Yuichi Goto
Kyushu University
Shuntaro Tsubouchi
The University of Tokyo
Hohto Bekki
Saga University
Profile of Fellows 2025-27
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Could you tell us what motivated you to apply for the fellowship?
AWhile 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.
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What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
AI 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.
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What are your goals or dreams for your future research?
AI 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.
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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?
AI plan to stay at CREST-ENSAE (Institut Polytechnique de Paris) in France.
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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 ?
AI 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.
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What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
AMy 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.
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What are your goals or dreams for your future research?
AThe 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.”
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Q
Could you tell us what motivated you to apply for the fellowship?
AWhen 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.
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What kind of research have you been working on, and could you explain it in a way that non-experts can understand?
AI have been working in number theory, especially onthe special values of L-functions. L-functions are certainanalytic functions naturally associated 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.
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What are your goals or dreams for your future research?
ACurrently, 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.
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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?
AI am currently collaborating with researchers at the Max Planck
Institute for Mathematics in Germany and at the University of Oxford in the UK.
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Could you tell us what motivated you to apply for the fellowship?
AI 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.
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What kind of research have you been working on,and could you explain it in a way that non-expertscan understand?
AI 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.
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What are your goals or dreams for your future research?
AOne 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.
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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?
AI hope to visit Busan National University in South Korea and McMaster University in Canada.