:::

數學組簡介

:::

宗旨及運作現況

Introduction

National Center for Theoretical Science (NCTS) in Taiwan was established on August 1, 1997 fully funded by the National Science Council (NSC) in Taiwan. The Center is hosted in Hsinchu jointly by National Tsing Hua University (NTHU) and National Chiao Tung University (NCTU). The first funding phase was six years (1997-2003). At the beginning of the second phase (2004-2008), an administrative decision was made by NSC to expand the structure of the NCTS by adding two subprojects: Subproject-I in Taipei hosted by National Taiwan University (NTU) and Subproject-II in Tainan hosted by National Cheng Kung University (NCKU) while the headquarter remains in Hsinchu. National Central University (NCU) joined NTHU and NCTU to become one of the hosting institutions in 2009, the beginning of the third phase (2009-2014).
The Center consists of two separate, equally funded divisions, Mathematics and Theoretical Physics. The total budget for 2013 is 75million NT dollars. Wen-Ching Winnie Li of Penn State University and NTHU is the current NCTS director, who also serves as the head of the Mathematics Division. She started this position in 2009, succeeding Jing Yu. During the semester she is in the US, Sze-Bi Hsu of NTHU is the acting Director. Xiao-Gang He of NTU and NTHU is the head of the Physics Division. Each subproject also has two divisions; Jung-Kai Chen of NTU and Ching-Hung Lam of Academia Sinica (AS) are currently in charge of the mathematics division in Subproject-I and Subproject II, respectively. In the history of NCTS, the mathematics division has had three division heads, who also served as directors of the center: Chang-Shou Lin (now at NTU), Jing Yu (now at NTU) and Wen-Ching Li.
The missions of NCTS are

1. To foster world class outstanding researchers, and attract top young researchers to do cutting edge research in theoretical sciences;

2. To attract worldwide outstanding theoretical scientists to do research in Taiwan;

3. To develop international and inter-disciplinary scientific research programs;

4. To promote international cooperation and collaborations, aiming to become a leading research institution in Asia and in the world.


Administrative Structure

In the Mathematics Division, policies and decisions are made by two committees. The program committee is concerned with the scientific activities of the center, and the executive committee makes decisions on policies and hiring. Currently, program committee members are Gerard Jennhwa Chang (discrete mathematics) from NTU, Jungkai Chen (algebraic geometry) from NTU, Shun-Jen Cheng (representation theory and Lie superalgebra) from AS, Yng-Ing Lee (differential geometry and geometric analysis) from NTU, Tai-Chia Lin (nonlinear PDE, math physics) of NTU, Yuan-Chung Sheu (probability theory) of NCTU, Chih-Wen Shih (dynamical systems) from NCTU, Dong-Ho Tsai (differential geometry and geometric analysis) from NTHU, Eugene Zhu Xia (algebraic geometry) from NCKU, and Chia-Fu Yu (arithmetic geometry) from AS. The executive committee consists of Chiun-Chuan Chen (nonlinear PDE) of NTU, Jung-Kai Chen (algebraic geometry) of NTU, Sze-Bi Hsu (dynamical systems and mathematical biology) of NTHU, Ming-Chih Lai (scientific computation) of NCTU, Ching-Hung Lam (vertex operator algebra) of AS, Wen-Ching Li (number theory) of NCTS, and Shuenn-Jyi Sheu (probability theory) of NCU.

The International Scientific Advisory Committee (ISAC) is formed to give advice and guidance of the future direction of the Mathematics Division. ISAC committee members are Ching-Li Chai (University of Pennsylvania and Academia Sinica), Bernold Fiedler (Free University of Berlin), Thomas Yizhao Hou (Cal Tech), Ker-Chau Li (UCLA), Shigefumi Mori (RIMS, Kyoto University), Richard Schoen (Stanford University), Horng-Tzer Yau (Harvard University), Shing-Tung Yau (Harvard University), and Shouwu Zhang (Princeton University).



Scientific Staffs

Modeled after MSRI at Berkeley, NCTS has no permanent scientists. Each year the center invites numerous short- and mid-term visitors. From time to time, there are long term visitors. For example, Der-Chen Chang of Georgetown University spent his sabbatical year visiting NCTS (Dec 2012-July 2013). The long term scientific research personnel in Mathematics Division consist of center scientists, postdoctoral fellows, and research associates.

