Could you tell us what motivated you to apply for the fellowship?
While I was developing the details of a joint research project with an overseas collaborator, I learned about the Research Fellowship for Promoting International Collaboration through a mailing list and decided to apply. Although research can progress via email and online meetings, I believe that sharing the same physical space enables more spontaneous and nuanced communication. It allows us to discuss subtle ideas and small questions that are difficult to convey in writing, which deepens the research and often leads to the discovery of new areas to explore. Since staying abroad incurs significant costs, the support provided by this fellowship made it possible for me to plan such a research stay.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
I have been conducting research in the field of time series analysis, which involves using statistics to analyze data that change over time, such as stock prices or temperature records, in order to uncover their underlying structure and characteristics. In one of my studies, I developed a method of analysis called “analysis of variance” that is applicable to time series data. Using this method, we were able to classify regions of the North Sea based on the amount of zooplankton collected, without relying on specialized biological or geographical knowledge.
What are your goals or dreams for your future research?
I aim to develop statistical methods that balance theoretical advancement with practical utility. In the future, I hope to create tools that are not only useful to researchers in theoretical statistics, but also accessible to practitioners in various fields who use statistical methods in their work.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
I plan to stay at CREST-ENSAE (Institut Polytechnique de Paris) in France.
Could you tell us what motivated you to apply for the fellowship? Also, if you don’t mind sharing, could you tell us which country you hope to stay in ?
I was informed of the fellowship in December 2024. At that time, I was already scheduled to stay in Parma, Italy for six months from around September 2025, as a visiting researcher at the University of Parma. I applied for this fellowship to receive support for my research activities in Italy. For regularity theories, Italy is one of the strongest countries. I believe that this stay will be an excellent opportunity to further advance my research.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
My research interest lies in elliptic and parabolic regularity theory for anisotropic singular diffusion problems. Regularity theory aims to realize the extent to which the smoothness (regularity) of weak solutions, solutions that should be treated in a weak sense, can be recovered. This is one of the important issues in the mathematical analysis of partial differential equations. Regularity theory is often developed under the assumption of isotropic spatial diffusion structures. In my research, however, we have to deal with an anisotropic singular diffusion operator, called the one-Laplace operator. My research over a few recent years has focused on showing the continuity of spatial gradients.
What are your goals or dreams for your future research?
The significant progress in my research was the encounter with a regularity theory for anisotropic degenerate diffusion problems, which has been studied in Europe. For the anisotropic diffusion problems in both cases, we find regularity results strikingly similar, as they were just like siblings. It would be one of my dreams to establish a unified theory that can explain the relationship between the two problems. Except for one paper co-authored with Professor Yoshikazu Giga, I have conducted most of my research alone. However, the discovery of a guiding “star” prevented me from feeling despair or pessimism. I would like to envision a future where the two theories unite to form a “constellation.”
Could you tell us what motivated you to apply for the fellowship?
When I applied for the fellowship, I was a postdoctoral researcher atthe Max Planck Institute for Mathematics in Bonn and hadalready begun several joint projects with researchers inEurope. I thought it would be a great opportunity to becomea fellow and continue these collaborations.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
I have been working in number theory, especially onthe special values of L-functions. L-functions are certainanalytic functions naturally Associationd with various interestingarithmetic objects, such as number fields, algebraic varieties,Galois representations, and automorphic forms, etc. The values ofL-functions at integers are called their special values, and theyhave many intriguing properties. For example, in the case ofthe Riemann zeta function ζ(s), which is the most basic exampleof an L-function, Euler computed its value at s=2 as ζ(2)=π^2/6.This is a fascinating formula because it relates an arithmeticobject (1,2,3,...) to a geometric constant ( π ), which are,a priori, unrelated. My research is motivated by such surprisingphenomena surrounding the special values of L-functions.
What are your goals or dreams for your future research?
