is an Associate Research Fellow of Research • Mainly for focus group members Center for Adaptive Data Analysis, National Irregular seminars (sponsorship: IPAS / NCTS) Central University, and Joint-appointment • Assistant Research Fellow of Institute of Physics, Specified meetings for Knowledge-enrichment Academia Sinica. • Invited talks

Highlights of Programs -›› III-16 • For people interested in the seminars Complexity and Life focus group and give lectures. For example, Prof. Gang Hu (Beijing We encourage junior colleagues and students to normal university, China) gave lectures in our participate in our activities, thus several measures group meeting, and NCTS summer workshop have been proposed. For example, in 2012, we in Institute of Physics, Academia Sinica, and in have hosted Dynamic Days Asia Pacific 7 Department of Physics of National Central (DDAP7): The 7th International Conference on University. Furthermore, David B. Saakian Nonlinear Sciences and the 11th Taiwan was invited by Prof. Gang Hu to visit Beijing International Symposium on Statistical Physics normal university. (homepage http://www.phys.sinica.edu. tw/~statphys/activities/conference/2012/), in (2) Chin-Ning Chen and Yu-Hsin Hsieh (PhD which there were 191 participants from 15 student of National Taiwan University) joined countries, among which 75 were students who the working group of Chin-Kun Hu and Mai only needed to pay half of the registration fees and Suan Li (Polish Academy of Sciences) to study part of them also received financial supports. simple models for protein aggregation, via the Outstanding presentation awards (sponsored by interactions in the activities of the focus group. EPL) were awarded to six students who gave good (3) Ming-Chya Wu and Xuhui Xiao (PhD student oral presentations and posters to encourage their of National Taiwan University) started to study participations. fibrillation transitions of protein secondary Our other activities (bio-monthly workshop structures, inspired by the lectures given by series; for details please visit the webpage: http:// Prof. Jian-Min Yuan (Department of Physics, proj1.sinica.edu.tw/~statphys/activities/workshop. Drexel University, Philadelphia, USA) in our html) also encourage young colleagues and workshops in 2011 and 2012. students to present their works in the meetings. (4) Two PhD students (Ms. Fangyan Ouyang and Local workshops are designed especially for Mr. Xinfei Jiang of Zhejiang University) visit students: they can present in Chinese or English Taipei for 45 days from Aug 5, to study depending on their wishes. We have 8 new group financial systems with our focus group. The members (2 faculties, 1 postdoc, 5 students) exchange program was confirmed in April joined us in summer of 2012 after attending our when his advisor, Prof. Bo Zheng visited activities (DDAP7 and workshops). Institute of Physics, Academia Sinica and gave a talk in our workshop in April. III. Visitors and International Collaborations IV. Highlights of Research Results Our focus group have been benefit much from A. Discovery of a new universal geometrical the supports of Institute of Physics, Academia factor of protein conformation, which can be Sinica, which funds NCTS for inviting visitors used to validate protein 3D structures (EPL, 96, abroad. In this year, our group members have 68005 (2011)). This work was presented in the invited more than five scientists using the supports 17th Biophysics Conference, the annual of IPAS-NCTS fund (mainly for airfares) to visit meeting of the Biophysics Society of ROC and our focus group and establish collaborations. attracted lots of attentions. NCTS provided living supports to some of them. These include: B. The first definite and precise study on phase diagram and universality of the Lennard-Jones (1) Three speakers of DDAP7 conferences gas-liquid system, which shows the system (supported by NSC, IPAS, IPAS-NCTS funds) belongs to the Ising university class (JCP 136, stayed in Taiwan for one more week after the 204102 (2012)). This work has been listed as conference (living expenses supported by the top 10 most read paper of JCP in April and NCTS) to visit our focus group and the June of 2012.

III-17 ‹‹- Highlights of Programs V. Publications [10] S. G. Gevorkian, A. E. Allahverdyan, D. S. [1] D. B. Saakian, A. Martirosyan, C.-K. Hu and Gevorgyan and C.-K. Hu, “Glassy state of Z. R. Struzik, “Exact probability distribution native collagen fibril?”, EPL 95, 23001 function for multifractal random walk models (2011). for stocks”, EPL 95, 28007 (2011). [11] B. K. Singh, P. E. Parham and C.-K. Hu, [2] Z. Kirakosyan, D. B. Saakian and C.-K. Hu, “Structural perturbations to population “Finite genome length corrections for the skeletons: transient dynamics, coexistence of mean fitness and gene probabilities in attractors and rarity of chaos”, PLoS one 6, evolution models”, J. Stat. Phys 144, 198 24200 (2011). (2011). [12] M.-C. Wu, M. S. Li, W.-J. Ma, M. Kouza, [3] D. B. Saakian, C. K. Biebricher, C.-K. Hu, and C.-K. Hu, “Universal geometrical factor “Lethal Mutants and Truncated Selection of protein conformations as a consequence of Together Solve a Paradox of the Origin of energy minimization”, EPL 96, 68005 (2011). Life”, PLoS one 6, 21904 (2011). [13] F.-Y. Wu, W.-J. Tzeng, and N. Sh. Izmailian, [4] A. Martirosyan and D. B. Saakian, “Exact “Exact solution of a monomer-dimer results in the large system size limit for the problem: A single boundary monomer on a dynamics of the chemical master equation”, a nonbipartite lattice”, Phys. Rev. E 83, 011106 one dimensional chain of equations, Phys. Rev. (2011). E 84, 021122 (2011). [14] D. B. Saakian, “Directed random walks on [5] C. T. Shih, Y. Y. Cheng, S. Wells, Rudolf A. hierarchical trees with continuous Romer, and C. L. Hsu, “Charge Transport in branching:A renormalization group Cancer-Related Genes and Early approach”, Phys. Rev. E 85, 011109 (2012). Carcinogenesis”, Comp. Phys. Commu. 182, [15] D. B. Saakian, M. W. Deem and C.-K. Hu, 36 (2011). “Finite population size effects in quasispecies [6] C. T. Shih, H.-W. Lin, A.-S. Chiang, model with single-peak fitness landscapes”, “Statistical Analysis and Modeling of the EPL 98, 18001 (2012). Temperature-Dependent Sleep Behavior of [16] D. B. Saakian, “The calculation of multi- Drosophila”, Comp. Phys. Commu. 182, 195 fractal properties of directed random walks (2011). on hierarchic trees with continuous [7] C.-H. Yang, C.-L. Hsu, N.-Y. Chen, and C.-T. branching”, J. Stat. Phys. P04007 (2012). Shih, “Temporal Dynamics of Site Percolation [17] D. B. Saakian, “Markov-switching in Nanoparticle Assemblies”, Comp. Phys. multifractal models as another class of Commu. 182, 71 (2011). random-energy-like models in one- [8] A.-S. Chiang, C.-Y. Lin, C.-C. Chuang, H.-M. dimensional space”, Phys. Rev. E 85, 031142 Chang, C.-H. Hsieh, C.-W. Yeh, C.-T. Shih, (2012). J.-J. Wu, G.-T. Wang, Y.-C. Chen, C.-C. Wu, [18] V. Galstyan, and D. B. Saakian, “Dynamics G.-Y. Chen, Y.-T. Ching, P.-C. Lee, C.-Y. Lin, of the chemical master equation, a strip of H.-H. Lin, C.-C. Wu, H.-W. Hsu, Y.-A. Huang, chains of equations in d-dimensional space”, J.-Y. Chen, Hsin-Jung Chiang, C.-F. Lu, R.-F. Phys. Rev. E. 86, 11125 (2012). Ni, C.-Y. Yeh, and J.-K. Hwang, “Three- Dimensional Reconstruction of Brain-wide [19] O. S. Rozanova, J.-L. Yu, and C.-K. Hu, “On Wiring Networks in Drosophila at Single-Cell position of vortex in a two-dimensional Resolution”, Current Biology 21, 1 (2011). model of atmosphere”, Nonlinear Anal. Real World Appl. 13, 1941 (2012). [9] K. G. Petrosyan and C.-K. Hu, “Protein- mediated Loops and Phase Transition in [20] N. Sh. Izmailian, “Universal amplitude ratios Nonthermal Denaturation of DNA”, J. Stat. for scaling corrections on Ising strips with Mech. P01005 (2011). fixed boundary conditions”, Nucl. Phys. B 854, 184 (2012).

Highlights of Programs -›› III-18 [21] M.-C. Wu, “Damped oscillations in the ratios [26] D. B. Saakian, Z. Kirakosyan, and C.-K. Hu, of stock market indices”, EPL 97, 48009 “Biological Evolution in a Multidimensional (2012). Fitness Landscape”, Phys. Rev. E, accepted. [22] N. Sh. Izmailian, P. Ruelle, and C.-K. Hu, [27] Z. Kirakosyan, D. B. Saakian and C.-K. Hu, “Finite-size Corrections for Logarithmic “Eigen model with correlated multiple Representations in Critical Dense Polymers”, mutations and solution of error catastrophe Phys. Lett. B 711, 71 (2012). paradox in the origin of life”, J. Phys. Soc. Jpn., accepted. [23] C.-L. Chang, D. Y. Lando, A. S. Fridman, and C.-K. Hu, Thermal Stability of DNA with [28] D. Y. Lando, E. N. Galyuk, C.-L. Chang, and Interstrand Crosslinks, Biopolymers 97, 807 C.-K. Hu, “Temporal behavior of DNA (2012). thermal stability in the presence of platinum compounds. Role of monofunctional and [24] H. Watanabe, N. Ito, and C.-K. Hu, “Phase bifunctional adducts”, J. Inorg. Biochem., diagram and universality of the Lennard- accepted. Jones gas-liquid system”, J. Chem. Phys. 136, 204102 (2012). [25] K. G. Petrosyan and C.-K. Hu, “Stepwise transition to higher degrees of coherence in a random network of phase oscillators”, EPL 99, 10008 (2012).

III-19 ‹‹- Highlights of Programs Focus Group on Complexity and Life

Coordinators: Chun-Chung Chen (NCTS; email:[email protected]), Chi-Lun Lee (National Central University; email:[email protected])

I. Brief Description on more specialized topics. Starting this year, a new joint seminar series is held between NCTS and the Physics Department of NTHU on soft-matter physics. This is a omplexity and Life focus group aims to student-oriented series consists mostly of promote collaboration and facilitate introductory talks by researchers from various research efforts in the field of complex systems institutes in Taiwan on their current research, as and biophysics. This field is characterized by a well as presentations by students reporting on wide range of research topics ranging from published work of recent advances in the field. molecular scale to global social and ecological This seminar series has successfully attracted systems, as well as fast moving progresses and more than 40 students including some graduate shifting focuses driven by technical advances. students from different research backgrounds and The current research interests of the group the regular participation of above 5 faculty members include molecular motors, protein members. It is serving well to encourage the folding, and DNA interaction with nano participation of new researchers to the field. structures; membrane dynamics, motility, and bacterial dynamics; neural networks and cardiac Besides the regular seminar series, visitors, muscular interaction; hydrodynamics of structured sponsored meetings and conferences, there are 3 particles, granular and chain dynamics, colloids major workshops this year: and foams; disorder in crystal defects and The 2012 Bio-Soft Matter Winter School was crumbling sheets; bioinformatics, complex held in January 15~17 in NCKU, allowing the PIs networks, traffic, and evolutionary dynamics, etc. in the research field to present and discuss their As a diverse field, fragmentation is a nature research results in details. This event was tendency. However, as a fast moving field, the arranged right before and in coordination with the risks of duplicated efforts and repeated failures are annual meeting of PSROC, so that the two events high. The focus group direct its effort at building did not share the same invited speakers. In this a efficient research network in Taiwan by meeting, 18 PIs in the field of the FG presented improving communication between group their research results. In contrast with the talks at members and promoting participation of new PSROC, plenty of time was allocated after each researchers. talk so that the participants could discuss their works extensively. A future meeting of the same nature will also be held in 2013 on Eastern II. Activities Taiwan, right before the annual meeting of PSROC. We plan to organize such a meeting The main activities of the focus group include annually in such a way that each PI in the field of five seminar series and feature workshops. In the FG will have a chance to report findings and NCU, the Bio-Soft Matter Seminars is a student- receive feedbacks on his/her work every 2 to 3 oriented series serving as a forum for PIs to years. introduce their research topics and for young researchers to present their endeavors. While, the The Complex Systems Symposium was a System Biology Colloquium provides a channel student symposium held in May 25~27, featuring for the researchers of the field to present their 21 student speakers of graduate and undergraduate recent advances. In NCHU, the Biophysical levels, reporting on the general topics of their Journal Club is geared to a more general audience researches in the field. Through this symposium, while the Nonlinear Phenomena Seminars focus the students had chances to present to and discuss

Highlights of Programs -›› III-20 their research works with other students, postdocs membrane protein in the membrane can be and PIs of the field. Plenty of discussion time was simulated for hundreds of cycles. This result will arranged to encourage such discussions so that the be presented in an invited article in the European students could receive critical feedbacks from the Journal of Physics E. participants, and the PIs of the field could also In a 2011 Physical Review Letter, Prof. Pik- share with each other the ideas of their research Yin Lai firstly constructed a theory on excitable and activities in their groups. The event took systems that are capable tuning their oscillation place in National Chiao Tung University and frequency through mutual interactions. This attracted about 50 participants. provides a mechanism for tuning and stabilizing One of the topics with growing interests of cellular and biological clocks and successfully fellow PIs in the field is the dynamics of self- explained the frequency variations in driven systems. Following the Complex Systems synchronized beating of cardiac muscular cells Symposium, we have chosen, as a topical meeting that has been observed experimentally in this direction, to hold a "2012 Workshop on (Europhyics Letter 2009). This work opened up a Self-Driven Systems" in the October. This fundamental descriptions for information workshop will invite both local and international propagation (Phys. Rev. E 84, 041921, 2011) as speakers with expertise on the subject to share well as tunability of biological clocks through their knowledge and ideas with the students and non-linear coupling in excitable systems, and can members of the focus group. The event will be be applied to general biological/physiological held at NCPU in Puli during October 26~28. systems. Using the concept of reaction kinetics, Prof. Chi-Lun Lee revisited the famous Gibbs paradox III. Visitors and International and showed that the thermodynamic behavior of Collaborations the systems is identical regardless whether or not Prof. Mikhailov (Fritz-Harber-Institute of the particles are distinguishable, even in the Max-Planck Society, Berlin, Germany) visited classical regime. As a byproduct of this Hsuan-Yi Chen's group in NCU to work on discussion, he showed the existence of a residual particle simulations of biomembranes and mixing entropy for identical particles. An analogy membrane proteins. of this was drawn to the mixing of counterions in colloidal systems when two colloidal particles Prof. Wada (Yukawa Institute of Theoretical come close to each other, where the increase in Physics) visited Hsuan-Yi Chen's group in NCU to entropy could be evidenced by counterion number work on gliding bacteria motility model. fluctuations via computer simulations. Using the sign-in system for employees in NCHU, Prof. Sy-Sang Liaw's group performed IV. Highlights of Research Results minority-game experiments for as long as two and The research group of Hsuan-Yi Chen (NCU a half years. In a paper published in Europhysics Physics and NCTS) in collaboration with Prof. Letters 2012, they compared the results with Mikhailov (Fritz-Harber Institut MPG, Berlin) and similar experiments they had done on Prof. Kapral (Univ of Toronto) developed a mosquitofish and concluded that the fish did have coarse-grain simulation for lipid membranes with memory and, similar to humans, would adopt multiparticle collision dynamics. This new different strategies to help them “win” the games. simulation approach can simulate lipid membrane Using molecular dynamic simulations in dynamics from picosecond to millisecond range addition to experiments on crumbling papers, while still preserve lipid structure in the Prof. Tzay-Ming Hong's group is finishing up membrane. The first report of this simulation three preprints on the powerlaw relationship method was published in Journal of Chemical between size of and external force on crumbled Physics and was featured in the cover of the Aug paper, stored potential energy and the length of the 7th issue of the journal. The dynamics of a model creases, as well as average crease length and

III-21 ‹‹- Highlights of Programs density of crumbled paper. They explored the [10] Wei-Yin Chiang, Pik-Yin Lai, C. K. Chan, possibility of a thermodynamic description of “Frequency Enhancement in Coupled Noisy compounded crumbling of thin films. They have Excitable Elements”, Phys. Rev. Lett. 106, also completed experimental setups of 254102 (2011). sonoluminescence and successful setup and [11] E. Avalos, Pik-Yin Lai, C. K. Chan, “Spiral observed X-ray as well as light emission in tape- waves in the heterogeneous excitable peeling processes. Kuramoto model”, Europhys. Lett. 94, 60006 (2011). [12] Fei Fang Chung, Sy-Sang Liaw and Wei V. Publications Chun Chang, “Collective motion of inelastic [1] I.-H. Lin, R.-K. Wu, and C.-M. Chen, 2011, particles between two oscillating walls”, “Synchronization in a Noise-driven Granular Matter 13, 787 (2011). Developing Neural Network”, Phys. Rev. E 051923 (2011). [13] Panupat Chaiworn, Fei Fang Chung, Cheng- Yen Wang, and Sy-Sang Liaw, “Brazil nut [2] C.-Y. D. Lu, “Theory of the polyelectrolyte effect in annular containers”, Granular Matter dielectric function”, Phys. Rev. E, 84 (2011). 13, 379 (2011). [3] Chun-Chung Chen and David Jasnow, “Event- [14] Mu-Jie Huang, Raymond Kapral, Alexander driven simulations of a plastic, spiking neural S. Mikhailov, and Hsuan-Yi Chen, “Coarse- network”, Phys. Rev. E 84, 031908 (2011). Grain Model for Lipid Bilayer Self-Assembly [4] Hsin-Hui Liang and Hsuan-Yi Chen, “Strength and Dynamics: Multiparticle Collision of adhesion clusters under shared linear Description of the Solvent”, J. Chem. Phys. loading”, Phys. Rev. E 83, 061914 (2011). 137, 055101 (2012). (Selected as the journal cover featured in Volume 137 Issue 5 on 7 [5] Peilong Chen and Qiyi Zhang, “Dynamical August 2012) solutions for migration of chiral DNA-type objects in shear flows”, Phys. Rev. E 84, [15] Mu-Jie Huang, Hsuan-Yi Chen, and 056309 (2011). Alexander S. Mikhailov, “Nano-swimmers in biological membranes and propulsion [6] Chi-Lun Lee, Chia-Ling Huang, “Asymptotic hydrodynamics in two dimensions” invited Dynamics of Self-driven Vehicles in a Closed article submitted to Euro. J. Phys. E (2012). Boundary”, J Stat. Phys. 144, 813 (2011). [16] Fu-Lai Wen, Kwan-tai Leung, Hsuan-Yi [7] Wei-Yin Chiang, Yue-Xian Lai, Pik-Yin Lai, Chen, “Curved trajectories of actin-based “Simple models for quorum sensing: motility in two dimensions”, Europhys. Lett. Nonlinear dynamical analysis”, Phys. Rev. E 98, 38005 (2012). 84, 041921 (2011). [17] Chang, J. Y.; Lai, Pik-Yin, “Uncontrolled [8] Wei-Chang Lo, H. C. Hong, H. J. Choi, et al., growth resulting from dedifferentiation in a “Stretching and migration of DNA by solvent skin cell proliferation model”, Phys. Rev. E elasticity in an oscillatory flow”, Phys. Rev. E 85, 041926 (2012). 84, 021802 (2011). [18] Ruey-Tarng Liu, Fei Fang Chung, and [9] Xuan Zhan, Pik-Yin Lai, C. K. Chan, “Effects Sy-Sang Liaw, “Fish play Minority Game as of glial release and somatic receptors on humans do” Europhys. Lett. 97, 20004 bursting in synchronized neuronal networks”, (2012). Phys. Rev. E 84, 011907 (2011).

Highlights of Programs -›› III-22 Highlights of Programs Condensed Matter Physics

Focus Group on Mesoscopic Physics and Strongly Correlated Systems

Coordinators: Ming-Chiang Chung (NCTS; email: [email protected]), Chung-Hou Chung (National Chiao Tung University/NCTS; email: [email protected])

I. Brief Description 1. Mesoscopic and Spin Physics Workshop, Dec 9-10, 2011, NCTS/NCTU Since 1999, our FG has hosted an annual winter workshop on mesoscopic and spin physics. he focus group is formed to promote This year, our annual mesoscopic and spin research topics on mesoscopic physics workshop is focused on quantum transport at and strongly correlated systems and provide nano-scales, such as: Luttinger liquid physics in opportunities for condensed matter theoreticians 1D nanowires/nanotubes, non-equilibrium effect interested in different materials and methods to in Kondo quantum dots, topological insulators/ increase the interaction and cooperation. In recent superconductors, spin transport in spintronic four years this focus group serves as a platform devices. among NCTS in Taiwan, junior research groups in APCTP (Asian Pacific Center for Theoretical We have invited several internationally well- Physics) and HKUST to facilitate the international known physicists to this workshop, including: collaborations, especially with young talented Jens Paaske Neiels Bohr Institute, U. of researchers from the Asian Pacific region (China, Copenhagen, Denmark, Stefan Kirchner, Korea, Japan and Taiwan). In addition we MPIPKS, Dresden, Germany, Gleb Kinkelstein financially support students and young researchers (Duke U.), KT Vic Law (HKUST, Hong Kong), to participate international conferences. Keiji Ono (RIKEN, Japan). Our domestic speakers, C.H. Chung, J.J. Lin, Wei-Ming Zhang, We have over 70 sing-up members in this focus had fruitful discussions with the international group and around 1/3 of the members have been speakers. Students and postdocs benefited much actively participating the group activities. The from the series of lectures given by some of the research topics are addressed on spintronics, key speakers. Through this workshop, possible topological insulators, graphenes, multiferroic new collaborations have been formed between materials, quantum transport, entanglement in local and international speakers, especially on the condensed matters and nanostructures, dynamics Kondo effect in graphene and dissipative quantum out of equilibrium and cold atomic systems phase trasnsitions in nanowires. applied in condensed matter physics. We expect that this workshop has formed an important platform for long-term international collaborations in our FG members. II. Activities 2. Quantum Condensation 2012 (Aug 12-25) In the past year (Oct. 2011 - Sep. 2012), our APCTP, Pohang, Korea focus group has organized (or co-organized) the following activities: The idea of QC workshop was initiated by

III-23 ‹‹- Highlights of Programs Prof. Peter Fulde (Director of APCTP). The goal Australia (Dr. McCulloch). The goal of this school of this workshop is to intensively increase the was to offer students at Master and PhD levels an collaboration among the condensed matter introduction to entanglement and out of physicists working in the asian pacific countries. equilibrium physics in condensed matter physics. In this 2-week’s workshop we want to create a In particular the school covered the following laid-back atmosphere for participants for building topics: exact diagonalization (ED), Bose Hubbard trust and long-term collaborations. In 2009 our Quench, entanglement spectra, classical and focus group helped Prof. Xin Wan (APCTP) quantum out of equilibrium dynamics, time organize QC09 in APCTP, Pohang Korea. In 2010 evolution using matrix product states and tensor QC10 was held in NCTS, Hsinchu organized by network. The school also focused on hands-on one of our coordinators (Ming-Chiang Chung). In experience via the extensive coding sessions. 2011 QC11 was organized by Prof Tai-Kai Ng in Hong-Kong university of sciences. The topics of the summer school: QC12 was held in APCTP Pohang this year • Exact diagonalization, Bose Hubbard quenches (2012) from 12-25 August. QC12 invited 34 and entanglement spectra (Prof. Laeuchli) participants from all over the Asia (Taiwan, China, • Aspect of classical and quantum out of Hong Kong, Korea, Japan and Spain). 6 equilibrium dynamics (Prof. Cugliandolo). Taiwanese researchers and postdocs participated this workshop. This year, QC12 had two panel • Efficient time evolution of one-dimensional topics: advanced topics in cold atoms and systems (Dr. Pollmann). unconventional superconductivity. • Matrix product algorithms for ground-states and Since 2009, QC 12 has been grown to one of dynamics. the most important workshops in asia. More and The students claimed that they had learned a more young talented researchers from Asia and lot in this summer school. The lecturers offered even from Australia and Europe would like to enough materials for them to start the study in the participate this workshop. The laid-back out of equilibrium dynamics. discussions in each talk has inspired a lot of 4. International workshop on Correlations and collaborations among those participants. Our Entanglement in Many-body Systems Out of focus group always plays an important role in the Equilibrium (Sep 10-13) organization of QC workshop. We bring a strong team to the international community and create Together with the FG “Numerical methods on the interaction among the physicists in the Asian strongly correlated systems (NMSCS)”, Prof. pacific region. In 2012, Prof Nagoasa from Japan Miguel Cazalilla from Spain and Prof Anibal Iucci and Prof Peter Fulde participated the workshop from Argentina, we organized a workshop on very actively and we had very successful Correlations and Entanglement in Many-body discussions. Please see website: https://www. Systems Out of Equilibrium due to a new field apctp.org/plan.php/qc12/ interplayed with entanglement and out of In 2013 QC13 will be held in NCTS, Hsinchu, equilibrium dynamics. In this workshop we Taiwan. invited 9 international speakers and 5 local speakers to participate this workshop. (See the list 3. Summer School for Entanglement and Quench below.) Dynamics in Condensed Matter Physics (Sep 5-7) The main topics of this workshop are Our focus group and FG (numerical methods in • The dynamics of the quantum systems strongly correlated systems) organized together a • The thermalization process summer school for entanglement and quench • Entanglement evolution dynamics in condensed matter physics. We invited 4 experienced physics in those field from • Interplay between entanglement and out of Germany (Dr. Pollmann), France (Prof. equilibrium dynamics Cugliandolo), Austria (Prof Laeuchli) and • Entanglement of tensor network

Highlights of Programs -›› III-24 The speakers are either world-known (5) Prof. Andrey Kolovsky (Kirensky Institute of physicists or young talented physicists coming physics, Krasnoyarsk, Russia) from Mar. 15 - from USA, Austria, Spain, Argentina, France and 24 2012. India. In this workshop they interacted a lot with (6) Prof. Rajesh Rajaranan (Indian Institute of local physicists, postdocs and students interested Technology, Chennai, India)from Mar. 27 - 31 in working on the topics and they are very also 2012. interested in collaborating with local Taiwanese physicists. This workshop is among one of few 2. Summer School for Entanglement and Quench international workshops which address this Dynamics in Condensed Matter Physics (Sep fundamental important issues of out-of- 5- 7) equilibrium dynamics and entanglement. (1) Prof. Andreas Laeuchli (University of 5. Internal seminars and discussions Innbruck, Austria) This year we invited different individual (2i) Prof. Leticia Cugliadolo (Laboratoire de speakers (see the list below) and have had several Physique Théorique et Hautes Energies seminars together with NTNU and FG NMSCS. Université Pierre et Marie Curie - Paris VI, We have announced all the seminars through a France) websites. We also brought all the visitors to (3) Dr. Frank Pollmann (Young research group different groups talking to interested physicists. leader, Max-Planck-Institute for physics of 6. Travel support for students/postdocs: complex systems, Dresden, Germany) With limited travel supports, we already (4) Dr. Ian McCulloch (Queensland university, supported 2 graduate students and 2 postdocs to Brisbane, Australia) attend international conferences. This channel of 3. International workshop on Correlations and supports is precious for the talented young bloods Entanglement in Many-body Systems Out of and their exposure to the international community Equilibrium has given them a glimpse about the outside world. In addition, we hope to attract young talents into (1) Prof.Miguel Cazalilla (Donostia International condensed matter physics via summer school, Physics Center NUS - Sigapore) workshops/miniprograms and journal clubs. So far (2) Prof. Anibal Iucci (University of La Plata, Arg we have already spent 90 K in sending the entina) postdocs and students to the international conferences. (3) Dr. Frank Pollmann (Max-Planck-Institute for physics of complex systems, Dresden, Germany) III. Visitors and International (4) Prof.Diptiman Sen (Indian Institute, India) Collaborations (5) Dr. Viktor Eisler (University of Vienna, Austri 1. Individual visitors a) (1) Dr. Frank Pollmann (Young research group (6) Dr. Jean-Marie Stephan (University of leader, Max-Planck-Institute for physics of Virginia, USA) complex systems, Dresden, Germany) from (7) Prof. Natan Andrei (Rutger University, USA) Feb. 13 - 17 2012. (8) Prof. Hosho Katsura (Gakushuin Univeristy, (2) Dr. Ian McCulloch (Queensland university, Tokyo, Japan) Brisbane, Australia) from Feb. 25 - Mar. 1 4. International Workshop on Mesoscopic and 2012. Spin Physics, Dec 9-10, 2011. (3) Prof. Tetsuya Takimoto (APCTP, Korea) from (1) Prof. Jens Paaske (Neiels Bohr Institute, U. of Mar. 8 -11 2012. Copenhagen, Denmark) (4) Prof. Masatoshi Sato (Nagoya university, (2) Dr. Stefan Kirchner, MPIPKS, Dresden, Nagoya, Japan) from Mar. 8-11 2012. Germany

