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137 labs · 7 student voices
Faculties at Nagoya University ›
Hisashi Naito, Professor
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Prof. Naito studies discrete geometric analysis and geometric variational problems. Viewing the structure of a crystal as a graph of points and lines embedded in space, the lab constructs good crystal lattices from a geometric standpoint and studies them. Nonlinear partial differential equations on manifolds, derived from variational problems originating in differential geometry, are also objects of study. For small graduate-level classes, the professor wants to take computers and the mathematics related to them as themes, and hopes students will study with a balance of "theory and practice," realizing theory on the computer.
Taro Nagao, Professor
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Prof. Nagao studies the theory of random matrices and their applications. A random matrix is a matrix whose entries are random numbers; the concept was conceived in the field of mathematical statistics at the beginning of the 20th century. Today it is widely applied across many fields, including analytic number theory, elementary particle physics, solid-state physics, ecology, and financial engineering. The lab aims to deepen the fundamental theory by opening up new application areas, and to create a cycle in which that development in turn gives rise to new applications.
Makoto Nakashima, Associate Professor
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Associate Professor Makoto Nakashima studies probability theory, focusing especially on branching processes, a population model in biology. Probability theory here means measure-theoretic probability, in which probability is defined using measures. In polymer models, one of the objects of study, a phase transition appears in which the shape changes greatly through interaction with impurities. The professor is also interested in how the scaling limits of discrete models reveal connections to partial differential equations and stochastic partial differential equations.
Tomoki Nakanishi, Professor
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Professor Tomoki Nakanishi's lab studies the algebraic structures called cluster algebras. Cluster algebras are a class of commutative algebras introduced around 2000, and they generalize the commutative algebras that appear in Lie theory. They can be regarded as a kind of extension of root system theory, and they are being actively studied as algebraic and combinatorial structures that appear in many areas of mathematics. In the graduate school's list of research fields, the lab is classified under representation theory, infinite-dimensional integrable systems, and mathematical physics.
Yusuke Nakamura, Associate Professor
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Associate Professor Yusuke Nakamura's lab studies birational geometry, a branch of algebraic geometry. Birational geometry divides complex algebraic varieties into birational equivalence classes, and aims to find a well-behaved representative in each class. One method for finding such representatives is the minimal model program. The lab aims to solve the termination of flips problem, which concerns whether this program terminates, using singularity theory. The lab is also interested in applications of minimal model theory, and it also conducts research in pure combinatorics that has no direct connection to algebraic geometry.
Shin Nayatani, Professor
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Prof. Nayatani studies geometry from the viewpoint of differential geometry. He is mainly interested in conformal geometry and the geometry of spaces of negative curvature. Starting from research on the rigidity of discrete groups, he also studies discrete objects such as buildings, and combinatorial harmonic maps, which are a discrete version of harmonic maps. In the 2026 undergraduate thesis research, students will read a book on spectral geometry, which studies eigenvalues of the Laplacian in connection with properties such as the curvature of a shape, in a group reading format.
Henrik Bachmann, Associate Professor
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Prof. Bachmann studies a wide range of topics in number theory related to multiple zeta values and the theory of modular forms. Multiple zeta values are real numbers that naturally generalize the values of the Riemann zeta function, and they appear in many areas of mathematics and physics. The lab draws on methods from number theory, the theory of modular forms, and combinatorics, and often incorporates computer experiments using PARI/GP, Mathematica, and Sage into its research.
Masashi Hamanaka, Lecturer
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Prof. Hamanaka's research themes are particle theory and mathematical physics. Prof. Hamanaka is interested in the mathematics behind particle theory and string theory in general, and has worked on extending soliton theory and integrable systems to noncommutative spaces. In the small graduate classes, the plan is to focus on a unified understanding of soliton theory and integrable systems from the framework of string theory. The particle theory faculty of the graduate school, together with departments such as Physics, hold seminars with invited experts and study sessions on presenting papers, and graduate students also give presentations at the study sessions.
Takahiro Hayashi, Associate Professor
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Prof. Hayashi studies quantum groups and their representation theory. A quantum group is not a group, but if you look at it with a generous mind, it is an algebraic structure that is not entirely unlike a group. Quantum groups are deeply connected with many areas of mathematics, including mathematical physics, low-dimensional topology, combinatorics, and operator algebras. In recent years, Prof. Hayashi has been generalizing quantum groups further and exploring new connections with the representation theory of classical groups.
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.
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