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33 labs · 9 student voices
Other departments in School of Science ›Faculties at Hokkaido University ›
Akira Sakai, Professor
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The Mathematical Sciences group pursues research in applied mathematics and mathematical sciences that connect with the other sciences. Like Boolean algebra and Turing's computing machine, mathematics has changed the workings of society while asking what thinking is. Building on partial differential equations, ergodic theory, nonlinear dynamical systems, and probability theory, each faculty member and graduate student pursues a theme of their own. Another feature is the wide range of styles, from theoretical research to research that uses computers to help analyze phenomena.
Yasuhide Numata, Professor
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Prof. Numata studies combinatorial objects that appear in representation theory and ring theory from the viewpoint of enumerative combinatorics. The main objects of study are Young diagrams, which control symmetric functions and irreducible representations. The lab is interested in objects in general that admit combinatorial arguments, and also looks at structures that appear in computational algebraic statistics and topological data analysis. For graduate studies, Prof. Numata is affiliated with the Graduate School of Information Science and Technology rather than the Graduate School of Science.
Keiji Matsumoto, Project Professor
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Prof. Matsumoto studies the theory of special functions, using geometric methods to investigate functions defined by integrals. Many functions have integral representations, including the gamma function, the beta function, zeta functions, and hypergeometric functions. By viewing these integrals as pairings between cohomology groups and homology groups, the lab understands the functions geometrically. The lab also works on finding new automorphic functions and automorphic forms through the study of period maps for families of algebraic varieties.
Genki Ouchi, Associate Professor
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Prof. Ouchi studies algebraic geometry, which investigates algebraic varieties. A space that can be described as the common zero set of several polynomials is called an algebraic variety. High-dimensional shapes are difficult to build physically or draw directly, but they can still be written down and reasoned about in the language of mathematics. In particular, he prefers to study Calabi-Yau varieties in a broad sense, such as K3 surfaces and holomorphic symplectic varieties.
Yuanqing Cai, Associate Professor
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Prof. Cai studies automorphic representations and their L-functions, in a field spanning number theory and representation theory. Automorphic representations and L-functions are objects that encode many properties of numbers, and they remain an active area of research today. In this field, a wealth of results has been found on the theta correspondence and the doubling method. Prof. Cai works on the theory of L-functions for classical groups, using a recently discovered extension of the doubling method.
Travis Scrimshaw, Associate Professor
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Prof. Scrimshaw studies how to express representation theory in the language of combinatorics. Representation theory is a field that uses linear algebra to study algebraic objects and to understand the symmetries of physical systems. Using Prof. Kashiwara's crystal theory, Prof. Scrimshaw works on representations of Kac-Moody Lie algebras and Lie superalgebras. Prof. Scrimshaw applies this to Schubert calculus, which deals with the geometry of subspaces of vector spaces, and also explores connections with physics and probability theory.
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.
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