III-25 ‹‹- Highlights of Programs (3) Prof. Gleb Kinkelstein (Duke U.), orbit interaction on the topological property of HgTe quantum well (4) Prof. K.-T.Vic Law (HKUST, Hong Kong) 6. Domestic collaborations (5) Prof. Keiji Ono (RIKEN, Japan). 5. International collaborators • Ming-Chiang Chung (NCTS)+ Po-Chung Chen (NTHU) • Chung-Hou Chung (NCTU) + Prof TK Ng • Chung-Hou Chung (NCTU) + Yu-Wen Lee (HKUST) ) on nonequilibrium transport via (THU) + Yu-Li Lee (NCHNU) functional bosonization approach. • Hsiu-Hau Lin (NTHU) + Chung-Hou Chung • Chung-Hou Chung (NCTU) + Prof. Miguel (NCTU) Cazalilla, (Centro de F´ısica de Materiales (CFM) Spain) on interaction effects of • Kwai-Kong Ng (THU) + Ming-Fong Yang topological insulators. (THU) • Chung-Hou Chung (NCTU) + Prof. Dr. • Yu-Wen Lee (THU) + Yu-Li Lee (NCUE) Matthias Vojta (TU Dresden) + Karyn Le Hur • Hsiu-Hau Lin (NTHU) + D.J. Huang (NSRRC) (CNRS, Paris, France) + Prof. Dr. Peter Woelfle (KIT, Karlsruhe, Germany) on quantum phase transitions in Kondo systems. IV. Highlights of Research Results • Chung-Hou Chung (NCTU) + Dr. Stefn Kirchner (MPIPKS, Dresden Germany) on two- 1. Quantum criticality of Kondo quantum dot channel Kondo physics in graphene. coupled to helical edge states of 2D topological insulators • Chung-Hou Chung (NCTU) + Prof. Qi-Miao Si (Rice Univ.) on exotic Kondo phases in heavy Via field-theoretical Renormalization Group fermion systems. (RG) approach, Chung-Hou Chung and his coworkers discover theoretically for the first time • Ming-Chiang Chung (NCTS) + Prof. Ingo the quantum phase transition (QPT) between the Peschel (Free university berlin) on quantum one-channel Kondo (1CK) and two-channel information applied in condensed matter. Kondo (2CK) fixed points in a quantum dot • Ming-Chiang Chung (NCTS)+ Prof. Miguel coupled to helical edge states of interacting 2D Cazallila (Centro de F´ısica de Materiales topological insulators (2DTI). We propose and (CFM) Spain) + Prof. Anibal Iucci (Universidad argue that the quantum critical behaviors near Nacional de La Plata, Argentina) on quench 1CK-2CK QPT can also be accessed dynamics of solvable models. experimentally. • Ming-Chiang Chung (NCTS) + Prof. Pochung 2. Quantum criticality out of equilibrium in the Chen(NTHU) + Prof. Sungkit Yip (Academia pseudogap Kondo model Sinica) + Prof. Ian McColluch (Unversity of Quantum phase transitions out of equilibrium Queenzland, Australia) on spin 2 bosnons in one are outstanding emergent subjects in condensed dimension. matter physics with great fundamental importance • Ming-Chiang Chung (NCTS) + Prof. Carlos and challenges. Chung-Hou Chung and his Trallero-Gino (Departamento de Fisica Teorica, co-workers discover new non-equilibrium Universidad de La Habana, Cuba) on BEC in universal scaling behaviors in transport properties one dimension. of a Kondo dot coupled to two voltage-biased fermionic leads with power-law density of states • Hsiu-Hau Lin (NCHU) + Toshiya Hikihara (DOS) with respect to their Fermi levels, so called (Hokkaido University) and Jian-Ming Tang the pseudogap Kondo model. (University of New Hamshire) on Graphenes. 3. Unconventional Superconductivity • Chon-Sar Chu (NCTU) + R. Winkler (Department of Physics, Northern Illinois Possibility of unconventional University) on the effects of Dresselhaus spin- superconductivity in newly discovered iron-

Highlights of Programs -›› III-26 vacancy ordered AyFe2-xSe2 is investigated. It is following a quantum quench is related to the found that the broken reflection symmetry implies nonergodic way in which operators sample, in the the rotation of the Cooper pair relative to the limit of infinite time after the quench, the quantum lattice becomes a free parameter and is an correlations present in the initial state. The important feature for iron-vacancy ordered iron nonergodicity of the correlations is thus shown superconductors. Furthermore, the Hund's rule analytically to imply the equivalence with the coupling is shown by Chung-Yu Mou and his generalized Gibbs ensemble for quantum Ising coauthors to be able to induce transition of pairing and XX spin chains as well as for the Luttinger symmetry from s-wave to d-wave in iron- model the thermodynamic limit, and for a broad superconductors. The research on unconventional class of initial states and correlation functions of superconductivity has been an important focus of both local and nonlocal operators. our FG and these researches result from It is analytically shown by them that the accumulated effort since past. asymptotic correlations following a quantum 4. Entanglement Hamiltonian and Spectra quench in exactly solvable models can sometimes look essentially thermal provided the initial Ming-Chiang Chung and his collaborator Ingo coupling between the system eigenmodes induces Peschel show that a proportionality between the a large gap. They study this phenomenon using entanglement Hamiltonian and the Hamiltonian of simple models, which also illustrate the a subsystem exists near the limit of maximal relationship between the entanglement spectrum entanglement under certain conditions. Away from of the initial state and the generalized Gibbs that limit, solvable models show that the coupling ensemble describing the long-time correlations range differs in both quantities and allow to after the quench. They also show that the effective investigate the effect. temperature characterizing the correlations is not 5. Exotic quantum phases related to spinor BEC related to the energy fluctuations after the quench, in an optical lattice and therefore does not have thermodynamic Ming-Chiang Chung and his coworkers study meaning. The latter observation implies a the phase diagram for spin-2 bosons loaded in a breakdown of the fluctuation–dissipation theorem. one-dimensional optical lattice. By using the non- 7. Rashba-type spin accumulation near a void at Abelian density matrix renormalization group a system edge: Phys. Rev. B 84, 125327 (2011) (DMRG) method they identify three possible Chon-Saar Chu in this work shows that spin- phases: ferromagnetic, dimerized, and trimerized Hall effect can be restored in a diffusive 2D phases. They sketch the phase boundaries based electron systems that consists of a Rashba-typed onDMRG. They illustrate two methods for spin-orbit interaction (RSOI), when the driving identifying the phases. The first method is based field is nonuniform. Even more importantly, when on the spin-spin correlation function, while in the this occurs near a boundary, we have established second method one observes the excitation gap as an unambiguous connection between a bulklike a dimerization, or a trimerization superlattice is spin flow and the spin accumulation Sz that occurs imposed. The advantage of the second method is at the boundary. This bulklike spin flow is that it also can be easily implemented in expected to be a primary impetus for local spin experiments. By using the scattering lengths in the injection when a local protrusion occurs at the literature we estimate that 83Rb, 23Na, and 87Rb boundary. can be ferromagnetic, dimerized, and trimerized, respectively. 8. Effects of edge potential on an armchair- graphene open boundary and nanoribbons, 6. Thermalization and quench dynamics Phys. Rev. B 85, 155444 (2012) Shown by Ming-Chiang Chung and his Chon-Saar Chu in this work shows that edge- coworkers, the generalized Gibbs ensemble states can be generated at an armchair-graphene introduced for describing few-body correlations in edge by the application of an edge-potential. In exactly solvable systems contrast to the edge-states at a zig-zag-graphene

III-27 ‹‹- Highlights of Programs boundary, the edge-states we find are dispersive, (2) Invited talk, Chung-Hou Chung, “Quantum which will contribute to conductance in a ribbon criticality of Kondo quantum dot coupled to configuration. The mechanism for the formation edge states of 2D topological insulators”, of these edge-states is understood, which is HangZhou international workshop on quantum associated with the pseudospin-flipping effect of matter, 2012, HangZhou, China, April 8, 2012. the edge-potential, and thus is different from that (3) Shun-Jen Cheng, “Crucial excitonic properties for the Tamm states in semiconductors. The of quantum dots as advanced light sources: mechanism supports generation of out-of-plane spin relaxation, optical fine structure and pseudospin density at an armchair-graphene open polarization anisotropy”, BIT’s 1st Annual boundary when a valley-polarized beam is World Congress of Nano-S&T, October 23-26, incident upon it. 2011, Dalian, China 9. Geometrical impacts of unstrained GaAs (4) Shun-Jen Cheng, “Electronic and Magnetic quantum dots on optical polarizations Properties of Magnetic Ion Doped In collaboration with experimental team at Semiconductor Quantum Dots”, 4th National Institute for Materials Science in Japan, Worldwide Universities Network (WUN) Prof. Shun-Jen Cheng (NCTU) reveals that the International Conference on Spintronics, lateral elongation of a quantum dot is not the sole Sydney, Australia, 23-25 July 2012. dominant cause of optical anisotropy, as commonly thought. They presented a theory based on the four-band Luttinger-Kuhn k.p model which VII. Selected Publications yields transparent analysis for the observed polarized photoluminesence of droplet epitaxial [1] Chung-Hou Chung and Kenneth Yi-Jie Zhang, GaAs quantum dots and confirms the essential “Quantum criticality out of equilibrium in the role of the vertical confinement in the optical pseudogap Kondo model”, Phys. Rev. B 85, anisotropies. To the best of our knowledge, it is 195106 (2012). the first time to fabricate unstrained GaAs QDs [2] D. Bolmatov, C.Y. Mou, “Graphene-based with in-situ controlled geometries and modulation-doped superlattice structures”, successfully account for the geometric impacts on Journal of Experimental and Theoretical the observed optical polarizations theoretically. Physics (JETP) 112, 102 (2011). [3] Shin-Ming Huang and Chung- Yu Mou, “Effective tight-binding model for the iron V. Honors and Awards vacancy ordered KyFe1.6Se2”, Phys. Rev. B Chung-Hou Chung obtained the poster award 84, 184521 (2011). in International conference on quantum criticality [4] Bor-Luen Huang, Ming-Che Chang,Chung-Yu and novel phases (QCNP 2012), Aug. 25-29, Mou, “Persistent currents in a graphene ring 2012, Drsden, Germany, Title: "Quantum with armchair edges”, J. Phys: Condens. criticality of Kondo quantum dot coupled to edge Matter 24, 245304 (2012). states of 2D topological insulators". [5] Chun-Yu Lin, Nan-Yow Chen, Chung-Yu Mou, “Folding a protein with equal probability of being helix or hairpin”, Biophysical Journal VI. Invited talks/Important International 103, 99 (2012). Visits [6] Shin- Ming Huang and Chung-Yu Mou , (1) Invited talk, Chung-Hou Chung, “Designing “Unconventional superconducting gap via spin heterostructures with higher temperature fluctuations in iron-vacancy ordered AyFe2- superconductivity”, Japan-Korea-Taiwan xSe2”, Phys. Rev. B 85, 184519 (2012). Conference on strongly correlated electron systems, March 16-18, 2012, National Sun-Ye- [7] L.Y. Wang and C.S. Chu, “Rashba-type spin Sun University, Kaohsiung, Taiwan. accumulation near a void at a system edge”, Phys. Rev. B 84, 125327 (2011).

Highlights of Programs -›› III-28 [8] C.H. Chiu and C.S. Chu, “Effects of edge [13] M.-C. Chung, M.A. Cazalilla and A. Iucci, potential on an armchair-graphene open “Thermalization in Systems with Bipartite boundary and nanoribbons”, Phys. Rev. B 85, Eigenmode Entanglement”, New. J. Phys. 14, 155444 (2012) 075013 (2012). [9] I. Peschel and M.-C. Chung, “On the relation [14] Yiwei Cai, Wen-Min Huang and Hsiu-Hau between entanglement and subsystem Lin, “Renormalization-group exponents for Hamiltonian”, Eur. Phys. Lett. 96, 50006 superconducting phases in two-leg ladders”, (2011). arXiv:1111.4373, accepted for publication in Phys. Rev. B (2012). [10] P.C. Chen, Z.L. Xue, I. P. McCulloch, M.-C. Chung and S.K. Yip, “Dimerized and [15] Yu-Huai Liao, Chien-Chih Liao, Chih-Hao trimerized phases for spin-2 Bosons in a Ku, Yu-Chen Chang, Shun-Jen Cheng*, onedimensional optical lattice”, Phys. Rev. A Masafumi Jo, Takashi Kuroda, Takaaki (Rapid Comm.) 85, 011601 (2012). Mano, Marco Abbarchi, and Kazuaki Sakoda,”Geometrical impact on the optical [11] M.A. Cazalilla, A. Iucci and M.-C. Chung, polarization of droplet epitaxial quantum “Thermalization and quantum correlations in dots”, accepted by Phys. Rev. B. exactly solvable models”, Phys. Rev. E 85, 011133 (2012). [16] Kwai-Kong Ng and Min-Fong Yang, “Thermal Phase transitions in attractive [12] C. Trallero-Giner, V. Lopez-Richard, N. extended Bose-Hubbard Model with three- Nurez-Fernadez, M. Oliva and M.-C. Chung, body constraint”, Phys. Rev. B 83, 100511(R) “Superfluidity and collective oscillations of (2011). trapped Bose-Einstein condensates in a periodical potential”, Eur. Phys. J. D 66, 177(2012).

III-29 ‹‹- Highlights of Programs Focus Group on Numerical Methods for Strongly Correlated Physics

Coordinators: Hong-yi Chen (National Taiwan Normal University; email: [email protected]) Po-Chung Chen (National Tsing Hua University/ NCTS; email: [email protected])

I. Brief Description visitor is invited to talk about new developments in the field. The talks are mostly informal. Discussion on details is strongly encouraged. Through the joined group meeting, members can he main goal of the “Numerical Methods get to know each other’s research topics and learn for Strongly Correlated Physics” new technique together. The informal talk (NMSCP) focus group (FG) is to build a strong atmosphere provides an opportunity for students local community in the field of numerical to learn to give presentations and to interact with simulation and to apply these techniques to a wide each other to broaden their perspectives. It also range of physics problems. In particular we aim to creates peer pressure on students to do more forge domestic and international collaborations as research. We also support participation from well as boost the international visibility of the institute with limited research resource. For local community. In 2012, Prof. Pochung Chen example we support Prof. Yu-Kun Huang from and Prof. Hong-yi Chen serve as the coordinators NJIT, which is not a research-oriented institute, to of the FG. Together with other six executive attend the meeting. This results in a new committee members: Prof. Ying-Jer Kao, Prof. collaboration with a paper by Prof. Yu-Kun Yu-Cheng Lin, Prof. Yung-Chung Chen, Prof. Huang, Prof. Pochung Chen, and Prof. Ying-Jer Chao-Cheng Kaun, and Prof. Hung-Chung Hsueh Kao and invited talks in international workshops. they represent the core members of the FG. In To broaden the vision of the members and to addition, there are about twenty active faculty identify potential new applications of the members and forty junior members (postdocs and numerical methods we organize bi-weekly students). The average age of the committee condensed matter seminar at NTNU. International members is about forty, indicating this is a young and domestic speakers in all subfield of condensed and energetic focus group. This is also due to the matter physics are invited to give formal talks generation gap that in Taiwan very few senior about their research. Traditionally there is no faculties are doing research along this direction. regular condensed matter seminar at NTNU but As a result it is important for the FG to foster a there are quite a few young faculties in this field strong local community that is sustainable in the joining NTNU in recent years. This seminar hence long run. Main research topics include (1) tensor aims to integrate NTNU faculties into local network algorithms, (2) classical and quantum community and help them to build international Monte-Carlo algorithms, (3) density functional connections. theory, (4) exact diagonalization, and (5) strong disorder RG. Within the focus group these To train young physicists, we organize schools numerical methods are applied to study a wide and workshops. This year we co-organize one range of problems in the field of condensed domestic summer school with MPS+SCS focus matter, cold-atom, and quantum information, group and co-organize one international winter which will be mentioned in highlights of research school with international DMRG community. The results. summer school focuses on “Quench dynamics and entanglement”. We invite world-leading experts II. Activities Prof. Leticia F. Cugliandolo, Prof. Andreas Läuchli, Prof. Frank Pollmann, and Prof. Ian To facilitate interaction among members we McColluch to give lectures and hold hand-on organize bi-weekly joined group meeting, which sessions. The school aims to help junior members is held at NTU or NTHU. In this meeting series, to bootstrap research in this direction. Students are either members of the FG report on their recent from various institutions and many of them lack progress or new technique, or an international the opportunity to learn these topics in their own

Highlights of Programs -›› III-30 school. We also encourage local physicists to poster. We sent Jhih-Shih You to attend the “2012 interact with invited speakers during their stay to Eurasia pacific summer school and conference on forge potential collaborations. Prof. Leticia F. strongly correlated electrons”, ITAP, Turkey. We Cugliandolo is currently the director of Les also sent Chia-Min Chung to ITP, Univ. Houches Physics School. She appreciated the Innsbruck, Austria as an exchange student to work opportunity to visit Taiwan and would like to with Andreas Läuchli for a year. encourage local community to send more students To boost the international visibility and to Les Houches School in the future. facilitate international collaborations we organize In December we co-organize second international workshops. This year we co-organize “International DMRG winter school” following “Workshop on correlations and entanglement in the first successful installment last year in many-body systems out of equilibrium” with Waterloo, Canada. The goal is to bring students, MSP+SCS focus group. This is a novel topic that postdocs, and faculties from around the world to has attracted lots of attention recently and there is gain an introductory understanding of the DMRG. an on-going program with similar topic at KIPT The lectures will be pedagogical but some of the this year. Invited international speakers include cutting-edge researches using DMRG will also be Prof. Natan Andrei, Prof. Miguel Cazalilla, Prof. highlighted. World-leading experts including Prof. Anibal Iucci, Prof. Hosho Katsura, Prof. Frank Andrian Feiguin, Prof. Miles Stoudenmire, Prof. Pollmann, Prof. Lea Santos, Prof. Diptiman Sen, Ian McCulloch, Dr. Hong-Chen Jiang, Prof. Tao Dr. Viktor Eisler, and Dr. Jean-Marie Stephan. Xiang, Dr. Robert Peters, Dr. Román Orús, Dr. Domestic invited speakers include Prof. Feng-Li Glen Evenbly, Dr. Fabian Heidrich-Meisner, Dr. Lin, Prof. Yu-Cheng Lin, Prof. Pochung Chen, Ivan Gonzalez, and Prof. Roger Melko will give Prof. Ying-Jer Kao, and Dr. Ming-Chiang Chung. lectures. There will also be some contributed talks It is expected that local community can learn and a poster session. Through this winter school, recent rapid development in this direction. There domestic young members have an excellent are several potential new collaborations initiated opportunity to learn DMRG from experts in a during this workshop. Prof. Miguel Cazalilla is pedagogical fashion. Faculty members will have a interested in using MERA or MPS to study Kondo chance to learn about the cutting edge research in related problems. Prof. Diptiman Sen is interested this direction and also to interact with invited in studying quench dynamics numerically. Prof. speakers as well as the international participants. Hosho Katsura would like to collaborate on From the list of participant we find that many combining Bethe ansatz and tensor network major international DMRG groups will attend this method. Prof. Frank Pollmann would like to school. We believe that by co-organizing this compare results with strong disorder RG. It is international winter school the international expected that the workshop also boost the visibility of the local community will be boosted. international visibility of local community. We emphasize that the international organization committee of the school decide to hold the school III.Visitors and International in Taiwan because the local community has gain Collaborations enough local strength and some international Typically we invite several international connections in the world-wide simulation visitors to stay for a week or longer. During the community due to the FG activities in recent visit the visitor will give talks at one or more years. institutes to facilitate interaction with people in To broaden the vision of student members we different institutes. We expect that the visitor send them to attend workshops and schools interact strongly with the visitor. Other members abroad. This year we sent Yun-Da Hsieh and who would like to interact with visitor are Yu-Chin Tzeng to attend the “Workshop on encouraged to meet visitors at host institutes. computational physics”, Lanzhou, China where During the last year we have Prof. Guang-Min they were invited to give presentations. We sent Zhang, Prof. Anders Sandvik, Prof. Ang Li, Prof. Y-Hao Jhu to attend “Quantum condensation Nocolae Atodiresei vising us. When organizing 2012”, APCTP, Korea where he presented a schools or workshops we usually arrange the

III-31 ‹‹- Highlights of Programs international visitor to stay extra days to interact Prof. Pochung Chen and coworkers study two- with local community. When inviting international species bosons in a 2D square lattice by QMC visitors, we value highly the potential of method and establishes the existence of pair- collaborations. Through the FG activities in last supersolid phase. The quantum and thermal few years, several visitors have become recurring transitions out of such phase are characterized. It and new international collaborations have been is found that there is a direct first-order transition formed. In particular, Prof. Anders Sandvik, Prof. from the pair-supersolid phase to the double- Frank Pollmann, and Prof. Ian McColluch have superfluid phase without an intermediate region. written papers with local community. As Upon heating, first the pair superfluid is destroyed mentioned in proceeding section, other new via a KT transition, then the solid order melts via collaborations are initiated through the workshop an Ising transition. (Phys. Rev. B). hold this year. Prof. Pochung Chen and Prof. Ying-Jer Kao have invited talks in “Quantum Condensation IV. Highlights of Research Results 2012”, APCTP Korea. Prof. Ying-Jer Kao and coworkers study spin ice, in which magnetic monopoles emerge as Prof. Pochung Chen and Prof. Ying-Jer Kao, classical defects. These magnetic charges are and Prof. Yu-Kun Huang have invited talks in carried by spinons, which can undergo BEC “Workshop on computational physics”, Lanzhou, through a first-order transition via the Higgs China mechanism. They report evidence of a Higgs Prof. Chao-Cheng Kaun has invited talk in transition from a magnetic Coulomb liquid to a “International Conference on Emerging Electronic ferromagnet in single-crystal Yb2Ti2o7. They Materials and Device Physics”, Chengdu, China. explain experimental results on the basis of a quantum spin-ice model (Nature V. Publications Communications). [1] L.-J Chang, S. Onoda, Y. Su, Y.-J Kao, K.-D Prof. Ying-Jer Kao and Dr. Derek Larson study Tsuei, Y. Tasui, K. Kakurai, and M. R. Lees, the interplay of superfluidity, glassy and magnetic Nature Communications, 3, 992, (2012). orders in the XXZ model with random Ising [2] P. Chen, Z. Xue, I. McCulloch, M. Chung, and interactions on a 3D cubic lattice. The QMC S.-K Yip, Phys .Rev. A, 85, 011610, (2012). simulation results show that quantum fluctuations stabilize the superglass while the [3] C. Chung, S. Fang, and P. Chen, Phys. Rev. B, antiferromagnetic order coexists with superfluidity 85, 214513, (2012). to form a supersolid. (Phys. Rev. Lett.). [4] M. Chung, Y, Jhu, P. Chen, and C. Mou, arxiv- Prof. Yu-Chen Lin, Prof. Ander Sandvik, and 1205.6951 (2012). coworkers proposed new valence-bond based [5] Y. Yuang. P. Chen, and Y. Kao, arxiv- variational wavefunctions and employed QMC 1203.4848 (2012). method to explore Neel-spin liquid-valence bond solid transition and emergent U(1) symmetry. [6] F. Iglói, Z. Szatmári, and Y.-C. Lin, Phys. Rev. (Phys. Rev. B). B, 85, 094417 (2012). Prof. Yu-Chen Lin and coworkers study the [7] D. Larson and Y.-J Kao, arxiv-1202.3908, to quench dynamics in disordered system. They find appear in Phys. Rev. Lett. (2012). unconventional non-equilibrium behavior in [8] Y.-C. Lin, Y. Tang, J. Lou, and A. W. Sandvik, quantum entanglement of disordered systems. arxiv-1206.6803, to appear in Phys. Rev. B (Phys. Rev. B). (2012). Prof. Pochung Chen, Prof. Ian McCulloch, and [9] J.-F. Yu and Y.-J. Kao, Phys. Rev. B, 85, coworkers study the phase diagram for spin-2 094407 (2012). bosons in a 1D lattice using DMRG. They find ferromagnetic, dimerized, and trimerized phases and phase boundary are determined. . (Phys. Rev. A).

Highlights of Programs -›› III-32 Focus Group on Computational Materials Research

Coordinator: Chih-Kai Yang (National Chengchi University; email: [email protected])

I. Brief Description (梁贊全, CCU), Ching-Ming Wei (魏金明, Academia Sinica), and Chih-Kai Yang (楊志開, coordinator, NCCU). Noted former members of the executive committee include M.-H. Tsai (蔡民 he primary purpose of this focus group is 雄, NSYSU, retired), Guang-Yu Guo (郭光宇, to promote computational materials NCCU/NTU), Ming-Hsien Lee (李明憲, TKU) research (CMR) based on first-principles and Shiow-Fon Tsay (蔡秀芬, NSYSU). They calculation methods in Taiwan, by providing a have contributed greatly to the success of the platform for the exchange of ideas among group focus group. The executive committee is tasked to members and encouragement of both domestic distribute the funds, to initiate research activities, and international collaborations, and also by to invite long-term and short-term visitors, and to attracting promising young scholars into this field. review financial supports for graduate students and junior scientists attending international The CMR focus group presently consists of 29 schools, conferences, or workshops, which are registered and active faculty members. According otherwise inaccessible to them. to their research interests and expertise and taking into account the current trend of physics, four research areas are specifically identified and accommodated by the corresponding study II. Activities groups: calculation of the electronic excited states 1. Training courses for first-principles (ES), quantum Monte Carlo methods (QMC), computational materials research quantum transport (QT), and low dimensional April 28-29, 2012 : Introductory level, for materials (also called nanomaterials or NanoMat). group I (49 enrolled) Members of CMR are free to choose and attend May 19-20, 2012 : Introductory level, for group study-group meetings led by senior members. II (46 enrolled) They are also entitled to recommend domestic and July 23-27, 2012 : Advanced level (42 enrolled) international scholars who may be invited to 2. Program-Wide Activities address their research interests in dedicated Feb. 9-10, 2012 : Winter Meeting for the CMR workshops or general meetings sponsored by Focus Group CMR. Two program-wide meetings are held each July 8-10, 2012: 12th Workshop on First- year and all CMR members and their students and Principles Computational Materials Physics associates have the opportunity to report the progress of their research activities. 3. Mini-school and workshop May 8, 2012: Quantum Matter: Topological CMR is managed through an executive Insulators, Superconductors, and Nano-dots committee consisting of ten members, with one of July 4-7, 2012: The 2nd Workshop on them serving as coordinator. Four of them are also Nanoscience: Carbon Relate Systems and in charge of the operations of study groups. They Nanometerials are Hung-Chung Hsueh (薛宏中, TKU) for ES, Chun-Ming Chang (張俊明, NDHU) for QMC, 4. Study group meetings Chao-Cheng Kaun (關肇正, Academia Sinica) for April 23, 2012: QMC study group meeting QT, and Feng-Chuan Chuang (莊豐權, NSYSU) May11, 2012: Low Dimensional materials for NanoMat. Other current committee members study group meeting are Yu-Chang Chen (陳煜璋, NCTU), Ching Sep. 7, 2012: GW one-day studying group Cheng (鄭靜, former coordinator, NCKU), meeting Michitoshi Hayashi (NTU), Tsan-Chuen Leung

III-33 ‹‹- Highlights of Programs Training courses for first-principles perspective in the field involving graphene and computational materials research were organized carbon nanotubes to local researchers and by Tsan-Chuen Leung (CCU) and given at the launched collaboration among the attendees. introductory level in the spring and at the The QMC study group meeting covered the advanced level in the summer. The purpose was to implementation of Wannier functions into the help beginners learn the theoretical background QMC methods, the description of van der Waals and practical use of popular codes available to interactions for insulating and ionic bilayer researchers. Enrollments were high in both systems using QMC methods and their classes, with the former having to open two comparisons to those using DFT methods with separate sessions to accommodate the applicants. different density functional schemes, and Graduate students, research scientists, and magnetic moments of small metallic clusters using professors from a variety of disciplines signed up QMC methods. for the popular courses, indicating the usefulness of computational methods, especially density The NanoMat study group meeting was functional theory, in dealing with various focused on graphene and related materials such as problems beyond the domain of physics. nanotubes and nanowires. The group has a fine record of productivity and is expanding to the area Two program-wide meetings were held in the of topological insulators, hoping to publish papers winter and summer, both encouraging PhD on this subject based on DFT calculation. students and postdocs to report the progress of their research under the guidance of advisors. The ES study group meeting was held to study Plenary talks were also given by invited domestic and implement the methods of GW and Bethe- and international scholars with the purpose of Salpeter equation to address the problem of the introducing cutting-edge research, novel methods, electronic excited states. Developed at the and initiation of collaboration between members University of California at Berkeley, the code has and the speakers. Prof. Hong Guo of McGill proved to be highly effective in this respect. University in Canada, for example, was invited to CMRFG encourages PhD students, postdocs, address the summer meeting, whose two-part and junior faculty members to attend international lectures on latest development in the theory of conferences, workshops and schools. Due to cut- quantum transport greatly informed the general back in the grant awarded to CMR, full cover of audience and may result in more formal expenses is generally impossible for applicants cooperation in the future. Invitation was extended seeking travel to North America or Europe. by Feng-Chuan Chuang to Prof. Arun Bansil of However, a special program is set up to subsidize Northeastern University in Boston to organize a graduate students and postdocs going to the 15th mini-workshop on May 8 in NCTS headquarters Asian Workshop on First-Principles Electronic in Hsinchu. The topic was about quantum matter: Structure Calculations, which is to convene in topological Insulators, superconductors, and nano- Taipei in November. dots. It is in the hope that researchers in Taiwan would be more aware of the development in this field, especially the topological insulators. There is already a paper published in Nature Physics as a III. Visitors and International result of the international collaboration in which Collaborations three Taiwanese theorists contribute toward the Examples of collaborations between CMRFG analysis of a magnetic topological insulator. members are listed as follows CMR also co-sponsored the second Workshop 1. CM Chang (NDHU), C Cheng (NCKU) and on Nanoscience: Carbon Related Systems and CM Wei (AS) on the applications of the Nanomaterials. There are over 100 participants Quantum Monte Carlo methods. from eight countries attending the workshop, 2. GY Guo ( NTU), TC Leung (CCU) and HC including such prominent foreign physicists such Hsueh (TKU) on the ab initio study for the as Sumio Iijima, Riichiro Saito, Francisco Guinea, excited states of nanomaterials. etc. The meeting provided a much needed

Highlights of Programs -›› III-34 3. CC Kaun (AS) and TC Leung (CCU) on 3. Electronic structures of an epitaxial graphene quantum transport in graphene nanoribbons and monolayer on SiC(0001) after metal nanomachines. intercalation (metal=Al, Ag, Au, Pt, and Pd): A first-principles study, authored by CMR 4. CM Wei (AS) and JL Kuo (AS) on the high- member Feng-Chuan Chuang and his students, pressure phases of ice. as well as Vidvuds Ozolins at UCLA, the paper 5. CK Yang (NCCU) and BR Wu (CGU) on is published on Applied Physics Letters and graphene and graphane. reveals the Rashba spin-orbit splittings among International collaborations are listed as follows other effects. 1. TC Leung (CCU) and CT Chan (Hong Kong) on optical properties of nanomaterials. V. Publications 2. CM Wei (AS) and N Drummond (UK) on [1] “Single-molecule refrigerators: Substitution applications of Quantum Monte Carlo methods. and gate effects”, Yu-Shen Liu and Yu-Chang 3. HC Hsueh (TKU) and SG Louie (USA) on Chen APPLIED PHYSICS LETTERS 98, Excitonic properties in nanomaterials and 213103 (2011). defects. [2] “The quantified NTO analysis for the 4. HC Hsueh (TKU) and Wei Ku (USA) on electronic excitations of molecular many-body Dynamic behavior of strongly bounded systems”, J.-H. Li, J.-D. Chai*, G. Y. Guo, M. excitons. Hayashi, Chemical Physics Letter 514, 362- 5. GY GuO (NCCU/NTU) and V Klimov (Russia) 367 (2011). on metamaterials. [3] “Justification of the total ionic 6. CC Kaun (AS) and H GuO (Canada) on pseudopotentials in first-principles methods”, quantum transport. T. L. Li* and W. S. Su, Chinese Journal of Physics 49(3), 802-808 (2011). 7. HT Jeng (NTHU), A Bansil (USA), and MZ Hasan (USA) on topological insulators. [4] “Exploring the interaction between the boron nitride nanotube and biological molecules”, 8. FC Chuang (NSYSU) and Vidvuds Ozolins Chih-Kai Yang, Computer Physics (USA) on nanomaterials. Communications 182 (2011) 39–42. [5] “Low-energy electronic structures of nanotube-nanoribbon hybrid systems”, C. H. IV. Highlights of Research Results Lee, S. C. Chen, C. K. Yang, W. S. Su*, and 1. Excitonic effects in the optical properties of a M. F. Lin*, Computer Physics SiC sheet and nanotubes, authored by CMR Communications 182 (2011) 68–70. members H. C. Hsueh and G. Y. GuO in [6] “An ab initio study of the magnetic and collaboration with Steven G. Louie of the electronic properties of Fe, Co, and Ni University of California at Berkeley, the paper nanowires on Cu (001) surface”, J.C. Tung and is published on Physical Review B and a G.Y. Guo, Computer Physics Communications demonstration of the powerful GW+BSE 182 (2011) 84–86. method dealing with difficult optical properties of nanomaterials. [7] “A first-principles study on the electromechanical effect of graphene 2. Recognizing nucleotides by cross-tunneling nanoribbon”, W.S. Su, B. R. Wu, and T. C. currents for DNA sequencing, authored by Leung, Computer Physics Communications CMR member Chao-Cheng Kaun and his 182 (2011) 99–102. postdoc, the paper is published on Physical Review E and a novel demonstration of how [8] “Electronic structure and transport properties DNA molecules can be screened by the of SrAl2Si2: Effect of Yttrium substitution”, transport properties. C.S. Lue, C.P. Fang, A.C. Abhyankar, J.W.

