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702 labs · 51 student voices
Daisuke Matsushita, Associate Professor
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Prof. Matsushita studies symplectic manifolds defined over the field of complex numbers. The definition is just that of an ordinary symplectic manifold, with the number system changed to the complex numbers. Even so, these manifolds are known to have rich symmetries not seen in the real case. Prof. Matsushita's goal is to follow this phenomenon and build “holomorphic symplectic geometry.”
Toshiyujki Akita, Professor
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Prof. Akita's main research subject is the cohomology of groups. Group cohomology is defined algebraically, yet it also coincides with the cohomology of the space determined by the group, placing it at the intersection of topology and algebra. The professor studies the cohomology of Coxeter groups, Artin groups, and mapping class groups of closed surfaces. Recently, the professor has also been working on algebraic systems closely related to topology, such as quandles.
Junichi Inoguchi, Professor
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Prof. Inoguchi studies geometric objects related to Lie groups and differential equations. Conversely, the professor also investigates differential equations in which geometric structures or backgrounds are hidden, using the geometry of Lie groups and homogeneous spaces. Differential equations that allow this back-and-forth are infinite-dimensional integrable systems, equipped with a geometry-derived 'mechanism of solvability.' As a result, a field fusing infinite-dimensional integrable systems with differential geometry has emerged, and in recent years it has come to be called integrable geometry.
Shimpei Kobayashi, Professor
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Prof. Kobayashi studies the area where differential geometry and integrable systems overlap. In differential geometry, 'curved spaces' such as curves, surfaces, and manifolds are investigated using curvature, connections, differential forms, Lie groups, and differential equations. In certain special geometric problems, a parameter enters Cartan's structure equations, allowing them to be deformed, and they become part of an integrable system. The professor works on themes where geometry and differential equations intersect, including constant mean curvature surfaces, constant Gaussian curvature surfaces, harmonic maps, statistical manifolds, and convex optimization.
Hitoshi Furuhata, Professor
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Prof. Furuhata uses the methods of differential geometry to study more general figures that abstract the properties of curves and surfaces. The study of shape has long been pursued across a wide range of fields, from the natural sciences and engineering to architecture and art. Even the beautiful curves and surfaces around us have meaningful mathematical structure. Recently, it has been shown that elegant figures also arise from fields such as statistics, which seem unrelated to shape.
Morimichi Kawasaki, Associate Professor
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Prof. Kawasaki specializes in symplectic geometry. Symplectic geometry is a field rooted in the Hamiltonian systems of analytical mechanics, and in recent years it has drawn attention through its relationships with various other fields. Of particular interest are the metric and group structures of the Hamiltonian diffeomorphism group, one of the transformation groups of a symplectic manifold. As an application, non-displaceable fibers of integrable systems are also studied.
Yuta Nozaki, Associate Professor
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Prof. Nozaki studies the global properties of shapes and spaces. Specifically, Prof. Nozaki is interested in surfaces, knots, and 3- and 4-dimensional manifolds. These are objects that can, in an appropriate sense, be made visible as shapes, but uncovering their geometric essence is not easy. Prof. Nozaki is also interested in interdisciplinary research and is engaged in collaborations related to, for example, computer science and physics.
Hideo Kubo, Professor
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Prof. Kubo studies the wave equation, which describes how waves propagate. The wave equation is a representative partial differential equation with a very simple form, yet the mathematical structure it contains is very rich. Since graduate school, Prof. Kubo has continued to think about how solutions change when small changes (perturbations) are made to the nonlinearity of the equation, the domain, or the metric of the space. Recently, Prof. Kubo has also become interested in systems of equations in mathematical physics that reduce to the wave equation, and in the noncommutative structure of differential equations.
Masaharu Kobayashi, Professor
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Prof. Kobayashi studies the properties of functions from the standpoint of harmonic analysis and real analysis. By examining the various “quantities” a function has, one can read off properties such as boundedness, continuity, differentiability, and integrability. The yardsticks for measuring these quantities are norms and the function spaces defined by norms. In particular, using function spaces called modulation spaces as a starting point, Prof. Kobayashi studies pseudodifferential operators and operators related to partial differential equations.
Akihito Hora, Project Professor
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Prof. Hora studies the boundary region between probability theory and the representation theory of groups. The guiding idea is the concept of a measure, and a tendency to take detours along the way is what gives this approach its character. Interest centers on bridging the finite and the infinite, with limit theorems, asymptotic representation theory, and noncommutative harmonic analysis as keywords. The current main interest is the analysis of probabilistic phenomena generated by the actions of huge groups.
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