Report on the invitation program for distinguish researchers 2008
 Host Researcher
Name: 
Yoshiaki Maeda
Professor of Faculty of Science and Technology、Keio University 
 Invited eminent scientist (name, title and affiliation, nationality)
Maxim Kontsevicch
I.H.E.S. France, Professor
France
 Duration of the stay
October 325, 2008(23days)
 Schedule during the stay (date, research activities, name of the places to visit, and description of the visits )
October 3 
Arrived at Narita Airport, Checked in at Tokyu Excel Hotel Shibuya Meetings with Maeda on schedules 
October 45 
Visiting the University of Tokyo, School of Mathematical Science for giving lectures at Takagi Lecture Series and at the meeting with high school students 
October 6 
Visiting Keio University, Faculty of Science(discussion on deformation quantization with Maeda) 
October 78 
FrenchJapanes Scientific Forum at the University of Tokyo (discussion) 
October 9 
FrenchJapanes Scientific Forum at Keio University (lecture and discussion) 
October 10 
FrenchJapanes Scientific Forum at Keidanren Hall (discussion) 
October 1112 
Discussion with Maeda on the deformation quantization problem 
October 1314 
Visiting IPMU, The University of Tokyo(lecture and discussion with K.Saito) 
October 15 
Visiting JSPS(discussion with Prof.Ono and received the award by JSPS) Discussion with young researchers at Keio University(afternoon) 
October 1620 
Visiting Kyoto University(lecture and discussion with K.Fukaya and M.Kashiwara) 
October 2024 
Visiting Kinosaki algebraic geometry workshop (lecture and discussion) 
October 25 
Leaving from Kansai Airport 
 Description of and results from the invitation
Professor Maxim Kontsevich, who was invited by the JSPS program, is a professor at the Institute des Hautes Etudes Scientifique (IHES). His research includes a wide range of areas in mathematics, including algebra, geometry, topology, analysis and combinatorics, and has had a broad influence internationally in the area in mathematics. His work also contributes to physics, namely string theory and quantum field theory. He has given new mathematical descriptions of physical phenomena, leading towards the construction of a new research area in mathematics, the socalled quantum mathematics, or the mathematics of noncommutativity. His main contributions to mathematics includes deformation quantization of Poisson manifolds, quantum invariants of knots, and mirror symmetry. He received the Fields Medal in 1988. Fields Medals are given to young researchers who are expected to become leaders in mathematics, and almost all Fields Medalists have filled this role. Kontsevich has taken a leadership role in mathematics research, and he is now recognized as a one of the best mathematicians in the world. It is an honor to invite Professor Maxim Kontsevich to Japan for discussions with Japanese researchers on his recent work. For this occasion, we arranged conferences, informal seminars with young researchers, and a meeting with high school students. He kindly accepted these events and gave lectures.
We mention some of main activities in Japan as follows.
1) Takagi Lecture: This was held October 45, with participation by Professors J. P. Bourguignon, E. Ghys, N. Nekrasov and M. Kontsevich, and with over 200 participants at the University of Tokyo. M. Kontsevich gave a talk on Dmodules and positive characteristics, which is a very new mathematical approach. 2)
2) FrenchJapanese Scientific Forum: Perspectives in Mathematical Physics: This was held at the University of Tokyo and Keio University on October 79 to discuss current problems in mathematics, physics and biomathematics with 14 invited speakers from France and Japan. M. Kontsevich gave a talk on a new approach to hyperKahler geometry.
3) Kinosaki algebraic geometry workshop:This ran October 2024. M. Kontsevich visited Kionsaki, where the algebraic geometry workshop and others. M. Kontsevich gave a talk and had many mathematical discussions, even in the evenings. In particular, many young researchers came into contact with M. Kontsevich and have been influenced by his mathematical thought.
4) Discussion at Keio: Y. Maeda had discussions with M. Kontsevich on deformation quantization, a common research interest, which will continue during the next year.
5) Discussion at IPMU: K. Saito invited M. Kontsevich to IPMU at the University of Tokyo to discuss the period integrals and the moduli space of discrete groups. They have common interests in these problems and will develop these discussions further during the next years.
6) Discussion at Kyoto University: Prof. K. Fukaya invited M. Kontsevich to Kyoto University for October 1620 to discuss Floer homology and mirror symmetry. M. Kashiwara, who is the director of RIMS, also invited him to discuss Dmodule problems.
 Contributions to the Host Institute
It was a very good opportunity to have hosted Professor Maxim Kontsevich at Keio University. Keio University established the Center for Integrative Mathematical Sciences after the 21th Century Center for Excellence, and now is developing a premier Japanese research center for mathematical sciences. One aim of this center is to be an international research center in mathematics. To accomplish this, the center is inviting many overseas visitors. Thanks to the support of the JSPS, this center had the opportunity to host such a distinguished researcher, which strengthens our international appeal. By cooperating with the university of Tokyo and Kyoto University the center for Integrative Mathematical Sciences, Keio University has a good opportunity to develop the international activity. We organized informal seminars with young researchers and Professor Maxim Kontsevich, which had a great influence on the researchers. One of our research projects is to study noncommutative structures in mathematics, which is a strong common interest of Professor Maxim Kontsevich. He agrees with the advisor for [direction of?] our project and agrees to coopearate with our research. He plans to return to Keio in 2009 and 2010, which will help develop our project in noncommutative mathematics.
 Others
1) We organized a meeting called High School Students Meets Mathematicians, which encouraged high school students to study mathematics. We invited over 80 high school students from several parts of Japan together with more than 20 high school teachers and university students who have received medals at the Mathematics Olympiad. We organized a question and answer session for high school students with Professors Hironaka,who received the Fields medal as Japanese, and Kontsevich.
2) Videos
We recorded several events during his stay, and will soon distribute lectures and workshops via the internet.