III-35 ‹‹- Highlights of Programs Lin, H.W. Lee, C.M. Chang*, Y.K. Kuo*, S. Su, C. P. Chang, M. F. Lin*, and T. L. Li*, Intermetallics 19 (2011) 1448-1454. JOURNAL OF APPLIED PHYSICS 110, 014312 (2011). [9] “Structural and electronic properties of bismuth and lead nanowires inside carbon [18] “Magnetic anisotropy and spin-spiral wave in nanotubes Chi-Hsuan Lee and Chih-Kai V, Cr and Mn chains on Cu(001) surface: Yang*”, J. Phys. Chem. C 2011, 115, 10524– First principles calculations”, J. C. Tung, Y. 10530. K. Wang and G. Y. Guo, Journal of Physics D: Applied Physics 44, 205003 (2011). [10] “Atomic-Scale Field-Effect Transistor as a Thermoelectric Power Generator and Self- [19] “Structural and electronic properties of Powered Device”, Yu-Shen Liu, Hsuan-Te hydrogen adsorptions on BC3 sheet and Yao, and Yu-Chang Chen*, J. Phys. Chem. C graphene: a comparative study”, Feng-Chuan 2011, 115, 14988–14996. Chuang, Zhi-Quan Huang, Wen-Huan Lin, Marvin Albao, and Nanotechnology 22 [11] “Conductance of Stretching Oligothiophene (2011) 135703 (9pp). Single-Molecule Junctions: A First-Principles Study”, Y.-H. Tang , V. M. K. Bagci , J.-H. [20] “Electronic structures of an epitaxial Chen , and C.-C. Kaun*, J. Phys. Chem. C graphene monolayer on SiC(0001) after gold 2011, 115, 25105–25108. intercalation: a first-principles study”, Feng- Chuan Chuang, Wen-HuanLin, Zhi-Quan [12] “Effect of Thermoelectric Cooling in Huang, Chia-Hsiu Hsu, Chien-Cheng Kuo, Nanoscale Junctions”, Yu-Shen Liu, Bailey Vidvuds Ozolins and V Yeh, Nanotechnology C. Hsu, and Yu-Chang Chen, J. Phys. Chem. 22 (2011) 275704 (6pp). C 2011, 115, 6111–6125. [21] “Optical magnetic response in three- [13] “Size effect of Pd clusters on hydrogen dimensional metamaterial of upright adsorption”, H. W. Lee, and C. M. Chang, J. plasmonic meta-molecules”, W. T. Chen, C. Phys.: Condens. Matter 23 (2011) 045503 J. Chen, P. C. Wu, S. Sun, L. Zhou, G. Y. (5pp). Guo, C. T. Hsiao, K.-Y. Yang, N.I.Zheludev [14] “The dielectric properties of La(Mg(0.5) and D. P. Tsai, Optics Express 19, 12837 Ti(0.5))O(3) ceramics studied by Raman- (2011). scattering, infrared reflectivity spectroscopy, [22] “Structural and electronic properties of and first-principles calculations”, Hsiang-Lin graphene nanotube-nanoribbon hybrids”, Liu, Hung-Chung Hsueh, I-Nan Lin, Ming-Ti Chi-Hsuan Lee, Chih-Kai Yang, Ming-Fa Yang, Wei-Chung Lee, Yi-Chun Chen, Chia- Lin*, Cheng-Pong Chang*, and Wang-Sheng Ta Chia and Hsiu-Fung Cheng, J. Phys.: Su, Phys. Chem. Chem. Phys., 2011, 13, Condens. Matter 23 (2011) 225901 (8pp) 3925–3931. [15] “Influences of twist boundaries on optical [23] “Counting statistics in nanoscale junctions”, effects: Ab initio studies of the deep Yu-Shen Liu and Yu-Chang Chen*, ultraviolet”, Z. S. Lin, Lei Bai, Lijuan Liu, PHYSICAL REVIEW B 83, 035401 (2011). M. H. Lee, J. Xu, Xiaoyang Wang, and C. T. Chen, Journal of Applied Physics 109, [24] “Seebeck coefficients in nanoscale junctions: 073721 (2011) Effects of electron-vibration scattering and local heating”, Bailey C. Hsu, Yu-Shen Liu, [16] “Giant spin Hall effect of Au films with Pt Sheng Hsien Lin, and Yu-Chang Chen*, impurities: Surface-assisted skew scattering”, PHYSICAL REVIEW B 83, 041404(R) B. Gu, T. Ziman, G. Y. Guo, N. Nagaosa, and (2011). S. Maekawa, JOURNAL OF APPLIED PHYSICS 109, 07C502 (2011). [25] “Ab initio studies of spin-spiral waves and exchange interactions in 3d transition metal [17] “Electronic structures and work functions of atomic chains”, J. C. Tung and G. Y. Guo, BC3 nanotubes: A first-principle study”, W. Physical Review B 83, 144403 (2011).

Highlights of Programs -›› III-36 [26] “Excitonic effects in the optical properties of [33] “Effect of Electron–Vibration Interactions on a SiC sheet and nanotubes”, H. C. Hsueh, G. the Thermoelectric Efficiency of Molecular Y. Guo, Steven G. Louie, PHYSICAL Junctions”, Bailey C. Hsu, Chi-Wei Chiang, REVIEW B 84, 085404 (2011). and Yu-Chang Chen, Nanotechnology 23 (2012) 275401 (9pp). [27] “High Chern number quantum anomalous Hall phases in graphene ribbons with [34] “Fabrication of three dimensional split ring Haldane orbital coupling”, T.-W. Chen, Z.-R. resonators by stress-driven assembly Xiao, D.-W. Chiou, and G. Y. Guo, method”, Chen, CC; Hsiao, CT Sun, SL; PHYSICAL REVIEW B 84, 165453 (2011). Yang, KY Wu, PC Chen, WT Tang, YH; Chau, YF Plum, E; Guo, GY Zheludev, NI [28] “Recognizing nucleotides by cross-tunneling Tsai, DP, Optics Express, Vol. 20 Issue 9, currents for DNA sequencing”, V. M. K. pp.9415-9420 (2012). Bagci, and C.-C. Kaun*, PHYSICAL REVIEW E 84, 011917 (2011). [35] “Coherent perfect nanoabsorbers based on negative refraction”, Klimov, V; Sun, SL [29] “Tuning the electronic properties of Guo, GY Optics Express, Vol. 20, Issue 12, monolayer graphene by the periodic aligned pp. 13071-13081 (2012). graphene nanoribbons”, C. H. Lee, S. C. Chen, W. S. Su, R. B. Chen*, and M. F. Lin*, [36] “Significant role of the DNA backbone in Synthetic Metals 161 (2011) 489–495. mediating the transition origin of electronic excitations of B-DNA - implication from long [30] “Electronic structures of graphane with range corrected TDDFT and quantified NTO vacancies and grapheme adsorbed with analysis”, Li J. H. , Chai J. D. , Guo G. Y., fluorine atoms Bi-Ru Wu and Chih-Kai Hayashi M., Phys. Chem. Chem. Phys., 2012, Yang*”, AIP ADVANCES 2, 012173 (2012). 14, 9092–9103. [31] “Electronic structures of an epitaxial Of the 29 papers published in 2011, 17 are from graphene monolayer on SiC(0001) after domestic collaborations among CMR members metal intercalation (metal5Al, Ag, Au, Pt, and and 7 are from international collaborations. Pd): A first-principles study”, Chia-Hsiu Hsu, Wen-Huan Lin, Vidvuds Ozolins, and Feng- Of the 9 papers already published in 2012, 3 of Chuan Chuang, APPLIED PHYSICS them are from domestic collaborations among LETTERS 100, 063115 (2012). CMR members and 4 are international. [32] “Enhanced magnetization and conductive phase in NiFe2O4”, Ching Cheng, Journal of Magnetism and Magnetic Materials.

III-37 ‹‹- Highlights of Programs Highlights of Programs Particles and Fields

Focus Group on Cosmology and Particle Astrophysics

Coordinator: Chao-Qiang Geng (National Tsing Hua University/NCTS; email: [email protected])

I. Brief Description • Establishing exchange programs with foreign research organizations and conducting exchange activities. Our current main research focus of FGCPA he Coordinator of FGCPA has been Chao- contains three specific topics: (1) Dark Matter, (2) Qiang Geng (National Tsing Hua Dark Energy and (3) Neutrino Physics. Univeristy and NCTS) since 2011. The Core Members of FGCPA are Pisin Chen (National Taiwan University), Guey-Lin Lin (National Chiao Tung University), Wolung Lee (National II. Activities Taiwan Normal University), Guo-Chin Liu 1. Seminars (Tamkang Univeristy), W-Y. Pauchy Hwang Taipei Chapter: This seminar series is located at (National Taiwan University), Kin-Wang Ng LeCosPA, NTU. It has been (Academia Sinica), and Chuan-Hung Chen holding seminars every week (National Cheng Kung University). In addition to during the semesters. the Core Members, there are many professors, researchers and postdocs (~10) as well as PhD and Hsinchu Chapter: This seminar series is located at Master students (~10) participate in this FG. NTHU/NCTS. It was originally planned to be a bi-weekly one The goals of FGCPA are as follows. but it has been becoming a • Organization of short cosmology and particle regular weekly seminar on astrophysics courses to students, posdocs and every Friday since 2012 during researchers. the semesters. • Invitation of short-term foreign visitors to give Tainan Chapter: This series is located at NCKU. seminars, talks and lectures. Since there are relatively fewer FG members in southern Taiwan, • Encouraging and promoting cooperation and/or it was decided that this series is joint research projects among domestic research held non-regularly and jointly groups. with the existing seminar series in • Training of graduate students and postdocs the Physics Department of through their attendance of international schools NCKU. or visits to foreign research institutes. 2. Working Groups • Invitation of distinguished cosmologists and Between 2009-2010, FGCPA was pursuing the particle astrophysicists for short or long-term following 5 research topics organized jointly with visits to initiate research projects.

Highlights of Programs -›› III-38 LeCosPA: Cosmic Rays and Neutrinos: Guey-Lin Physics and Cosmology, May 7-12, 2012, Lin (orgainzer); Baryon Asymmetry of the Chongqing, China. Seven of them have Universe (BAU): Chao-Qiang Geng (organizer); presented talks related to CPA at the meeting. Dark Energy Phenomenology: Je-An Gu • Two students: Ling-Wei Luo (Ph.D) and Jia- (organizer); String Cosmology: Debaprasad Maity Liang Shen (Master) had a 4-week visit to (organizer); Gravity and Structure Formation: Chongqing University of Post and Antonio Enea Romano (organizer). Since 2011, Telecommunication (CQUPT) during the although some of the five groups are still in summer (July 11-Aug. 3) of 2012 to learn some active, in particular the groups based on LeCosPA, recent progresses made by Prof. Y.G. Gong and NTU, the emphasis of the working groups at Prof. F.W. Shu on Massive Gravity and Dark NTHU and NCTU has been concentrated on Energy. topics related to dark matter, dark energy and neutrino physics. In addition, at the main center of • Chao-Qiang Geng attended “the International NCTS located at NTHU, we have a weekly Conference on Flavor Physics and regular group meeting chaired by the coordinator Cosmophysics 2012 (ICFPC2012)”, Aug. 8-12, between 10:00-12:00 on Tuesday to discuss the 2012, Weihai, China, where he presented a recent progress on CPA. plenary talk on “Teleparallel Dark Energy”. 3. Joint Meetings and Retreats • One PhD student: Yi-Peng Wu has been attending the KITPC program of “Cosmology • rd 3 NCTS-FGCPA and LeCosPA Joint Meeting and Astroparticle Physics”, KITPC, Beijing, on Dark Energy, April 25, 2012, NCTS/NTHU, between September 7- 24, 2012. Hsinchu, Taiwan • One PhD student: Yi-Peng Wu will attend the • th 4 NCTS-FGCPA and LeCosPA Joint Meeting RESCEU Symposium on “General Relativity on Dark Energy, June 21, 2012, AS, Taipei, and Gravitation”, Nov. 12-16, 2012, University Taiwan of Tokyo, Japan. • 5th NCTS-FGCPA and LeCosPA Joint Meeting on Dark Energy, Oct. 20, 2012, NTU, Taipei, Taiwan III. Visitors and International • 3rd Joint retreat on LHC physics and Cosmology, Collaborations Nov. 2-4, 2012, NCTS, Hsinchu, Taiwan Visitors 4. Workshops • Dr. Kazuharu Bamba of Kobayashi-Maskawa • Mini-Workshop on Neutrino Physics, May 26, Institute for the Origin of Particles and the 2012, NCTS/NCTU, Hsinchu, Taiwan Universe, Nagoya University, Japan visited NCTS under the support of FGCPA between • 9th Symposium on Cosmology and Particle May 16--30, 2012. He gave two special lectures Astrophysics (CosPA), Nov. 13-15, Taipei and on “Modified Gravity Theories”. Dr. Bamba has Nov. 16-17, Hsinchu, Taiwan finished two research papers with NCTS as • 3rd International Conference on Dark Matter, Affiliation based on this visit. Dark Energy and Matter-antimatter Asymmetry, • Dr. Zong-Kuan Guo of Institute of Theoretical Dec. 28-29, 2012, NCTS/NTHU, Hsinchu, Physics, Beijing will visit NCTS under the Taiwan support of FGCPA between Nov. 1 –Nov. 5, 5. Attendance of International Activities 2012. He is one of the invited speakers for the • Ten Ph.D students: Chung-Chi Lee, Ling-Wei 3rd Joint retreat on “LHC physics and Luo, Huan-Hsin Tseng, Po-Yan Tseng, Chi- Cosmology”, Nov. 2-4, 2012 at NCTS. He is an Fong Wong, and Yi-Peng Wu from NTHU; Pei- expert on CMB. Hung Yuan from NCTU; and Yu-Hsiang Lin, • Dr. Yu-Feng Zhou of Institute of Theoretical Che-Min Shen and Nien-En Tung from NTU Physics, Beijing will visit NCTS under the attended 2012 Cross-strait Meeting on Particle support of FGCPA between Nov. 1 –Nov. 5,

III-39 ‹‹- Highlights of Programs 2012. He is one of the invited speakers for the Germany), Chuan-Hung Chen (NCKU/NCTS) 3rd Joint retreat on “LHC physics and and Chao-Qiang Geng (NTHU/NCTS) on CP Cosmology”, Nov. 2-4, 2012 at NCTS. He is an violation. expert on Dark Matter. • Collaborations of Pisin Chen (NTU) with many • Prof. Yong-Chuan Huang and Prof. Hao Wei of others on Cosmology and Astroparticle physics. Beijing University of Technology will visit See the publication list with NCTS as NCTS under the support of FGCPA between Acknowledgement. between Nov. 1 –Nov. 5, 2012. They are invited speakers for the 3rd Joint retreat on “LHC physics and Cosmology”, Nov. 2-4, 2012 at VI. Highlights of Research Results NCTS. We would like to highlight our research results • Dr. T. Araki of Maskawa Institute, Kyoto since the last report along our current three main Sangyo University, Japan will visit NCTS under research directions: Dark Energy, Dark Matter and the support of FGCPA between Nov. 14-Dec. 9, Neutrino Physics. 2012. Dark Energy • Dr. Rong-Jia Yang of Hebei University, China will visit NCTS for one month under the Using the “teleparallel” equivalent of General support of FGCPA between Dec. 1-31, 2012. Relativity as the gravitational sector, which is based on torsion instead of curvature, we have • More visitors will be invited to NCTS at the end proposed a new dark energy model [1,7], so called of 2012 to attend the 3rd International the “Teleparallel Dark Energy” model, by adding Conference on Dark Matter, Dark Energy and a canonical scalar field and allowing for a non- Matter-antimatter Asymmetry, Dec. 28-29, minimal coupling with gravity. Although the 2012, NCTS/NTHU, Hsinchu, Taiwan. Some of minimal case is completely equivalent to standard them may stay longer to have more time to quintessence, the non-minimal scenario has a interact with students and researchers at the richer structure, exhibiting quintessence-like or center. phantom-like behavior, or experiencing the International Collaborations phantom-divide crossing. The richer structure is manifested in the absence of a conformal • Collaboration between Dr. E.N. Saridakis (UA, transformation to an equivalent minimal-coupled Greece) and Chao-Qiang Geng (NTHU/NCTS) model. We have also used data from Type Ia on dark energy models. Supernovae (SNIa), Baryon Acoustic Oscillations • Collaboration between Dr. E.N. Saridakis (UA, (BAO), and Cosmic Microwave Background Greece) and Dr. T. T. Qiu (NTU) on Inflation. (CMB) observations to constrain this teleparallel dark energy scenario. Using the power-law, the • Collaboration between Dr. Kazuharu Bamba exponential and the inverse hyperbolic cosine (KMI, Japan) and Chao-Qiang Geng (NTHU/ potentials, we have shown that the scenario is NCTS) on modified gravity theories and large- compatible with observations. In particular, the scale magnetic fields. data favor a non-minimal coupling, and although • Collaboration between Dr. R. Takahashi (Osaca the scalar field is canonical the model can describe University, Japan) and Chuan-Shu. Chen both the quintessence and phantom regimes. (NCTS) on neutrino physics. Recently, we have also investigated the • Collaboration between Dr. S.H. Ho (MIT, USA) teleparallel dark energy model with purely non- and Chao-Qiang Geng (NTHU/NCTS) on Kalb- minimal coupling and without potential [29]. We Ramond fields. have found the analytic solutions of the scalar field in the radiation, matter, and scalar field (or • Collaboration between Mr. L. Yang (UCLA, dark energy) dominated eras, respectively. These USA) and Chao-Qiang Geng (NTHU/NCTS) on solutions indicate the tracker behavior in the singularity phenomena in viable f(R) gravity. radiation and matter dominated eras, while the • Collaborations between Dr. W. Wang (DESY, equation of state of the teleparallel dark energy is

Highlights of Programs -›› III-40 determined by the non-minimal coupling constant V. Publications but insensitive to the initial condition. We remark NCTS as Affiliation that this work was started when Dr. Saridakis had one month visit to NCTS under the support of [1] “Teleparallel' Dark Energy”, C.Q. Geng, C.C. FGCPA in 2011. The Coordinator of FGCPA, Lee, E.N. Saridakis and Y.P. Wu, Phys. Lett. Chao-Qiang Geng, has presented a plenary talk B704 (2011) 384.  based on the above results at the International [2] “Large 13 from finite quantum corrections in Conference on “Flavor Physics and Cosmophysics quasi-degenerate neutrino mass spectrum”, T. 2012 (ICFPC2012)”, Aug. 8 to 12, 2012, Weihai, Araki, C.Q. Geng, JHEP 1109 (2011) 139. China. [3] “Kinematically Blocked Curvaton”, L.Y. Lee, Dark Matter C.M. Lin, C.S. Chen, Mod. Phys. Lett. A26 We have studied magnetic dipole moments of (2011) 2731-2737. right-handed neutrinos in a keV neutrino dark [4] “Matter Bounce Cosmology with the f(T) matter model [12]. This model is a simple Gravity”, Y.F. Cai, S.H. Chen, J.B. Dent, S. extension of the standard model with only right- Dutta, E.N. Saridakis. Class. Quant. Grav. 28 handed neutrinos and a pair of charged particles (2011) 215011. added. One of the right-handed neutrinos is the candidate of dark matter with a keV mass. Some [5] “Thermodynamics of cosmological horizons in bounds on the dark matter magnetic dipole f(T) gravity”, K. Bamba, C.Q. Geng, Journal moment and model parameters are obtained from of Cosmology and Astroparticle Physics 1111 cosmological observations. Motivated by the (2011) 008. discovery hint of the SM Higgs mass around 125 [6] “Cosmon as the Modulon: Non-Gaussianity GeV at the LHC, we have examined the vacuum from Dark Energy”, C.S. Chen, C.M. Lin, stability and perturbativity bounds on Higgs scalar Phys. Lett. B705 (2011) 161-164. of the SM extensions including neutrinos and dark [7] “Observational Constraints on Teleparallel matter [1]. Dark Energy”, C.Q. Geng, C.C. Lee and E.N. Neutrino Physics Saridakis, Journal of Cosmology and We have shown a finite quantum correction to Astroparticle Physics 1201 (2012) 002. the tri-bimaximal (TB) neutrino mixing in several [8] “Study of B→pρ(Φ) and B→ΛΛK*”, C.Q. generic classes of neutrino models. We have found Geng, Y.K. Hsiao. Phys. Rev. D85 (2012) that all three mixing angles can depart from the 017501. TB values. In particular, the deviation for 12 can [9] “Vacuum stability, neutrinos, and dark matter”, be large due to the degeneracy between the C.S. Chen, Y. Tang, JHEP 1204 (2012) 019. neutrino masses of m1 and m2. The model- independent upper bounds on 23 and 13 are also [10] “π→pγ*γ Transition Form Factor within obtained. After the large value of 13 reported by Light Front Quark Model”, C.C. Lih and C. T2K and MINOS as well as Double Chooz before Q. Geng, Phys. Rev. C85 (2012) 018201. Daya Bay and RENO, we studied [2] the finite [11] “Entropic Force Scenarios and Eternal quantum corrections for several well known Inflation”, T. Qiu, E.N. Saridakis. Phys. Rev. neutrino mixing matrices to see if they can be use D85 (2012) 043504. to account for the data. However, we find that it is hard to do it. To nicely reproduce all [12] “Magnetic dipole moment and keV neutrino experimentally favored neutrino mixing angles dark matter”, C. Q. Geng and R. Takahashi, and masses, we also proposed a new neutrino Phys. Lett. B710 (2012) 324. mixing pattern [2]. [13] “Searching for Z' Gauge Boson in an Anomaly-Free U(1)' Gauge Family Model”, J.Y. Liu, Y. Tang and Y.L. Wu, J. Phys. G39 (2012) 055003.

III-41 ‹‹- Highlights of Programs [14] “Exotic fermion multiplets as a solution to [23] “Study of pesudoscalar transition form baryon asymmetry, dark matter and neutrino factors within light front quark model”, C.Q. masses”, C.H. Chen, S.S.C. Law, Phys. Rev. Geng, C.C. Lih, Phys. Rev. C36 (2012) D85 (2012) 055012. 038201. [15] “Comment on Reparametrization Invariance [24] “Gravitational waves in viable modified of Quark-Lepton Complementarity”, G.N. Li, gravity theories”, C.Q. Geng, Journal of H.H. Lin, X.G. He, Phys. Lett. B711 (2012) Physics: Conference Series 384 (2012) 57. 012030. [16] “CP violation in D 0(K–K +, π–π +) from NCTS as Acknowledgement diquarks”, C.H. Chen, C.Q. Geng and W. [25] “Probing annihilations and decays of low- Wang, Phys. Rev. D85 (2012) 077702. mass galactic dark matter in IceCube [17] “Hints of Standard Model Higgs Boson at the DeepCore array- Part I : track events”, Fei- LHC and Light Dark Matter Searches”, X.G. Fan Lee, Guey-Lin Lin, Phys. Rev. D85 He, B. Ren, J. Tandean, Phys. Rev. D85 (2012) 023529. (2012) 093019. [26] “Confronting Tracker Field Quintessence [18] “Study of rare B→Λpνν decay”, C.Q. with Data”, Pao-Yu Wang, Chien-Wen Chen, Geng, Y.K. Hsiao. Phys. Rev. D85 (2012) Pisin Chen, JCAP 1202 (2012) 016. 094019. [27] “Near-Field Effects of Cherenkov Radiation [19] “Large-scale magnetic fields from inflation Induced by Ultra High Energy Cosmic due to a CPT-even Chern-Simons-like term Neutrinos”, C.Y. Hu, C.C. Chen and P. Chen, with Kalb-Ramond and scalar fields”, K. Astropart. Phys. 35 (2012) 421. Bamba, C.Q. Geng, S.H. Ho, W.F. Kao. Eur. [28] “Stringy Stability of Charged Dilaton Black Phys. J. C72 (2012) 1978. Holes with Flat Event Horizon”, Y.C. Ong, [20] “Hierarchically Acting Sterile Neutrinos” Pisin Chen, JHEP 1208 (2012) 079. C.S. Chen and R. Takahashi, Eur. Phys. J. Reference C72 (2012) 2089. [29] “Tracker Teleparallel Dark Energy with [21] “Singularity phenomena in viable f(R) Purely Non-minimal Coupling to Gravity”, gravity”, C.C. Lee, C.Q. Geng and L. Yang, J.A. Gu, C.C. Lee, C.Q. Geng, Prog. Theor. Phys. 128 (2012) 415. arXiv:1204.4048 [astro-ph.CO]. [22] “Implications of LHC Searches for Massive Graviton”, Y. Tang, JHEP 1208 (2012) 078.

