## Outline of IMI

In today’s functionally advanced society, mathematics is like a light in the darkness that never goes out. Mathematics is actually the foundation of almost all advanced technologies driving modern society such as information security, network systems, CT scans, MRIs, and other medical technologies, airplane and automobile development technologies, smelting-furnace and nuclear-reactor control technologies, scheduling in the transport and distribution sectors, and finance and insurance support systems, as well as technologies for resource exploration, disaster prediction, and even entertainment. Today, there is a need like never before in many scientific and technical fields for research personnel skillful in mathematics and the mathematical sciences, and there is no doubt that this need will continue to grow in the years to come on an international scale.

To meet this global demand, the Institute of Mathematics for Industry (IMI) at Kyushu University was founded on April 1, 2011 as the first institute in Asia for industrial mathematics based on diverse fields of mathematics research. IMI was also authorized as the MEXT Joint Usage/Research Center entitled “Center for Collaborative Research in Advanced and Fundamental Mathematics for Industry” from the Ministry of Education, Culture, Sports, Science and Technology on April 1, 2013.

Mathematics for Industry (MI) is a new research area that will serve as a hub for creating future technologies. It was born with the aim of responding to the needs of the industrial sector by reorganizing and merging pure and applied mathematics into flexible and versatile forms. The IMI is involved in the following activities to promote MI.

- Joint research in response to the needs of industry inside and outside Japan and various types of mathematics research in support of joint projects
- Organization of joint researches as the MEXT Joint Usage/Research Center
- Education and training of junior researchers. In particular, producing future leaders in the global situation.
- Organization of workshops and international conferences
- Organization of study groups (training camps for solving outstanding problems in industry and other fields)
- Organization of joint seminars between academia and industry and other fields
- International cooperation with particular focus on Asia-Pacific area
- Technical consultation
- Tutorials on mathematical key technologies
- Publication of International Journal of Mathematics for Industry (IJMI), proceedings of international conferences, Lecture Note Series and Preprint Series
- Matching and managing internships (long-term doctoral programs, medium-term master’s programs)
- Education from the viewpoint of mathematics beneficial to society (Graduate School of Mathematics, Department of Mathematics of the Faculty of Science) and awareness campaigns

The following departments have been established in IMI to promote the above activities in an efficient manner.

**(1) Division of Advanced Mathematics Technology**

This department promotes joint research with companies and researchers in other fields. Researching groundbreaking mathematical technologies, it works to solve mathematical problems that companies have by joint or commissioned research.

**(2) Division of Applied Mathematics**

This department develops mathematical methods to refine existing mathematical techniques and investigates theories having broad application to demonstrate the universality of mathematics. The members of this department will perform joint research on occasion with members of industry and researchers in various scientific fields and will promote theoretical research with an eye to application.

**(3) Division of Fundamental Mathematics**

This department is staffed with pure mathematicians having an interest in application, who, in cases where the problem is clear but the mathematical technique for solving the problem is not, perform basic research to clarify that technique. The department performs basic research to drive technical innovation.

**(4) Division of Intelligent Societal Implementation of Mathematical Computation**

This division implements cutting edge mathematical technologies for highly convenient social designs in large scale through collaboration with many industrial partners, and thus leads IMI’s industry-academia cooperation. By creatively amalgamating leading techniques in mathematical modeling with AI, we contribute to the construction of ultra-smart society based on Society 5.0.

**(5) Australia Branch**

Australia Branch was established in La Trobe University (Melbourne, Australia) in March, 2015, and is managed by the academic staffs employed in Australia to be the hub for promoting the activities such as joint researches with institutes in Oceania area, student exchanges and international internships. It also coordinates the cooperation with major research institutes in Australia and New Zealand.

**(6) Laboratory of Mathematical Design for Advanced Cryptography**

Recent advances in information and telecommunication technologies bring forward new applications of cryptographic theory. In turn, newly developed cryptographic methods and constructions as well as their security evaluation require application of a wide range of mathematical theories, beyond those conventionally used for cryptography. The Laboratory of Mathematical Design for Advanced Cryptography, leveraging the cooperation between academic research institutes, industry and the governmental institutions, aims at development of the next-generation cryptographic technologies featuring a wide variety of secure functionalities, with the ultimate goal of achieving safe and sustainable society. Through the cooperation between academia, industry, and the governmental institutions, the Laboratory will continue to promote the newest advances in mathematical cryptography towards design and development of the next-generation cryptographic constructions meeting the highest international standards.

