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703 labs · 48 student voices
Masahito Hayashi, Professor
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Prof. Hayashi is a Professor in the fields of information theory, quantum information theory, and quantum networks. The faculty profile lists quantum information theory, quantum statistical inference, and information theory as topics for the small-group class in the Master's program. The profile says that, because this is a relatively new research field, students can reach the level of writing research papers earlier than in other fields, depending on their own aptitude and effort. The faculty profile says that, except in January, Prof. Hayashi is on research leave from Nagoya University and working at Southern University of Science and Technology; Nagoya University students are supervised mainly online within the scope of an academic exchange agreement, and only students who can handle the minimum on their own are accepted.
Tomoyuki Hisamoto, Associate Professor
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Prof. Hisamoto uses partial differential equations to study the geometric properties of algebraic varieties. Prof. Hisamoto is particularly interested in the relationship between canonical metrics on manifolds and K-stability. Recently, Prof. Hisamoto has also become interested in Fano varieties that are not K-stable, and works on research using parabolic partial differential equations. In the seminar for undergraduate thesis research, students learn Riemann surfaces and the theory of complex manifolds; in the small-group class in graduate school, students work on problems matching their own interests and write a paper.
Toshiaki Hishida, Professor
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The lab of Professor Toshiaki Hishida studies nonlinear partial differential equations, in particular the Navier-Stokes equations, the fundamental equations of fluid dynamics. Within the physical settings of different domains, such as flow past an object or flow through a gap between walls, the lab seeks to clarify the mathematical properties of the equations and the behavior of their solutions. In the small classes of the master's program, the topics include the fundamental theory of second-order elliptic equations and the mathematical analysis of stationary and nonstationary problems for the Navier-Stokes equations.
Hiroshi Hirai, Professor
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In the lab of Professor Hiroshi Hirai, research covers optimization, algorithms, and discrete mathematics. The lab is attempting to develop the theory of optimization and algorithms on metric spaces of nonpositive curvature, which have properties similar to Euclidean space. It also works on combinatorial optimization that uses computations such as determinants, and on compact representations of lattices and related algorithms. For undergraduate thesis research, students read texts on optimization, algorithms, and combinatorics in a reading group, and the lab states that programming ability is not required.
Kazuhiro Fujiwara, Professor
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Professor Kazuhiro Fujiwara studies arithmetic algebraic geometry, a field that spans both number theory and algebraic geometry. The objects of study are varieties over finite fields and rings of integers. The methods tend to be abstract, but many of the results obtained can be seen concretely. There is a remarkable phenomenon in which arithmetic properties appear as analytic properties of analytic functions called L-functions, and the lab is currently studying the connection between arithmetic varieties and L-functions. The lab also places emphasis on establishing non-abelian class field theory, a generalization of the classical class field theory that dates back to Teiji Takagi and Artin.
Hidekazu Furusho, Professor
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Prof. Furusho specializes in number theory and conducts research from the perspective of fundamental groups. Prof. Furusho re-examines objects such as Galois representations, periods, and p-adic periods from the viewpoint of fundamental groups rather than cohomology. In mathematics, one way to advance a subject is to move to higher dimensions or to p-adicize it, but Prof. Furusho's motto is "Make it multiple!" Prof. Furusho's doctoral thesis developed the theory of p-adic multiple zeta values.
Lars Hesselholt, Professor
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Prof. Hesselholt studies algebraic K-theory and algebraic topology. In algebraic K-theory, a topological space is assigned to a ring, and its homotopy groups are called the algebraic K-groups. Understanding the structure of these groups is a deep problem, and in some cases it is equivalent to a conjecture in number theory. Topics listed for the small-group classes in the master's program include de Rham cohomology, characteristic classes, and algebraic K-theory.
Shinichiroh Matsuo, Associate Professor
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Prof. Matsuo studies geometric analysis and differential geometry. The professor's three major research themes are "infinity, space, and complexity." From the viewpoint of infinite-dimensional geometry, the professor has studied the spaces formed by solutions of nonlinear partial differential equations. Recently, the professor has become interested in the discretization of space and works on mathematics arising from lattice gauge theory. In the master's program, to acquire the typical methods for nonlinear problems in geometric analysis, students begin by choosing one landmark paper and reading it thoroughly together.
Kazuhiko Minami, Associate Professor
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Prof. Minami studies statistical mechanics and mathematical physics. The professor investigates the properties of models in which spins are placed on lattice points and interact quantum mechanically. Centered on exact solutions of one-dimensional quantum spin chains, the lab works on solvable lattice models.
Hitoshi Moriyoshi, Professor
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Prof. Moriyoshi is interested in the study of manifolds in general, and works on topology and differential geometry. The professor is particularly interested in generalizations of the Atiyah–Singer index theorem, which connects the analytic invariants and the geometric invariants of manifolds. The professor believes the appeal of the index theorem lies in the way it brings together fields of mathematics with entirely different backgrounds. The seminar for undergraduate thesis research takes "Introduction to Geometry and Manifolds" as its theme. In a reading format where students take turns presenting, they learn the basic knowledge needed to study manifolds.
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