Highlights of Programs -›› III-42 Focus Group on Gravitation

Coordinator: Hing-Tong Cho (Tamkang University; email: [email protected])

I. Brief Description II. Activities A. 2012 Asia-Pacific School/Workshop on Cosmology and Gravitation The main activity of our FG this year is the he Focus Group on Gravitation was co-organization of the "2012 Asia-Pacific School/ established five years ago as an effort to Workshop on Cosmology and Gravitation” at the bring together researchers in Taiwan working on Yukawa Institute in Japan. It was held from March the theory of gravitation. As the numbers of 1 to March 4. There were more than one hundred people working on this area in different institutes participants mainly from the Asia-Pacific are quite small, the Focus Group becomes an ideal countries. As to our group we have 25 people setting to encourage interactions and attending with 10 faculties, and 15 postdocs and collaborations among them. With these in mind, students. This was indeed a great occasion for the the Focus Group on Gravitation has the following members of our group to interact and to initiate main goals: possible collaborations with researchers in the 1. To generate long-term collective force in field of gravity in countries like Japan, Korea, and Gravitation research among the local communities China. Thus it accomplishes one of the main goals and the Asia-Pacific area; 2. To generate of our group. interdisciplinary and cutting-edge research In fact, this event was initiated by our group 5 activities on Gravity; 3. To create both academic years ago, and it has become an annual activity and career opportunities for talented graduate ever since. In 2008 it was held at the National students and postdocs. Taitung University. Subsequently, the event was The activities this year, as well as in the held at APCTP (Pohang, Korea), National Taitung preceding years, are organized to accomplice University, Shanghai Normal University, and this these goals. year at the Yukawa Institute. Next year it will be There are 12 core members in our FG: Chiang- held in Korea with S. P. Kim and G.W. Kang as Mei Chen (National Central University), Hing- the local organizers. In 2014 this event will be Tong Cho (Coordinator, Tamkang University), rotated back to Taiwan. Chung-Hsien Chou (National Cheng-Kung In the school part of the workshop in Yukawa University), Da-Shin Lee (National Dong-Hwa there were four lecturers: Larry Ford (Tufts U), University), Shih-Yuin Lin (National Changhua Jun'ichi Yokoyama (U of Tokyo), Akihiro University of Education), James M. Nester Ishibashi (Kinki U), and Gregory Gabadadze (National Central University), Wei-Tou Ni (NYU), giving introductory lectures in various (National Tsing Hua University), Chopin Soo topics in gravity. These are really beneficial to the (National Cheng-Kung University), I-Ching Yang students. Moreover, in the workshop the postdocs (National Taitung University), Hwei-Jang and the students are especially encouraged to give (National Cheng-Kung University), Hoi-Lai Yu presentations, with awards (sponsored by the (Institute of Physics, Academia Sinica), Chun- Europhysics Letters, IOP Publishing) given to the Hsien Wu (Soochow University). best ones among them. There are 10 such In addition there are around 5 postdocs and 15 presentations given by our group, with Jen-Tsung students. This year we already have had three Hsiang receiving the award. visitors (Bei-Lok Hu, Wade Naylor, and Niall This constitutes an important part of our O'Murchadha) and two more in October (Gerard ‘t training for our postdocs and students. Going to Hooft) and in December (Larry Ford), this school/workshop they have the rare respectively. opportunity to visit a prestige research institute, to meet with foreign researchers working in their

III-43 ‹‹- Highlights of Programs research areas, and also to present their works to initiated last year. This year we continue on with an international audience. this activity. So far we have had 6 PhD seminars B. Six miniworkshops organized in 2012 held at Tamkang U, National Cheng Kung U, National Central U, and National Dong Hwa U. Since the members of our group are from institutes all over Taiwan, in order to bring them III. Visitors and International together in a regular basis so as to enhance their Collaborations collaborative efforts, we have planned 6 In 2012 we have planned to have 5 foreign miniworkshops in this year. The first one is held in visitors to our group. The first visitor is Bei-Lok the Institute of Physics, Academia Sinica on Feb Hu (University of Maryland). He stayed at the 22 with the title “Miniworkshop on “Problem of National Changhua University of Education for Time””. In this workshop, Jim Nester, Chun-Yen nearly a month in January. With Shih-Yuin Lin, Lin (UC, Davies), Hoi-Lai Yu, and Chopin Soo they worked on the theory of relativistic quantum talked on their recent work on the problem of time information. With Hing-Tong Cho, they in gravitational theories. The second considered the stress tensor fluctuations in various miniworkshop was organized at the National curved spacetimes. The second visitor is Wade Changhua University of Education on April 28 Naylor (Osaka University). He stayed at Tamkang with the title “Miniworkshop on Field Theory in University for a week, collaborating with Hing- Curved Space”. Jen-Tsung Hsiang, I-Chin Wang, Tong Cho on the physics of higher-dimensional Shun-Pei Miao (Utrecht U), and Chih-Hung Wang black holes. The third visitor is Niall gave talks on their recent research, mainly in the O’Murchadha (University College, Ireland), who area of quantum field fluctuations applied to stayed at National Central University for two different physical situations. weeks. He collaborated with Jim Nester, Chopin The next miniworkshop is held at NCTS on Soo, and Hoi-Lai Yu on the theory of canonical June 9 with the title “Miniworkshop on Canonical gravity. Approaches and Numerical Methods in Gravity”. The next visitor is Gerard ‘t Hooft (Utrecht U), Wei-Tou Ni, Niall O Murchadha (U College, who was the Physics Nobel Laureate in 1999. He Ireland), Dah-Wei Chiou, and Alf Tang talked will give a seminar at the Institute of Physics, about works on canonical gravity, while Hwei- Academia Sinica on Oct 19 and then he will visit Jang Yo talked on methods in numerical relativity. the National Cheng Kung U in Oct 20-21 to have The fourth miniworkshop is in Aug 4 at the discussions with our group members. He will also National Central University with the title give a seminar at the National Dong-Hwa U on “Miniworkshop on Spacetime Physics”. Otto Oct 24. The last visitor this year is Larry Ford Kong, Wai Bong Yeung, and Jim Nester gave talks (Tufts U), who will visit Soochow University in on various aspects of the theories of relativity and December for three weeks. He will collaborate gravitation. with various people on the topic of quantum field The fifth miniworkshop has just been held at fluctuations in curved spacetimes. the National Cheng Kung University with the title Foreign visitors are very helpful to us. That is “Workshop on Recent Advances in Gravitational the case especially for Bei-Lok Hu and Larry Ford Physics”. It was a two-day event on Sep 14-15. who visit us regularly, almost once a year. They There were 11 talks for people to report on the are both world experts in quantum field theory in works they had done on the various main research curved spacetime, and they are instrumental in directions of our FG during the summer. The last pushing forward our program on quantum field miniworkshop will be held on Dec 28-29 at fluctuation phenomena. Soochow University. It will also be a two-day event on the physics of gravitational wave and Other than the visitors members of our group dark energy. have collaborated with the following foreign C. PhD student seminars researchers: Eyo Ita, Ray J. Rivers, Jorma Louko, R. B. Mann, Rong Zhou, R. B. Behunin, Zhoujian In order to give the students opportunities to Cao, Sang Pyo Kim, A. S. Cornell, and Jason have presentations in institutes other than their Doukas. own, a series of PhD students seminars was

Highlights of Programs -›› III-44 IV. Highlights of Research Results submission. In 2011 we have published 21 papers, The main research directions of our group are: and 1 preprint. Below we list some of the 2012 Canonical Gravity, Quantum Field Fluctuations, papers according to their related research areas. Gravitational Wave, and Black Hole Physics. NCTS as Acknowledgement A. Canonical Gravity Quantum Field Fluctuations Finding a consistent theory of quantum gravity is an important issue in theoretical physics. [1] B. L. Hu, Shih-Yuin Lin, and Jorma Louko, Chopin Soo and Hoi-Lai Yu have worked on this “Relativistic Quantum Information in direction. Beginning with a new formalism of the Detectors-Field Interactions”, to be published Horava gravity, they have put forth a in Class. Quantum Grav. (2012). revolutionary proposal of realizing gravitation Black Hole Physics through 3d diffeomorphism invariance to understand the problem of time and to formulate a [2] Chiang-Mei Chen, Sang Pyo Kim, I-Chieh consistent theory of quantum gravity. Jim Nester Lin, Jia-Rui Sun, and Ming-Fan Wu, and Chiang-Mei Chen continue their effort to find “Spontaneous Pair Production in Reissner- the appropriate quasilocal expressions for the Nordstrom Black Holes”, Phys. Rev. D85 gravitational energy. (2012) 124041. B. Quantum Field Fluctuations [3] H. T. Cho, A. S. Cornell, Jason Doukas, T.-R. Huang, and Wade Naylor, “A New Approach Shih-Yuin Lin and Chung-Hsien Chou, with to Black Hole Quasinormal Modes: A Review Bei-Lok Hu, have used the influence functional of the Asymptotic Iteration Method”, Adv. method to explore how to describe quantum Math. Phys. 2012 (2012) 281705. measurement consistently in relativistic quantum field theory. Hing-Tong Cho, with Bei-Lok Hu, Reference has also applied this method, also known as the Canonical Gravity stochastic gravity theory, to consider quantum field fluctuations in curved space. Niall O Murchadha, Chopin Soo, and Hoi-Lai Yu, C. Gravitational Wave “Intrinsic Time Gravity and the Lichnerowicz- York Equation”, arXiv:1208.2525 (2012). Gravitational wave is expected to be detected in the near future, most probably by advanced 1. Chopin Soo and Hoi-Lai Yu, “General LIGO. Since the noise level is very high, accurate Relativity Without Paradigm of Space-Time numerical templates are needed to identify the Covariance: Sensible Quantum Gravity and signal. Hwei-Jang Yo has been working on the Resolution of the “Problem of Time””, numerical simulation of binary black hole arXiv:1201.3164 (2012). coalescences, which are the expected candidates Quantum Field Fluctuations for detection. 2. Shih-Yuin Lin, Kazutomu Shiokawa, Chung- D. Black Hole Physics Hsien Chou, and B. L. Hu, “Quantum Chiang-Mei Chen has explored the Teleportation between Moving Detectors in a holographic descriptions, related to the AdS/CFT Quantum Field”, arXiv:1204.1525 (2012). approach, of Kerr and charged RN black holes. 3. B. L. Hu, Shih-Yuin Lin, and Jorma Louko, Hing-Tong Cho, with Wade Naylor, has “Relativistic Quantum Information in considered various aspects of higher-dimensional Detectors-Field Interactions”, to be published in rotating black holes. Class. Quantum Grav. (2012). Gravitational Wave V. Publications In 2012 the members of our group have 4. Hwei-Jang Yo, Zhoujian Cao, and Chun-Yu published 6 papers and 3 more are accepted for Lin, “Modifications for Numerical Stability of publication. There are also 7 preprints under Black Hole Evolution”, arXiv:1205.5111 (2012)

III-45 ‹‹- Highlights of Programs Focus Group on Lattice QCD and Hadron Physics

Coordinator: Chung Wen Kao (Chung Yuan Christian University; email: [email protected])

I. Brief Description II. Activities Lots of activities have been organized to induce new ideas and collaborations: Regular activities: (a) Lattice QCD and oordinators: Chung Wen Kao, Chung Hadron physics seminar at NTU (b) Seminars Yuan Christian University Series at NCTU, co-funded by LQCDHP and Committee members: Juinn-Wei Chen Cosmology focus groups (c) Seminars Series at (National Taiwan University), Ting-Wai Chiu NDHU , co-funded by LQCDHP and Cosmology (National Taiwan University) Tung -Han Hsieh focus groups . (Academia Sinica) Fu-Juin Jiang (National Taiwan Schools and Workshops: (a) Mini-workshop Normal University) Chi-Jen David Lin (National on Beyond Standard Model Lattice Simulations Chiao-Tung University), Cheng-Pang Liu (June 14, 2012, NCTU) (b) The 16th Taiwan (National Dong-Hwa University) Nuclear Physics Winter School (July.2-5, 2012, There are seven members in our execute NTNU) (c) The 1st Winter School of committee. Our focus group consists of eight “Nonperturbative aspect of Gauge Field Theories” faculty members with their postdoctoral research (January 15-18, 2013, NTU). associates and students including graduate and We benefit from those activities a lot. The undergraduate students. Our scientific goal is to speakers of the seminars are mainly the foreign investigate the nonperturbative aspect of gauge visitors we have invited. field theories with the numerical and/or analytical methods. Among those gauge field We also support following travel budget theories the most important one is the theory of requests: the strong interaction, QCD. Our members (Lin, (1) Dr Kenji Ogawa (Postdoc of C.-J. David Lin) Chiu) are working on the projects of using lattice attended “lattice field theory conference”at methods to study the properties of the hadrons. On Caims, Australia and gave a talk there. the other hand some of us also work on the projects of using effective field theories and/or (2) Dr Alvin Kiswandhi (Postdoc of Shin Nan other theoretical tools such as Ads/CFT or adapt Yang) visited Dr Dong, Yu-Bing at Peking the models to study the properties of the hadrons University for their collaboration such as EDM of the hadrons (Liu), the (3) Mr. Chih-Liang Wu (J.W. Chen’s master fragmentation functions (Kao) and the phase student) will visit 2012 Shanghai Particle structure of quark-gluon plasma (Chen). Physics and Cosmology Symposium Furthermore our research also goes beyond QCD. (SPCS2012) on Sep. 15-16, 2012 For example, our members also study Technicolor and Shanghai International Summer School of theory using lattice method (Lin) and the Neutrinos and Dark Matter (SSNuDM) on condensed matter systems such as anti- Sep. 17-20, 2012, both at Shanghai Jiao Tong ferromagnets by effective field theory and Monte University (SJTU), Shanghai. Carlo simulation (Jiang). Although our object of research appears very diversed, essentially they all III. Visitors and International belong to the category of the nonperturbative Collaborations aspect of gauge theories. Our focus group succeeds to stimulate the collaboration between the local members, for

Highlights of Programs -›› III-46 example, C.P.Liu and J.W. Chen have written an This is the first lattice calculation on these article together with Chen’s student,Shen-His coupling constants which are essential quantities Yu(arXiv1209.2552). C.W.Kao and F.J.Jiang are in predicting the strong decays of these hadrons, working on the Monte Carlo calculation of quark as well as in controlling the chiral extrapolations jet contribution to fragmentation function with for all matrix elements involving heavy hadrons. Jiang’s new Ph.D student, D-H Yang. The In this projects, it was demonstrated that a high- following international collaborations have also precision computation for these couplings can be been set up by the help of NCTS: achieved with all the systematic errors under control. This project has led to three journal (1) Collaboration with William Detmold’s group papers, incuding one in Physical Review Letters (MIT) and Matt Wingate’s group and two in Physical Review D. (Cambridge) on lattice b physics. (C.-J. David Lin) (b) In collaboration with Hiroshi Ohki and Eigo Shintani, C.-J. David Lin and Kenji Ogawa (2) Collaboration with Karl Jansen’s group at performed study of the running coupling constant DESY Zeuthen on lattice Higgs-Yukawa in SU(3) gauge theory with 12 flavours. This model simulations. (C.-J. David Lin) theory can be one of the candidates for the (3) Collaboration with individuals (Hiroshi-Ohki walking technicolour scenario for dynamical at Nagoya University and Eigo Shintani at electroweak symmetry breaking. There has been Brookhaven National Lab) on lattice controversies about whether or not this theory is simulations for technicolour models. (C.-J. conformal in the IR. Our data and analysis has David Lin) added new information in this debate, and (4) Collaboration with individuals (Christopher indicated that indeed there is an IR fixed point in Aubin at Fordham University and Amarjit Soni this theory. Results from this study have been at Brookhaven National Lab) on new lattice published in JHEP. (c) With Christopher Aubin approaches to non-leptonic B decays. (C.-J. and Amarjit Soni, C.-J. David Lin worked out the David Lin) applicability of hard-pion chiral perturbation theory to the B decays into the D-K or D-pi final (5) Collaboration with Nam, Seung-il (KAIS) on state. This approach, when implemented with fragmentation function calculation based on numerical lattice calculations, can help tighten the non-local chiral-quark model. (C.W.Kao) constraint on the CP-violating angle, gamma, in (6) Collaboration with Jens Braun (Jena) Jain the b-d unitarity triangle in CKM physics. This Deng (ShangDong) Joaqun E. Drut (UNC) on work has been published in Phys. Lett. B. (d) Simulation of ultracold atom. (J.W. Chen). Together with Karl Jansen’s group at DESY Drut is the lecturer of the 16th summer school. Zeuthen and the NTU-HEP group led by Prof. He joined the collaboration after school. George Hou, C.-J. David Lin and Kenji Ogawa have been performing simulations for the Higgs- (7) Collaboration with F. Kämpfer, B. Bessire, M. Yukawa models are strong Yukawa couplings. Wirz, U.-J. Wiese (Bern) and C. P. Hofmann This year, they worked out the bulk phase (Colima) on anti-ferromagnet. (F. J. Jiang). structure of the theory, and now they are (8) Collaboration with U.-J.Wiese (Bern) and C.P. investigating whether the new second order phase Hofmann(Colima) and N. D. Vlasii (Kyiv) on transition in this regime is in the same universality skymion in a doted ferromagnet. (F. J. Jiang). class with the pure O(4) model. If it is not, then it will be very interesting to study the spectrum in this regime and there may be alternatives for IV. Highlights of Research Results accommodating the 125 GeV Higgs signal with some new physics beyond the standard model. C.-J. David Lin C. -J. David Lin has been invited to present the (a) C.-J. David Lin collaborated with William above work at seminars at many institutions, Detmold and Stefan Meinel on lattice computation including Yale University and the Kobayashi,- of heavy hadron axial current matrix elements. Maskawa Institute in Nagoya, as well as several

III-47 ‹‹- Highlights of Programs workshops held in Europe and North America. Monte Carlo data they reached are in consistence Because of these projects, this year C.-J. David with the established numerical values for the Lin was invited to co-organise a b-physics critical exponents, including the confluent workshop at the European Centre for Theoretical exponent, in the $O(3)$ universality class. Nuclear Physics and Related Areas in Trento, as (b) Jiang and his collaborators used the low- well as to serve on the International Advisory energy effective field theory for holes coupled Committee for The 30th International Symposium to the staggered magnetization to investigate on Lattice Field Theory (2012) in Cairns. the localization of holes on a Skyrmion in a J. W. Chen square lattice antiferromagnet. They find that when two holes get localized on the same A glance at the imaginary world of ultracold Skyrmion, the hole-pair forms a bound state. In atoms: From ultracold atoms to quantum particular, using the method of collective modes chromodynamics, reliable ab initio studies of quantization of the Skyrmion, Jiang and strongly interacting fermions require numerical colalborators determine the quantum numbers of methods, typically in some form of quantum the bound state. Remarkably, for p-wave states the Monte Carlo. Unfortunately, (non-)relativistic quantum numbers are the same as those of a hole- systems at finite density (spin polarization) pair bound by one-magnon exchange. They generally have a sign problem, such that those ab further find that two holes localized on a initio calculations are impractical. It is well Skyrmion with winding number $n = 1$ or 2 may known, however, that in the relativistic case have s- or d-wave symmetry as well. Their study imaginary chemical potentials solve this problem, might provide useful information relevant to the assuming the data can be analytically continued to preformed Cooper pairs of high-temperature the real axis. Is this feasible for non-relativistic superconductors. systems? Are the interesting features of the phase diagram accessible in this manner? Introducing (c) Jiang determines the low-energy complex chemical potentials, for real total particle constants, namely the staggered magnetization number and imaginary polarization, the sign density per spin, the spin stiffness , and the problem is avoided in the non-relativistic case. To spinwave velocity $c$ of the 2-d spin-1/2 give a first answer to the above questions, Heisenberg model on the honeycomb lattice by J.W.Chen Jens Braun, Jian Deng, Joaqun E. Drut, using first principles Monte Carlo method. The Bengt Friman, Chen-Te Ma, and Yu-Dai Tsai, periodic boundary conditions (PBCs) performed a mean field study of the finite- implemented in his investigation lead to a temperature phase diagram of spin-1/2 fermions honeycomb lattice covering both a rectangular and with imaginary polarization. The result is written a parallelogram-shaped region. Remarkably, while with the title: A glance at the imaginary world for quantum antiferromagnets on the rectangular of ultracold atoms and submitted to archive: area, it has been demonstrated that the use of arXiv:1209.3319. Monte Carlo data and predictions of magnon F. J. Jiang chiral perturbation theory can lead to accurate determination of the low-energy constants, by (a) Jiang and his students study the phase utilizing a similar approach, the numerical values transitions induced by dimerization of the of $\tilde{{\cal M}_s}$, $\rho_s$, and $c$ he herringbone- and ladder-dimer quantum obtains on the periodic honeycomb lattice Heisenberg models on the square lattice using covering a area of different shapes are consistent Monte Carlo method. While the obtained Monte with each other quantitatively. The numerical Carlo data for both the models considered in their accuracy he reached is greatly improved. investigation are compatible with the recently proposed scenario of an enhanced correction to scaling, they find it is likely that the enhanced correction to scaling manifests itself as V. Publications (After Oct 2011) amplification of the nonuniversal prefactors [1] William Detmold, C.-J. David Lin, Stefan appearing in the scaling forms. In other words, the Meinel, “Calculation of the heavy-hadron axial

Highlights of Programs -›› III-48 couplings g1, g2, and g3 using lattice QCD”, [7] F. Kämpfer, B. Bessire, M. Wirz, C. P. Phys. Rev. D 85, 114508 (2012). Hofmann, F.-J. Jiang*, and U.-J. Wiese, “Systematic low-energy effective field theory [2] Christopher Aubin, C.-J. David Lin, Amarjit for magnons and holes in an anti- Soni, “Possible lattice approach to B→Dπ(K) ferromagnet on the honeycomb lattice” Phys. matrix elements”, Phys. Lett. B 710, 164 Rev. B 85, 075123 (2012). (2012). [8] F.-J. Jiang*, “Monte Carlo simulations of an [3] William Detmold, C.-J. David Lin, Stefan unconventional phase transition for a two- Meinel, “Aial Couplings and Strong Decay dimensional dimerized quantum Heisenberg Widths of Heavy Hadrons”, Phys. Rev. Lett. model”, Phys. Rev. B 85, 014414 (2012). 108, 172003 (2012). [9] S.i.Nam and Chung Wen Kao, “Fragmentation [4] William Detmold, C.-J. David Lin, Stefan and quark distribution functions for the pion Meinel, “Axial couplings in heavy-hadron and kaon with explicit flavor-SU(3)-symmetry chiral perturbation theory at the next-to- breaking”, Phys.Rev.D 85, 094023 (2012). leading order”, Phys. Rev. D 84, 094502 (2011), published 9 November 2011. [10] S.i.Nam and Chung Wen Kao, “Fragmentation functions and parton [5] C.-J. David Lin, Kenji Ogawa, Hiroshi Ohki, distribution functions for the pion with the Eigo Shintani, “Lattice study of infrared nonlocal interactions”, Phys. Rev. D 85, behaviour in SU(3) gauge theory with twelve 034023 (2012). massless flavours”, arXiv:1205.6076, JHEP 1208 (2012) 096. [11] J.W. Chen, S.H. Dai, N.E. Lee, D. Maity, 2012, Novel Parity Violating Transport [6] J.W. Chen, N.E. Lee, D. Maity, W.Y. Wen, “A Coefficients in 2+1 Dimensions from Holographic Model for Hall Viscosity”, Phys. Holography, e-Print: arXiv:1206.0850 [hep- Lett. B713 (2011). th] To appear at JHEP.

III-49 ‹‹- Highlights of Programs Focus Group on LHC Physics

Coordinator: Chuan-Hung Chen (National Cheng Kung University; email: [email protected])

I. Brief Description II. Activities To promote the research quality and the cooperation among researchers and benefit students, we have organized many schools, regular TLAS and CMS at the LHC has observed seminars and workshops. They are introduced as a new boson at the level of 5σ follows: significance in the mass region around 125-126 Schools GeV this year. Recently, LHCb firstly measures an unexpected large CP asymmetry difference in 1. We sponsor the 25th spring school on particle D-meson decays, and the anomaly is confirmed by and files held April 5-8 at NTU. Each lecturer CDF. Apparently, LHC-related physics becomes gave a series of lectures to introduce the basic very important fields in particle physics in next concept and the recent progress on that field. decade. 2. To study the sophisticated processes of LHC The Goals of the LHC focus group (FG) are (1) physics, we organized Taipei School on to train the students and young postdocs to know MadGraph for LHC Physics, which was held and study the new trends in and frontier of high May 25-27 at NTU/NTHU. One of organizer is energy physics effectively; (2) to establish the Prof. Hagiwara from KEK Japan. The main local and international collaborations and increase audiences are students including 5 from China. the international visibility; (3) to respond to the Seminars important idea and hot topics in the field and make contributions in a timely manner. As stated Weekly seminars and journal clubs are in original proposal, the scientific goals of this regularly scheduled at NTU, NCU, CYCU and focus are (a) investigation of physics of NTHU. Beside the lecture fee, we also support electroweak symmetry breaking and Higgs the accommodation if the speaker stays additional mechanism; (b) physics beyond the standard time for collaborations and discussions. model; (c) probing the nature of dark matter; (d) Workshops flavor physics and CP violation. 1. 2012 LHC Focus Group Miniworkshop was The FG consists of six coordinators from 5 held on 16 June at CYCU, organized by K.C. universities and one institute. They are Tzu- Yang. The invited speakers included students Chiang Yuan of AS, Cheng-Wei Chiang of NCU, and postdocs. This provided a platform for them Chuan-Hung Chen of NCKU, Kwei-Chou Yang to present the recent research achievements. and Kingman Cheung of NTHU. This year we Collaboration could be formed by such have a new coordinator Chuan-Ren Chen of miniworkshop. NTNU instead of Xiao-Gang He who now is the director of physics division NCTS. The chief 2. Summer Institute 2012, a Japan traditional coordinator is alternation and will take charge of activity, was held Aug 18-24 in Sun-Moon Lake the detailed matter for that year. In addition, there Taiwan this year, organized by Otto Kong and are 25 other faculty and 15 postdoc members from K. Cheung etc. Last time in Taiwan was 2008. various universities and institutes. The students The agenda included lectures, session talks and who work on high energy physics are welcome to poster session. Students presented their research participate our academic activities. results in the poster session that induced a lively discussion.

Highlights of Programs -›› III-50 Furthermore, the planning workshop and Ayyad U. Morocco, see [6] and [8] in the school are publication list, respectively. • A 3-day workshop entitled Joint Retreated on • C.W. Chiang collaborated with V. Barger of U. Cosmology and LHC Physics will be held Nov of Wisconsin and W.Y Keung and with T. Han 2-4, organized by C.H. Chen and C.Q. Geng. of U. of Wisconsin-Madison, see [10] and [20] The invited speakers are more then 30 and the in the publication list, respectively. He also involved countries are Taiwan, China, Korea collaborated with A. Arhrib of faculty of science and Japan etc. Morocco, D.K. Ghosh of India and R. Santos of Portugal, see [17]. • Third Taiwan Winter Camp on Numerical Simulation in High Energy Physics will be held Jan 19-26 2013, organized by Dr. Chung-Lin Shan. IV. Highlights of Research Results Research results are classified by topics and we highlight a few selected achievements. III. Visitors and International Collider Physics Collaborations • In the beginning of 2011, CDF announced that Visitors the top-quark forward-backward asymmetry • Prof. Pyung-Won Ko of KIAS Korea visited (FBA) has very strange behaviors in the large NCTS from Mar 27 – April 3 for collaboration rapidity-difference region and in the large with Dr. Jae-Sik Lee of NTHU. invariant mass region. The top FBA is large as 61% in the large invariant mass. Cheung and • Dr. Wei-Chih Huang visited NCTS from 11-20 Yuan [2] investigate a W’ contribution and April for collaboration with K. Cheung. discuss an easy way to test the model. Chen and • Prof. Wai-Yee Keung of U. of Illinois at his collaborators study the problem in unparticle Chicago visited NTHU and NTU from Jul 2- physics [8]. Aug 22. He collaborated with Cheung, Chiang • Chiang and his collaborators study the and Yuan. implications of the searches based on H→τ+τ− • Prof. Muneyuki Ishida of Meisei U. Japan by the ATLAS and CMS collaborations on the visited NTU and NTHU from 2-8 July. parameter space of the two Higgs doublet model • Dr. Hiroaki Sugiyama of Toyama U. Japan (2HDM). They also discuss the implications for visited NCU between 24-29 Aug for the 2HDM of the recent di-muon search by the collaboration with Prof. Chiang’s group. ATLAS collaboration for a CP-odd scalar in the mass range 4-12 GeV [10] • Prof. Victor Chernyak of Institutes of Nuclear Dark Matter Physics, Novosibirsk will visit Taiwan for QCD workshop at AS from 25 Oct to 5 Nov. He will Cheung and Yuan [1] use an effective gave lectures at NTU and AS. interaction approach to describe the interactions of Prof. Rachid Benbrik of Cadi Ayyad U. the dark matter particle with the standard model Morocco will visit NCTS and NCKU for (SM) particles. collaboration with C.H. Chen and participating the They estimate the lower bounds on the new workshop in November. interactions based on the condition of thermalizing International Collaborations dark matter particle in the early Universe. They found the latest antiproton data from PAMELA • K.C. Yang collaborated with T.M. Aliev of can put a strong constraint on the size of the faculty of Arts & Sciences Turkey, see [7] ] in interactions. the publication list. Flavor Physics and CP Violation • C.H. Chen collaborated with C.S. Kim of • Yonsei U. Korea and with R. Benbrik of Cadi To understand the unexpected large CP

III-51 ‹‹- Highlights of Programs asymmetry (CPA) difference in D0→(K–K+, π– [3] K. Cheung, T. –J. Hou, J. S. Lee, E. Senaha, π+) observed by LHCb and confirmed by CDF, “Higgs-mediated electric-dipole moments in Cheng and Chiang study the phenomenon in the the next-to-minimal supersymmetric standard SM in detail, and conclude the SM cannot solve model: An application to electroweak the anomaly, see [18,20]. For solving the baryogenesis”, Phys. Rev. D84, 015002 (2011) problem, Chen and Geng study the contributions [arXiv:1102.5679 [hep-ph]]. from colored scalar boson in [15]. [4] Chun-Fu Chang, Kingman Cheung, Tzu- • Yang used Gell-Mann-Okubo mass formulas Chiang Yuan “2011 Global Study of Electron- and data from f1(1285)→(Φγ, ργ) to Quark Unparticle Interactions”, Eur. Phys. J.

determine the mixing angle of f1 (1420) and C71 (2011) 1611 [arXiv:0912.1849 [hep-ph]].

f1(1285). In this work, the strange quark mass [5] Chian-Shu Chen, Thomas W. Kephart and and the condensate are also calculated [6]. Tzu-Chiang Yuan, “An A_5 Model of Four • Chiang and his collaborators explore a Z' boson Lepton Generations”, JHEP 1104 (2011) 015 with family-nonuniversal couplings to charged [arXiv:1011.3199 [hep-ph]].

leptons. They perform a comprehensive study of ++ [6] Kwei Chou Yang, “1 Nonet Singlet-Octet constraints on the leptonic Z' couplings from Mixing Angle, Strange Quark Mass, and currently available experimental data on a Strange Quark Condensate”, Phys. Rev.D 84, number of flavor-conserving and flavor- 034035 (2011) [arXiv:1011.6113 [hep-ph]]. changing transitions [11]. [7] T.M. Aliev, M. Savci and Kwei-Chou Yang, Interdisciplinary → “Tensor form factors of B K1 transition from Using the nonobservance of missing mass QCD light cone sum rules”, Phys. Lett. events in the leptonic kaon decay K→μX, Chiang B700:55-64 (2011). and his collaborators place a strong constraint on [8] C.H. Chen, G. Cvetic and C.S. Kim, exotic parity-violating gauge interactions of the “Forward-backward asymmetry of top quark right-handed muon. For illustration, they apply it in unparticle physics”, Phys. Lett. B 694, 393 to explain the proton size anomaly, where the (2011) [arXiv:1009.4165 [hep-ph]]. gauge boson decays invisibly or is long-lived are constrained [17]. [9] C.H. Chen and Gaber Faisel, “Axigluon on b like-sign charge asymmetry A sl , FCNCs and In summary, we have published 19 papers with CP asymmetries in B decays”, Phys.Lett.B696, NCTS affiliation and 16 papers with 487 (2011) [arXiv:1005.4582 [hep-ph]]. acknowledgement to NCTS since 2011, where the former and the latter includes one paper in [10] A. Arhrib, R. Benbrik, M. Chabab and C.H. Physical Review Letters, respectively. Moreover, Chen, “Pair production of neutralinos and we also have 5 and 3 preprints that affiliate and charginos at the LHC: the role of Higgs acknowledge NCTS. bosons exchange”, Phys. Rev. D 84, 115012 (2011)[arXiv:1109.0518 [hep-ph]]. [11] Cheng-Wei Chiang, Yi-Fan Lin, and Jusak V. Selected Publications Tandean, “Probing leptonic interactions of a [1] Kingman Cheung, Po-Yan Tseng and Tzu- family-nonuniversal Z’ boson”, JHEP 1111, Chiang Yuan, “Cosmic Antiproton Constraints 083 (2011). on Effective Interactions of the Dark Matter”, [12] Vernon Barger, Cheng-Wei Chiang, Wai-Yee JCAP 1101 (2011) 004 [arXiv:1011.2310 [hep- Keung, and Danny Marfatia, “Proton size ph]]. anomaly”, Phys. Rev. Lett. 106, 153001 (2011). [2] Kingman Cheung and Tzu-Chiang Yuan, “Top [13] Chuan-Hung Chen, Cheng-Wei Chiang, Quark Forward-Backward Asymmetry in the Takaaki Nomura, Yu Fusheng, “A Light charged Large Invariant Mass Region”, Phys. Rev. D Higgs boson in two-Higgs doublet model for CDF 83 (2011) 074006 [arXiv:1101.1445 [hep-ph]]. Wjj anomaly”, Phys. Rev. D 85, 075018 (2012).