Center Scientists are responsible for organizing activities for the center. In return for their service, their teaching loads in their home institutions are reduced. Current Center Scientists are: Der-Chen Chang (differential geometry and geometric analysis) from Georgetown University, Kuo-Chang Chen (dynamical systems) from NTHU, I-Liang Chern (nonlinear PDE and scientific computation) from NTU and NCTU, Hung-Lin Chiu (differential geometry and geometric analysis) from NCU, Sze-Bi Hsu (dynamical systems and mathematical biology) from NTHU, Ming-Chih Lai (scientific computation) from NCTU, Wen-Ching W. Li (number theory and applications) from Penn State University and NCTS, Chih-Wen Shih (dynamical systems) from NCTU, Shuenn-Jyi Sheu (probability theory) from NCU, and Yifan Yang (number theory) from NCTU. This list is adjusted annually.

In Hsinchu there are 5 postdoctoral fellows (Xiaoqing He, Hau-Wen Huang, , Linfeng Mei, Yong-Li Tang, Fang Ting Tu) and 3 research associates (His Wei Hsieh, Chung-Yun Hsieh and Min-Chun Wu). The postdoctoral position is for one year and renewable for another year. Most of the postdoctoral fellows remain in academia after leaving NCTS. The research associates spend one year at NCTS to strengthen their mathematical background and research skills while preparing themselves for studying abroad. This is one of the several ways NCTS help young people to pursue their career in mathematics. NCTS has been quite successful in doing this. This August, Wong will go to Queens University in Canada to study analytic number theory with Ram Murty, and Shih will study scientific computation at Stony Brook in US.

In Taipei, there are 3 postdoctoral fellows (Hyunjoo Cho, Hao Feng and Mounir Hajli ) and 1 research associates (Kai-Chieh Chen).



Administrative Staff

The division has a team of able administrative staff to provide support and take care of all details related to day-to-day smooth operation of the Center. All visitors are deeply impressed by their efficiency and courtesy. They are: Wendy Huang (黃雍雅), Vickey Sun(孫毓孜), Chiayu Twu (涂佳玉), Sophie Wang (王寶珍)in Hsinchu; Shu Hui Haung (黃淑惠) and Szuchia Chiu (邱思佳) in Taipei; and Teresa Pan(潘蒔儀) in Tainan.



Research Programs

Scientific activities are primarily carried out by director/division head, PI and co-PI of subprojects, center scientists, and focus program coordinators, with assistance from honorary researchers, Chern fellow, and young theorists.

The Mathematics Division has 10 focus programs and 2 regional programs. The focus programs and coordinators are as follows:


1. Algebraic Geometry, coordinator: Jungkai Chen

2. Discrete Mathematics, coordinators: Gerard Chang and Li-Da Tong

3. Dynamical Systems, coordinator: Kuo-Chang Chen

4. Geometric Analysis and Differential Geometry, coordinators: Jih-Hsin Cheng, Yng-Ing Lee, D-M. Nhieu, Chiung-Jue Sung, Dong-Ho Tsai, and River Chiang

5. Mathematical Biology, coordinators: Sze-Bi Hsu, Chih-Wen Shih, and Je-Chiang Tsai

6. Number Theory, coordinators: Wen-Ching W. Li, Liang-Chung Hsia, Yifan Yang, and Chia-Fu Yu

7. Partial Differential Equations, coordinators: Jong-Sheng Guo, Tai-Chia Lin, Jenn-Nan Wang, Jann-Long Chern, Yung-Fu Fang, and Chiun-Chuan Chen

8. Probability Theory, coordinators: Shuenn-Jyi Sheu and Yuan-Chung Sheu

9. Representation Theory, coordinators: Shun-Jen Cheng, Ching-Hung Lam, and Wen-Fong Ke

10. Scientific Computation, coordinators: Ming-Chih Lai, Wen-Wei Lin, Wei-Cheng Wang, Soon-Yi Wu, and I-Liang Chern.

In addition, there are two regional programs in Statistics, one in Hsinchu coordinated by H. Wang, N.-J. Hsu and S.-T. Tseng, and one in Tainan run by Tiee-Jian Wu.

Each focus group, based on its needs and goals, determines its own priority and the appropriate scientific activities. At the end of each calendar year, NCTS presents written and oral reports to the review committee (called by the NSC), which examines the performance of all programs and checks how the funds were used.



