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157 labs · 25 student voices
Faculties at Hokkaido University ›
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.
Naofumi Honda, Professor
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Prof. Honda works in algebraic analysis, focusing on the classification problem for holonomic systems (maximally overdetermined systems) with irregular singularities. Algebraic analysis is a field that combines analysis and algebra to approach a wide range of problems, and it was initiated by Japanese researchers. Holonomic systems are higher-dimensional systems of equations with properties similar to systems of ordinary differential equations in one variable, and they have influenced many areas of mathematics. For regular singularities, results based on the Riemann-Hilbert correspondence are known, but for irregular singularities, entirely different phenomena such as the Stokes phenomenon occur.
Tadahiro Miyao, Professor
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Prof. Miyao studies the mathematical structures of the diverse phenomena that appear in condensed matter physics. The tools are methods from analysis, such as operator algebras, stochastic analysis, and spectral analysis. The aim is not only to elucidate phenomena but also to deepen the theories used for that purpose. Keywords include quantum field theory, quantum statistical mechanics, and topological phases.
Yuhei Suzuki, Associate Professor
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Prof. Suzuki studies operator algebras, especially C*-algebra theory. C*-algebra theory is a system that provides a framework for understanding infinite-dimensional, noncommutative structures. When studying structures such as groups, topological dynamical systems, and metric spaces, C*-algebras often appear naturally as a powerful tool. Rather than such applications, Prof. Suzuki is interested in developing new insights and phenomena in C*-algebra theory itself.
Takahiro Hasebe, Associate Professor
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Prof. Hasebe studies probability theory, combinatorics, graph theory, functional analysis, complex analysis, and representation theory, with probability theory at the center. Particular emphasis is placed on noncommutative probability (free probability). This field is something like a fusion of all the fields listed above, and Prof. Hasebe writes that it suits students who like mathematics broadly without narrowing their specialization too much. Current interests are free probability, branching processes, and topology optimization.
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