Highlights of Programs -›› III-52 [14] Chuan-Hung Chen and Sandy S.C. Law, [19] Hai-Yang Cheng and Cheng-Wei Chiang, “Exotic fermion multiplets as a solution to “Direct CP violation in two-body hadronic baryon asymmetry, dark matter and neutrino charmed meson decays”, Phys. Rev. D 85, masses”, Phys. Rev. D 85, 055012 (2012) 034036 (2012); Erratum-ibid 85, 079903 [arXiv:1111.5462 [hep-ph]]. (2012). [15] Chuan-Hung Chen, Chao-Qiang Geng and [20] Hai-Yang Cheng and Cheng-Wei Chiang, Wei Wang, “CP violation in D0→(K–K+, π –π+) “Revisiting scalar and pseudoscalar couplings from diquarks”, Phys. Rev. D 85, 077702 with nucleon”, JHEP 1207, 009 (2012). (2012) [arXiv:1202.3300 [hep-ph]]. [21] Hai-Yang Cheng and Cheng-Wei Chiang, [16] Cheng-Wei Chiang, Takaaki Nomura, Koji “SU(3) symmetry breaking and CP violation Tsumura, “Search for doubly charged Higgs in D --> PP decay”, Phys. Rev. D 86, 014014 bosons using the same-sign diboson mode at (2012). the LHC”, Phys. Rev. D 85, 095023 (2012). [22] Cheng-Wei Chiang, Neil D. Christensen, [17] Vernon Barger, Cheng-Wei Chiang, Wai-Yee Gui-Jun Ding, and Tao Han, “Discovery in Keung, and Danny Marfatia, “Constraint on Drell-Yan processes at the LH”, Phys. Rev. D parity-violating muonic forces”, Phys. Rev. 85, 015023 (2012). Lett. 108, 081802 (2012). [18] Abdesslam Arhrib, Cheng-Wei Chiang, Dilip Kumar Ghosh, and Rui Santos, “Two Higgs Doublet Model in light of the standard model H --> τ+τ− search at the LHC”, Phys. Rev. D 85, 115003 (2012).

III-53 ‹‹- Highlights of Programs Focus Group on String Theory

Coordinator: Yi Yang (National Chiao Tung University; email: [email protected])

I. Brief Description (2) The 5th Taiwan School on String and Field will be held at NCU (main organizer: Chiang-Mei Chen) during Dec.13-16, 2012. This workshop is one of our important annual events in he string theory focus group is one of the summarizing the recent development and earliest founding units of the NCTS reviewing our own progress in the past year. Physics Division. Our research goal is to make To provide a better educational platform and theoretical study of the string theory as a unified encourage young researchers to collaborate framework of quantum gravity and apply string with other research fields, we decide to theory methods to other physics fields such as reorientate our annul Taiwan String Workshop hadrons physics and condensed matter physics. to Taiwan School on String and Fields from Our group committee consists of 14 faculty this year. In addition, we organized a mini- members: Heng-Yu Chen (NTU), Wu-Yen Chuang workshop on cosmology on Aug. 3. (NTU) Pei-Ming Ho (NTU), Hsien-Chung Kao (3) We have several journal clubs and study (NTNU), Feng-Li Lin (NTNU), Choon-Lin Ho groups on some special topics: (TKU), Chiang-Mei Chen (NCU), Wen-Yu Wen (a) SYSY; (b) BFSS Matrix model; (c) BCFW (CYCU), Chong-Sun Chu (NTHU), Jen-Chi Lee and string amplitudes; (d)AdS/QCD (e) AdS/ (NCTU), Yi Yang (NCTU), Chuan-Tsung Chan CMT (THU), Chen-Pen Yeh (NKHU), and Kzzuyuki Furuuchi (NCTS). The current coordinator is Yi We found that these journal clubs and study Yang (Department of Electrophysics, NCTU). In groups are extremely useful for young addition to faculty members, the active group researchers to learn the new developments, members include 34 post-docs researchers and propose their research directions and seek the students. We have various research teams which collaborations. Many of our recent papers are select their individual research topics based on benefit from these programs. Some of the their interests and expertise (the details are given programs involved research topics in other in below). focus groups, such as hardon physics and condensed matter physics, and increased the opportunity to communicate with other focus groups. II. Activities In addition, there is a summer school on The major activities of our string theory focus Symmetries in physics and mathematics during group consist of four major categories: Aug.6-10 held by NCTS, North. (1) We have regular seminar series in three major (4) It is our policy to support post-doc and universities: students to attend international conferences (a) NTU string seminar; (b)NTNU HEP and/or schools in order to get more solid seminar; (c)NCTU HEP seminar. trainings. We have supported Dr. Horotaka Irie We invite many international and local visitors to visit CERN (1/9-1/14), Dr. Tomino Dan and to report on the recent progress of String Dr. Shoichi Kawamoto to attend the workshop theory. Through the discussions with the "Progress in Quantum Field Theory and String speakers, we hope to create more opportunities Theory" in Osaka (4/3-4/7). In addition, we of collaboration. In the year of 2011-2012, we will support Dr. Shang-Yu Wu, Dr. Shou- have held more than 70 seminars and invited Huang Dai and Dr. Shoichi Kawamoto to 25 international visitors to present in our attend the YITP workshop on "From Gravity seminar series. to Strong Coupling Physics" (10/15-10/19).

Highlights of Programs -›› III-54 III. Visitors and International theory. Their study on the Stokes phenomena Collaborations has led to interesting discovery of integrable To provide more opportunities to communicate structures of the non-critical String/M theory. and collaborate with the international researchers, (5) Study the phase structure of RN black hole, we spent most of our budget to invite international Kerr-AdS black hole, Kerr-Newman black visitors. During the last 8 months of 2012, we hole, Kerr-Newman-AdS-dS black holes and have invited 25 foreign visitors to visit Taiwan their holographic dual. and give talks in our various seminars and mini- (6) Study 1uasi-local Energy in spherically workshop. Among the 39 papers that our focus spacetimes group members have finished, there are 15 papers are collaborated with international authors. In (7) Study gauge symmetry on fazzy geometry. December, we will organize the 5th Taiwan (8) Study cosmological constant, no-cloning School on String and Fields. Four international theorem and baryogenesis in inflating invited speakers will give a series lectures on (1) scenario. High Energy Physics in Primordial Density Perturbations, (2) Scattering Amplitudes and the Conference Presentations Role of Spacetime, (3) Scale invariance vs. [1] Hirotaka Irie, “Stokes Phenomena and Conformal invariance and (4) Black Holes and Quantum Integrability in the Multi-cut Matrix Non-Perturbative Effects in Higher Spin Theories. Models” at UK-Japan Winter School 2012 on String Theory, Geometry and Mathematical Physics, January 4-8, 2012, Oxford University, IV. Highlights of Research Results UK. We have finished 39 research papers in the [2] Hirotaka Irie, “Matrix Models and Stokes period from 2011 to 2012. Among them the Phenomena” at Workshop on Matrix Model highlight results are: and Around, February 18-21, 2012, Rikkyo University, Japan. (1) Application of gravity/gauge duality to strongly correlated systems. [3] Chong-Sun Chu, “Non-abelian action of M5-branes” at workshop on Mathematical • Build various holographic models to study aspects of string and M-theory, Issac Newton superconductor, topological insulator, dipole Institute of mathematical science, March 3, coupling effect, Hall viscosity, Unruh effect, 2012. Entanglement Entropy and violating transport coefficients in condensed matter [4] Wen-Yu Wen, “Dipole Coupling Effect of theories. Holographic Fermion in Charged Dilatonic Gravity” at International Conference on • Study holographic QCD at Finite Density. Progress in Quantum Field Theory and String (2) By studying the non-Abelian self-dual gauge Theory, April 3-7, 2012, Osaka. theory, we try to write down the action of [5] Yi Yang, “Phases in Holographic QCD" at M5-brane and D-brane in R-R Field 2012 Cross Strait Meeting on Particle Physics Background. This is crucial to understand the and Cosmology”, May 7-11, 2012, Chongqing, M theory. PRC. (3) Study high-energy string scattering amplitudes [6] Chong-Sun Chu, “A proposal for a non-abelian in Regge limit in the cases of supersymmetric theory of multiple M5-branes” at CQUeST and compactified spacetime, respectively. We EU-FP Autumn workshop 2012, September conjectured and proved a series of identidies 13, 2012, Seoul. between string amplitude in Regge limit and hard limit. [7] Chong-Sun Chu, “A proposal for a non-abelian theory of multiple M5-branes” at Autumn (4) Suggeste to use multi-cut matrix model as a Symposium on string/M-theory, September 19, constructive definition of non-critical M 2012, Seoul.

III-55 ‹‹- Highlights of Programs V. Selected Publications [11] Chiang-Mei Chen, Sang Pyo Kim, I-Chieh [1] Jen-Chi Lee, Yoshihiro Mitsuka, Yi Yang, Lin, Jia-Rui Sun, Ming-Fan Wu, “Higher Spin String States Scattered from “Spontaneous Pair Production in Reissner- D-particle in the Regge Regime and Factorized Nordstrom Black Holes”, arXiv:1202.3224. Ratios of Fixed Angle Scatterings”, Prog. [12] Wen-Yu Wen, Shang-Yu Wu, “Dipole Theor. Phys. 126 (2011), 397-417. Coupling Effect of Holographic Fermion in [2] Kazuyuki Furuuchi, Takeo Inami, Kazumi Charged Dilatonic Gravity”, Okuyama, “Gauge-Higgs Unification In arXiv:1202.6539. Spontaneously Created Fuzzy Extra [13] Masafumi Ishihara, Feng-Li Lin, Bo Ning, Dimensions”, JHEP11 (2011) 006. “Refined Holographic Entanglement Entropy [3] Ming-Fan Wu, Chiang-Mei Chen, Jian-Liang for the AdS Solitons and AdS black Holes”, Liu, James M. Nester, “Optimal Choices of arXiv:1203.6153. Reference for a Quasi-local Energy: [14] Shih-Hao Ho, Feng-Li Lin, “Anti-de Sitter Spherically Symmetric Spacetimes”, Space as Topological Insulator and arXiv:1109.4738. Holography”, arXiv:1205.4185. [4] Jiunn-Wei Chen, Nien-En Lee, Debaprasad [15] Ming-Fan Wu, Chiang-Mei Chen, Jian-Liang Maity, Wen-Yu Wen, “A Holographic Model Liu, James M. Nester, “Quasi-local Energy For Hall Viscosity”, arXiv:1110.0793 for Spherically Symmetric Spacetimes”, [5] Yi Yang, Jen-Chi Lee, “String Scattering arXiv:1206.0506. Amplitudes in High Energy Limits”, [16] Pei-Ming Ho, Chen-Te Ma, Chi-Hsien Yeh, arXiv:1112.6077. “BPS States on M5-brane in Large C-field [6] Yu-Dai Tsai, X.N. Wu, Yi Yang, “Phase Background”, arXiv:1206.1467. Structure of Kerr-AdS Black Hole”, Phys. Rev. [17] Chuan-Tsung Chan, Hirotaka Irie, Chi-Hsien D 85, 044005 (2012). Yeh, “Analytic Study for the String Theory [7] Jen-Chi Lee, Catherine H. Yan, Yi Yang, Landscapes via Matrix Models”, “High-Energy String Scattering Amplitudes arXiv:1206.2351. and Signless Stirling Number Identity”, [18] Pei-Ming Ho, Yutaka Matsuo, “Note on non- SIGMA 8 (2012), 045. Abelian two-form gauge fields”, [8] Chuan-Tsung Chan, Hirotaka Irie, Chi-Hsien arXiv:1206.5643. Yeh, “Stokes Phenomena and Non- [19] Shih-Hao Ho, Feng-Li Lin, Xiao-Gang Wen, perturbative Completion in the Multi-cut Two- “Majorana Zero-modes and Topological matrix Models”, Nucl.Phys. B854 (2012) Phases of Multi-flavored Jackiw-Rebbi 67-132. model”, arXiv:1207.1620. [9] Kazuyuki Furuuchi, Chia-Min Lin, “Affleck- [20] Song He, Jen-Chi Lee, Yi Yang, “Exponential Dine baryogenesis in inflating curvaton fall-off Behavior of Regge Scatterings in scenario with O($10-10^2$TeV) mass moduli Compactified Open String Theory”, accepted curvaton”, JCAP03 (2012) 024. by Prog. Theor. Phys. [10] Chiang-Mei Chen, Jia-Rui Sun, “The Kerr- [21] Qing-Guo Huang, Feng-Li Lin, Newman/CFTs Correspondence”, “Cosmological constant, inflation and arXiv:1201.4040. no-cloning theorem”, accepted by Phys. Lett. B.

Highlights of Programs -›› III-56 Highlights of Programs Interdisciplinary Fields

Focus Group on Atomic-Molecular-Optical Physics

Coordinator: Daw-Wei Wang (National Tsing Hua University; email: [email protected])

I. Brief Description Atoms and Molecules in Teacher’s Hostel, organized by Daw-Wei Wang, Shih-Chuan Guo, and Ming-Shien Chang. We invited several world- leading-edge theorists and experimental groups to oordinator: Daw-Wei Wang (National introduce their work on ultracold atoms and Tsing Hua University) molecules. This includes Daniel Comparat (Laboratoire Aimé Cotton, France), Olivier Dulieu Committee members: Wen-Chin Wu (NTNU), (Laboratoire Aimé Cotton, France), Gediminas Shih-Chuan Gou (NCUE), Ming-Chiang Chung Juzeliunas (Vilnius U, Lithuania ), Henning (NCTS), Jiang-Nan Liu (FCU), Yi-Wei Liu Moritz (U. of Hamburger, Germany), Pierre Pillet (NTHU), Ying-Cheng Chen (IAMS), Te-Kuei (Laboratoire Aimé Cotton, France), Cheng Chin Fang (FCU), Wei-Chi Liu (NTNU), Ray-Kuang (Chicago U., USA), Lode Pollet (University of Lee (NTHU), Chin-Chun Tsai (NCKU), Ming- Munich, Germany), Ian Spielman (National Shien Chang (IAMS) Institute of Standard Technology, USA). The Group size: Active faculty members are about major topic is about the synthetic gauge field and 40 (including experimentalists), and students are polar molecules. about 120, based on the participants in annual Some of our invited speakers have built close activities. collaboration with researchers in Taiwan. For Goal: 1) To encourage more cooperation example, Prof. Spielman was the adviser of Prof. between researchers in this community, Yu-Ju Lin (IAMS), working together in synthetic especially cooperation between different institutes gauge field of fermionic atoms. Prof. Juzeliunas and between theorists and experimentalists. 2) To has a close collaboration with Prof. Ite Yu attract more researchers and students to join (NTHU) and Shi-Chuan Guo (NCUE) in EIT and related research and to form a stable research slow light physics. Furthermore, Prof. Comparat, environment. 3) To enhance the research quality Dulieu, and Pillet from Laboratoire Aimé Cotton by actively cooperating with international will like to build a long-term collaboration with frontier researchers. cold atom experimental groups in IAMS and NTHU. Major Research direction: (1) Strongly correlated physics in cold atoms/molecules, (2) AMO Summer School: In Aug. 2012, we held Dynamical properties of weakly interacting Bose the 9th AMO summer school in National Chung- gases, (3) Light and atom interaction and quantum Cheng University, organized by Prof. Dien-Jung manipulation, (4) Atomic structure theory and Han. In the summer school, we provide basic spectroscopy. training and knowledge to students and postdocs about recent development in AMO fields, II. Activities including precision measurement, cold atom, cold International Workshop: In the May 2012, molecules, polariton-exciton condensation, EIT we held an International Workshop on Ultracold and slow light etc. We also have a good tradition

III-57 ‹‹- Highlights of Programs by having a student session: students or postdocs International Cooperation from different groups provide lectures for their (1) D.-W. Wang (NTHU) recently has continue research results, so that they could know each collaboration with M. A. Cazalilla (NUS, other better and have more discussion for the Singapore), E. Demler (Harvard U.), and possible collaboration in future projects. Nikolaj Zinner (Aarhus U., Demark) etc. (ii) Prof. R.-K. Lee (NTHU) has collaboration with Prof. Yuri S. Kivshar and Prof. Wieslaw III. Visitors and International Krolikowski (Australian Nat’l U)., Prof. Wen- Collaborations Xing Yang, (Southeast U., China) , Prof. Ming Visitors Shen, (Shanghai U., China), Prof. Emmanuel Paspalakis (U. Patras, Greece), Prof. Boris A. (1) Regular international visitor: In recent years, Malomed, (Tel Aviv University, Israel), Prof. we have two regular international visitors. One Gaetano Assanto, (U. Studi Roma Tre, Italy), is Prof. Miguel Cazalilla, who had a long stay and Prof. Alexander P. Alodjants (Vladimir in NCTS during Feb. 15 and May 15, 2011. He State U., Russia). (iii) Prof. Chung-Hou Chung acknowledge NCTS’s hospitality for his (NCTU) has a collaboration with Prof. M. preparation of a review article in Rev. Mod Cazalilla. (iv) Prof. T.-K, Fang (FJU) Phys. [1]. In the last year, we also visited collaborates with Prof. T.-N. Chang (USC). (v) NCTS for three times: two was invited to Prof. Shih-Chuan Gou collaborates with Prof. Condensed matter theory focus group for two Makoto Tsubota (Osaka City U., Japan) and workshops and one by our focus group for Blair Blakie (U. Otago, New Zealand). (vi) short discussion. His visit brought a great Prof. Ming-Chiang Chung collaborates with impact to the AMO community in various Prof. Ingo Peschel (Free U. Berlin), Prof. ways: For example, Prof. Cazalilla has Miguel Cazallila (Centro de F´ısica de collaboration (i) with Prof. D.-W. Wang in Materiales (CFM), Spain), Prof. Anibal Iucci NTHU on the analytic renormalization group (U. Nacional de La Plata, Argentina), Prof. Ian theory of anisotropic superfluidity at zero and McColluch (U. Queenzland, Australia), and finite temperature, compared to the numerical Prof. Carlos Trallero-Gino (U. La Habana, quantum Monte Carlo results; (ii) with Dr. Cuba). M.-C. Chung in NTCS on thermalization of an exactly solvable model. The second regular visitor is Prof. Tu-nan IV. Highlights of Research Results Chang of USC. He continually leads the joint Strongly interacting cold atoms and polar experimental and theoretical team (including molecules: T. S. Yih, C. C. Chu, and J. I. Lo at the National Central University, H. S. Fung and Y. (1) Prof. Sungkit Yip (AS), Po-Chung Chen Y. Lee at the NSRRC, and T. K. Fang and C. (NTHU) and Ming-Chiang Chung (NCTS) H. Chen at Fujen University) on atomic investigated the quantum phase diagram of 1D structure study. spin-2 atoms by using both analytic as well as numerical techniques. Rich phase diagram and (2) Other visitors: In the last year, we have invited fundamental behaviors are reported [2]. several international researchers to visit NCTS (some of them give lectures in NTHU-PHYS (2) Daw-Wei Wang (NTHU) and Miguel Cazalilla or other institutes due to the host). It includes studied the quantum and thermal phase Cheng Chin (Chicago U., USA), Gediminas transition of anisotropic superfluid in 2D Juzeliunas(Vilnius U, Lithuania ), and Prof. optical lattice, showing nontrivial Kosterless Michael Fleischhauer (Universität Thouless trasition near the quantum critical Kaiserslautern). We will also invite several point [3]. They developed self-consistent others later in this year, include Prof. Krishna meanfield theory, renormalization group, as Dastidar (Indian Association for the well as quantum Monte Carlo calculation to Cultivation of Science), and Nikolaj Zinner understand such phase transition physics. (Arhus U., Denmark) etc.

Highlights of Programs -›› III-58 (3) Based on a mean-field approach, Wen-Chin quantum statistics and many-body effects of Wu (NTNU) and his collaborator have recently cold atoms. [9] investigated spontaneously crystalline ground Atomic structure and spectroscopy: states, called quantum crystals, of a trapped Rydberg-dressed Bose-Einstein condensate. In Tu-nan Chang (USC) and Te-Kuei Feng (FJU) a quasi-two-dimensional geometry, a study the disappearance of bound states for two- hexagonal lattice of condensate droplets electron atoms subjected to external plasma manifests when dressed coupling is above a environment [10]. Their quantitative estimates critical value. [4]. have resolved the qualitative disparity on the disappearance of the bound states between the Quantum dynamics of Bose-Einstein one- and two-electron atoms suggested implicitly Condensate: by other recent theoretical studies. (1) Prof. S,-C. Guo (NCUE) and collaborators develop modulation theory for undular bores (dispersive shock waves) in the framework of V. Selected Publications the Gardner equation. Using a reduced version of the finite-gap integration method we derive [1] M. A. Cazalilla, R. Citro, T. Giamarchi, E. the Gardner-Whitham modulation system in a Orignac, and M. Rigol, Rev. Mod. Phys. 83, Riemann invariant form and show that it can 1405 (2011). be mapped onto the well-known modulation [2] Pochung Chen, Zhi-Long Xue, I. P. system for the Korteweg--de Vries equation. McCulloch, Ming-Chiang Chung, and S.-K. [5] Yip, Phys. Rev. A 85, 011601(R) (2012) (2) Prof. S.-C. Gou (NCUE) and collaborators [3] Jhih-Shih You, Hao Lee, Shiang Fang, Miguel study the nonequilibrium dynamics of a A. Cazalilla, and Daw-Wei rapidly quenched spin-1 Bose gas with spin- Wang, arXiv:1207.2122, (submitted to Phys. orbit coupling. They show that crystallization Rev. A) of half-skyrmions (merons), can occur in a spinor condensate of Rubidium 87. [6] [4] C.-H. Hsueh, T.-C. Lin, T.-L. Horng, and W. C. Wu, Phys. Rev. A 86, 013619 (2012). (3) Daw-Wei Wang (NTHU) and Ray-Kuang Lee (NTHU) investigate the quantum tunneling [5] A. M. Kamchatnov, Y.-H. Kuo, T.-C. Lin, T.-L. behavior of a 1D soliton of Bose-Einstein Horng, S.-C. Gou, R. Clift, G. A. El, R. H. J. condensate in different parameter regime. Grimshaw, arXiv:1205.2749 (accepted by Their results show how the particle-wave Phys. Rev. E) duality to present in the tunneling properties of [6] S.-W. Su, I.-K. Liu, Y.-C. Tsai, W. M. Liu and a single soliton. [7] S.-C. Gou, Phys. Rev. A 86, 023601 (2012) Light-atom interaction and manipulation: [7] C.-H. Wang, T.-M. Hong, R.-K. Lee, and (1) Prof. Ray-Kuang Lee (NTHU) and his D.-W. Wang, arXiv:1206.1606 (accepted to be collaborator theoretically and experimentally published in Optical Express) generate stationary crescent surface solitons [8] C. P. Jisha, YuanYao Lin, Tsin-Dong Lee, and pinged to the boundary of a microstructured Ray-Kuang Lee, Phys. Rev. Lett. 107, vertical cavity surface emission laser. Their 183902 (2011). results provide an alternative and general [9] H. H. Jen, Xiong Bo, Ite A. Yu, Daw-Wei method to control lasing characteristics as well Wang, arXiv:1208.0118 (accepted by Phys. as to study optical surface waves. [8] Rev. A). (2) Daw-Wei Wang (NTHU) and Ite Yu (NTHU) [10] The preliminary result of this work will be developed a full quantum theory for the EIT presented in an invited talk by T. N. Chang at and slow light physics in quantum degenerate AISAMP10 in Taipei, Oct. 23-30, 2012. T. N. atomic gases, showing how the slow light Chang and T. K. Fang, to be resubmitted. spectrum can be a good method to reflect the

III-59 ‹‹- Highlights of Programs Focus Group on Quantum Information Science

Coordinators: Chung-Hsien Chou (National Cheng Kung University; email: [email protected]), Alec Maassen van den Brink (Academia Sinica; email: [email protected])

I. Brief Description 3. Summer Miniworkshop on Quantum Measurement and Quantum Information Science, July 23, 2012 (Taipei, Taiwan). 4.The 2012 Summer workshop on Quantum he main mission of the Quantum Science and Technology, Sep. 8~10, 2012 (Chi- Information Science (QIS) focus group is Tou, Taiwan). to build a platform of communication and discussion for researchers in this area in Taiwan. 5. Miniworkshop on Quantum Information In the last few years, we have brought QIS Science, to be held on Oct. 19, 2012 (Taipei, researchers in Taiwan to work and discuss Taiwan). research together and to hold activities, such as 6. Minischool on quantum information science, to scientific seminars, workshops and short-term be held on Dec. 22, 2012 (Tainan, Taiwan) schools. We have also been seeking to establish 7. The 7th Winter School on Quantum Information links and exchanges as well as to initiate Science, to be held in Jan. 19~22, 2013 collaborations with other QIS researchers (Kaohsiung, Taiwan) worldwide. 8. QIS seminars at NCKU, NTU, and CYCU. Coordinators: Chung-Hsien Chou (NCKU) and Alec Maassen van den Brink (AS) Beneficiaries Committee members: Yia-Chung Chang (AS), 1. The beneficiaries The Winter School on Yueh-Nan Chen (NCKU), Chi-Yee Chueng (AS), Quantum Information Science every year Hsi-Sheng Goan (NTU), Li-Yi Hsu (CYCU), (Activities (1) & (7)) is three-fold: 1. To Feng-Li Lin (NTNU), Shih-Yuin Lin (NCUE), continue the success of the schools on Zheng-Yao Su (NCHC), Wei-Min Zhang 'Quantum Information Science' held annually in (NCKU). Taiwan , supported by NCTS. 2. To promote and enhance the interaction between the Size of the Focus Group: Currently we have distinguished overseas speakers and local 11 active faculties and 7 postdocs. The average participants. 3. To educate graduate students to participants for the QIS winter schools are about enter the research frontier. 80 people. 2. Activities (2) & (4) are workshops for local Focused topics: Quantum Decoherence, researchers to exchange ideas and establish Entanglement, non-Markovian dynamics and future collaborations. They also provide a relativistic quantum information. useful platform for experimentalists and theorists to share their own research. II. Activities and Beneficiaries 3. Activities (3), (5) are one-day miniworkshops on special topics in quantum information Activities science, where several world-renowned experts 1. The 6th Winter School on Quantum Information working in this area are invited to present their Science, Feb. 12~14, 2012 (Nan-Tou, Taiwan) most recent experimental observations and theoretical investigations. We hope that these 2. Miniworkshop on Recent Developments in activities will serve the purpose to interest and Quantum Information Science, May 26, 2012 attract students and young scientists to the field (Hsinchu, Taiwan). of quantum information, and to promote the

Highlights of Programs -›› III-60 interaction between the international speakers 13. Prof. J. Oppenheimer, College University of and local researchers. London, (Oct. 19, 2012) Training of young-generation physicists 14. Prof. Anton Zeilinger, University of Vienna, (Oct. 19, 2012) 1. Financial supports for international collaborations International Collaborations We have supported Prof. Che-Min Li to visit Prof. Y. N. Chen + Prof. Buchleitner (Freiburg): Prof. Nori’s group at RIKEN and initiate new Project on photosynthesis. research projects and he is now a faculty Prof. C. M. Li, Dr. G. Y. Chen and Prof. Y. N. member at NCKU. Chen + Prof. Nori (Riken, Japan): (1) Research We also supported Mr. Matisse Wei-Yuan Tu visiting; (2) Project on Quantum Measurement. (Ph. D. student) to visit Prof. Nori’s group at Prof. C. M. Li and Prof. Y. N. Chen + Prof. J. W. RIKEN. Pan: (1) Research visiting of Prof. C. M. Li; (2) Project on Quantum Entanglement. Prof. H.-S. Goan + Prof. Vidar Gudmundsson III. Visitors and International (Iceland): Quantum transport of electrons through Collaborations a photon cavity Visitors Prof. W. M. Zhang + Prof. Amnon Aharony and 1. Prof. Bei-Lok Hu, University of Maryland, Prof Ora Entin-Wohlman (Israel): Project on USA (Dec. 24, 2011~ Jan. 23, 2012) transient quantum transport in mesoscopic physics 2. Prof. Marcos Cesar de Oliveira, Universidade Prof. W. M. Zhang + Prof. Tzyh-Jong Tarn (USA): Estadual de Campinas, Brazil (February, 2012) Project on quantum feedback control theory. 3. Prof. Barry C. Sanders, University of Calgary, Prof. W. M. Zhang + Prof. Daniel Braun (France): (February, 2012) Project on Decoherence Free Space in non- 4. Prof. Xin-Qi Li, Beijing Normal University, Markovian open systems. China (February ~ March, 2012) Prof. S.-Y. Lin, Prof. C.-H. Chou + Prof. B. L. Hu 5. Prof. Ora Entin-Wohlman, Ben Gurion (Maryland), Mr. Rong Zhou (Maryland), Dr. R. B. University of the Negev, Israel, (Feb. 24~27, Behunin (LANL): Project on entanglement 2012) dynamics in relativistic systems. 6. Prof. Amnon Aharony, Ben Gurion University Prof. S.-Y. Lin + Prof. R. B. Mann (Waterloo), Dr. of the Negev, Israel, (Feb. 24~27, 2012) Jason Doukas (NII): Project on non-equilibrium physics beyond the Unruh effect. 7. Prof. Kai Chen, University of Science and Technology, China, (Jun. 17~26, 2012) Prof. S.-Y. Lin + Dr. Andrzej Dragan (Warsaw): Project on quantum measurement in relativistic 8. Dr. Guin-Dar Lin, Harvard University, USA, quantum field theory.IV. Highlights of Research (July, 2012) Results 9. Dr. Haixin Miao, California Institute of Technology, USA, (July, 2012) IV. Highlights of Research Results 10. Prof. Ora Entin-Wohlman, Ben Gurion University of the Negev, Israel, (Sept. 13~24, A. Quantum Entanglement 2012) We investigate the entanglement generation 11. Prof. Amnon Aharony, Ben Gurion University between two quantum dots coupled to nanoring of the Negev, Israel, (Sept. 13~24, 2012) surface plasmons with asymmetric coupling strength g1 and g2. The dynamics of concurrence is 12. Prof. Lajos Diosi, Research Institute for obtained by solving the corresponding master Particle and Nuclear Physics, Hungary, (Oct. equation. High entanglement can be generated at 19, 2012)

III-61 ‹‹- Highlights of Programs appropriate times through the scatterings of the investigated the quantum coherence dynamics of incident field and its scattered field. Furthermore, the nanoscale double quantum dot Aharonov- we find that maximum entanglement can be Bohm (AB) interferometers, and discovered a new

created when r≡g1/g2 is the ratio of odd numbers. phenomena of phase localization, namely the Contrary to intuition, relative high entanglement relative phase between two double-dot charge (C 1) can remain even if the ratio r is far off the states is localized to a fixed value with varying the required values, which is useful in real magnetic flux threading into the symmetric AB experiments. [19]. ring [15]. Recently, we find that the coherence control between the two-dot charge states through In addition, we have also investigated the Fano the magnetic flux can be realized under a very resonance of the scattering spectra in a system unusual condition, namely the double dots consisting of a metal nanowire coupled to two asymmetrically couple to electrodes under a large colloidal quantum dots. By varying the coupling bias, which is usually forbidden in the coherence strengths and the energy spacings of the QD manipulation. And we also explored qubits, we find that both the lineshapes and the systematically, for the first time in the literature, presence of the Fano resonance can be controlled. the transient transport dynamics of nanoscale AB Furthermore, the degree of two-qubit interferometers. Besides, we studied the real-time entanglement can vary from unity to zero when dynamics of single-electron turnstiles and the Fano resonance occurs. This indicates that pumpings, and find the up-limit of the operating there exists the correlations between the two-qubit frequency for the single electron pumps [1]. This entanglement and the Fano resonance [26]. work has received a considerable attention of two experimental groups, one from the National B. Quantum coherence and quantum transport Institute of Standard technology of USA and the phenomena other from the National Physical Laboratory of UK. We established and developed the theory of dissipative photonic quantum transport for photonic networks [17]. The theory is based on C. Quantum Control Theory the exact master equation we derived in the past We introduce an efficient optimal-control few years, incorporating the dynamics equation of theory based on the Krotov method for a non- the reduced density matrix with the Schwinger- Markovian open quantum system with a time- Keldysh’s nonequilibrium Green functions. In nonlocal master equation in which the control particular, the quantum coherence and parameter and the bath correlation function are decoherence as well as the non-Markovian correlated. As an illustration, the optimal-control memory structure, the two main features in method is applied to find the control sequences for quantum transport, are fully taken into account in high-fidelity Z gates and identity gates of a qubit this theory. Applying this theory to nanocavities embedded in a non-Markovian bath. Z gates and coupled to waveguides imbedded in photonic identity gates with errors less than 10−5 for a wide crystals, we discovered that the non-Markovian range of bath decoherence parameters can be dynamics, due to the strong coupling between the achieved for the non-Markovian open qubit system and its environment and the structured system with control over only the σz term. The (engineering) reservoirs, can effectively suppress presented quantum optimal-control method is the coherence loss [14]. We also find that two shown to be a powerful tool, capable of separated squeezed states located in two distant facilitating new implementations of various nanocavities can be stably entangled through a quantum information tasks against decoherence. weak coupling to a waveguide [3]. The required information is knowledge of the bath Meanwhile, we explored the quantum or noise spectral density, which is experimentally coherence and quantum transport phenomena in accessible. By virtue of its generality, our method nanoelectronic systems, based on the exact master will find useful applications in many different equation and the quantum electronic transport branches of the sciences. The result was published theory we developed. In particular, we in [21].

