Introduction

Home
Outline of MIMS
Introduction / Collaborative Research Project

Principle

Objective and Establishment

Meiji University established Meiji Institute for Advanced Study of Mathematical Sciences (MIMS) in 2007. MIMURA Masayasu is the Founder of MIMS.
The mission of MIMS is to develop mathematical sciences for the purpose of deepening our understanding of a wide variety of phenomena in society and nature. We are also focusing on returning our research results to society and on fostering young researchers through various programs. With these activities, we aim at forming a leading international research center.

MIMS Research divisions:
(1) Fundamental Mathematics Division
(2) Mathematical Modeling and Analysis Division
(3) Mathematical Education Division
(4) Art-and-Science Integration Division
(5) Integrated Division of Mathematical Modeling and Life Sciences
(6) Advanced Mathematical Science Division

Organization FY2026

FY2026 Collaborative Research Project

Interdisciplinary Research Project on Mathematical Dynamics of Opinion Formation

Objective:

　The rapid development of social media and generative AI has created a new information environment in which large numbers of agents, including both humans and AI systems, interact and form opinions. In such an environment, opinions do not simply converge toward consensus or polarization. Rather, the collective state may evolve in complex ways through interactions among individuals, memory of past interactions, trust relationships, coupling among multiple topics, and the continual emergence of new information and issues. Understanding such opinion formation as a new form of collective dynamics in society has therefore become an important challenge for the mathematical sciences.
　The purpose of this project is to develop a new mathematical framework for understanding the relationship between microscopic interactions and macroscopic collective dynamics in opinion formation, through collaboration among researchers in nonlinear dynamics, mathematical modeling, data analysis, information science, and generative AI. In addition to consensus, clustering, and polarization, which have been the primary focus of conventional mathematical models of opinion formation, we will investigate temporal dynamics such as oscillations, metastability, switching, itinerancy, and self-organization, and identify the interaction structures responsible for generating such dynamics through both mathematical models and data-driven approaches.
　We will further employ natural-language interactions among artificial agents based on large language models (LLMs) as a novel computational experimental system, while feeding insights from nonlinear dynamics and complex systems back into the design of LLM agents and social simulations. Through these activities, the project aims to establish a cross-disciplinary research network connecting mathematical sciences, information science, and the study of social phenomena, and to develop “the mathematical dynamics of opinion formation” as a new interdisciplinary research area centered at MIMS.

Research Outline:

　This project views opinion formation as nonlinear collective dynamics arising from interactions among multiple agents, and investigates it by combining mathematical theory, mathematical modeling, data analysis, and computational experiments with LLMs.
　First, building on conventional opinion dynamics models such as the DeGroot, Deffuant, and Hegselmann–Krause models, we will introduce interaction mechanisms including nonreciprocity, memory and forgetting, trust, interest and habituation, coupling among multiple topics, and adaptive networks. We will investigate mathematical mechanisms that generate not only consensus and polarization but also oscillations, metastability, switching, and itinerant dynamics. Concepts and methods from nonlinear dynamics and complex systems, including slow–fast dynamics, bifurcation theory, heteroclinic dynamics, and self-organization, will be employed to clarify the relationship between interaction structures at the individual level and temporal dynamics at the collective level.
Second, we will use natural-language interactions among LLM agents as a computational experimental system and analyze their conversations as high-dimensional trajectories in semantic space. We will investigate convergence and divergence of conversations, metastable states, transitions among topics, and their dependence on memory and interaction structures. By combining data-driven methods with mathematical modeling, we will seek to extract low-dimensional dynamical structures underlying these high-dimensional conversational processes.
　Third, we will explore the possibility of controlling and designing the dynamics of collective natural-language interactions by implementing, in LLM agents, mechanisms identified through mathematical models as generators of complex temporal dynamics. By establishing a cycle between “discovering mathematical structures from data and LLM experiments” and “designing new artificial-agent dynamics from mathematical structures,” we aim to create a new interface between research on opinion formation, nonlinear dynamics, and artificial intelligence.
　MIMS will serve as a hub for this interdisciplinary activity. Through seminars, workshops, and collaborative research involving researchers in mathematical sciences, information science, complex systems, and social simulation, we will promote both domestic and international collaboration. By seeking mathematical principles that are not restricted to particular models or particular LLMs, the project ultimately aims to establish a broad research foundation for the “mathematical dynamics of opinion formation,” encompassing opinion formation, collective decision-making, and societies of artificial agents.