Highlights of Activities

The Center is a lively and intellectually stimulating place for all, from undergraduate students to senior researchers. We offer regular seminars and winter/summer schools to train undergraduate and graduate students, weekly research seminars for graduate students, postdoctoral fellows, and faculty members. Continuous efforts are made to invite domestic and international experts to offer special topic courses designed to discuss cutting edge research progress, aiming to identify research topics and start research collaborations. The numerous visitors report on their recent advances in diverse areas of mathematics. Each focus program organizes at least one workshop/conference in its field every year to showcase results by Taiwanese researchers and to provide a platform for domestic researchers to interact with the international experts. In recent years mathematicians and physicists have jointly organized workshops and summer schools to promote further communications between the two divisions of the Center.

The special year in the Mathematics Division was initiated in 2010. The purpose is to allocate more resources to a targeted area to give it a strong push. The themes are: number theory (2010), geometry (2011), applied mathematics (2012), algebraic geometry and representation theory (2013), and number theory (2014). It has been very fruitful. As a result, interactions and collaborations among people from different institutions have remarkably increased, and through jointly organized inter-disciplinary and cross-area activities, people have broadened their horizon.

The “Distinguished Lecture Series” are the most prestigious lectures in the Mathematics Division. Its inaugural speaker was Jean-Pierre Serre of College de France in 2009. Beginning 2010, we incorporate this lecture series with activities of the special year. We are very fortunate that Don Zagier of Max Planck Mathematics Institute, Bonn, and College de France (2010), Gerhard Huisken of Max Planck Institute of Gravitational Physics (2011), Fang-Hua Lin of Courant Institute of Mathematical Sciences (2012), Jean-Pierre Serre of College de France (2013), and Manjual Bhargava of Princeton University (2014) have accepted our invitation to deliver the Distinguished Lecture Series.

In 2012 the Mathematics Division launched a new “Meet with Professor …” series to devote one day to feature a famous mathematician. Activities include lectures to highlight his/her research achievements and a forum discussion to show his/her human side. The purpose is for the audience to learn from very successful people their mathematics and how to handle challenges in mathematics. We have featured Sun-Yung Alice Chang of Princeton University, Yum-Tong Siu of Harvard University, Ching-Li Chai of University of Pennsylvania and Academia Sinica, and Chang-Shou Lin of National Taiwan University in 2012, and will feature Jean-Pierre Serre of College de France, John Coates of University of Cambridge, and Horng-Tzer Yau of Harvard University in 2013.

To promote international cooperation and collaboration is one of our main tasks. In recent years, the Mathematics Division has signed MOU with prestigious institutions in the world. These include: Pohang Mathematics Institute, Korea (2010), Russian-French Poncelet Lab, Russia (2011), Independence University of Moscow, Russia (2011), University of Bergen, Norway (2012), Tsinghua University Mathematical Sciences Center, China (2013). There have been regular exchanges between NCTS and the MOU partners. The most frequent one is the rotating annual workshop in number theory or PDE between PMI and NCTS since 2009. There have been biannual conferences in number theory (resp. PDE) between NCTS and Waseda (resp. Tohoku) University in Japan. Beginning 2012, Taiwan has become a member country of the Pan Asian Number Theory community, with Director Li serving on its Scientific Committee representing Taiwan. These agreements provide more opportunities to elevate the visibility and quality of research of Taiwanese mathematicians. They have also resulted in international collaborations.

The Center also seeks cooperation with international funding agencies. We have successfully organized three conferences jointly supported by NCTS and the National Science Foundation in US: Workshop on PDE Model: Biological Process (2010), Workshop on Fluid–Structure Interaction Problems (2011), International Conference on Galois Representations, Automorphic Forms, and Shimura Varieties (2011). This kind of international cooperation was first in Taiwan.




Awards and nurturing young talents

The foremost mission of NCTS is to nurture young talents. A substantial portion of our funds is used for this purpose. We strongly encourage young researchers, including Ph.D. students, postdoctoral fellows, and junior faculty members to attend important programs abroad or spend an extended period of time to work with international experts. Those interested can apply for CTS fellows to support such activities. This has been an important and effective way to foster young generations. Many people have benefited from this program.

