Center for Integrated Mathematical Sciences

Director: Masato Kurihara (Professor, Faculty of Science and Technology)

Primary Campus: Yagami

In today's advanced and complex society, mathematics and mathematical sciences are playing an increasingly important role in solving a wide range of problems. The resolution of key issues inherent to mathematics and mathematical sciences, along with the mathematical theories and methods developed in the process, is expected to be highly beneficial for collaboration with other research fields due to their versatility. From this perspective, the Center for Integrated Mathematical Sciences brings together researchers in mathematics and mathematical sciences within Keio University to promote research in these fields, provide mathematical theories and methods to the wider society, and conduct interdisciplinary research with various other fields.

Mathematics, mathematical sciences, integrated and interdisciplinary mathematical sciences

■ Activities Continuing from the Previous Fiscal Year: Background, Rationale, and Goals

We intend to continue actively promoting the activities that have been successful for this center, such as internal collaborative research, support for young researchers, international collaborative research, and various interdisciplinary collaborations. Following last year's efforts, we will also continue to actively dispatch young researchers abroad. There is no doubt that establishing a foundational hub for mathematical sciences within Keio University will bring significant benefits both inside and outside the university. For this reason, we wish to continue the center's activities.

■ New Activity Goals, Content, and Implementation Background for the 2017 Fiscal Year

With the goal of advancing mathematical sciences research within Keio University, we aim to promote internal collaborative research, support for young researchers, international collaborative research, and various interdisciplinary collaborations. We will continue to send many faculty members and students to international research conferences, providing numerous opportunities for graduate students and young faculty to be active on the international stage. By actively and regularly holding colloquia and seminars hosted by the Center for Integrated Mathematical Sciences, featuring invited distinguished researchers from Japan and abroad, we will provide a place where mathematical sciences researchers, young researchers, and graduate students within Keio University can gather informally, while also aiming for the further revitalization and development of mathematical sciences and related fields. As before, the colloquia will regularly feature lectures that offer new insights and spark new interests in research outside the members' own specializations. We will promote new collaborative research and partnerships, conducting vigorous and functional activities. We also plan to continue actively welcoming researchers from overseas to the center. Through the continuation of these activities, we hope to further develop mathematical sciences research at Keio University.

■ Implementation Details, Research Outcomes, and Degree of Achievement for the Fiscal Year's Business Plan

In fiscal year 2017, continuing from the previous year, we conducted activities with the following key business plans:

1) Promotion of advanced mathematical sciences research

2) International collaboration in mathematical sciences

3) Interdisciplinary research with other fields

Our research is advanced along two main pillars: pure mathematics, including foundational areas like algebra, geometry, and analysis, and applied mathematics, focusing on statistics, discrete mathematics, and numerical analysis. We promote research in each of these areas while also fostering their mutual integration. This fiscal year, we conducted our activities using approximately 40 million yen in Grants-in-Aid for Scientific Research and core-to-core program funding. In particular, numerous international collaborative projects were carried out this year through the JSPS Core-to-Core Program "International Research Network for Mathematical Sciences centered on Number Theory and Geometry," which was adopted as an activity of the Center for Integrated Mathematical Sciences. The annual Boston-Keio Summer Workshop was held in June 2017 with a focus on geometry, and the center was involved in its preparation, dispatching many students. With Boston University as a central partner, there were many participants from the American side, providing an invaluable experience for the students and young researchers who attended from Japan. Additionally, we dedicated significant effort to preparing for the international research conference "Iwasawa 2017," held at the University of Tokyo. This was a large-scale conference with over 40 invited speakers from overseas alone, attracting a total of 236 participants from 16 countries (98 from overseas). As in previous years, we also worked to promote information exchange and discussion among center members through colloquia in the field of mathematical sciences.

As in previous years, members of this research center have achieved results in fields such as number theory, arithmetic geometry, dynamical systems, complex deformation quantization problems, rigidity problems, graph theory on surfaces, optimization problems, nonlinear analysis of fluids, stochastic processes and stochastic analysis, mathematical finance, and statistics. In terms of international projects, we again dispatched many young researchers to numerous summer and winter schools, where they gained experience and achieved significant results. For the Boston-Keio Summer Workshop, we changed the timing to make it easier for participants from the American side to attend. The UK-Japan Winter School is also held annually and has become a well-known project among mathematicians in the UK and Japan. A particularly noteworthy achievement was the "Iwasawa 2017" research conference, which was primarily organized by this center. It was a great success, attracting 236 researchers from Japan and abroad (138 domestic, 98 international). Furthermore, the actuarial training seminars, conducted for graduate and undergraduate students aiming to take actuarial exams, have once again proven to be extremely useful in meeting student needs this fiscal year.