Research period: October 1,2026－March 31,2031

Project leader: OGAWA Toshiyuki (Professor, School of Interdisciplinary Mathematical Sciences, Meiji University)

Project Member:
NISHIMORI Hiraku（Professor, MIMS, Meiji University）
NISHIMOTO Keita（Associate Professor, School of Interdisciplinary Mathematical Sciences, Meiji University）
ICHIDA Yu（Senior Assistant Professor, School of Science and Technology, Meiji University）
OHNO Kota（Specially Appointed Associate Professor, School of Science and Engineering, Chuo University）

K.Sugihara, A.Sekisaka, T.Ogawa and T.Miura, Segmented wavetrains and sites of reversal in the mouse seminiferous tubules, Math. Biosci. 396, 109672 (2026).
K.Ikeda, T.Kan and T.Ogawa, Existence of traveling wave solutions in continuous optimal velocity models, Physica D {\bf 471}, 134430 (2025).
S.-I.Ei, H.Ikeda and T.Ogawa, Bifurcation of co-existing traveling wave solutions in a three-component competition diffusion system, Physica D {\bf 448}, 133703 (2023).

Interdisciplinary Research Project for the Mathematical Reconciliation of Economic Solvency and Asset-Liability Management

Objective:

　Economic Value-Based Solvency Regulation (ESR) was introduced to the insurance industry in 2026, following international discussions on the Insurance Capital Standard and domestic deliberations by the Financial Services Agency's expert panel. It was expected to align with asset-liability management (ALM), which is one of the most powerful risk management tools for insurance companies. However, unforeseen inconsistencies have emerged in the mathematical properties of the two approaches, which could lead to undesirable consequences in risk management. This project is conducted by a collaborative research group involving insurance and actuarial science researchers, who played a central role in the expert panel, as well as practitioners from insurance companies implementing cutting-edge, accurate ALM. The project aims to propose a new, integrated framework that mathematically reconciles ESR and ALM, thereby contributing to realistic domestic and international discussions regarding their future evolution.

Research Outline:

　The study will clarify the inconsistencies between advanced ALM practices and ESR within the context of the three pillars (minimum capital requirements, internal controls, and information disclosure), and investigate strategies to harmonize them. In collaboration with data provider companies, the study will focus particularly on yield curve models (extrapolation and adjusted spreads) and lapse models, which currently differ significantly between solvency evaluations and ALM purposes. The study will construct an integrated framework for the mathematical reconciliation of the two.

Research period: Until March 2028

Project leader: MATSUYAMA Naoki (Professor, School of Interdisciplinary Mathematical Sciences, Meiji University)

Interdisciplinary Research Project for Application of Topology to Engineering and Life Science

Purpose of the project:

　By performing interdisciplinary research for topology, engineering, and life science, we promote collaborations among researchers in these areas from the point of view of mathematical sciences. Nowadays, topology has been applied for various research fields such as sensor networks and motion planning in engineering and analysis of complex geometric structures of proteins in life science etc. We aim to perform research among these areas beyond the traditional boundary of disciplines. We study fundamental theory which can be shared by researchers of various areas and also collaborate to develop the interface by means of the techniques in computing topology.

Summary of research:

　　　　　　　　　　　　　　　　Topology is a branch of mathematics which has been rapidly developed from the middle of the 20th century. We apply contemporary techniques in topology to engineering and life science. Especially, we study topological data analysis such as persistent homology theory in relation with various research areas including material science and life science. Our research will include applications of knot theory to genetic research, graph theory for networks, and application of the theory of configuration spaces to robotics. For the purpose of supporting research of various disciplines, we will develop computer software including the ones for VR and archive such digital information. Our activity will also cover the visualization in geometry and art. We perform research in collaboration with Kyushu University Institute of Mathematics for Industry, The University of Tokyo Virtual Reality Educational Research Center, Art Center the University of Tokyo.

Period of research project: Until March 2026 (the period of the collaborations)

Project leader: KOHNO Toshitake (Professor, The University of Tokyo/ MIMS Fellow)

Interdisciplinary Research Project for Mathematical Sciences and Biology

Goal:

　The international research network on Reaction-diffusion systems in Mathematics and Biomedicine (GDRI ReaDiNet) has been started from 2015 under the cooperation among six research institutions of MIMS and Department of Mathematical Sciences of University of Tokyo (Japan), Paris-Sud University and University of Nice Sofia Antipolis (France), Kaist (Korea), National Center for Theoretical Sciences (Taiwan).
Since 2020, due to the reorganization of the CNRS project, the name has been changed to the IRN-ReaDiNet project, and the activities have continued.