Each year NCTS offers Young Theorists Awards to young faculty members. The recipients in mathematics this year are Ming-Lun Hsieh of NTU (number theory), and Ching-Hsiao Cheng of NCU (nonlinear PDE); together with Chieh-Yu Chang of NTHU (number theory), Wan-Keng Cheong(Algebraic Geometry), Wu-Yen Chung(String Theory), and Kung –Chien Wu(Nonlinear PDE).there are six young theorists at present. We are very proud that in the past decade all NSC 吳大猶Award winners in mathematics have been NCTS young theorists. Kuo-Chang Chen of NTHU (dynamical systems) is the current Chern Fellow (2010-2014), the most prestigious award of the Mathematics Division.

Mathematicians active in NCTS have won important international and domestic recognitions in recent years. International awards include:

ICCM Morningside awards: Chin-Lung Wang of NTU (silver medal 2001), Chiun-Chuan Chen of NTU (silver medal 2007), Jung-Kai Chen of NTU (silver medal 2010);
ICCM Chern award: Song-Sun Lin of NCTU (2001), Wen-Ching Li (2010);
AMS inaugural fellow: Wen-Ching Li of NCTS (2012), Jing Yu of NTU (2012);
SIAM fellow: Sze-Bi Hsu of NTHU (2013).

Within Taiwan, the former director Jing Yu of NTU was elected Academician of Academia Sinica in 2012; Chiun-Chuan Chen of NTU, Chin-Lung Wang of NTU, Wen-Wei Lin of NCTU, and Sze-Bi Hsu of NTHU were named the prestigious Ministry of Education National Chair Professor (教育部國家講座); Shun-Jen Cheng of AS, Gerard Chang of NTU, Jung-Kai Chen of NTU, and Meng-Kiat Chuah of NTHU received Ministry of Education Outstanding Research Award (教育部學術獎).

The NSC distinguished award recipients in the past decade are all avid participants of NCTS, many of them benefited greatly from NCTS. Among them Chieh-Yu Chang of NTHU is the only assistant professor receiving this honor. C.-Y. Chang was a postdoctoral fellow at NCTS for four years before joining NTHU.

 

The Impact of NCTS to Theoretical Sciences in Taiwan

In the past 16 years, the research in theoretical sciences in Taiwan has improved remarkably. It is generally believed that the superb job done by NCTS played the pivotal role. Some statistical data support the above statement. In the year before 1993, the total number of articles in mathematics in SCI journals is less than 100. The quantity grew dramatically after 1998, one year after NCTS started its operation. Not only the quantity, but also the overall quality of the research work is improved strikingly as well. Here are some statistics in mathematical sciences as of 2012. Taiwan ranked number 17th internationally in terms of the total number of papers appeared in SCI ranked journals, ranked 21st in terms of total number of citations, and ranked

40th in terms of the number of citations per paper. The figure below shows the relative impact factor to mathematics in 5 year trends, with impact factor 1 being world average.

A. The international standing of Mathematics in Taiwan


2007-2011 Relative impact factors : Denmark (1.13)、USA (1.30)、Netherlands (1.23)、France (1.12)
China (1.00)、Taiwan (0.99)、South Korea (0.85) 、Japan (0.83)

B. Number of high quality papers in Mathematics

In the past 15 years, the research in theoretical sciences in Taiwan has improved remarkably. The following table shows the growth of publications in high quality journals in pure math., applied math., and statistics. We list the number of papers ranked A* (= top 7%) and A (next
19%) according to ERA journal ratings for mathematics; total means the number of all papers in
that category. This is expressed graphically below the table.

year
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
 
NCTS as affiliation
A*
0
1
1
0
2
3
1
5
10
17
12
10
18
A
1
0
0
1
4
8
10
27
18
17
17
14
14
total
1
1
1
3
10
16
28
52
54
81
53
59
78
 
acknowledging
 
NCTS
A*
1
1
0
0
5
10
10
15
19
20
17
13
11
A
1
0
0
2
8
9
16
22
24
27
24
26
31
total
2
2
4
5
25
33
43
57
108
114
75
88
99
other
A*
1
0
0
0
0
1
2
1
2
0
0
0
2
A
0
0
0
0
0
0
1
6
0
0
0
0
1
total
1
0
0
0
11
3
7
16
23
0
0
0
10

最後修改者 : 睿綸數位 2014-04-07 14:10:20
web_use_log