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, we plan to hold research meetings in the following fields and organize public lectures to introduce the cutting edge of research to the general public.

1) Transformation of Academia Crossing the Boundaries Between Humanities and Sciences
①Mathematical geographical modelling
 We will explore mathematical approaches to fields in the humanities, such as history, geography, and literature.
 Senior Research Fellow
  AOKI Takaaki         Professor, Shiga University
②AI and the Science of Science
 In light of the significant impact AI is having on academia across all disciplines, we will discuss the future of scholarship and research.
 Senior Research Fellow
  FUJIWARA Naoya      Professor, Tohoku University
  AOKI Takaaki         Professor, Shiga University
③Generative Science
 In collaboration with “Institute of Generative Science,” Kyoto University, we will discuss the evolution of academia and science in the age of AI from diverse perspectives, including physics, mathematics, computer science, philosophy, literature, and law.
 Senior Research Fellow
  HASHIMOTO Koji       Professor, Kyoto University

2）Mathematical Approach to Environmental History
①Hydrological Climatology of Monsoon Asia
 Using specific examples from monsoon regions of Asia, such as Bangladesh and the Kizugawa River basin, we will adopt an environmental history approach based on mathematical models and field data.　
 Senior Research Fellow
  TERAO Toru           Professor, Kagawa University
  MURAYAMA Satoshi      Professor Emeritus, Kagawa University
                   Co-Convener, International Consortium for Earth and Development Sciences,
                   Kagawa University

3）Mathematical Conditions for Life
①Algorithms of Life
 We aim to elucidate the mechanisms underlying biological phenomena, such as the movement of organisms, using theoretical and numerical methods.
 Senior Research Fellow
  ISHIMOTO Kenta         Professor, Kyoto University
②Habitable Planets
 We will discuss the surface environments of exoplanets from both theoretical and observational perspectives, with a focus on habitable environments (the habitable zone).
 Senior Research Fellow
  ISHIWATARI Masaki    Professor, Hokkaido University
  HAYASHI Yoshiyuki      Academic Fellow and Professor Emeritus, Kobe University

4）Research in Mathematical Methods and Pure Mathematics
①Phenomena and Mathematics
 We use mathematical approaches to uncover the mechanisms underlying the complex phenomena that occur in nature and society.
 Senior Research Fellow
  KOBAYASHI Miki         Professor, Rissho University
  ISHIMOTO Kenta        Professor, Kyoto University
  OBUSE Kiori            Professor, Okayama University
②Representation Theory
 We will hold research conferences in the field of Representation Theory in pure mathematics.
 Senior Research Fellow
  KOBAYASHI Toshiyuki   Professor, The University of Tokyo
③Symplectic geometry
 We will hold research conferences on Symplectic geometry, a branch of geometry.
 Senior Research Fellow
  ONO Kaoru         Professor, RIMS, Kyoto University
④New Developments in Mathematical Fluid Dynamics: Information, Causality, and Spontaneous Probability
 We will address nonlinear problems found in fluid dynamics (stability, turbulence, and mixing) and information science (machine learning, data assimilation, and random number generation), as well as the application of information science methods to fluid dynamics.
 Senior Research Fellow
  INUBUSHI Masanobu   Associate Professor, Tokyo University of Science