There are many universal structures in our world, such as Newtonian mechanics and thermodynamics describing macroscopic physics, and quantum mechanics describing microscopic physics. My interest is to find their intimate relations mathematically and physically.

I used to study minimal surfaces and harmonic maps, and now I study discrete geometry, such as graph theory.

I study string theory, which contains ample contents in Mathematics and Physics (e.g. geometry, elementary particles, etc.). I also study quantum entanglement.

There are four interactions in nature; gravity, weak interaction responsible for the radioactive decay of atoms, strong interaction that confines quarks, and electromagnetic interaction. The other interactions than gravity are described by the standard model, and the unified theory including gravity is an important theme in theoretical particle physics. String theory is regarded as a promising candidate, and several matrix models have been proposed as the nonperturbative definition of string theory. In string theory, the dimensionality of the spacetime is restricted to 10 (1-dim time and 9-dim space) from theoretical consistencies. My interest is to elucidate how the interactions between matters and our 4-dimensional spacetime (1-dim time and 3-dim space) dynamically emerge from matrix models, via numerical simulations using (super)computers.

Many natural phenomena, such as water (or viscous fluid) running down walls or thermal convection, are non-linear. My interest is to interpret these non-linear phenomena mathematically using analytical methods.

My research interest is integrable systems. Although there is no clear definition of the term “integrable,” systems that can be solved exactly are called the integrable systems. In particular, the main topics of my research are conformal field theories (CFTs) required for particle physics, representation theory of algebras associated with CFTs, and the eigenvalue problems of the Macdonald and Ruijsenaars operators obtained from one-dimensional many-body systems.