Advanced Mathematical Sciences Research Center

The workings of modern society cannot be considered without the development and application of mathematical sciences. Mathematical sciences are used in various modern activities, and their importance is ever-increasing (for example, cryptography for managing security systems and big data analysis, to name just a few).

Furthermore, not only are its results applied in various fields, but mathematical thinking is also incorporated into many disciplines, becoming a cornerstone of modern societal development.

In relation to this, Keio University has faculty members related to mathematical sciences in various departments. The purpose of establishing this center is to bring together mathematics-related faculty members at Keio University to conduct not only research on problems specific to mathematics but also interdisciplinary research across various fields and to engage in international activities. We aim to evolve and develop this foundation, built by the Research Center for Integrated Mathematical Sciences which was active until 2017, to conduct even more advanced research activities.

Mathematical sciences, interdisciplinary research, international collaboration

■ Activities Continuing from FY2019: Background, Rationale, and Goals for Continuation

The annual Boston-Keio Summer School is scheduled to be held at Boston University in June 2020 with a focus on geometry. Additionally, to commemorate its 20th anniversary, the UK-Japan Winter School will be held at the University of Warwick from May 11 to 15, 2020, as a special program titled "Geometry, Stochastics & Dynamics - Celebrating 20 years of UK-Japan Winter Schools," focusing on geometry, stochastics, and dynamical systems. As before, we also plan to hold lectures by leading international researchers. Through these research meetings and projects, we hope to provide students and young researchers with international experience, enhance their global perspective, and produce talent that can compete on the world stage. We plan to continue promoting interdisciplinary and international collaborative research as we have in the past.

■ New Activity Goals, Content, and Implementation Background for FY2020

With the goal of advancing mathematical sciences research within Keio, we aim to promote support for on-campus collaborative research, assistance for young researchers, international joint research, and collaboration between 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 colloquia and seminars hosted by the Research Center for Integrated Mathematical Sciences, featuring prominent researchers from Japan and abroad, we aim to provide a place where mathematical sciences researchers, young researchers, and graduate students within Keio can gather informally, while also striving for the further revitalization and development of mathematical sciences and related fields. We also plan to actively welcome researchers from overseas to our center. Next fiscal year, we intend to promote colloquia.

As a specific project for 2020, we plan to host the Pan Asian Number Theory Conference, an international research meeting on number theory, at the Research Institute for Mathematical Sciences, Kyoto University in July, and we will invite many leading researchers of Asian origin from around the world. For example, Mr. Ngo from Vietnam, a recipient of the Fields Medal, which is the Nobel Prize of mathematics, is also scheduled to be invited. The Advanced Mathematical Sciences Research Center is set to play a central role in organizing this research meeting.

By continuing these activities, we hope to further develop mathematical sciences research at Keio University.

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

This fiscal year, the Boston-Keio Summer Workshop, which has been held between Boston University in the US and Keio University for over 10 years, was conducted with number theory as its theme. The faculty specializing in number theory at Boston University and Keio University know each other very well, and it is a field where collaboration has yielded significant results. This year, we held a summer school centered on young researchers and students, covering diverse topics in number theory. We succeeded in further deepening the collaboration between young researchers from Japan and the US.

The UK-Japan Winter School, which had been held annually in January, was scaled up this year to commemorate its 20th anniversary. Instead of a winter school, it was held in May at the University of Warwick as a special program titled "Geometry, Stochastics & Dynamics - Celebrating 20 years of UK-Japan Winter Schools," focusing on geometry, stochastics, and dynamical systems. Therefore, unlike in previous years, the January school was not held. However, with the Advanced Mathematical Sciences Research Center playing a central role, we successfully secured funding, the venue and speakers have been decided, and active preparations are underway.

In addition, various interdisciplinary research projects, including AI research, are being conducted, and the activities of the Advanced Mathematical Sciences Research Center are progressing smoothly.

Papers: 38

35 others

Conference Presentations: 13

10 others

We consider it a major achievement that we have provided students and young researchers with international experience by holding international research meetings and workshops such as the Boston-Keio Summer School.