IRL FJ-LMI, a laboratory of excellence in mathematics in Tokyo
The first Franco-Japanese laboratory dedicated to mathematics, located in Tokyo, the FJ-LMI embodies the dynamic exchanges between French and Japanese researchers. This international research laboratory of the CNRS, created in the fall of 2023, is part of a tradition of scientific collaboration that has shaped major advances in the discipline.
Franco-Japanese collaborations that have left their mark on the history of mathematics
The University of Tokyo (Tōdai), the oldest and certainly the most prestigious university in Japan, was founded in 1877 by the Meiji government as the country's first modern national university at the time of its opening up to the outside world. Since then, it has distinguished itself through its academic excellence – among its former students, there are seven Nobel Prize winners and one Fields Medal recipient – and its central role in international research. At the crossroads of scientific innovation and Japanese traditions, it offers a stimulating environment for scientists from all over the world.
The University of Tokyo has built up a rich history of collaboration with many French partners, particularly the CNRS. This institutional cooperation began in the early 1990s with the creation of one of the very first joint international units in the field of micromechatronics. In October 2022, the strategic partnership between the CNRS and the University of Tokyo was further strengthened with the creation of an International Research Center (IRC) bringing together five IRLs and eleven IRNs led by these two organizations. The Franco-Japanese Laboratory of Mathematics and their Interactions (FJ-LMI) is the latest to be created in this context in the fall of 2023 and is the first Franco-Japanese laboratory in Mathematics.
The Japanese supervisory body of the FJ-LMI is the “Graduate School of Mathematical Sciences” of Tōdai. This entity is the successor to the mathematics department of the Faculty of Science, which has a history going back almost 150 years. Today, it brings together almost 60 professors and 150 Master's and doctoral students working in various fields of fundamental and applied mathematics, thus perpetuating a long tradition of scientific excellence in research and doctoral training.
Among the first notable examples is the publication of Claude Chevalley's doctoral thesis on the theory of class groups in the Journal of the Faculty of Sciences of the University of Tokyo in 1933. Among other fundamental results, Chevalley introduced the notion of Takagi groups, in reference to the work of Teiji Takagi, considered the founder of the modern mathematical school of Japan and professor at the University of Tokyo for nearly 40 years.
Other scientific interactions have played a fundamental role, demonstrating that these multiple exchanges have always been stimulating collaborations rather than competitions. These interactions have opened up new perspectives and shaped entire fields in mathematics, leading to numerous applications:
- the creation of stochastic calculus by Kiyosi Itō, Paul Malliavin and Marc Yor;
- the revolutionary advances in algebraic geometry due to Heisuke Hironaka and Alexander Grothendieck and in number theory due to Kenkichi Iwasawa and Jean-Pierre Serre or André Weil, Gorō Shimura and Yutaka Taniyama in particular following the famous Nikko-Tokyo conference.
- the development of microlocal analysis and the theory of hyperfunctions under the impetus of Mikio Sato and the schools of Jean Leray and Alexander Grothendieck;
Since then, several generations of mathematicians have contributed to the edifice, including:
- Luc Illusie, Kazuya Kato and Takeshi Saito in arithmetic geometry, and
- Masaki Kashiwara, Michèle Vergne and Pierre Schapira, in algebraic analysis in relation to representation theory.
The FJ-LMI: a center of excellence for mathematical research
The activities of the FJ-LMI are currently structured around four thematic areas:
- Arithmetic geometry (Prof. Takeshi Saito)
- Representation theory and Lie theory (Prof. Toshiyuki Kobayashi and Michael Pevzner)
- Interactions with biology and life sciences (Prof. Hiroshi Matano)
- Analysis and control of PDEs, applied inverse problems (Prof. Masahiro Yamamoto)
In the future, new topics will be gradually developed.
Since last year, the laboratory has already welcomed 2 long-stay researchers and 21 short-stay researchers. A thesis, obtained in response to a call from the Mission for Transversal and Interdisciplinary Initiatives of the CNRS and in partnership with the Institut Camille Jordan in Lyon, began in October 2024 and four Master's students will carry out their research internship in Tokyo in the spring of 2025.
The inaugural conference in April 2024 was attended by more than 200 participants. A conference on the geometric aspects of Painlevé equations took place in September 2024, and another on arithmetic geometry is planned for April 2025. A series of lectures on ramification and reciprocity theory will be held in March 2025, followed by a CNRS thematic school on the representation theory of Lie groups in October 2025.
Testimonial from Bruno Kahn, research director at IMJ-PRG, on a mobility program at FJ-LMI
At the FJ-LMI for 6 months, I have the chance to work regularly with four of my collaborators. I have already had the opportunity to participate in a conference in my research areas, and I am organizing a series of presentations with Takeshi Saito. This event, supported by the IRL, is aimed at students and researchers in arithmetic geometry; it is a pleasure to carry out this project, which is generating a great deal of interest. I have just finished an article, prompted by a discussion with a Japanese colleague. I also have total freedom, particularly psychological freedom, because I am not under the pressure of Paris. I am accommodated on campus, a 15-minute walk from my office, in a quiet, wooded environment. In short, I am very happy with this stay, which has been both relaxed and fruitful!
Springer Nature has just launched a new series of Lecture Notes in Mathematics dedicated to the FJ-LMI, with a first volume to be published in May 2025 on the spectral analysis of locally homogeneous spaces by Fanny Kassel (IHES) and Toshiyuki Kobayashi (UT & FJ-LMI).
Applying for a position or being hosted as a visiting researcher at the IRL FJ-LMI means joining a stimulating environment and benefiting from numerous opportunities:
- Collaborative projects: participate in transdisciplinary and international initiatives with experts from the University of Tokyo and its IRLs as well as with colleagues from the Greater Tokyo Area, which includes several dozen universities.
- Exceptional resources: access to cutting-edge infrastructure, regular seminars and a scientific network that is as dense as it is varied.
- Funding and support: possibility of accessing mobility programs and specific funding via both the CNRS and JSPS portals.
- Living in Tokyo: enjoy cultural immersion in Japan while evolving in an exceptional scientific environment.