Currently, I aim to understand these remarkable phenomena andthe structures behind the special values of L-functions by usingso-called Eisenstein cocycles, which have natural connections toboth the arithmetic and geometric worlds.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
I am currently collaborating with researchers at the Max Planck
Institute for Mathematics in Germany and at the University of Oxford
in the UK.
Could you tell us what motivated you to apply for the fellowship?
I had already been in touch with researchersfrom countries such as the United States, Poland,and South Korea before applying. I was eager todeepen those academic relationships and developcollaborative research projects. That desire tobuild on existing connections and foster jointresearch led me to apply for this fellowship.
What kind of research have you been working on,and could you explain it in a way that non-expertscan understand?
I work in the field of mathematics called topology,which is a branch of geometry that focuses on theproperties of shapes that don’t change when theyare stretched or deformed. Within topology,I’m particularly interested in knot theory andfour-dimensional topology.Knot theory studies tangled loops, like piecesof string tied up in complicated ways. It’s quitea visual area of math—something that people canoften understand through diagrams. In contrast,four-dimensional topology deals with objects andspaces that we can’t see directly, because theyexist in four dimensions rather than the usual three.My motivation comes from trying to understand thisinvisible four-dimensional world using the morevisible and intuitive tools provided by knot theory.A key concept connecting these two areas is the ideaof a “2-knot,” which is like a knot made from a sheetinstead of a string. I’ve worked on ways to representand understand these 2-knots.In doing so, I also use algebraic structures called"quandles" that help describe the properties of knotsin a systematic, symbolic way.
What are your goals or dreams for your future research?
One major goal of my research is to contribute tothe classification of 2-knots. In four-dimensional topology,there’s a famous conjecture known as the "Smooth PoincaréConjecture in Dimension Four." It’s one of the big openproblems in topology, and it's connected to the study of 2-knots.I hope to contribute to this area in some meaningful way.I’m also very interested in developing a more comprehensivepicture of the whole landscape of 2-knots. What kinds of2-knots are out there? How are they related to one another?These are some of the fundamental questions that drive my work.
If you don’t mind sharing, could you tell us whichinstitution or country you hope to stay in, or whichinstitutions your research collaborators are affiliated with?
I hope to visit Busan National University in South Korea and McMaster University in Canada.
Could you tell us what motivated you to apply for the fellowship?
I learned about this fellowship through the Topology-ML. I received the announcement while I was staying in the US, where I was experiencing the differences in living costs and exchange rates. With the hope of continuing to carry out research visits abroad in the future, I decided to apply for this fellowship in the hope of receiving its support.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
My research focuses on the characteristic classes of fiber bundles. A fiber bundle is a shape with a certain kind of twisting, such as the Mobius band. (The Mobius band is the shape obtained by twisting a rectangular strip of paper once and gluing the opposite edges together.) In general, a (higher-dimensional) fiber bundle is hard to visualize, and characteristic classes are fundamental tools to study them. They are described using diffeomorphism groups, which are very large and complicated groups. I'm studying algebraic and dynamical properties of diffeomorphism group that are related to characteristic classes.
What are your goals or dreams for your future research?
The theory of characteristic classes of fiber bundles and the cohomology theory of diffeomorphism groups contains vast unexplored territory. Even in the case where the fiber is a circle, many important problems remain unsolved. My goal is to deepen our understanding of these objects.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
I am considering research visits to Purdue University in the US and KIAS in South Korea.
Could you tell us what motivated you to apply for the fellowship?
At the time of my application, I was working on several joint research projects with Westlake University in China. I applied for this fellowship because I believed that these activities were well aligned with the purpose of the program.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
I have been studying the nonlinear partial differential equations that describe the motion of fluids such as water and air. In particular, I have worked on the Navier–Stokes equations, which are fundamental equations in fluid mechanics. My research focuses on problems such as whether solutions exist globally in time and whether the energy equality holds. These problems are important for understanding the mathematical aspects of turbulence, and they may also provide a mathematical basis for the validity of numerical analysis.
What are your goals or dreams for your future research?
