My research explores the mathematical connections between quantum mechanical scattering, nonlinear waves, and seismic waves to understand how mathematical methods and analysis can potentially gain new insights and develop novel approaches.
Finding and understanding the mathematical connections that exist between different fields and phenomena is what makes mathematical research so fascinating.

In the word of mathematics, the symmetric structures on spaces are described by groups.
We call such symmetric space a space with group action.
My research interest lies in geometry and topology of the spaces with torus actions.
In this decades, the area so-called toric topology has been emerged.
Roughly speaking, toric topology can construct bridges among different areas (geometry, algebra and combinatorics) by the study of the spaces with torus actions.
In the near future, I would like to continue to study toric topology more deeply and challenge to solve open problems.

Inverse problem can be found in various fields, for examples, X-ray CT in medical fields, and non-destructive evaluations in engineering fields.In our laboratory, we make a mathematical analysis of inverse problems, especially, inverse source problems for wave equations and inverse scattering problems. We develop a numerical procedure to apply our mathematical results to practical problems.

We also study mathematical and numerical analysis for abnromal diffusion process in the soil.

There are analogies between algebraic number fields and function fields of one variable over finite fields. Number theory has developed on both fields. Using Dedekind sums which are special numbers, I study functions in number theory – zeta functions, L-functions, Dirichlet series, modular forms, and modular functions, for example. Using these functions, I also study numbers.

My field of expertise is algebraic geometry. There we consider a set of zero points (algebraic variety) of polynomials. For example, lines, circles, hyperbolas, and parabolas are algebraic varieties. The set of all geometric objects with certain properties is called a moduli space.
Moduli spaces of stable vector bundles on complex algebraic surfaces X are actively investigated as concrete examples of algebraic varieties.

For an algebraic variety M, the Kodaira dimension is determined.
The Kodaira dimension of M is an important invariant related to the curvature of M. Also, there is the minimal model theory to understand higher dimensional varieties. In this theory, one simplifies a variety by exploding and contracting its subspaces to get a simple variety, called minimal model.

I am interested in singularities, the Kodaira dimenson and the minimal model program of moduli space M.
(1) For large classes of surfaces X, I described the minimal model program of M by using words of moduli theory.
(2) I examined singularities of M, and in case where the structure of X is relatively simple, I showed that singularities of M are “good”. As a result, I calculated the Kodaira dimension of M.

I am interested in hit problem. The Steenrod algebra acts on polynomial algebras over the field of two elements. Hit problem is to find a minimal generating set of polynomials over the Steenrod algebra. General linear groups act on polynomial algebras, and this commutes with the action of the Steenrod algebra. These are motivated by problems in topology, I consider this problem from various viewpoints.

(1) Electric materials for the next 6G system
　We have synthesized a new polymer with the lowest dielectric constant in all-aromatic hydrocarbon-type polymers, and are developing it for electric materials of the next 6G system.

(2) Production of green hydrogen
　The catalysts and materials for production of green hydrogen are studied such as artificial photosynthesis and electrolysis of water by renewable energy.

(3) Secondary battery with ultra-high capacity
　The new cathode materials with ultra-high capacity in lithium ion battery are developped to increase driving distances for EV.

The aim of the research is to clarify the origin and evolution of the Solar System using various types of meteorite samples. Analytical techniques I am using for the studies are optical microscope, scanning electron microscope, electron probe micro analyzer (EPMA) and Micro Raman spectroscopy etc. Our target bodies are all of the celestial bodies include Earth. I am also joining the deep space exploration. My E/PO activities are exhibitions of meteorites and public lectures.

Graphene, integrated into the 3D nanoarchtecture with the smoothly interconnected curved surface, is promissing to clarify the novel properteis of the curved atomic layers adding to the amplifications of various material performance per unit projected area. We experimentally clarify the basic properties of the electrical transport on the 3D curved surface utilizing the high quality 3D graphene materials (so-called 3D nanoporous graphene). We also focus on the coexistence of the localized and itinerant electron properties originating from nitrogen-doping induced the local structural deformation of the 3D curved surface toward applications for the catalyst electrodes and thermoelectric materials using multifunctional electronic properties.

The integral of a function is intuitively the “area under the graph”, but it is now generalized in many ways. And when functions “converge” the function in some sense, do their integrals also converge it? The question “is this true?” can be a yes or no. The answer depends on the situation. By clarifying the nature of the concept of integrals, I am trying to clarify the mechanism by which such things do or do not happen.
Also, probability and integration are closely related. The so-called “expected value” or “variance (standard deviation)” is the integral of a random variable, and stochastic integrals are used to analyze stochastically varying processes such as stock prices.
However, the concept of “probability” that currently prevails in mathematics does not match well enough the image that people have of “probability. For this reason, there is still a debate among philosophers as to what probability is. This also has a negative impact on probability in school education. By resolving this issue, the human way of thinking about probability should evolve.

Conduction electrons in organic conductors behave simultaneously as quantum waves and classical particles. Due to the dual nature of these electrons, molecular solids demonstrate a variety of unconventional properties. Our group is investigating the possibility of finding a ferroelectric material that is polarized by a change of electron distribution, using techniques such as IR-Raman spectroscopy, nonlinear optics, and thermo-electric measurements. The unusual macroscopic polarization resulting from electron ordering could pave the way for future applications of organic solids in fast-switching devices and opto-electronic transducers.

