The International Workshop on Commutative Algebra was successfully held at Thai Nguyen University of Sciences from the 4th to the 7th of January 2017. The workshop is one of a series of activities in the program to strengthen research capacity and specialized training on Algebra by the Japanese mathematicians to support faculty and research students of Thai Nguyen University (TNU). The mandate of the workshop is "by and for Japan-Vietnam Young Mathematicians", but many senior mathematicians also attended and supported the event.
There were 40 participants attending the workshop, including 13 faculties and PhD students of Thai Nguyen University; 14 Japanese delegates from Meiji University, Nagoya University, Hokkaido University of Education, Chiba University, Yamaguchi University, Osaka University; 5 delegates from Hanoi Institute of Mathematics, and some representatives from universities in Ha Noi, Vinh Phuc, Phu Tho, Vinh and Ho Chi Minh City. Many famous senior mathematicians also attended the workshop such as professors Shiro Goto and Ryo Takahashi – the Japanese outstanding mathematicians; prof. Ngo Viet Trung, prof. Nguyen Tu Cuong, prof. Le Tuan Hoa - the three winners of the Ho Chi Minh Prize in 2016; prof Dao Hai Long from Kansas University of America who won two gold medals in International Mathematical Olympiad; prof Pham Ngoc Anh from Hungary Institute of Mathematics – the Vietnamese young man brilliant at mathematics in the 1980s – 1990s of the previous century.
The Organizing and Program Committee of the workshop includes young mathematicians of Japan (Naoyuki Matsuoka, Kazuho Ozeki), Hanoi's Institute of Mathematics (Doan Trung Cuong, Hoang Le Truong) and the young faculty of Thai Nguyen University. The workshop was very special with no showy displays, no opening and closing ceremonies, no interpreters, no tour visits, and all participants even had lunch at the seminar room. The entire 4 days, from 8.30 am to 7 pm, were spent on scientific reports and discussions. In total, 18 reports were presented at the workshop, lasting from one to two hours each. The Japanese delegations had 10 presentations of Naoki Taniguchi and Kaori Shimada (Meiji University); Shin-ichiro Iai and Futoshi Hayasaka (Hokkaido University of Education); Shinya Kumashiro and Ryotaro Isobe (Chiba University); Tao Suzuki and Kazunori Matsuda (Osaka University); Kazuho Ozeki (Yamaguchi University); Hiroki Matsui (Nagoya University). For Vietnam, all 8 rapporteurs are faculty and PhD students of TNU namely Tran Duc Dung, Luu Phuong Thao, Do Van Kien, Nguyen Thu Hang, Pham Hong Nam, Nguyen Van Hoang, Tran Do Minh Chau, and Hoang Ngoc Yen.
The language of the workshop is English. Many reports have high scientific content, presenting new research results around the topics of interest among world community of mathematics such as almost Gorenstein rings; Hilbert functions and coefficients; depth functions and combinatorial computations; reductions of multigraded modules; Koszul algebras; Balmer spectra; free resolutions; canonical module; dualizing complex; homological conjectures; reducibility index; and local cohomology modules. Many young rapporteurs of TNU who had the first experience in presenting in such a prestigious scientific forum, had carefully prepared the report and presented it enthusiastically and impressively. Many questions and comments from the participants added to the effectiveness of the workshop.
The program to support research and professional training on Algebra of Japanese mathematicians to faculty and research students of TNU of Vietnam has been implemented since the beginning of 2016 with the strong support of prof. Shiro Goto and Naoyuki Matsuoka (Meiji University) and colleagues in Japan. From February to November 2016, two PhD. students (Do Van Kien, Nguyen Thi Thu) and 2 TNU lecturers (Dr. Tran Nguyen An, Dr. Tran Do Minh Chau) were sponsored to study at Meiji University under the supervision of professors Shiro Goto, Naoyuki Matsuoka and Naoki Taniguchi. In March 2016, the International School of Commutative Algebra was first held at Thai Nguyen University of Sciences (TNUS) with a series of lectures by professors Shiro Goto, Naoyuki Matsuoka, Shin-ichiro Iai and Kazuho Ozeki. In June 2016, the professors continued to have lectures at the International School of Commutative Algebra in TNUS for the second time. In November 2016, two mathematicians representing the research team of TNU were funded by the Japanese partner to present at the Symposium on Commutative Algebra of Japan held in Tokyo. Significantly, nearly 100 precious specialized books have been donated to TNUS by Japanese professors. Two accounts have been given to TNU researchers for free access to library materials of Meiji University. With the efforts from both sides, 6 research articles by TNU faculty and PhD. students (Le Thị Thanh Nhan, Nguyen Van Hoang, Tran Do Minh Chau, Do Van Kien, Tran Nguyen An, Nguyen Thi Dung) co-authored with the mathematicians of Meiji University have been completed in which 4 articles have been or accepted to be published in the international journals of mathematics.
The year 2017 has a nice opening by the success of the International Workshop on Commutative Algebra. The research team of Thai Nguyen University had a chance to present their research results, to join the discussions and to experience intensive team work with the Japanese mathematicians as well as with professors of mathematics in Vietnam and in the world. At the same time, this workshop is a great opportunity for young staffs of the universities in the country in general and of TNU in particular to learn how to work seriously, precisely, effectively with full of energy and passion, with the will and the responsibility of the Japanese experts. We believe that the new year 2017, the second year to implement the program to support research and specialized training on Algebra at Thai Nguyen University of Vietnam, will be more effective and successful.