Introducing ICIAM's New Officer-at-Large Kenji Kajiwara

Brief History

I graduated from the Department of Mathematical Engineering at The University of Tokyo, Japan, in 1989, obtained a Master of Engineering and then a Ph.D. (Engineering) at the Department of Applied Physics at The University of Tokyo in 1994. Then, I was employed by Doshisha University, a private university in Kyoto, as a Lecturer and then an Associate Professor at the Department of Electrical Engineering (1994-2001). I moved to the Faculty of Mathematics, Kyushu University, in 2001 as an Associated Professor, then became a Professor in 2009. I moved to the Institute of Mathematics for Industry (IMI) in 2011 upon its inauguration, then I served as Deputy Director (2019-2022) and Director (2022-). I was awarded by JST one of the prestigious grants of CREST (250,000,000 JPY, 2019-2025) as PI and leading an interdisciplinary research project of mathematics, architecture, industrial design, and computational geometry. I am a member of the Japan SIAM, Australian Mathematical Society, and SIAM. I am also a member of the Asia Pacific Consortium of Mathematics for Industry and serving as Secretary since 2021. In JSIAM, I served as a Board Member (2012-2014, 2022-) and a Vice President (2020-2022), then I was elected as a Fellow in 2023. I took the role of a JSIAM Delegate to ICIAM (2020-2023), and then I contributed to ICIAM2023 in Tokyo as a member of the Organizing Committee and the Executive Committee.

Research Description

My background is mathematical physics, particularly the theory of integrable systems. My interest lies in discrete objects, such as differential-difference, difference, and so-called ultra-discrete equations. I have been studying the (discrete) Painlevé equations and their generalizations, with a particular focus on the particular solutions (hypergeometric type solutions and algebraic/rational solutions) and underlying algebraic and geometric structures [1]. I shifted my main research to integrable (discrete) differential geometry on the occasion of moving to IMI, with an expectation of interdisciplinary activities and possible joint research with industry. My recent work, done during the task of the Director, is on the characterization of “aesthetic” curves and surfaces used for industrial design and architecture [2]. It arises from a rediscovery of similarity geometry, a Klein geometry associated with the similarity transformation group (Euclidean motion + scale change), and collaboration with integrable systems, with the new light of motivation from industrial design. I think that this is a small but typical example of “Mathematics for Industry”.

Developing “Mathematics for Industry”

Mathematics for Industry (MfI) is an idea of a new area of research in mathematics that serves as a foundation for future technologies and which as well is valuable as mathematics in itself. It is formed through the challenge of responding to the demands of society and industry by reorganizing and merging pure and applied mathematics into flexible and versatile forms. The IMI was founded in 2011 as the first research institute of industrial and applied mathematics in Japan, with the mission of sharing the idea and developing MfI. Since its inauguration, we have been making a lot of efforts in:

  1. Promotion of research and collaboration with industry and diverse scientific fields.
  2. Management of Joint Use Research Center.
  3. Human Resource Development.
  4. International Collaborations.

As a Faculty Member, I have contributed mainly to (2) and (4). In particular, I have organized and managed the IMI Australia Branch at La Trobe University in Melbourne since 2015. As Director, I have been making those activities more systematic on a larger scale with extensive support and collaborations from the government and industry. One such challenge is “Mathematics for Industry Platform,” a network of 17 mathematical institutes spread over Japan that started in October 2023. I hope to have a chance to report on our activities and the current status of industrial and applied mathematics in Japan.

  1. Kenji Kajiwara, Masatoshi Noumi and Yasuhiko Yamada, Geometric aspects of Painlevé  equations, J. Phys. A: Math. Theor. 50(7)(2017) 073001. doi:10.1088/1751-8121/50/7/073001 
  2. Jun-ichi Inoguchi, Kenji Kajiwara, Kenjiro T. Miura, Yoshiki Jikumaru and Wolfgang K. Schief, Log-aesthetic curves: similarity geometry, integrable discretization and variational principles, Comput. Aided Geom. Design 105(2023) 102233. doi:10.1016/j.cagd.2023.102233
Author: 

Kenji Kajiwara

Kenji Kajiwara is Director of the Institute for Mathematics in Industry, Kyushu University and Officer at Large of ICIAM. He obtained his PhD from the University of Tokyo. His research is in integrable systems and, more recently, in geometric design.
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