The goal of my research is to understand fundamental problems arising from the nonlinearity of the equations. In particular, the global well-posedness for the three-dimensional Navier–Stokes equations is known as a major open problem related to the Millennium Prize Problems, and I hope to contribute to progress on this problem. Furthermore, I would like to apply the perspectives and techniques obtained through this research not only to this equation, but also to the development of the theory of nonlinear partial differential equations.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
Westlake University, China.
Could you tell us what motivated you to apply for the fellowship?
I had previously visited Jean Monnet University, my prospective host institution, for several months through the “Overseas Challenge Program for Young Researchers (JSPS).” Even after returning to Japan, I continued joint research with host professor and postdoctoral researchers there. Around September 2025, I learned about this fellowship and decided to apply in order to continue and accelerate our ongoing research.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
I am studying certain complex functions with several variables, called multiple zeta functions.
One of the most fundamental tasks in mathematics is “counting objects.” In analytic number theory, which is my field, even when it is impossible to count something exactly, we often try to obtain accurate approximations instead. For example, suppose we want to know how many prime numbers are less than or equal to a given number N. Although the exact number is generally difficult to determine, we can obtain accurate approximations in terms of N.
Regarding other difficult counting problems, it is known that multiple zeta functions are very powerful tools for approximation. For instance, in recent years, values of multiple zeta-functions — more precisely, their generalizations called zeta-functions of root systems — at the origin have been used to derive detailed asymptotic formulas for the number of n-dimensional irreducible representations of semisimple Lie algebras (= difficult counting objects).
Related to this topic, it has also been revealed in recent years that the values of zeta-functions of root systems at non-positive integers are closely connected with relations among the well-known, classical Eisenstein series. I am particularly interested in such interactions between multiple zeta-functions and related areas of mathematics.
What are your goals or dreams for your future research?
Historically, research on multiple zeta functions first developed through the study of their special values. Compared with this, research on the functions themselves has not been explored extensively. Moreover, even the study of special values may not be widely recognized in the world.
However, I strongly believe that the study of multiple zeta functions and their values is both rich and fascinating. One of my goals is to communicate this appeal to the international mathematical community and, together with researchers around the world, deepen our understanding of the mysterious phenomena exhibited by multiple zeta-functions.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
I plan to stay at the Camille Jordan Institute (ICJ) at Jean Monnet University in France.
Could you tell us what motivated you to apply for the fellowship?
I first learned about the Overseas Research Fellowship through an announcement on the academic mailing list. At that time, I was already planning to conduct research in Italy, and I was also considering participating in research workshops in Greece and France. I decided to apply because receiving support for travel and accommodation expenses would enable me to carry out my research activities in a more substantial and meaningful way.
What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
I have been studying the existence of solutions to elliptic equations associated with coupled nonlinear Schrödinger systems, mainly by employing variational methods. Variational methods provide a framework for guaranteeing the existence of critical points of functionals, that is, points where the derivative vanishes. In particular, one characterizes solutions of the equation as critical points of a suitable functional and then establishes their existence through variational techniques. Recently, I have been working on coupled nonlinear Schrödinger equations with point interactions. Since point interactions are actively studied in Italy, I hope to further develop this research theme during my stay in Italy.
What are your goals or dreams for your future research?
I have so far focused my research mainly on the existence of solutions. However, proving existence alone only tells us that “a solution exists under certain conditions,” and it does not allow us to conclude whether solutions fail to exist once those conditions are no longer satisfied. I felt a certain sense of insufficiency in my results, as if the research remained incomplete and had not yet reached a fully satisfactory stage.
This led me to consider situations in which solutions do not exist and to aim at clarifying the boundary between existence and nonexistence. I believe that identifying such a threshold would add greater depth and significance to the results I have obtained on the existence of solutions.
If you don’t mind sharing, could you tell us which institution or country you hope to stay in, or which institutions your research collaborators are affiliated with?
I am planning to visit Italy (Polytechnic University of Bari), Greece (National and Kapodistrian University of Athens), and France (Sorbonne University).