Highlights of Programs -›› III-62 D. Relativistic Quantum Information Science Prof. Wei-Min Zhang We explicitly showed the consistency of 1. Nov. 2012 (to be), Invited Speaker, instantaneous projective measurement in a International workshop on Entangled Coherent relativistic quantum field when the measurement State and Its Application to QIS, Toyao, Japan. events are spatially local in a detector-field theory 2. Oct. 2012 (to be), Invited Speaker, the BIT's [25]. We studied the non-equilibrium physics of 2nd Annual World Congress of Nano-S&T, non-uniformly accelerated Unruh-DeWitt Qingdao, China. detectors moving in a quantum field, and looked at the entanglement dynamics and quantum 3. Jun. 2012, Invited Speaker, the 3rd International teleportation between an inertial detector and a Workshop on Entanglement, Decoherence and non-inertial detector undergoing non-uniform Quantum Control, Shanghai, China. accelerations [23]. Now we are working on the 4. Dec. 2011, Invited Speaker, the 5th physics in the detectors in oscillatory or circular International Workshop on Solid-State motion, the entanglement dynamics in the twin Quantum Computing, Hong Kong paradox, in dielectric medium, and in compact space, as well as the nonlocal measurement in relativistic quantum field theory. V. Publications Cooperation with experimental group The number of NCTS papers(since 2011) Prof. Yueh-Nan Chen is collaborating with which are results of Prof. Che-Ming Li’s group at NCKU. (1) collaborations of domestic institutes: 1 Interdisciplinary new collaboration (2) collaborations of international institutes: 13 Prof. Yueh-Nan Chen and Prof. Che-Ming Li’s group collaborate with Prof. Yuan-Chung Cheng [1] C. Y. Lin and Wei-Min Zhang, Appl. Phys. (Department of Chemistry, NTU) on a new Lett. 99, 072105 (2011). emerging subject, quantum biology and obtain [2] X. Z. Yuan, H.-S. Goan and K. D. Zhu, New J. some preliminary results. Phys. 13, 023018 (2011). Invited presentations [3] H. T. Tan, W. M. Zhang and G. X. Li, Phys. Prof. Hsi-Sheng Goan Rev. A 83, 062310 (2011). 1. Oct. 2012 (to be), Invited Speaker, the [4] G. Y. Chen, N. Lambert, C. H. Chou, Y. N. International Workshop on Horizons of Chen and F. Nori, Phys. Rev. B 84, 045310 Quantum Physics: from Foundation to (2011). Quantum-Enabled Technologies, Taipei, Taiwan [5] H. B. Chen, G. Y. Chen and Y. N. Chen, Opt. 2. Oct. 2012 (to be), Invited Speaker, the BIT's Commun. 284, 4529 (2011). 2nd Annual World Congress of Nano-S&T, [6] H. T. Tan and W. M. Zhang, Phys. Rev. A 83, Qingdao, China 032102 (2011). 3. Jun. 2012, Invited Speaker, the 3rd International [7] H.-S. Goan, P. W. Chen and C. C. Jian, J. Workshop on Entanglement, Decoherence and Chem. Phys. 134, 124112 (2011). Quantum Control, Shanghai, China [8] J. Y. Lien, Y. N. Chen, and C. H. Chou, New J. 4. Dec. 2011, Invited Speaker, the 5th Phys. 13, 083036 (2011). International Workshop on Solid-State [9] C. H. Chou, B. L. Hu and Y. Subasi, J. Phys.: Quantum Computing, Hong Kong Conf. Ser. 306, 012002 (2011). Prof. Shih-Yuin Lin [10] C. H. Chou, B. L. Hu and Y. Subasi, J. Phys.: 1. Invited Speaker, Relativistic Quantum Conf. Ser. 330, 012003 (2011). Information 5 Workshop, University of [11] S.-Y. Lin, J. Phys.: Conf. Ser. 306, 012060 Queensland, Brisbane, Australia, November (2011). 28-29, 2011.

III-63 ‹‹- Highlights of Programs [12] S.-Y. Lin, J. Phys.: Conf. Ser. 330, 012004 [23] D. C. M. Ostapchuk, S.-Y. Lin, R. B. Mann, (2011). and B. L. Hu, JHEP 1207, 072 (2012) [arXiv:1108.3377]. [13] W. Chen, G. Y. Chen, and Y. N. Chen, Opt. Lett. 36, 3602 (2011). [24] B. L. Hu, S.-Y. Lin, and J. Louko, Class. Quantum Grav., Special Issue on Relativistic [14] C. U. Lei and Wei-Min Zhang, Phys. Rev A Quantum Information (invited review, to 84, 052116 (2011) appear in November 2012) [15] Matisse Wei-Yuan Tu, Wei-Min Zhang and [arXiv:1205.1328]. Jinshuang Jin, Phys. Rev. B 83, 115318 [25] S.-Y. Lin, Ann. Phys. (N.Y.), accepted (2011) [arXiv:1104.0772]. [16] P.-W. Chen, C.-C. Jian and H.-S. Goan, Phys. [26] G. Y. Chen and Y. N. Chen, Opt. Lett., Rev. B 83, 115439 (2011) accepted (2012). [17] Lei, Chan U. and Zhang, Wei-Min, Ann. [27] H. N. Xiong, Wei-Min Zhang, M. W. Y. Tu, Phys. 327, 1408-1433 (2012). and D. Braun, Phys. Rev. A 86, 032107 [18] O. Jonasson, C.-S. Tang, H.-S. Goan and V. (2012). Gudmundsson New J. Phys. 14, 013036 [28] M. W. Y. Tu, Wei-Min Zhang, J. S. Jin, O. (2012). Entin-Wohlman and A. Aharony, "Transient [19] Guang-Yin Chen, Che-Ming Li, and Yueh- quantum transport in double dot Aharonov- Nan Chen, Opt. Lett., Vol. 37, 1337-1339, Bohm interferomenters", Phys. Rev. B 86, (2012). accepted (2012). [20] Li-Yi Hsu, Phys. Rev. A 85, 032115 (2012). [21] B. Hwang and H.-S. Goan, Phys. Rev. A 85, 032321 (2012). [22] V. Gudmundsson, O. Jonasson, C.-S. Tang, H.-S. Goan and A. Manolescu, Phys. Rev. B 85, 075306 (2012).

Highlights of Programs -›› III-64 Research Activities of Individuals

Research Activities on Particle Physics

Chian-Shu Chen (email: [email protected]) Postdoctoral researcher, 2010/08/01~2012/07/31; Assistant research scholar, 2012/08/01~present

n 2012 my research activity in NCTS has mixing matrix (CKM matrix) and lepton mixing been concentrated on neutrino physics matrix (PMNS matrix) in this model. And we may   and physics beyond the Standard Model. The have the relation of c ~ 13 which agrees with the topics cover from the mass generation of tiny experimental results. We find that the masses of neutrino masses, field theory issues, flavor fermions, including the heavy sectors, can be symmetry, dark matter, matter-antimatter accommodated with the limits of experimental asymmetry, and collider physics. Two main results. And at leading order the CKM matrix is theoretical puzzles have been settled by the the identity and the PMNS matrix corresponds to experiments in this year. The first one is the tribimaximal mixings.  mixing angle 13 and the second is the Standard Confronting with the neutrino oscillations and Model Higgs which have been searched for more cosmological observations. The tension between than forty years since it was proposed. The the standard three flavor oscillation picture and question “how small is the lepton mixing angle  ” some experimental results exists. The oscillation 13 had a convincing answer in a surprising  anomalies of MiniBooNE and LSND look for short time, 13 9°, a large value comparable to the explanation. The muon neutrino to electron previous experimental limit. It defines a new neutrino transitions anomaly indicates at least one epoch in the neutrino physics. A door to search sterile neutrino with mass at the eV-scale. It was leptonic CP phase and the determination of shown that the oscillation data can be neutrino mass hierarchy is open. The second is the accommodated in this so-called 3+1 scheme. signal of the long searching Higgs particle have Meanwhile dark matter constitute of 25% of been discovered by ALTLAS and CMS at LHC. energy density in our universe and we still do not For flavor symmetry we instead of studying know the nature of it. It was also shown that the flavor symmetry among three generations of the keV sterile neutrino is a good candidate of dark fundamental fermions, we investigate the flavor matter. In this case the dark matter is a decaying symmetry for the possible existence of forth dark matter. The mixing between this field to generation [1]. Our previous study concentrate on other active neutrinos is constrained to be small in the extended one more generation in the lepton order to keep it long-lived. Hence the terms from sector based on the discrete group A_5 (the even this field through seesaw mechanism do not permutation of five objects), in which the best contribute to the atmospheric and solar neutrino features of the three family model survive, mass scales. The question “why matter is including the tribimaximal pattern of three dominated over antimatter” remains one the generation neutrino mixings. We further extend biggest puzzles awaiting the resolution. Dr. Ryo this model to include four generation quarks[2]. Takahashi and I proposed a scenario, named And the flavor symmetry is replaced by a binary hierarchically acting sterile neutrinos, trying to icosahedral symmetry (I’ symmetry). We discover explain the three puzzles in this scenario[3]. We that there is an interesting relation between quark proposed that a hierarchical spectrum of sterile

III-65 ‹‹- Research Activities of Individuals neutrinos (eV, keV, 1013-15 GeV) to as the lepton conserving theory and can be used to explanations for MiniBooNE and LSND explain the baryon asymmetry in our universe. oscillation anomalies, dark matter, and baryon The paper will be also finished soon. An asymmetry of the universe respectively. And interesting process in the International Linear finally the baryon asymmetry can be achieved in a Collider (ILC) is investigating with Dr. Sugiyama combination of GUT baryogenesis and heavy and Dr. Koji Tsumura san from Nagoya sterile neutrino decays. University. We concentrate on the doubly charged Higgs interactions. And hope the process will Motivated by the discovery evidence of the compensate the study of those in the LHC. Standard Model Higgs mass around 125 GeV at the LHC, Dr. Yong Tang and I study the vacuum Many exciting results of neutrino are stability and perturbativity bounds on Higgs scalar discovered, and I will continue my investigation of the Standard Model extensions including along the line in neutrino physics and it neutrinos and dark matter[4]. Guided by the applications in related topics. Standard Model gauge symmetry and the minimal changes in the Higgs potential we consider two extensions of neutrino sector (Type-I and Type-III References in 2012 seesaw mechanisms) and dark matter sector (a real [1] Chian-Shu Chen, Thomas W. Kephart, and scalar singlet (darkon) and minimal dark matter Tzu-Chiang Yuan, “An A_5 Model of Four (MDM)) respectively. The darkon contributes β Lepton Generations”, Journal of High Energy positively to the function of the Higgs quartic Phys.1104:015(2011). coupling λ and can stabilize the Standard Model [2] [2011] Chian-Shu Chen, Thomas W. Kephart, vacuum up to high scale. Similar to the top quark and Tzu-Chiang Yuan, “Binary Icosahedral in the Standard Model we find the cause of Flavor Symmetry for four Generations of instability is sensitive to the size of new Yukawa Quarks and Leptons”, arXiv:1110.6233. couplings between heavy neutrinos and Higgs boson, namely, the scale of seesaw mechanism. [3] Chian-Shu Chen and Ryo Takahashi, MDM and Type-III seesaw fermion triplet, two “Hierarchically Acting Sterile Neutrinos”, Eur.

nontrivial representations of SU(2)L group, will Phys. J. C72,2089(2012). bring the additional positive contributions to the [4] Chian-Shu Chen and Yong Tang, “Vacuum gauge coupling g2 renormalization group stability, neutrinos, and dark matter”, Journal evolution and would also help to stabilize the of High Energy Phys.1204,019(2012). electroweak vacuum up to high scale. [5] Chian-Shu Chen and Lu-Hsing Tsai, work in Recently, a new postdoc from NTHU, progress. Lu-Hsing Tsai, and I are working on a model that [6] Chian-Shu Chen, Hiroaki Sugiyama, and Ryo the Peccei-Quinn symmetry breaking is the origin Takahashi, work in progress. of Dirac neutrino mass[5]. The advantage of this [7] Chian-Shu Chen, Hiroaki Sugiyama, and Koji model is that the dark matter can be naturally Tsumura, work in progress. embedded in the neutrino physics. The Nambu- Goldstone boson of U(1) Peccei-Quinn symmetry, axion, can be easily accommodate the distribution of dark matter in our universe. We can also predict large lepton flavor violating processes in the near future. The paper will be finished soon. In the meantime, I also collaborate with some of my Japanese colleagues recently: Dr. Ryo Takahashi from Hokkaido University and Dr. H. Sugiyama san from Toyama University and I are working on neutrinogenesis can be realized in a loop-induced Dirac Yukawa couplings. The interesting point is that leptogenesis can be realized in the model of

Research Activities of Individuals -›› III-66 Research Activities on Biophysics

Chun-Chung Chen (email: [email protected]) Assistant research scholar, 2009/10/01~present

volutionary Dynamics the RGB model, it has been shown that the extinction time of a species can be drastically Under the pressure of genetic mutation, a prolonged. We found that this prolongation is dilemma forms in the competition for dominance linked to a short correlation length in the system. between species: whether to optimize the fitness The earlier work of Reichenbach et al [2] has with a highly specific genetic sequence or to shown spiral waves can be observed with the compromise it for a less specific combination addition of particle mobility. The centers of these that's more robust to the mutation. Using the spiral have the likeness of vortices seen in 2D XY variational approach developed earlier [3], we model in statistical physics, which gives rise to the mapped out the phase diagram for this peak-mesa Kosterlitz–Thouless transition [1] at a critical competition in Eigen's quasispecies model (Figure temperature. Under these premise, I have 1a) and derived an analytic expression of the developed computer programs to calculate various minimal mesa fitness for the existence of a mesa stationary properties and visualize the dynamics domain (Figure 1b). of these vortices (Figure 2). From a pure statistical physics point of view, the segregation of degree of freedom in many body systems is an important mechanism how macroscopic phenomena can emerge from microscopic interactions. In our model of cyclic competition, we will demonstrate that the front (domain wall between species) propagation can be considered the fast-varying degree of freedoms of the system that can be integrated out at long time scale, leaving the slow- varying vortex dynamics of the system that dictates the extinction time of the system. Neural Network One of the ultimate goals of studying networks of neurons is to understand the working of animal brains. However, such a high goal can be hard to reach without proper stepping stones. One of these stepping stones in neurobiology is the study of relative small networks of cultured neurons. Over Figure 1. (a) Phase diagram for peak-mesa competition in the the past year, I have started a collaboration with fitness landscape of Eigen model for different Prof. Chi Keung Chan in Academic Sinica to sequence lengths. There is a minimum mesa fitness model the dynamical behavior his group observed (intersect of the phase boundaries) below which the mesa species has no impact on the quasispecies in networks of neurons they cultured. Specifically, transition (vertical line). The rescaled plot (inset) they have observed reverberation behavior in their shows collapse of the diagram for different sequence network similar to an earlier study by Volman et al lengths. (b) Analytical expression of the minimum mesa fitness (dashed line) predicted with only the [4]. But unlike previous study, the spike patterns diagonal components compared with result of in Prof. Chan's network are more scattered and numerical diagonalization (asterisks) of the matrix. can be manipulated into a broad range of Adding spatial distribution into cyclic dynamical patterns through various biochemical competition of a rock-paper-scissors-like game, agents. In order to match the experimental efforts

III-67 ‹‹- Research Activities of Individuals and improved simulation flexibility, I have developed a series of interactive programs allowing runtime manipulation of various modeling parameters (Figure 3). So far, we have been able to attribute the scattering of the reverberation pattern to a stronger asynchronous release of neural transmitters and a more localized network in the cultures. With the help to the program, we are hoping to elucidate the role played by various biochemical treatments that have been seen to influence the spiking dynamics.

References [1] J M Kosterlitz and D J Thouless, “Ordering, metastability and phase transitions in two- dimensional systems,” Journal of Physics C: Solid State Physics, 6(7):1181, 1973. [2] Tobias Reichenbach, Mauro Mobilia, and Erwin Frey, “Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games,” Nature, 448(7157):1046, 2007. [3] Min-Feng Tu, Ching-I Huang, Hsiu-Hau Lin, and Chun-Chung Chen, “Variational ansatz for Figure 2. Visualization of the RGB model of cyclic competition. quasispecies in the eigen model,” Three species are represented by different color on arXve:1011.5098, 2010. the top panel. The red (blue) points on the bottom panel mark the positions of (anti-)vortices. The line [4] Vladislav Volman, Richard C. Gerkin, Pak- segments on the bottom panel point to the direction Ming Lau, Eshel Ben-Jacob, and Guo-Qiang of propagation fronts. Bi, “Calcium and synaptic dynamics underlying reverberatory activity in neuronal networks,” Physical Biology, 4(2):91, 2007. Hsiu-Hau and Chen, Chun-Chung, “Variational ansatz for quasispecies in the Eigen model” unpublished, arXiv. org:1011.5098.

Figure 3. An interactive computer experiment on a network of spiking (Morris-Lecar) neurons showing network reverberation. The time on the firing polygram runs to the right with each red dot represents a firing event of a neuron. The firing rate is shown with green lines at the lower part of the diagram. The W-V space plot shows the state of each neuron with a dot while the network connection is show by the lines. All model parameters of the simulation can be adjusted dynamically allowing an easy exploration of the phase space that is not possible in physiological experiments.

Research Activities of Individuals -›› III-68 Research Activities on Soft Matters and Biophysics

Hsuan-Yi Chen (Department of Physics, National Central University and Institute of Physics, Academia Sinica; email: [email protected]) Center scientist, 2010/08/01~2014/07/31

n the past year I have been working on On the theoretical side, in the past few years I computational and theoretical models for have been working on the physics of actin- subcellular processes. The published results propelled motion [3]. In physiological condition, include a new simulation approach for actin monomers self-assemble into a double-strain biomembranes [1], swimming nanomachines in a polar filament. ATP-actin monomers tend to join lipid membrane[2], and a phenomenological the plus end, afterwards their ATPs hydrolyze to model for Listeria-type motion in two- ADP, and ADP-actin monomers on the minus end dimensional space[3]. tend to leave the filament. In this way the actin monomer in the cell is recycled. In the presence In the computational study of biomembranes, of ATP supply, like in typical cells, this dynamics our research in collaboration with Prof. Mikhailov lead to a treadmilling motion of actin filaments (Fritz-Harber Institute of the Max-Planck Society, that powers cell crawling, small vesicle motion in Berlin) and Prof. Kapral (Univ. of Toronto) have cells, and even the motion of some bacteria (such developed a new lipids-resolved coarse-grain as Listeria monocytogenes) in host cells. An simulation that includes the solvent by multi- interesting observation is that experiments on particle collision dynamics[1]. This approach has dead Listeria and plastic beads coated with special successfully reproduced the gel and liquid phases proteins found that the trajectories of these objects of biomembranes, the short-time subdiffusive and in cell extract are often non-straight geometrical long-time diffusive in-plane motions of lipids, the trajectories. Circles, figure-eight, s-shape, and elastic properties of the membrane, and the other geometrical trajectories have been observed. in-plane flow properties of a liquid membrane. th We constructed a phenomenological theory for The result was featured in the cover of the Aug 7 such actin-based motility based in symmetry issue of Journal of Chemical Physics. consideration. We are able reproduce all We further combined this simulation with a experimental observed trajectories from the bead-and-spring model for active membrane numerical simulation of our model. The result of protein that can change its conformation when our study reveals the feedback mechanism that specific ligand molecule binds or leaves it. With destabilizes a straight trajectory. It also put strong this efficient simulation technique, for the first restriction on the type of microscopic mechanism time the motion of an active cyclic membrane that is responsible for such curved trajectories of protein is simulated for hundreds of cycles [2]. Listeria and plastic beads in cell extracts. Our simulations of a toy model three-domain Currently my postdoc researcher Dr. Wei-Chang protein shows that such a membrane protein Lo, my student Fu-Lai Wen and I are working on a behaves like a nanoswimmer in a membrane, model of actin gel in which the local elastic moving ballistically on time scale shorter than its properties of the gel is determined by the actin rotational diffusion time. The induced-flow of polymerization rate at the time when the gel was such a swimmer in the membrane falls off formed. We hope this model will help connecting logarithmically with distance, indicating a strong the microscopic actin dynamics to our hydrodynamic interaction between two membrane phenomenological model for Listeria motion. swimmers. In the future simulations the Besides research work, I have helped consequences of such long range hydrodynamic organizing the Dynamics Days Asia-Pacific held interactions will be further studied.

III-69 ‹‹- Research Activities of Individuals in Academia Sinica during Aug 6th to Aug 9th, [2] Nano-swimmers in biological membranes and 2012. During this meeting we have also decided propulsion hydrodynamics in two dimensions, to organize Bio-Complexity Taiwan 2013, a Mu-Jie Huang, Hsuan-Yi Chen, and Alexander satellite meeting of StatPhys25 from July 16th to S. Mikhailov, invited article submitted to Euro. July 19th, 2013. Dr. C.K. Hu (Academia Sinica) J. Phys. E (2012). and I will co-chair the organization committee. [3] Curved trajectories of actin-based motility in There will also be a NCTS Math-Phys joint two dimensions, Fu-Lai Wen, Kwan-tai Leung conference in Dec. 2012. The theme of this joint and Hsuan-Yi Chen, Europhys. Lett., 98, conference will be the mathematics and physics of 38005 (2012). complexity. In this two-day workshop, Prof. Kuo- Chang Chen (NTHU/NCTS Math) and I will invite about 10 mathematicians and physicists working on nonlinear dynamics, networks, stochastic processes, and other subfields to introduce their research works and seek the possibility of further interactions and collaborations between the Taiwanese physicists and mathematicians working in this research area.

References [1] Coarse-Grain Model for Lipid Bilayer Self- Assembly and Dynamics: Multiparticle Collision Description of the Solvent, Mu-Jie Huang, Raymond Kapral, Alexander S. Mikhailov, and Hsuan-Yi Chen, J. Chem. Phys. 137, 055101 (2012). (Selected as the journal cover featured in Volume 137 Issue 5 on 7 August 2012)

Research Activities of Individuals -›› III-70 Research Activities on Particle Physics

Cheng-Wei Chiang (Department of Physics, National Central University and Institute of Physics, Academia Sinica; e-mail: [email protected]) Center Scientist, 2011/02/01~2013/01/31

y position of a Center Scientist at NCTS found that the strange quark contribution in both started from February 2011. This report types of couplings was smaller than previously shows my research results since my last report at thought. the beginning of this year. They are described as A third direction involved a detailed collider follows. study of doubly charged Higgs bosons predicted The first direction concerns the studies of in many new physics models with an extended direct CP violation in hadronic charmed meson Higgs sector that contained a Higgs triplet field, decays in collaboration with Prof. Cheng [1,5]. particularly the Georgi-Machacek (GM) model Motivated by the observation of the LHCb [3]. Current experimental searches had been Collaboration, we studied direct CP asymmetries focusing on the scenario where the same-sign in the standard model (SM) for the singly dilepton decay modes were dominant. We studied Cabibbo-suppressed (SCS) two-body hadronic instead the scenario where the vacuum expectation decays of charmed mesons using the combination value of the triplet field was sufficiently large of topological-diagram and QCD factorization (e.g., in the GM model) so that the associated approaches [1]. Our analysis made use of flavor charged Higgs bosons decayed dominantly to a SU(3) symmetry to relate certain hadronic pair of weak gauge bosons. A detailed simulation parameters. Our result indicated that the of signal and background events was performed measured value was higher than the SM for the CERN Large Hadron Collider (LHC) at the expectation by two standard deviation. In the collision energy of 8 TeV and 14 TeV. We had subsequent paper [5], we considered SU(3) optimized experimental cuts to improve the breaking and studied its effects on the direct CP discovery reaches in various scenarios. asymmetries. We found that the new result still A fourth topic was about nonstandard could not account for the experimental interactions of neutrinos with electrons arising observation. In addition, we computed the from a new light spin-1 particle with mass of tens predictions for the direct CP asymmetries of all of GeV or lower [4]. This boson was not SCS modes in two new physics models. Both necessarily a gauge boson and assumed to have no works were published in Physical Review D. Ref. mixing with standard-model gauge bosons. [1], in particular, was the first published paper on Adopting a model-independent approach, Dr. this issue. Tandean, Dr. Faisel, Mr. Lin and I studied Ref. [2], published in JHEP, came out of constraints on the flavor-conserving and -violating another enjoyable collaboration with Prof. Cheng. couplings of the boson with the leptons from a In this work, we studied how scalar and number of experimental data. pseudoscalar bosons interact with nucleons. Such With Dr. Tandean and Dr. Nomura, we an analysis is useful and meaningful because such explored the possibility of accommodating the scalars can mediate interactions between dark potential results of the Higgs boson search in a matter and nuclei. Based on recent new simple new physics model with discrete gauge developments in lattice calculations, we symmetry as well as light neutrino masses [6]. re-evaluated the relevant nucleon matrix elements Specifically, we studied collider and relic density and computed the scalar and pseudoscalar constraints on the new gauge coupling and couplings of the proton and neutron. We also predicted the cross section of the dark matter

III-71 ‹‹- Research Activities of Individuals scattering off nucleons, to be compared with related to the LHC FG. For example, I will current direct search data. We also discussed the organize the next Cross-Strait Conference on implications for Higgs searches if the dark matter Particle Physics and Cosmology and the first was sufficiently light. KIAS-NCTS Joint Workshop in the next year. In view of the fact that the decays of a Higgs boson to the γγ and Zγ final states were purely quantum mechanical phenomena that were closely related to each other, Dr. Yagyu and I studied the References effects of an extended Higgs sector on the decay rates of them [7]. We proposed that a [1] Hai-Yang Cheng and Cheng-Wei Chiang*, simultaneous determination of them and the ZZ Phys. Rev. D 85, 034036 (2012); Erratum-ibid mode was a useful way to see whether the Higgs 85, 079903 (2012) (arXiv: 1201.0785 [hep- boson recently observed by the LHC experiments ph]). was of the standard model type or could be a [2] Hai-Yang Cheng and Cheng-Wei Chiang*, member of a larger Higgs sector. JHEP 1207, 009 (2012) (arXiv: 1202.1292 The last three manuscripts mentioned above [hep-ph]). [4,6,7] are currently under peer reviews for [3] Cheng-Wei Chiang*, Takaaki Nomura, and journal publication. Koji Tsumura, Phys. Rev. D 85, 095023 (2012) In this year, I had served as the main contact (arXiv: 1202.2014 [hep-ph]). person for the KIAS-NCTS exchange program, [4] Cheng-Wei Chiang, Gaber Faisel, Yi-Fan Lin, aiming at promoting joint activities and research and Jusak Tandean*, arXiv: 1204.6296 [hep- collaborations between particle physicists of ph]. KIAS and NCTS. [5] Hai-Yang Cheng and Cheng-Wei Chiang*, I had been invited to various conferences. Phys. Rev. D 86, 014014 (2012) (arXiv: First, I was invited as a representative Taiwanese 1205.0580 particle physicist to participate in the 5th Symposium on France-Taiwan Frontiers of Science in June to advertise my research works to both French and Taiwanese colleagues in other fields. I was asked to review heavy flavor physics at the 2012 International Conference on BSM of Particle Physics in July held in Vietnam (NCTS- supported). Afterwards, I visited Nanjing University to talk about my studies on doubly charged Higgs bosons. Following that, I went to the 2012 International Conference on Flavor Physics and Cosmophysics in Weihai to talk about the works in Refs. [1,5]. Recently, I was invited to deliver a talk on the work of Ref. [7] at the 2nd KIAS Phenomenology Workshop. As a Center Scientist, I will continue to promote activities at the NCTS Headquarter. I will help organizing NCTS colloquia, a newly formed activity of the Center, and help selecting prospective postdocs in the field of particle phenomenology. If duties are called for, I will also help with the organization of those activities