**(7) Division of Fujitsu Social Mathematics**

This division was set up by Kyushu University, Fujitsu LTD. and Fujitsu Laboratories LTD. in September, 2014. It aims to develop mathematical technologies for modeling social system based on human behavioral and psychological factors, and to optimize the various policies of the social system with the model. It promotes the establishment of novel design methodologies for social systems based on interdisciplinary research that combines social science research, such as economics and psychology and data utilization techniques such as mathematical analysis, optimization and control. It also addresses to implement newly established design methodologies for resolving real social issues.

**(8) Office for Promotion and of Collaboration and Consultation**

This office is manned by a joint research coordinator in charge of promoting collaboration and providing technical consultation. It serves as an interface between industrial technologies and mathematics.

**(9) Visitors Section**

This section invites researchers from companies, research institutions, and other universities in Japan and overseas and researches advanced problems to deal with ever-changing problems in the industrial sector.

The IMI is a leading institute in the establishment and management of Asia-Pacific Consortium of Mathematics for Industry (APCMfI) which is a framework of international cooperation in Asia-Pacific area.

The IMI stands out from European and American research laboratories involved in applied mathematics and industrial mathematics in the following ways.

**・Adopting a long-term view, the IMI brings together researchers in pure mathematics to drive applied research for industry.**

While it cannot be predicted when and where mathematics can be applied, basic research in mathematics incorporates an explosive potential for application. For this reason, it is important to assemble a wide range of researchers from diverse fields such as statistics, algebra, and geometry in addition to applied analysis, which is the focus in Europe and the United States. In the IMI researchers in pure mathematics are also actively engaged in joint researches with industries.

**・Plans are being made to create a forum for obtaining feedback from industry and other fields for use in mathematics research.**

The IMI places importance on uncovering new mathematical problems and cultivating new techniques as a science and aims to enrich the field of mathematics itself through collaborative efforts with industry.

The activities IMI have the following ripple effects:

(1) The development of research personnel for both basic and applied mathematics through close cooperation with the Faculty of Mathematics of the Graduate School of Kyushu University. Personnel educated by the Graduate School of Mathematics will find that many opportunities are available to them both inside and outside Japan.

(2) Expanded collaboration with other fields of learning by promoting the interdisciplinary research of mathematics. In particular, the solution of mathematical problems in industrial technologies will help to facilitate collaboration between industry and academia.

(3) Promotion of joint research with top-tier researchers from industry and creation of a mechanism that would enable research exchanges with personnel trained at IMI and training for private-sector personnel also studying at the Graduate School of Mathematics. The Institute of Mathematics for Industry will also contribute to a new climate in mathematics research in Japan in which the exchange of researchers between universities and the industrial sector and public institutions will become the norm.

(4) International cooperation with emphasis on Asia-Pacific area yields a new international network based on MI. It activates the researches, and in addition, has a great effect for improvement of the motivation of research and international sense of young researchers, and thus it contributes to internationalization of Kyushu University and mathematical communities.

(5) Direct acquisition of knowledge on what industry expects of education at the Graduate School of Mathematics and adoption of a viewpoint emphasizing the smooth education and training of personnel in accordance with the needs of industry. The creation of a mutually cooperative system of mathematics and science education that includes the other graduate schools at Kyushu University can also be expected. This will contribute to exchanges between graduate-school students and postdoctoral researchers equipped with mathematical skills and research institutions and development sites in the industrial sector.

(6) The embedding in Japan of the importance of mathematics research for society and the development of highly competent personnel as a result. A positive effect on secondary education can also be expected.

(7) Development of appropriate evaluation methods for industrial mathematics. This will unveil an entirely new aspect of mathematics research in Japan.

The IMI aims to form one of the top research hubs in industrial mathematics in the world, based on the tradition and advantages of Kyushu University, and putting emphasis on international cooperation particularly with Asia-Pacific area. Furthermore, by maintaining its cooperative relationship with the Faculty of Mathematics, IMI aims to represent Japan as a world-class educational and research institute in mathematics.