Outline of the Research:

　Through Mathematical Sciences based on modeling and analysis, we focus on understanding of complex system arising in biomedicine and develop theoretical methods on analysis and numerical simulation under international cooperation with other research institutions.

Research Period: to December 2029 (which will be the final year of the IRN-ReaDiNet project)

Leader: MATANO Hiroshi (Distinguished Professor Emeritus, Organization for the Strategic Coordination of Research and Intellectual Properties, Meiji University)

Industrialized Project based on Origami engineering

Object:

　It is aimed to solve problems for industrialization of origami structures by merging advanced origami geometry, computational science simulation and manufacturing science. Because we meager origami geometry and computational science, we promote joint research with researchers and engineers in the manufacturing field. We aim to find solutions to problems common to all origami structures for their industrialization by acting as a hub between various fields.

Research overview:

　The research of origami engineering is entering its third period, which is expected to yield many fruitful results. The first period was filled with excitement about creating origami structures which are (1) light and rigid, or (2) has expansion and contraction functions. In the second period, efforts were focused on solving two issues that hindered origami engineering promotion. The first one was that maintaining stability after expansion or contraction was difficult and the other one was that it was difficult to find an inexpensive manufacturing method without losing the wonderful features of origami structure because the origami structure is generally more complicated than the general structure. It is shown that the origami group of MIMS is leading the way in this brilliant third period in SIAM（Society for Industrial and Applied Mathematics）newsletter.

　Furthermore, we aim to contribute from the cultural aspect of origami engineering. A characteristic of Japanese culture is beautiful simplification such that (1) Creating beautiful hiragana based on kanji, (2) Beautiful origami with simplified shapes, (3) Tanka and haiku that simplify written expressions, (4) Fan of simplified expression through pictures. Among them, the fan looks different depending on the angle from which it is viewed so that many great painters such as Jyakutyu Ito and Hokusai Katsushika, etc. in Edo period attempted to simplify expression through painting with fan. However, because the face of fan is distorted, the perfect circle on 2-dimensional fan picture becomes ellipse on 3-dimensional fan. And so, it was difficult to compose with fan so that fan's pictorial simplification was not always sufficient. To solve this, we have developed a mathematical model that can reproduce "distortion of fan face" with high precision　(Hagiwara, I., Yamazaki, K. and Abe, F., Fan, conversion device of fan picture, conversion method of fan picture and members of fan picture, Patent application No. 2020-149060,in Japanese). With this mathematical model, we have already developed a system where for example, if you look from the left, you can see images related to the above phrase and if you look from the right, you can see images related to the below phrase. Based on this mathematical model, we are aiming to create a new unique Japanese culture that handles Tanka simplified by text and fan of simplification through pictures (images) at the same time. At the same time, we will also promote second generation origami engineering with regard to related industrialization that treats not only sheet but also members such as fan and umbrella, etc. and has excellent characteristics that cannot be achieved with either one alone in contrast to conventional origami engineering that deals with sheets alone.

　Furthermore, through joint researches, we aim to commercialize related structures to the following patents such as

Hagiwara,I. and Nara,C., Container, Patent application No. 2017-201993,in Japanese,
Hagiwara,I. and Nara,C.,Folding structure, Patent application No. 2015-245594,in Japanese,
Hagiwara,I.and Zhao,X.,Crash energy absorption structure forming equipment ,crash energy absorption structure and crash energy absorption structure forming method, Patent application No. 2021-215790,in Japanese,
Hagiwara,I.and Zhao,X., Forming method of spherical tank and spherical tank, Patent application No.2022-097813,in Japanese,
Hagiwara, I. and　Zhao, X., Core panel, core panel forming method and core forming device, Patent application No. 2022-177019, ,in Japanese
Hagiwara ,I. and　Zhao ,X., Shock absorber, Patent application No. 2023-037761, ,in Japanese
and
Hagiwara,I. and Sasaki,T., Hat, Patent application No. 2023-194075,in Japanese.

Installation period: Until the end of March in 2026 when the joint research ends.

Project leader: HAGIWARA Ichiro (Meiji University distinguished professor emeritus, Organization for the Strategic Coordination of Research and Intellectual Properties)

↑ Page Top