Research Activities of Individuals -›› III-72 Research Activity on Bose-Einstein Condensate and Quantum Information Applied in Condensed Matter Physics

Ming-Chiang Chung (email: [email protected]) Assistant research scholar, 2010/02/01~2013/01/31

n 2012 my research activity in NCTS has (c) Thermalization and Quantum Correlations in been focused on two main topics: Bose- Exactly Solvable Models Einstein condensate (BEC) and quantum The generalized Gibbs ensemble introduced for information applied to condensed matter theory. In describing few body correlations in exactly the aspect of BEC I have been interested in solvable systems following a quantum quench is quench dynamics of solvable models and related to the way in which operators sample, in macroscopic quantities of BEC and the the limit of infinite time after the quench, the thermalization process, especially related to the quantum correlations present in the initial state. bipartite entanglement. For quantum information The emergence of the generalized Gibbs ensemble applied in condensed matter I have mainly is thus analytically demonstrated for the quantum focused on the entanglement of subsystems and its Ising and XX chains in the thermodynamic limit. relation to thermalization. For these models and a broad class of initial (a) On the relation between entanglement and states, which includes both translationally and subsystem Hamiltonians non-translationally invariant states, the validity of the generalized Gibbs ensemble for simple We show that a proportionality between the correlation functions of both local and nonlocal entanglement Hamiltonian and the Hamiltonian of operators is established [3]. a subsystem exists near the limit of maximal entanglement under certain conditions. Away from (d) Superfluidity and collective oscillations of that limit, solvable models show that the coupling trapped Bose-Einstein condensates in a range differs in both quantities and allow to periodical potential investigate the effect.[1]. Based on a unified theoretical treatment of the (b) Trimerized and dimerized phases for for spin- 1D Bogoliubov-de Genes equations, the 2 Bosons in a one-dimensional optical lattice superfluidity phenomenon of the Bose-Einstein condensates (BEC) loaded into trapped optical We study the phase diagram for spin-2 bosons lattice is studied. Within the perturbation regime, loaded in a one-dimensional optical lattice. By an all-analytical framework is presented enabling using non-Abelian density matrix renormalization a straightforward phenomenological mapping of group (DMRG) method we identify three possible the collective excitation and oscillation character phases: ferromagnetic, dimerized, and trimerized of a trapped BEC where the available phases. We sketch the phase boundaries based on experimental configurations also fit [4]. DMRG. We illustrate two methods for identifying the phases. The first method is based on the spin- (e) Thermalization in systems with bipartite spin correlation function while in the second eigenmode entanglement method one observes the excitation gap as a It is analytically shown that the asymptotic dimerization or a trimerization superlattice is correlations following a quantum quench in imposed. The advantage of the second method is exactly solvable models can sometimes look that it can also be easily implemented in essentially thermal provided the initial coupling experiments. By using the scattering lengths in the between the system eigenmodes induces a large literature we estimate that 83 Rb, 23 Na, and 87 gap. We study this phenomenon using simple Rb be ferromagnetic, dimerized, and trimerized models, which also illustrate the relationship respectively. [2] between the entanglement spectrum of the initial

III-73 ‹‹- Research Activities of Individuals state and the generalized Gibbs ensemble describing the long-time correlations after the quench. We also show that the effective References temperature characterizing the correlations is not [1] I. Peschel and M.-C. Chung, On the relation related to the energy fluctuations after the quench, between entanglement and subsystem and therefore does not have thermodynamic Hamiltonian, Eur. Phys. Lett. 96, 50006 meaning. The latter observation implies a (2011). breakdown of the fluctuation–dissipation theorem [5]. [2] P.C. Chen, Z.L. Xue, I. P. McCulloch, M.-C. Chung and S.K. Yip, Dimerized and trimerized (f) Quench Dynamics of Topological phases for spin-2 Bosons in a onedimensional Maximally-Entangled States optical lattice, Phys. Rev. A (Rapid Comm.) We investigate the quench dynamics of the 85, 011601 (2012). one-particle entanglement spectra (OPES) for [3] M.A. Cazalilla, A. Iucci and M.-C. Chung, systems with topologically nontrivial phases. By Thermalization and quantum correlations in using dimerized chains as an example, it is exactly solvable models, Phys. Rev. E 85, demonstrated that the evolution of OPES for the 011133 (2012). quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a [4] C. Trallero-Giner, V. Lopez-Richard, N. pseudo spin in a time-dependent pseudo magnetic Nurez-Fernadez, M. Oliva and M.-C. Chung, field S(k,t). The existence and evolution of the Superfluidity and collective oscillations of topological maximally-entangled edge states are trapped Bose-Einstein condensates in a determined by the winding number of S(k,t) in the periodical potential, Eur. Phys. J. D 66, k-space. In particular, the maximally-entangled 177(2012) edge states survive only if nontrivial Berry phases [5] M.-C. Chung, M.A. Cazalilla and A. Iucci, are induced by the winding of S(k,t). In the Thermalization in Systems with Bipartite infinite time limit the equilibrium OPES can be Eigenmode Entanglement, New. J. Phys. 14, determined by an effective time-independent 075013 (2012). pseudo magnetic field S_eff(k). Furthermore, when maximally-entangled edge states are [6] Ming-Chiang Chung, Yi-Hao Jhu, Pochung unstable, they are destroyed by quasiparticles Chen and Chung-Yu Mou arXiv: 1205.6951 within a characteristic timescale in proportional (submitted to EPL). to the system size [6]. My research plan of the future is based on the ongoing research of mine: one is the development on the theory of cold atoms and the other on the quantum information applied to condensed matter theory. The quantum dynamics of cold atomic systems and the spinor bosons are two important topics of my study on cold atoms and I am also focusing on topological properties and quantum quench of entanglement - an aspect of quantum information applied to condensed matter theory (see the overview of the research). I plan to do more researches on the topic of the dynamics of topological isulators to see the evolution of majorana edge mode. I also want to study the out- of-equilibrium dynamics related to the entanglement, especially to study wheather the system is going to have dynamics or not.

Research Activities of Individuals -›› III-74 Research Activities on String Theory

Kazuyuki Furuuchi (Department of Physics, National Tsing Hua University, email: [email protected]) Staff scientist, 2007/08/01~2012/07/31

n this academic year, I studied cosmology Dine (AD) baryogenesis. A flat direction of the together with Dr. Chia-Min Lin, then at supersymmetric standard model was the Institute of Physics, Academia Sinica. In Ref. responsible for this mechanism. [1] we studied possible roles of moduli fields in The mass scale of the moduli field and the flat the early Universe. Moduli fields are light scalar directions are constrained by the weak-scale fields which interact only with the strength of supersymmetry. It turned out that in this scenario, gravity. Moduli fields often appear in the the standard curvaton scenario does not work candidates of more fundamental theory such as because it produces baryon isocurvature string theory. Thus studying their possible roles in perturbation much larger than the observational Nature is very interesting. In particular, since upper bound. However, we found that if we moduli fields interact weakly, their lifetime could consider inflating curvaton scenario recently be relatively long. It has been noticed that if there proposed by Dimopoulos, Kohri, Lyth and exists a moduli field whose mass is below some Matsuda, we do not meet this problem. We 10 TeV scale, it will decay after the Big Bang showed that our scenario explains the primordial nucleosynthesis and ruin its success. On the other density perturbation by the inflating curvaton hand, if we assume the weak scale supersymmetry mechanism and at the same time can produce right to be the solution to the hierarchy problem amount of the matter – anti-matter asymmetry via regarding the mass of the Higgs field, the moduli the AD baryogenesis. Moreover, the dark matter fields cannot be too heavy. This motivates us to abundance is also explained by the non-thermal consider moduli fields whose masses are between decay of the moduli field via the Moroi-Randall 10 TeV to some 100 TeV. In cosmic inflation mechanism. Since our scenario is motivated by scenario, such light scalar fields are of particular particle physics and string theory, and explains interests, since they may play various roles in the many features of our Universe at the same time, history of the Universe. For example, the quantum we think this is a very interesting scenario. The fluctuation of one of such light scalar fields is near future finer observation of the CMB widely believed to be the origin of the Cosmic anisotropy and the experiments on the Higgs field, Microwave Background (CMB) anisotropy and supersymmetry and the dark matter may provide the large scale structure. additional inputs to, or the evidences of, our From the motivations explained above, in Ref. scenario. [1] we examined the scenario where I also get interested in quantum field theory on 1. The primordial density perturbation was de Sitter space. During the period of inflation the generated by the lightest moduli field whose space-time was approximately de Sitter space, mass is O(10-102 TeV) through the curvaton thus understanding the properties of quantum field mechanism. theory in de Sitter space is very important. However, unlike quantum field theory on the flat 2. The hierarchy problem of the Higgs mass is Minkowski place, there remain several explained by the weak-scale supersymmtry. The controversial issues in quantum field theory on de supersymmetry breaking is mediated by certain Sitter. I invited Prof. Yoshihisa Kitazawa and Dr. type of gravity mediation. Hiroyuki Kitamoto from KEK, who have 3. The asymmetry between matter and anti-matter published interesting results regarding the infra- in our Universe was generated by the Affleck- red effects in quantum field theory on de Sitter

III-75 ‹‹- Research Activities of Individuals space, and organized the lecture by Prof. Kitazawa theory, quantum field theory and cosmology, to at NCTS. I also discuss with Prof. Takeo Inami the students and the researchers in Taiwan, and and Mr. Yoji Koyama at Chuo University on this inspire discussions with the lecturers and among topic. We hope to understand the properties of them. I hope my efforts and works have made quantum field theory on de Sitter space and report some contributions to the progress of theoretical about them in the near future. physics in Taiwan. I would also like to report that the Ref.[2] I believe the reputation of the string theory which was a pre-print when I reported last year research at NCTS in the world has been was published in JHEP. established during these five years, building on the earlier efforts by the previous members. I am As I am finishing my 5-year term as a Staff sure that the string theory research activity at Scientist (Aug. 1st 2007- July 31 2012), I’d like to NCTS and in Taiwan will continue to grow in the briefly look back my activities in these five years. future, and I am very looking forward to seeing it. I also became a committee member of the NCTS String Theory Focus Group when I started this position. Since my research achievements have been reported in the past annual reports, here I just References would like to state that I am very happy that I [1] K. Furuuchi and C.-M. Lin, “Affleck-Dine could concentrate on research for five years in a baryogenesis in inflating curvaton scenario wonderful research environment of NCTS. with O(10-102 TeV) mass moduli Indeed, I will surely miss my cozy office, the c u r v a t o n , ” JCAP 1203, 024 (2012) discussion space with the glass boards, and the [arXiv:1111.6411 [hep-ph]]. coffee bar of the NCTS. The eight publications resulting from the work at NCTS are very [2] K. Furuuchi, T. Inami, K. Okuyama, “Gauge- important pieces in my research life. This having Higgs Unification In Spontaneously Created been said, below I focus on my activity Fuzzy Extra Dimensions,” JHEP 1111, 006 organization. (2011) [arXiv:1108.4462 [hep-ph]]. After I came to NCTS, more and more visitors from abroad began to visit us, as our research activity is known to the world. During 2007-2009, I organized several NCTS HEP Lecture Series given by the visitors, extending the weekly NCTS-NCTU-NTHU HEP journal club. After 2009, we had string seminars of the NCTS String Focus Group around once a month at NCTS, which are held at NTU in other weeks. We used the video meeting system to broadcast the string seminars to NTU. I also worked for organizing workshops. I was one of the organizers of the 1st Taiwan String Theory Workshop held at NTU in January 2009 and the 3rd Taiwan String Theory Workshop held at THU in December 2010. I was one of the speakers at the 2nd Taiwan String Theory Workshop held at NTNU in December 2009. Those activities were meant to introduce important developments in the field of string

Research Activities of Individuals -›› III-76 Research Activities on Particle Physics and Cosmology

Chao-Qiang Geng (Department of Physics, National Tsing Hua University; email: [email protected]) Center scientist, 2011/02/01~2013/01/31

ince Feb. 1, 2011, becoming a center In [2], we have shown that the crossing of the scientist, I have been in charge of the phantom divide can also be realized in the viable focus group of “Cosmology and Particle f(R) gravity model. We have also demonstrated Astrophysics,” which was established in 2009. My that the future crossing of phantom divide is a current research interests have been in particle generic feature in various popular viable f(R) physics and cosmology with specific topics gravity models as well as f(T) gravity theories [3]. related to dark energy, dark matter, neutrino and In [4], we demonstrate that it is possible to obtain flavor physics. a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological The standard model (SM) of the strong and background for a wide class of modified gravity electroweak interactions has an enormous success theories. This work shows that there is a in explaining all relevant existing experimental correlation between Dark Energy and Entropy in data. In particular, the recent experimental modified gravity theories. Recently, we have also searches at the LHC have almost confirmed the shown both pictures of equilibrium and non- existence of the last elementary particle in the SM, equilibrium thermodynamics on the apparent i.e., the Higgs boson, with its mass between horizon in f(T) gravity [5]. 124~126 GeV. However, in addition to containing a large numbers of free parameters, the SM leaves In [6], using the “teleparallel” equivalent of too many fundamental problems unanswered. For General Relativity as the gravitational sector, instance, why are there three families? What is the which is based on torsion instead of curvature, we explanation for fermion masses in view of the add a canonical scalar field, allowing for a non- tremendous range of their values, in particular, the minimal coupling with gravity. Although the small neutrino masses? What is the origin of CP minimal case is completely equivalent to standard violation? What are the real natures of dark matter quintessence, the non-minimal scenario has a and dark energy? My research focus since 2011 at richer structure, exhibiting quintessence-like or NCTS has been studying these important phantom-like behavior, or experiencing the problems in particle physics, cosmology and phantom-divide crossing. The richer structure is particle astrophysics. With the support of NCTS, manifested in the absence of a conformal so far I have published 26 research articles since transformation to an equivalent minimal-coupled 2011. I would like to highlight some of them as model. In [7], we use data from Type Ia follows: Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background In [1], we study the inert triplet models, in (CMB) observations to constrain the teleparallel which the SM is extended to have a new SU(2)L dark energy scenario proposed in [6]. Using the triplet scalar (Y=0 or 2) with an Z2 symmetry. We power-law, the exponential and the inverse show that the neutral component of the triplet can hyperbolic cosine potentials, we show that the be a good dark matter candidate. In particular, for scenario is compatible with observations. In the hypercharge Y=0 triplet model, the WMAP particular, the data favor a non-minimal coupling, data favors the region where the dark matter mass and although the scalar field is canonical the is around 5.5TeV, which is also consistent with the model can describe both the quintessence and direct detection experiments. In contrast, for the phantom regimes. Y=2 model, although dark matter with its mass around 2.8TeV is allowed by WMAP, it is In [8], we study gravitational waves in viable excluded by the direct detection experiments. f(R) theories under a non-zero background

III-77 ‹‹- Research Activities of Individuals curvature. In general, an f(R) theory contains an [4] K. Bamba, C.Q. Geng and Shinji Tsujikawa: extra scalar degree of freedom corresponding to a “Thermodynamics in Modified Gravity massive scalar mode of gravitational wave. We Theories”, Int. J. Mod. Phys. D20, 1363 illustrate our results in two types of viable f(R) (2011). models: the exponential gravity and Starobinsky [5] K. Bamba and C.Q. Geng: “Thermodynamics models. In both cases, the mass will be in the of cosmological horizons in f(T) gravity”, order of 10-33eV when it propagates in vacuum. JCAP 1111, 008 (2011). However, in the presence of matter density in galaxy, the scalar mode can be heavy. Explicitly, [6] C.Q. Geng, C.C. Lee, E.N. Saridakis and Y.P. in the exponential gravity model, the mass Wu: “'Teleparallel' Dark Energy”, Phys. Lett. becomes almost infinity, implying the B704, 384 (2011). disappearance of the scalar mode of gravitational [7] C.Q. Geng, C.C. Lee and E.N. Saridakis: wave, while the Starobinsky model gives the “Observational Constraints on Teleparallel -24 lowest mass around 10 eV, corresponding to the Dark Energy”, JCAP 1201, 002 (2012). lowest frequency of 10-9Hz, which may be detected by the current and future gravitational [8] L. Yang, C.C. Lee and C.Q. Geng: wave probes, such as LISA and ASTROD-GW. “Gravitational Waves in Viable f(R) Models”, Recently, we also discuss [9] the curvature JCAP 1108, 029 (2011); C.Q. Geng: oscillation as well as its singularity in viable f(R) “Gravitational waves in viable modified gravity models when the background density is gravity models”, J, of Phys: Conf. Ser. 384 dense. (2012) 012030. In [10], we study a finite quantum correction to [9] C.C. Lee, C.Q. Geng and L. Yang: “Singularity the tri-bimaximal (TB) neutrino mixing in several phenomena in viable f(R) gravity”, Prog. generic classes of neutrino models. We show that Theor. Phys. 128, 415 (2012). all three mixing angles can depart from the TB [10] T. Araki, C.Q. Geng and Z.z. Xing: “Finite  values. After the large value of 13 reported by quantum corrections to the tribimaximal T2K and MINOS as well as Double Chooz befor neutrino mixing”, Phys. Lett. B699, 276 Daya-Bay and RENO, we studied [11] the finite (2011). quantum corrections for several well known  neutrino mixing matrices to see if they can be use [11] T. Araki and C.Q. Geng: “Large 13 from to account for the data. However, we find that it is finite quantum corrections in quasi- hard to do it. To nicely reproduce all degenerate neutrino mass spectrum”, J. High experimentally favored neutrino mixing angles Energy Physics 1109, 139 (2011). and masses, we propose a new neutrino mixing pattern [11].

Reference [1] T. Araki, C.Q. Geng and K. I. Nagao: “Dark Matter in Inert Triplet Models”, Phys. Rev. D83, 075014 (2011); “Signatures of Dark Matter in Inert Triplet Models”, Int. J. Mod. Phys. D20, 1433 (2011). [2] K. Bamba, C.Q. Geng and C.C. Lee: “Phantom crossing in viable f(R) theories”, Int. J. Mod. Phys. D20, 1339 (2011). [3] K. Bamba, C.Q. Geng and C.C. Lee: “Equation of state for dark energy in f(T) gravity”, JCAP 1101, 021 (2011).

Research Activities of Individuals -›› III-78 Research Activities on Particle Physics

Yu-Kuo Hsiao (email: [email protected]) Assistant research scholar, 2011/08/01- 2013/07/31

n 2011 my research activity in NCTS has as well as BELLE and BABAR at the B factories. been focused on the particle physics, The new charmed baryon states studied in [4] especially the topics related to the semileptonic are proposed to explain a bunch of peaking data and three-body baryonic B decays. points in mD(*)0p invariant mass distributions of Similar to semileptonic decays, the decays. In the paper of Phys. Rev. study of semileptonic baryonic B decays is D85. 09101 (2012) by the BABAR collaboration, necessary, as the decays can be used to probe into the low-mass peaks in the mD(*)0p spectra with new physics. We hence studied the decays of seem puzzling as the data points and in the Starndard disagree with what expected from the uniform Model, which have been published in [1] and [2], phase-space model. We find that, unlike the peaks respectively. For , we find that the around the threshold area in the spectra, the decay branching ratios of ( ) low-mass peaks in the mD(*)0p spectra cannot be are about (1.0,1.0,0.5) ×10-4, respectively. In understood based on the pQCD effect in the particular, the electron mode is close to the creation of the dibaryon. We introduce the corresponding CLEO's upper limit of 5.2×10-3. resonant amplitudes to fit the invariant mass For , since in detection the can only spectra of D(*)0p. With the charmed baryon states be treated as missing energy, we sum over the denoted as Bc, these peaks are considered to arise branching ratios for the with through the 2-step processes of to be nearly of order 10-6. Clearly, the . As a result, among the fit LHCb and both B-factories of Belle and BaBar resonant states, two of them are identified as the Λ + Λ + should be able to observe these exclusive four- established states C(2880) and C(2940) , and + + body modes. We will also go further to study the the BC(2820) and BC(3820) have already been decays via the effective Hamiltonian signed by experiments. Besides, the rest of the of at the quark level. This requires to new charmed baryon states are found to have been define new matrix elements for the previously predicted theoretically in various transition with a tensor-type coupling. studies elsewhere. Therefore, it is promising for these new charmed baryon states to be further The study of the three-body baryonic B decays investigated in the future. of with V being a vector meson published in [3] is inspired by the BELLE’s paper In sum, my research of this year in NCTS is of Phys. Rev. D80, 11103 (2009), in which it is achieved to be interesting and aboundant, and stated that the branching fraction of is other projects related to cosmology and hadron about an order of magnitude larger than the decays are also in the progress. theoretical prediction. The theoretical calculation is hence improved, such that we can simultaneously explain the experimental data on References the decays of and based on the QCD counting rules and SU(3) flavor [1] C.Q. Geng and Y.K. Hsiao, Semileptonic symmetry. We also predict that the decay decays, Phys. Lett. B704, 495 branching ratios of and are (2011). 3.0 and 1.5×10-6, respectively, which are [2] C.Q. Geng and Y.K. Hsiao, Rare promising to be observed by the LHCb at CERN decay, Phys. Rev. D85, 094019 (2012).

III-79 ‹‹- Research Activities of Individuals [3] C.Q. Geng and Y.K. Hsiao, Study of and , Phys. Rev. D 85, 017501 (2012). [4] H.Y. Cheng, C.Q. Geng, and Y.K. Hsiao, Possibly New Charmed Baryon States from Decays, arXiv:1205.0117 [hep- ph].

Research Activities on Condensed Matter Physics

Wen-Ming Huang (email: [email protected]) Postdoctoral researcher, 2011/01/01~2012/07/31

uring my postdoctoral fellow in National Within renormalization-group analysis, we shows Center for Theoretical Science, Physics that the ground state is a phonon-dressed Division, from Jan. 2011 to Jul. 2012, my unconventional superconductor: the dominant researches mainly focus on the field of collective electronic interactions account for pairing fermionic systems, especially in graphene and mechanism while electron-phonon interactions are iron-based superconductors. subdominant. Meanwhile, because of the phonon dressing, the isotope effect of the critical In the superconductivity part, we study temperature can be normal or reversed, depending electron-phonon effect in recent discovery of on whether the retarded intra- or inter-band superconductivity in iron-based material. What interactions are altered upon isotope role phonons play for electron pairing always substitutions[1,2]. stimulates intense discussions when a new superconductor is discovered such as cuprates, One of my researches focus on the collective magnesium diboride, sodium cobalt oxide and phenomena in graphene framework. Recently a recently found iron-based superconductors. tunable bandgap by electronic gating realized in Experimentally, to reveal the role of phonons, bilayer graphene pronounces a temendous isotope effect in the superconducting temperature probability to build up a field-effect transistor in Tc is commonly used upon isotope substitutions. graphene network. However, defects in graphene However, in iron-based superconductor is framework is unavoidable and will strongly currently under debate with conflicting modify the electronic properties in graphene experimental reports on the isotope effect. transistors. For instance, in 2010 we clarify the zero-bias sharp peak in the local density of state To address this important issue, we employ the induced by a vacancy as a power-law singularity renormalization-group method to investigate the in monolayer graphene. Inspire of importance of competition between electron-electron and disorder in graphene, we study the variation of the electron-phonon interactions in these materials. local density of state in bilayer graphene when a

Research Activities of Individuals -›› III-80 point defect happens. There are two kinds of the zero-bias enhancement dependent on where a vacancy locates in bilayer. With both of analytical References and numerical methods, we show that one is a [1] Wen-Min Huang, Hong-Yan Shih, Fa Wang power-law singularity assembled by resonant and Hsiu-Hau Lin, arXiv:1112.4326. states as the same as in monolayer. The other is a [2] Yiwei Cai, Wen-Min Huang and Hsiu-Hau localized states in the Lorentzian shape with the Lin, Phys. Rev. B 85, 134502 (2012). broadening factor proportional to the interlayer hopping amplitude[3]. [3] Wen-Min Huang, Jian-Ming Tang and Hsiu- Hau Lin, preprint. In another work in graphene systems, we study effective field theory in graphene edges[4]. In our [4] Wen-Min Huang, Yen-Chen Lee, Toshiya previous study, a single-branch of ferromagnetic Hikihara and Hsiu-Hau Lin, magnon with linear dispersion is shown to exist near the (uncompensated) zigzag edge for Heisenberg model on honeycomb lattice. In this work, we develop a field-theory description for the edge magnon and find its dynamics is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterart, described by the two-dimensional Klein- Gordon equation. Furthermore, we also reveal how the parity symmetry relates evanescent modes on opposite edges in a honeycomb nanoribbon. By employing alternative methods, including Schwinger bosons and density-matrix renormalization group, we also demonstrate that the relativistic edge magnon is robust even when Xar1v10:7i0.2. the Neel order in the bulk is destroyed by quantum fluctuations. The edge magnon is a direct consequence of uncompensated edge and may be verified in realistic materials by experimental probes.

III-81 ‹‹- Research Activities of Individuals Research Activities on String Theory

Hirotaka Irie (Yukawa Institute for Theoretical Physics, Kyoto University; Email: [email protected]) Postdoctoral researcher 2011/01/01 ~ 2012/03/31

he period I have spent in NCTS was Our project on the non-perturbative completion really fruitful for me with wonderful started with the paper [1]. In the paper, we focused collaborations in Taiwan with Prof. Chuan-Tsung on a mathematical system called isomonodromy Chan (THU) and Dr. Chi-Hsien Yeh (NTU). We systems and the Riemann-Hilbert method. In succeeded revealing new non-perturbative aspects particular, we formulate the physical constraint on on string theory with new prospects on analytic non-perturbative completion which is required by structure of the string theory landscape. matrix models. In some sense, our result not only gives light to fundamental understanding of string My research areas are string theory and its theory, but also solves mathematical problems relevant mathematical physics, especially about with uses of physics. Fortunately, in June, 2011, non-perturbative completion of string theory. one of the pioneer of this mathematical theory String theory was proposed as a universal visited Taiwan (the host of Professor Chang-Shou framework for quantum gravity and is expected to Lin in TIMS at NTU). From that time, we started unify all the fundamental forces in our universe. communications with Professor Chang-Shou Lin Despite of this expectation, it still relies on the and with Professor Martin Guest in Tokyo perturbative formulation and is not completely Metropolitan University. This gives us countless formulated from non-perturbative points of view. valuable discussions. In particular, our current formulations are not enough to derive the particle-physics standard In the second paper of non-perturbative model and to predict physical laws for completion [2], we found that the physical observational cosmology, including dark matter constraint equations from the matrix model are and dark energy. Therefore, my main purpose of equivalent to T-systems in quantum integrable this research is to complete fundamental systems. This is a quite surprising result and I felt understanding of string theory, and eventually find that this indicates our approach directs to right a direct connection with the real world from the answer. We not only showed quantum integrability first principle. but also gave explicit expressions to Stokes phenomena in general isomonodromy systems. Motivated by these fundamental objectives, we This is a surprising result from the mathematical started focusing on Stokes phenomena in string points of view. Also from the physical points of theory. Mathematically, this is the information view, it is a quite strike result to show explicit which enables us to reconstruct a complete analytic structure in the information which cannot function from a given perturbative series with be seen in perturbative string theory. This result is their all possible non-perturbative effects. In fact, presented in international conference [2], “Strings in our current understanding, we know how to 2011”, in its gong show, and also in UK-Japan define the all-order perturbative series (from the Winter School 2012 [3] as an invited lecturer. worldsheet formulation) and their non- perturbative effects (mostly originated from After succeeding study of this project, we D-branes and instantons). Therefore, the Stokes recently submitted a new paper [4] which gives an phenomenon is the last step toward the non- insight into the string theory landscape. In this perturbative completion of string theory. paper, we complete all the physical constraints from the matrix models. What is more, we

Research Activities of Individuals -›› III-82 explicitly demonstrated a first-principle analysis [3] H. Irie, “Stokes Phenomena and Quantum of the landscape as a consequence of our physical Integrability in the multi-cut matrix models,” constraint. We here explicitly showed that with an invited lecturer in UK-Japan Winter School our considerations on “physical constraints on 2012 in Oxford, UK, January 4-January 8, non-perturbative completion” we can obtain 2012. analytic structure of the string theory landscape. [4] C.-T. Chan, H. Irie, C.-H. Yeh, “Analytic In particular, we are now able to calculate non- Study for the String Theory Landscapes via perturbative instability and decay rate and true Matrix Models,” arXiv: 1206.2351 [hep-th] (5 vacuum of perturbative string theory. Therefore, pages) we took a large step toward analytic study for the string theory landscape. In near future, we anticipate that our considerations will lead us to analytic derivation of the standard models from string theory.

