Research Center for Integrated Mathematical Sciences

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

Base Campus: Yagami

In today's highly advanced and complex society, the role of mathematics and mathematical sciences in solving various problems is growing. The resolution of important problems unique to mathematics and mathematical sciences, along with the mathematical theories and methods developed in the process, are expected to be highly beneficial for collaboration with other research fields due to their versatility. From this perspective, the Research Center for Integrated Mathematical Sciences aims to promote research in mathematics and mathematical sciences by bringing together researchers in these fields within Keio University. It also seeks to provide mathematical theories and methods to the broader society and conduct interdisciplinary research with various other fields.

Mathematics, mathematical sciences, integrative and interdisciplinary mathematical sciences

■ Ongoing Activities 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 collaborative research within the university, support for young researchers, international joint research, and collaboration with various different fields. As in the previous fiscal year, we will also actively promote the dispatch of young researchers. Establishing a foundational hub for mathematical sciences within Keio University will undoubtedly bring significant benefits both inside and outside the university (Juku). For this reason, we wish to continue the center's activities.

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

With the goal of advancing mathematical sciences research within Keio University, we aim to promote collaborative research within the university, support for young researchers, international joint research, and collaboration with various different fields. We will continue to send many faculty members and students to international research conferences to provide numerous opportunities for graduate students and young faculty to be active on the international stage. By actively and regularly holding colloquiums and seminars hosted by the Research Center for Integrated Mathematical Sciences, featuring invited prominent 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 for the colloquiums, we will continue to regularly hold lectures that can provide new insights and spark new interests, even on research outside the members' own areas of expertise. We will promote new collaborative research and partnerships, conducting vigorous and functional activities. As before, we plan to actively welcome 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 for the Fiscal Year's Action Plan, Research Outcomes, and Degree of Achievement

In fiscal year 2017, continuing from the previous year, our activities were based on the following key action plans:

1) Promotion of advanced mathematical sciences research

2) International collaboration in mathematical sciences

3) Fusion research with other fields

We have advanced our research based on two pillars: pure mathematics, including foundational areas like algebra, geometry, and analysis; and mathematics research with an emphasis on applications, such as statistics, discrete mathematics, and numerical analysis. We are promoting research in each of these areas while simultaneously fostering research through their mutual fusion. This fiscal year, we conducted our activities using approximately 40 million yen in scientific research funds and core-to-core program funding. In particular, numerous international collaborative projects were carried out this fiscal year through the JSPS Core-to-Core Program, "Formation of an International Center for Research in Mathematical Sciences with a focus on Number Theory and Geometry," which was adopted as an activity of the Research Center for Integrated Mathematical Sciences. The annual Boston-Keio summer workshop was held in June 2017 with geometry as its theme, and the center was involved in its preparation, dispatching a large number of students. There were many participants from the American side, centered around Boston University, and it proved to be an invaluable experience for the students and young researchers who participated from Japan. Additionally, we held the international research conference Iwasawa 2017 at the University of Tokyo, and a great deal of effort was put into its preparation. This was a large-scale research conference with over 40 invited participants from overseas alone, and a total of 236 people from 16 countries gathered (98 of whom were from overseas). As in previous years, we also strove to promote information exchange and discussion among center members through colloquiums in the field of mathematical sciences.

As in previous years, members of this research center have achieved results in areas 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 were able to dispatch many young researchers to numerous summer and winter schools again this year, allowing them to gain experience and achieve significant results. For the Boston-Keio summer workshop, we changed the timing of the event 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. Notably, the Iwasawa 2017 research conference, which was primarily organized by this center, was a great success, attracting 236 researchers from Japan and abroad (138 domestic, 98 international). Furthermore, the actuarial training seminar, conducted for graduate and undergraduate students aiming for actuarial exams, has once again been very useful in meeting student needs this fiscal year.