Core Program

This research explores the deepening of mathematical sciences, which form the foundation of various disciplines, and their collaboration with diverse academic fields. The fundamental philosophy of the International Institute for Advanced Studies (IIAS)—"Uncovering what must be studied for the future and happiness of humanity"—refers to the act of stepping into territories where only "beast trails" (unbeaten paths) exist. It expresses the high expectations for experimental and adventurous research in these frontier fields, which are often difficult to conduct within existing research institutions. In accordance with this philosophy, this study aims to deepen mathematical methods in STEM fields such as mathematics, biology, and informatics. Furthermore, it seeks various mathematical approaches to humanities fields where such research has traditionally been scarce—such as literature, history, archaeology, and geography—thereby expanding the academic horizon of mathematical sciences into these unexplored territories.
Fiscal year 2026 will be a phase for assessing the current status and exchanging information through joint discussions among researchers challenging mathematical approaches in frontier fields, with the goal of developing new mathematical methodologies. Specifically, the following fields and research meetings are planned. For each meeting, we expect the researchers to give lectures on the front lines of their research, aimed as much as possible at the general public.

1) Mathematical Geographical Modeling of Population and Environment
We will hold a research meeting in the field of "Mathematical Geographical Modeling," which studies geographical phenomena, including human geography, through mathematical modeling. Based on a partnership agreement with the Research Institute for Mathematical Sciences (RIMS) at Kyoto University, this meeting—previously a joint usage project of RIMS—will now be co-hosted with IIAS. It is scheduled to be held over two days in the fall of 2026 in cooperation with Kagawa University and others, with an expected 20 to 30 participants. Each year, new mathematical approaches to the humanities (literature, history, archaeology, etc.) are discussed. In 2026, the agenda includes organizing key points and sharing challenges regarding the current state of the "Science of Science" and research support through the utilization of AI.

2) Habitable Planets
This research meeting is related to astrobiology and focuses on habitable environments (habitable zones) on exoplanets, discussing planetary surface environments from both theoretical and observational perspectives. By taking a comparative planetology approach to the surface environments of planets and satellites in our solar system, as well as Earth's paleoclimate, the goal is to comprehensively understand the formation and evolution of "our environment" that can nurture life. It is scheduled for 2 to 3 days around February 2027, with an expected 20 to 30 participants. This meeting has been co-hosted by the Center for Planetary Science (CPS) at Kobe University and the Astrobiology Center (ABC) of the National Institutes of Natural Sciences, contributing significantly to the foundation of habitable planet theory. Hosting the meeting at IIAS from fiscal 2027 onwards is also under consideration.

3) Representation Theory Symposium
This is a leading domestic research meeting in the field of representation theory within pure mathematics. It is expected to have about 70 participants, including several from overseas each year. Following the November 2025 event at the Kanagawa Institute of Technology, it is scheduled to be held at IIAS in mid-November 2026.

4) Research Programs Under Consideration
i) Hydroclimatology of Monsoon Asia: Environmental History Approach through Mathematical Models and Observed Data

A research meeting to be held as part of the SATREPS project (Science and Technology Research Partnership for Sustainable Development) by JST and JICA. It involves the development and implementation of a high-precision flood forecasting system in Bangladesh. Related to regional studies, this international meeting will also address hydroclimatology in the Kizu River basin. We are considering holding this once per fiscal year for three years starting from 2026.

ii) Symplectic Geometry

An international research meeting in a field of pure mathematics, specifically geometry, is under consideration.