References [1] C.-T. Chan, H. Irie, C.-H. Yeh, “Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models,” Nuclear Physics, Section B 854 (2012) pp. 67-132 [arXiv:1011.5745 [hep-th]]. [2] C.-T. Chan, H. Irie, C.-H. Yeh, “Stokes Phenomena and Quantum Integrability in Non- critical String/M Theory,” Nuclear Physics, Section B 855 (2012) pp. 46-81 [arXiv:1109.2598 [hep-th]]; a talk in the Gong Show session, Strings 2011, Uppsala, Sweden, June 27-July 2, 2011

III-83 ‹‹- Research Activities of Individuals Research Activities on Plasmonic Metamaterials

Shulin Sun (email: [email protected]) Postdoctoral researcher, 2010/05/20~2013/05/19

am a postdoctoral fellow working for the Plasmonic Metamaterials Initiative of the Physics Division of NCTS at Taipei from May, 2010. In the past years, my research interests focus on gradient meta-surfaces, magnetic metamaterials, and plasmonic nanoabsorbers, etc. As is well known in optics community, light reflections/refractions at an interface between two different homogeneous media satisfy the famous Snell’s law. Beginning from 2011, rather unexpectedly, a series of works (Capasso’s group Science 2011, Shavalev’s group Science 2012) have shown that Snell’s law can be generalized when one of the media is replaced by a carefully designed inhomogeneous meta-material which Figure 1. Near-field characterizations of SWs excited on the provides an additional k vector to the momentum gradient meta-surface. conservation. Different from the former works to convert incident propagating waves (PWs) to anomalous reflected PWs, we further extended Despite of the great successes already achieved this idea to show that such a meta-surface can for the above introduced gradient mate-surfaces, convert PWs to surface waves with 100% these works still suffer some limitations. For efficiency [1]. These works are certainly of great example, available meta-surfaces so far designed importance to the optics community. Our system by these groups only work in the infra-red (IR) behaves as an efficient bridge between far field and microwave regimes, and the generalized and near field and hence is highly desired for the Snell’s law has not yet been tested in visible development of plasmonics. regime, which is certainly more challenging and interesting. Also, previously fabricated IR meta- surfaces (Capasso’s group & Shavalev’s group) support not only anomalous reflections/ refractions, but also support normal ones simultaneously, so that the desired effects do not exhibit high efficiency (~20% or so). Very recently, we theoretically and experimentally demonstrate a carefully designed gradient meta- surface that supports high-efficiency anomalous reflections governed by the generalized Snell’s law at ~850nm wavelength [2]. The anomalous reflected wave can be either non-specular propagating waves or surface waves determined by the incident angle of the input beams. Compared to previously fabricated gradient meta- surfaces in infra-red wavelength regime

Research Activities of Individuals -›› III-84 (Capasso’s group & Shavalev’s group), our samples work at a shorter wavelength regime with a broad bandwidth (700-900nm). The conversion efficiency to the anomalous reflection mode is up to about 80% and the polarization of the anomalous reflected beams keeps unchanged. This work has been submitted to Nano Letters.

Figure 3. Transmission spectra and eigen-modes field patterns of the upright SRR.

Recently, a fascinating concept of coherent Figure 2. Geometry of the metasurface and anomalous perfect absorbers (CPAs) has been suggested. It reflection demonstration. was demonstrated experimentally by the example of a symmetric Fabry-Perot cavity with small The split ring resonators (SRRs) are the most losses which was symmetrically irradiated by 2 common meta-molecules adopted in constructing coherent plane waves, which can be understood as the sub-wavelength metamaterials. Recently, Prof. an inverse effect of lasing. Nevertheless, its Tsai’s group has employed stress-driven assembly application to more complicated geometries is method [3] and femtosecond laser-induced difficult. So an effective nanoabsorber of forward-transfer technique [4] to fabricate SRRs. electromagnetic fields from a single atom or Different from the traditional fabricated flat SRRs molecule is highly desired. Recently, we propose a based on electron beam lithography method, concept of coherent perfect nanoabsorbers stress-driven assembly method can fabricate (CPNAs) for divergent beams [5]. This concept upright SRRs which can be excited by both the makes use of the properties of a slab with negative incident electric and magnetic field. It means that refraction and small losses. The proposed CPNA the upright SRRs has a stronger electromagnetic device would allow focusing radiation in response than flat ones. Besides, the femtosecond nanoscale regions, and hence could be applied in laser-induced forward-transfer technique is also optical nanodevices for such diverse purposes as used to fabricate SRRs. It makes the fabrication of reading the results of quantum computation which multilayer and three-dimensional plasmonic is based on single photon qubits. Analytical dipole structures easier. To understand the underlying model analyses and numerical finite element physics mechanism of the SRRs fabricated by method simulations are used to demonstrate its both methods, we calculated the transmittance property. spectra and field patterns by finite element simulation method (FEM). The eigen-modes of the SRRs can be excited by normal illumination with polarization state parallel to the erected SRRs.

III-85 ‹‹- Research Activities of Individuals [5] Vasily Klimov, Shulin Sun and Guang-Yu Guo. “Coherent perfect nanoabsorbers based on negative refraction”. Optics Express 20, 13071 (2012). [6] Hongxing Dong, Shulin Sun, Liaoxin Sun, Weihang Zhou, Lei Zhou, Xuechu Shen, Zhanghai Chen, Jun Wang, and Long Zhang. “Thermodynamic effect induced growth and UV lasing of hierarchical ZnO Fabry-Pérot resonators”. Journal of Material Chemistry 22, 3029 (2012). Figure 4. Electric field intensity distribution (logarithmic scale) in the coherent perfect nanoabsorber.

References [1] Shulin Sun, Qiong He, Shiyi Xiao, Qin Xu, Xin Li and Lei Zhou. “Gradient-index meta- surface as a bridge linking propagating waves and surface waves”. Nature Materials 11, 426 (2012). [2] Shulin Sun, Kuang-Yu Yang, Chih-Ming Wang, Ta-Ko Juan, Wei Ting Chen, Chun Yen Liao, Qiong He, Shiyi Xiao, Wen-Ting Kung, Guang-Yu Guo, Lei Zhou, Din Ping Tsai. “High-efficiency Broadband Anomalous Reflection of Visible Light by Gradient Meta- surfaces”. Submitted to Nano Letters. [3] Che Chin Chen, Chih Ting Hsiao, Shulin Sun, Kuang-Yu Yang, Pin Chieh Wu, Wei Ting Chen, Yu Hsiang Tang, Yuan-Fong Chau, Eric Plum, Guang-Yu Guo, Nikolay I. Zheludev, and Din Ping Tsai. “Fabrication of three dimensional split ring resonators by stress- driven assembly method”. Optics Express 20, 9415 (2012). [4] Ming Lun Tseng, Pin Chieh Wu, Shulin Sun, Chia Min Chang, Cheng Hung Chu, Yao-Wei Huang, Po-Li Chen, Nien-Nan Chu, Chung Hao Lu, Lei Zhou, Ding-Wei Huang and Din Ping Tsai. “Fabrication of multilayer metamaterials by laser-induced forward transfer”. Laser & Photonics Reviews 6, 702 (2012).

Research Activities of Individuals -›› III-86 Research Activities on Particle Physics Phenomenology

Yong Tang (email: [email protected]) Postdoctoral researcher, 2011/08/01~present

uring 2011/8--2012/7, my researches at contribution to the gauge coupling constant with NCTS were focused on particle physics an asymptotic free power-law running at one loop phenomenology both in collider and cosmology. near the Planck scale. The result get published on The research projects I finished include, “Z' JHEP 1111 (2011) 073. model and top charge asymmetry”, “gravitational The Higgs decay H to two photons due to the contributions to gauge theories”, “Higgs decay virtual W-loop effect is revisited in the unitary into two photon”, “vacuum stability with neutrino gauge by using loop regularization method. and dark matter” and “Implications of LHC Though the one-loop amplitude of H to two searches on massive graviton”. The following is photons is finite, it involves both tensor-type and the brief summary of these works. scalar-type divergent integrals which can in We study a simple ultraviolet complete and general destroy the gauge invariance without anomaly free Z' model based on a U(1)' gauge imposing a proper regularization scheme. We family symmetry without introducing extra explicitly show the absence of decoupling in the fermions beyond the standard model. The U(1)' limit M_W/M_H -> 0 and obtain a result agreed group is diagonal in the three family space in exactly with the earlier one in the literature. We which the U(1)' charges of the first and second then clarify the discrepancy between the earlier families are the same but different from those of result and the recent one obtained by R. the third family. After spontaneous symmetry Gastmans, S.L. Wu and T.T. Wu. The result is breaking, there exist in general both flavor- published on Commun. Theor. Phys. 57 (2012) conserving and flavor-changing couplings. We use 427-434. the latest dijet and dilepton search at the LHC to Motivated by the hint of the Standard Model constrain the mass and gauge couplings of Z'. Also (SM) Higgs mass around 125 GeV at the LHC, we we show that in this Z' model it can only study the vacuum stability and perturbativity contribute to part of the forward-backward bounds on Higgs scalar of the SM extensions asymmetry in the top quark pair production including neutrinos and dark matter (DM). We observed at the Tevatron by taking into account consider two extensions of neutrino sector and the constraint from same sign top production at DM sector (a real scalar singlet (darkon) and the LHC. The result is published on J. Phys. G 39, minimal dark matter (MDM)), respectively. The 055003, 2012. darkon contributes positively to the beta function We perform an explicit one-loop calculation of lambda and can stabilize the SM vacuum. for the gravitational contributions to the two-, Similar to the top quark in the SM, we find the three- and four-point gauge Green’s functions with cause of instability is sensitive to the size of new paying attention to the quadratic divergences. It is Yukawa couplings between heavy neutrinos and shown for the first time that the Slavnov-Taylor Higgs boson. MDM and Type-III seesaw fermion identities are preserved even if the quantum triplet, will bring the additional positive graviton effects are included at one-loop level. We contributions to the gauge coupling running and also present a regularization scheme independent would also help to stabilize the electroweak calculation based on the Vilkovisky-DeWitt's vacuum. The result is shown on JHEP 1204 effective action. In all the calculations, the (2012) 019. symmetry-preserving and divergent-behavior- Using the latest LHC searches on dijet and preserving loop regularization method can dilepton final states, I considered the constraints consistently lead to a nontrivial gravitational on the massive graviton and scale in Randall-

III-87 ‹‹- Research Activities of Individuals Sundrum model. The mainly constrained phase [5] Yong Tang, Implications of LHC searches for space here was not shown in the LHC search massive graviton, JHEP 1208 (2012) 078, results and this work can be regarded as arxiv:1206.6949. complementary to experiments' works.

References [1] Jin-Yan Liu, Yong Tang , Yue-Liang Wu, Searching for Z' Gauge Boson in an Anomaly- Free U(1)' Gauge Family Model, J. Phys. G 39, 055003, 2012, arXiv:1108.5012 [hep-ph]. [2] Yong Tang, Yue-Liang Wu, Gravitational Contributions to Gauge Green’s Functions and Asymptotic Free Power-Law Running of Gauge Coupling, JHEP 1111 (2011) 073, arXiv:1109.4001 [hep-ph]. [3] Da Huang, Yong Tang, Yue-Liang Wu, Note on Higgs Decay into Two Photons H to two photons, Commun. Theor. Phys. 57 (2012) 427-434, arXiv:1109.4846 [hep-ph]. [4] Chian-Shu Chen, Yong Tang, Vacuum stability, neutrinos, and dark matter, JHEP 1204 (2012) 019, arXiv:1202.5717 [hep-ph].

Research Activities on Atomic Physics

Daw-Wei Wang (Department of Physics, National Tsing Hua University; email: [email protected]) Center Scientist, 2010/08/01~2014/07/31

s a NCTS Center Scientist, I was Frankly speaking, I am not fully satisfied with the benefited by the resources and flexibility quality of these works, but expect some of them of this position to work deeper in my research. can be extended and bring more important impact Below I outline some important works and/or to the community. Below are brief description of activities I have done so far since the last fall related works. (2011 Sep.-2012 Aug.). (1) N. T. Zinner*, B. Wunsch, I. B. Mekhov, S.-J. Research Huang, D.-W. Wang, and E. Demler, Few- Body Bound Complexes in One-dimensional In the past year, my research direction was Dipolar Gases and Non-Destructive Optical moving gradually from many-body physics of Detection, Phys. Rev. A 84, 063606 (2011): polar molecules toward several other directions, We consider dipolar interactions between including condensate dynamics, EIT and slow heteronuclear molecules in low-dimensional light physics, QMC simulation in optical lattice, geometries. The setup consists of two one- synthetic gauge field and Rydberg atoms etc.

Research Activities of Individuals -›› III-88 dimensional tubes. We study the stability of behaves as a classical particle (matter wave) in possible few-body complexes in the regime of the limit of small (large) incident velocity. In repulsive intratube interaction, where the the intermediate regime, the classical and binding arises from intertube attraction. To quantum properties are combined via a finite observe these complexes we propose an (but not full) discontinuity in the tunneling optical non-destructive detection scheme that transmission coefficient. We demonstrate that enables in-situ observation of the creation and the formation of a localized bound state is dissociation of the few-body complexes. essential to describe such inelastic collisions, showing a nontrivial nonlinear effect on the (2) N. T. Zinner*, B. Wunsch, D. Pekker, and quantum transportation of a bright soliton. D.-W. Wang, BCS-BEC crossover in bilayers of cold fermionic polar molecules, Phys. Rev. (5) H.-H. Jen*, B. Xiong, Ite Yu, and Daw-Wei A 85, 013603 (2012): We investigate the Wang, Electromagnetic induced transparency quantum and thermal phase diagram of and slow light in interacting quantum fermionic polar molecules loaded in a bilayer degenerate atomic gases, arXiv: 1208.0118 trapping potential with perpendicular dipole (accepted by Phys. Rev. A): We systematically moment. We use both a BCS-theory approach develop the full quantum theory for the that is most reliable at weak coupling and a electromagnetic induced transparency (EIT) strong-coupling approach that considers the and slow light properties in ultracold Bose and two-body bound dimer states with one Fermi gases. The speed of light inside the molecule in each layer. The crossover can be atomic gases can be changed dramatically near driven by many-body effects and is strongly the Bose-Einstein condensation temperature, affected by the intralayer interaction which while the presence of the Fermi sea can was ignored in previous studies. destroy the EIT effect even at zero temperature. We further investigate the (3) S.-J. Huang*, Y. - T. Hsu, H. Lee, Y.-C. Chen, interaction effects on the EIT for a weakly A.G. Volosniev, N.T. Zinner, and D.-W. Wang, interacting Bose-Einstein condensate, showing Field-induced long-lived supermolecules, a nontrivial change of the light speed due to Phys. Rev. A 85, 013603 (2012): We the quantum many-body effects. demonstrate that the long-lived bound states (super-molecules) can exist in the dilute limit (6) J.-S. You, H. Li, S. Fang, M.A. Cazalilla, and when we tune the shape of effective potential D.-W. Wang, Tuning the Kosterlitz- Thouless between polar molecules by an external transition to zero temperature in Anisotropic microwave field. We explicitly show that the Boson Systems, arXiv: 1207.2122 (accepted by non- adiabatic transition rate can be easily Phys. Rev. A): We study the two-dimensional tuned small for such ground state super- Bose-Hubbard model with anisotropic molecules, so that the system can be stable hopping. Focusing on the effects of anisotropy from collapse even near the associated on the superfluid properties such like the potential resonance. Our results, therefore, helicity modulus and the normal-to-superfluid suggest a feasible cold molecule system to (Berezinskii-Kosterlitz-Thouless, BKT) investigate both novel few-body and many- transition temperature, two different body physics (for example, the p-wave BCS- approaches are compared: Large-scale BEC crossover for fermions and the paired Quantum Monte Carlo simulations and the condensate for bosons) that can not be easily self-consistent harmonic approximation accessed in single species atomic gases. (SCHA). The accuracy of the SCHA in the extremely anisotropic limit, where the BKT (4) C.-H. Wang, T.-M. Hong, R.-K. Lee*, and transition temperature is tuned to zero (i.e. into D.-W. Wang, Particle-wave duality in quantum a Quantum critical point) and therefore tunneling of a bright soliton, Optical Express quantum fluctuations play a dominant role, is 20, 22675 (2010): We report a systematic particularly striking. study of the quantum tunneling property for a bright soliton in ultracold atoms, which

III-89 ‹‹- Research Activities of Individuals Service I served as the coordinator of AMO focus group of NCTS. The annual budget is 800K and has about 40 faculties (including experimentalists). We organize an international workshop on ultracold atoms and molecules in May 2012, and a summer school in Aug. 2012. More details can be fund from the report of AMO focus group.

Research Activities on Phenomenology of heavy quarks and Higgs bosons at hadron colliders and lepton colliders

Hiroshi Yokoya (email: [email protected]) Assistant research scholar, 2011/01/01~2012/08/31

uring my career at the NCTS north, I have very important. worked on phenomenological studies for In collaboration with Dr. J. Alwall, Dr. T. high-energy collider experiments mainly at the Enkhbat and Prof. W.S. Hou, we further studied LHC. the collider analysis on the characteristic signature 4th generation quarks are, if they exist, expected of the exotic mesons which have color and isospin to have large Yukawa couplings with the Higgs- simultaneously [2]. We found the decay of the boson and also the Nambu-Goldstone boson color-octet and isospin-triplet scalar into W-boson according to their large mass. Therefore, they can and gluon can be seen with an additional W-boson form bound-states via the Yukawa force. In where the W-boson from the scalar is highly collaboration with Dr. T. Enkhbat and Prof. W.S. boosted. Therefore, hadronic observables from the Hou, we studied the expected spectrum of the W-boson are seen as a collimated fat jet with bound-states and their phenomenology at the LHC substructure. We performed the realistic [1]; the production cross-section, the decay simulation study for W-jet tagging and detector branching ratio and the possible signature, by simulation, and compared the significance of assuming degenerated 4th generation quarks and different decay modes of W-bosons for the mixing with the other three generations. Since the exclusion and discovery of such mesons. Our experimental bound on the mass of the 4th analysis shows that the LHC 2012 data has generation quark reaches the unitarity bound, an potential to exclude the mesons with the mass analysis on the consequence of the existence of around TeV. such heavy quarks and its collider signature is

Research Activities of Individuals -›› III-90 Furthermore, I have worked on the collider The mass determination of a particle which signatures of various extended Higgs scenarios, decays including missing momentum can not be such like a model with color-octet scalar [3,4] in straightforward. In collaboration with Ms. S. collaboration with Dr. T. Enkhbat, Dr. Y. Mimura Kawabata, Dr. Y. Shimizu, Prof. Y. Sumino have and Prof. X.G. He, two Higgs doublet model [5] developed a new method to find a correct mass of in collaboration with Dr. K. Tsumura and Prof. S. a particle by using only the lepton energy Kanemura, and Higgs triplet model [6] in distribution [8]. This method is quite general and collaboration with Dr. H Sugiyama and Dr. K. can be applied to any particle which is scalar or Tsumura. Since the determination of the Higgs unpolarized and which decays including lepton. sector for spontaneous electroweak symmetry As a demonstration of this method, we performed breaking is the most important task at the LHC, it a simulation study of the mass determination of is also important to study the collider signatures of the Higgs boson in vector-boson fusion process the Higgs sector which is different from the followed by Higgs boson decays into WW. We minimal standard model. The evidence of the found that since the lepton energy can be extended Higgs sector can appear, for example, in measured precisely, the mass determination is not the CP-odd asymmetry in top-quark pair affected by the uncertainties of parton distribution, production process, 4 tau-lepton production measurements of jet momentum and missing process, and also the production of the same-sign momentum. lepton resonances. I have studied the phenomenological analysis for such processes and the method to reconstruct the kinematics of the events including missing momentum to obtain the mass of the new scalars. References In addition, I have worked on the perturbative [1] T. Enkhbat, W.-S. Hou and H. Yokoya, Phys. QCD for the collider phenomenology. My interest Rev. D84, 094013 (2011). is the QCD correction to the heavy quark [2] J. Alwall, T. Enkhbat, W.-S. Hou and H. production at the hadron colliders and lepton Yokoya, arXiv:1208.1686 [hep-ph]. colliders. Close to the threshold, it is known that large corrections come from the logarithmic terms [3] T. Enkhbat, X.-G. He, Y. Mimura and H. by soft/collinear emission of gluons from initial/ Yokoya, JHEP 1202, 058 (2012). final states, and also the Coulomb gluon exchange [4] X.-G. He, G. Valencia and H. Yokoya, JHEP in the final states. I have developed the formalism 1112, 030 (2011). for resuming the all-order contributions of the [5] S. Kanemura, K. Tsumura and H. Yokoya, Coulomb exchange at hadron colliders. Due to Phys. Rev. D85, 095001 (2012). this resummation in a non-relativistic and non- perturbative treatment, the formation of the bound [6] H. Sugiyama, K. Tsumura and H. Yokoya, state can be described. We have performed the arXiv:1207.0179 [hep-ph]. detailed simulation study for the determination of [7] R. Yonamine, K. Ikematsu, T. Tanabe, K. Fujii, the top-quark Yukawa coupling in the Higgs- Y. Kiyo, Y. Sumino and H. Yokoya, Phys. Rev. associated top-quark pair production process at D84, 014033 (2011). the future international linear collider [7]. It was found that the effect of the all-order Coulomb [8] S. Kawabata, Y. Shimizu, Y. Sumino and H. summation is crucial to estimate the production Yokoya, Phys. Lett. B710, 658 (2012). cross-section and the accuracy of the Yukawa coupling measurement.

III-91 ‹‹- Research Activities of Individuals Introducing New Members

Dr. Sung-Po Chao

Postdoctoral researcher (Ph.D. Rutgers University Piscataway, USA) email: [email protected]

will work as a postdoc researcher starting Riverside, under Prof. Vivek Aji, during which I on Oct 1st , 2012 in the condensed matter worked on Kondo problems in grapheme, group in National Center for Theoretical Science transport and magneto properties of Dirac type (NCTS). I got my B.S. (95-99) and M.S, (99-01) (linear dispersions) material such as surface state in Physics from National Tsing Hua University of three dimensional topological insulator or under the supervision of Prof. Darwin Chang and grapheme. Chung-Yu Mou on the charge transport in Currently I will continue to work on superconducting -normal metal superlattice identifying phases of those linearly dispersing system. I got my Ph.D. (03-10) in Physics at novel materials and seek to work with the center Rutgers University under the supervision of Prof. scientists on various topics such as quenching of Natan Andrei. My thesis work is to apply the interactions in the cold atom system, noise Scattering Bethe Ansatz approach, a type of exact analysis in the transport of quantum impurity solutions to tackle nonequilibrium quantum system, phase transitions in heavy fermion impurity problems, on the steady state current of materials, etc. Glad to join the NCTS and happy to quantum dot system. Beteen 10-12 I worked as a work with you. postdoc researcher in University of California,

Prof. Chung-Hou Chung

Center scientist and associate professor (NCTU) email: [email protected]

tarting Fall of 2012, I become a center quantum phases in correlated many-body systems. scientist in the physics division of NCTS. Examples include: the two-channel Kondo ground I also work as an associate professor in state realized in nano-devices, unconventional Department of Electrophysics, National Chiao- superconductivity in cuprates and heavy-fermions, Tung University (NCTU). spin-liquid states in frustrated quantum magnets, fractionalized quasi-particle excitations in helical My current research interest is on novel Luttinger liquids of interacting 2D topological quantum phenomena in low-dimensional insulators. The understanding of these exotic condensed matter and mesoscopic systems with quantum phases often exceeds the scope of the strong electron correlations. In particular, I am well-known Laudau Fermi-liquid descriptions. interested in understanding newly realized exotic One goal of my research is to develop the proper

Introducing New Members -›› III-92 theoretical descriptions of these new quantum fermion materials near quantum criticality, and phases realized in various experiments. Another non-equilibrium quantum criticality of a equally important aspect is to study the possible dissipative resonant level quantum dot. Various continuous phase transition at zero temperature, analytical and numerical approaches are applied so-called “quantum phase transition” in these here to address these issues, including field- systems once other competing orders are also theoretical perturbative renormalization group present. Observables near the quantum critical (RG) approach, Green’s function approach in point (QCP) exhibit universal power-law scaling quantum many-body theory, large-N theories at low temperatures. Examples are: Kondo combined with the Non-Crossing Approximation breakdown and emergence of superconductivity or (NCA), mean-field theories. spin-liquid phase in Kondo lattice model of heavy

Dr. Shih-Hao Ho

Postdoctoral researcher (Ph.D. National Tsing Hua University, Taiwan) email: [email protected]

am starting this September first, 2012 as Taiwan Normal University, we have explored a research associate in the physics some aspects along the first topic [1] and these division of NCTS after being a visiting scientist at will also be my major research topics in the Center for theoretical physics at MIT for two following year. years. On the other hand, along with Professor Feng- My current research interest is the interface Li Lin and Xiao-Gang Wen, we also studied the between the condensed matter physics and high Jackiw-Rebbi model with more fermion species energy physics, especially the application of AdS/ and found that there exists a single Majorana zero CFT correspondence in condensed matter physics mode [2] [3]. We wish this can open the and its connection with the topological ordered possibilities to study the non-Abelian anyons in phases. three dimensional space, which are argued not existing in three dimension conventionally. This is The breakthroughs of AdS/CFT also one of my major research focus. correspondence provide us a powerful tool to study a strongly-coupled system through a classical gravity theory. On the other hand, since References the topological insulators and superconductors [1] S.-H. Ho and F.-L. Lin, “Anti-de Sitter space have been studied extensively, two natural as a topological insulator and holography,” questions arise: first, how to classify these various arXiv:1205.4185 [hep-th]. types of topological insulators/superconductors when they are (strongly) interacting systems, and [2] S.-H. Ho, F.-L. Lin and X.-G. Wen, “Majorana second what are the effective field theory of these Zero-modes and Topological Phases of Multi- various classes of topological insulators/ flavored Jackiw-Rebbi model,'' superconductors. I am convinced that the AdS/ arXiv:1207.1620 [hep-th]. CFT can help us to answer the first question while [3] This Majorana zero mode is a “projective the anomaly structures in quantum field theory topological mode”, i.e. it is not robust respect can help us advance the understanding of the to all the perturbation rather than the second one. perturbation respecting some discrete Along with Professor Feng-Li Lin at National symmetries.

III-93 ‹‹- Introducing New Members Prof. Yoshiaki Teranishi

Center scientist and assistant professor (NCTU) email: [email protected]

have been appointed as a new center spectroscopic methods utilizing the idea of scientist in the physics division of NCTS quantum control. since this August. I earned his Ph.D from the When an intense laser (typical intensity is Graduate University for Advanced Studies in 14 2 10 W/cm ) is irradiated to atoms or molecules, Japan. I came to Taiwan in 2007 as a postdoctoral highly nonlinear ionization take places. This fellow at the Academia Sinica. Since 2011, I have highly nonlinear ionization is utilized as the basic been an assistant professor of the Institute of mechanics of the cutting edge laser technologies, Physics at National Chiao-Tung University. My such as atto second pulses and X-ray lasers. current research interests include (1) laser Highly nonlinear excitation, however, is not paid quantum control of atomic and molecular much attention so far. Recently it is processes, (2) ultrafast dynamics of atoms and experimentally revealed that electronic excitation molecules in intense laser fields, and (3) atomic of molecules takes places when an intense laser is collision theories. irradiated. I have developed basic theory to Recent technologies in lasers realize complicated explain this process, and I am now trying to shaping of laser pulses. One of the big problems discuss the application of this theories. For still remain is how to find the optimal pulse shape example, this intense laser excitation can be to realize desired control. I am interested in basic utilized to remote lasing. problems in laser control, such as “How fast can I am studying also on the atomic collision we achieved a control?”, or “What is the relation processes with antiproton. I have proposed a between the uncertainty principle and the possible simple formula of capture cross section of fastest controlling time”. I also proposed new antiproton by atoms.

Dr. Jackson Wu

Assistant research scholar (PhD, University of Washington, USA) email: [email protected]

n Spring 2012 I joined the Physics the LHC has yielded tantalizing hints of possible Division of NCTS as a new assistant BSM physics in its decay channels, and new research scholar. I was previously postdoctoral bounds were derived by me and others that place fellows at TRIUMF, ITP Bern, and CQUeST. significant new constraints on various classes of BSM models. With more data forthcoming from My research interests have been wide, ranging the LHC, where BSM physics may lie in the from particle physics phenomenology to string parameter space will be determined with ever theory. In particle physics, one of my current higher precision. focus is on how to constrain models of beyond the SM (BSM) physics from collider experiments. In string theory, my interest is in applying the The recent, long-awaited discovery of the Higgs at method of gauge/gravity duality or “holography”

Introducing New Members -›› III-94 to study strongly-coupled systems such as QCD between a gravity theory and the gauge theory it and those found in condensed matter physics. The corresponds to is not always firmly established, or duality allows one to study these systems in a the duality is firm but the gauge theory is only weakly-coupled dual gravity picture, making similar to the one of interest. Take QCD again, calculations of correlation functions in a currently it has no known gravity dual. What has controlled fashion possible, which is not the case been constructed are all for QCD-like theories, in the original strongly-coupled gauge theory even which contain extra states not found in the QCD with numerical methods. An example is QCD at spectrum. Nevertheless, holography can offers finite density, which is very difficult to simulate important qualitative insights even with these on the lattice due to the notorious sign problem. imperfections. The obvious challenge are to But by using holography, I was able to explore its sharpen these dualities and finding new ones phase diagram at nuclear density. which will expand the validity and thus power of holography to answer questions still intractable in As with all things, there are limitations and strongly-coupled systems. shortcomings in holographic methods. The duality

Dr. Chi-Hsien Yeh

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

am starting this August 2012 as a new minimal string theory. Matrix model has fewer postdoctoral fellow in the physics degrees of freedom, so it is easily calculable. On division of NCTS. I got my Ph.D. degree from the other hand, it still shares the specific features National Taiwan University in January 2012. My with original string theory, so it will help us learn supervisor was professor Pei-Ming Ho. Our works more about the non-perturbative completion and focused on the M-theory, low-energy effective the structure of vacuum (Landscape) in string theory of D-brane, and Nambu-Poisson gauge theory. theory. These works help us understand more Recently, we analyze the landscape of matrix about the non-perturbative completion in string model. From instanton calculations, we can know theory. if the vacuum is stable or not. We also calculate From 2008, I also collaborated with Dr. the decay rate from meta-stable vacuum to true Hirotaka Irie, professor Chuan-Tsung Chan, and vacuum. We want to know that if these Sheng-Yu Darren Shih. We studied Matrix Model calculations can be applied to original string which is a simple version of 2D quantum gravity theory. It may help us to solve the landscape theory. This theory includes the gravity parts (2D problem in string theory. Moreover, we may Liouville theory) and matter parts (minimal understand why Standard Model is in this special conformal field theory), so it is also called vacuum.

III-95 ‹‹- Introducing New Members