The spatial resolution of images observed by the ground-based astronomical telescope is limited because of the wavefront distortion suffered by the turbulence of the earth atmosphere. In order to overcome this problem, we are studying the adaptive optics and developing the astronomical instruments with adaptive optics, which corrects the wavefront distortion in real-time. The applications of this technology into biological and medical fields are also being studied.
In addition, we are studying the internal structure, physical condition, formation, and evolution of the active galactic nuclei, which are active objects emitting a huge energy from the very compact region by mass accretion into the super-massive black hole at the center of galaxy, observing them with time-variability monitoring, polarimetry, and adaptive optics.

The latest cosmological observations strongly suggest the surprising fact that the Universe is undergoing an accelerated expansion at two very different times, immediately after the birth of the Universe and at the present time. However, this fact is incompatible with the property that gravity is an attractive force. An interesting fact is that the latest observational results suggest that a modification of general relativity may be manifested in the very early and current Universe. I believe that the key to the search for essentially new observables is to observe the “Dark Ages” and “Cosmic Dawn”, in which information about the very early Universe is preserved. Through radio observations that can probe these epochs, I aim to unravel the detailed history of the Universe.

Our research interests span various quantum phenomena such as magnetism, superconductivity, and multipolar ordering in strongly-correlated electron systems, as well as Weyl fermion excitations in what are known as topological Weyl semimetals. The nuclear magnetic resonance (NMR) techniques we use are advantageous because they allow us to investigate microscopic electronic states on the laboratory scale.

We also have a keen interest in developing a mobile and easily reproducible NMR spectrometer by leveraging the latest radio frequency technologies.

Microscopes are very important tools for studying biological samples. However, most of the microscopes cannot measure the vibrational molecular imaging based on molecular information. At the moment, only two microscopes are measureable. One is the Raman microscope, and the other is IR microscope, those are complementary relations. But these are not perfect. Especially, the IR microscope has very low spatial resolution about 10 µm, because of the diffraction limit by the IR wavelength. This is a serious problem for a microscope. To solve this problem, we have developed IR super-resolution microscope with a sub-micrometer spatial resolution by using vibrational sum-frequency generation (VSFG) detection, and have reported the applications to various biological samples such as human hair, avian feather, living cells and so on. By using this microscope, we can observe not only the vibrational molecular image with high spatial resolution but also the molecular orientation and chirality images.

Salmon milt, defatted soybeans, crab and shrimp shells, and cowhide have been discarded as an industrial waste around the world. Therefore, DNA, soy protein, chitin/chitosan, and collagen, which are obtained from these materials, are sustainable resources. Our research using sustainable resources is as follows; 1) removal of harmful organic compounds; 2) selective accumulation of metal ion; 3) development of anhydrous proton conducting material; and 4) development of bioplastic with the biodegradable property.

Metal complexes can exhibit functions and physical properties not achieved by organic or inorganic compounds alone by appropriately selecting the central metal ion and designing the organic π-electron ligands surrounding it. The characteristics of these complexes enable effective sunlight harvesting and various catalytic reactions utilizing its energy. In our laboratory, we are developing visible light-driven redox catalysts for photocatalytic H₂ production and CO₂ reduction using metal-porphyrin complexes, which can harvest visible light and catalyze various reactions. In research on functions and physical properties, we are developing coordination polymers with unique magnetic and dielectric properties based on mixed-valence states using redox-active ligands. Furthermore, we are developing one-dimensional d-electroninc metals based on partially oxidized one-dimensional dinuclear platinum complexes that exhibit stable metallic states at low temperatures.

Our research theme is development of new photoreaction using photoinduced electron transfer and its application to syntheses of functional materials. In present, we are working on (1) investigation of photochemical syntheses of indole derivatives which are considered to the important alkaloids widely found in nature, and (2) development of efficient photochemical synthetic methods for quinone imine dyes and their application. Because these target compounds indicate characteristic redox behavior, we also consider applying them to functional materials such as an OLED material while adopting their expected physical properties evaluated by quantum chemical calculation.

The kinds of polymers are relatively a few, which are used as plastics, rubber, and gels for daily life, since they exhibit versatile properties by hierarchical structure control ranging from nano- to micro-meter scales. In our laboratory, we focus to develop new polymeric materials by the hierarchical structure control and reveal the relationship between the mechanism and structure by microscope, scattering, and spectroscopy methods.

I’m working on migration behavior of elements in hydrosphere from a chemical view.

【Elucidation of mechanism of solid-liquid interfacial reaction】
One of the factors affecting migration behavior of elements in environment (especially in hydrosphere) is “adsorption of dissolved species on soil”. In recent years, it has been reported that various reactions to the adsorbed species occur. I’m trying to elucidate the mechanism of the reaction.

【Elucidation of nature of dissolved species in hydrosphere】
The dissolved species in hydrosphere is complex because several dissolved species coexists. I’m trying to elucidate the nature of the complicated dissolved species with theoretical calculation.