Report on the JSPS Invitation Award for Eminent Scientist

1. Invited Fellow Researcher
Name: Prof. Martin D. Kruskal
Institution and title: Professor of Rutgers University, USA


2. Duration of the Stay
December 28, 2004 to March 27, 2005 (90 days)


3. Hosting Environment
Accommodation: Tokyu Stay Shibuya
Research institute: Graduate School of Mathematical Sciences / The University of Tokyo
Status in the host institute: Visiting Professor


4. Schedule during the Stay
December 28, 2004 Arrived at Narita airport
Until his departure, he has continually joined in discussions on singular analysis of differential and difference equations, and theory of numbers at Graduate School of Mathematical Sciences, The University of Tokyo. Participants of the discussions were Junkichi Satsuma, Kazuo Okamoto, Tetsuji Tokihiro, Ralph Willox and students belonging to laboratories of the above mentioned professors. Besides this activity, he gave several lectures listed below.


January 14, 2005
Open lecture at the lecture hall of Graduate School of Mathematical Sciences.

Title: Surreal numbers - a new number system for the new millenium

This was a lecture on new number system, and several tens of audience attended the lecture.


January 19, 2005
Special class in College of Arts and Sciences.

Title: Past, Present and Future of Mathematics

Almost a hundred of student in College of Arts and Sciences attended and learned Prof. Kruskal's view point on mathematics and sciences.


February 14,2005
Invited talk in the international conference "Nonlinear integrable systems and their real world applications" sponsored by COE program and held at the lecture hall of Graduate School of Mathematical Sciences.

Title: Surreal numbers are THE numbers

This was a talk which emphasizes the importance of surreal numbers. About 80 participants were impressed by his talk.

Professor Kruskal also visited two universities. In each university he gave a lecture listed below and joined in discussion on singular analysis of differential and difference equations, and theory of numbers.


January 23 to 26, 2005
He visited Kyoto University, and gave a talk on 24th in Graduate School of Informatics.

Title: Early Days of Solitons

His talk concerned histrical matters of the discovery of solitons. About 30 people attended the lecture.


March 9 to 12, 2005
He visited Kyushu University, and gave a talk on 10th in Research Institute for Applied Mechanics.

Title: The dawn of soliton study

This is a special lecture of the research institute.


March 27, 2005 Departed from Narita airport to USA

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5. Description of and results from the invitation
Prof. Kruskal is renowned worldwide for pioneering research on nonlinear integrable systems. He is almost 80 years old, but still very active in research on singular analysis of differential and difference equations, theory of numbers and some others. In this nice opportunity of having him as a visiting proffesor, we organized seminars for researchers of our school, in particular for young scientists. From the seminar young scientists obtaied not only the knowledge on new direction of research but also proper advice for the research they were conducting.
We also organized an open lecture sponsored by graduate school of mathematical sciences to learn his point of view for research. In the lecture, Prof. Kruskal explained the new system of numbers plainly and inspired the audience including those from outside the university.
Moreover, we had a special talk for the first and second year students in college of arts and sciences. We believe that his talk gave strong motivation for study to almost a hundred students who joined the class.
In the international conference "Nonlinear integrable systems and their real world applications" sponsored by COE program, he was not only one of the key speakers but also an important adviser during the whole schedule of the meeting. He contributed the success of the conference very much.
Besides the activity in the university of Tokyo, he visited Kyoto university and Kyushu university and gave a talk in each institution. Prof. Ralph Willox accompanied him in both successful trips. Prof. Kruskal's talks in two universities were concerned with histrical matters of the discovery of solitons and impressed the audience strongly.

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6. Contribution by the invitee to the host institutes
   Research on nonlinear integrable systems is one of the hottest theme in the university of Tokyo. Prof. Kruskal's stay stimulated people in graduate school of mathematical sciences. In particular, young scientists were inspired very much. We believe that his attendence at the seminars played an important role to activate research in the graduate school. Moreover, his lectures are essential to develop new areas of research.
   Prof. Kruskal also had a big impact on students. Several undergraduate and graduate students told us that they were strongly impressed by his talk as well as his attitude during his talk. It is quite sure that his stay in Japan is also meaningfull in educational sense.
   Graduate school of mathematical sciences were chosen as one of the reseach bases of the 21st Century COE program and aimed to be a new mathematical development center to support scientific technology. In the international conference "Nonlinear integrable systems and their real world applications" sponsored by the program, several interesting results on the application of mathematics were reported. Prof. Kruskal's critical comments for all of the talks were very useful. Many of the participants said that this was one of the best conferences in recent years. The attendence of Prof. Kruskal is one of the main factors of getting such a reputaiton.