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46 labs · 0 student voices
Other departments in School of Science ›Faculties at Nagoya University ›
Sho Tanimoto, Professor
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Prof. Tanimoto studies algebraic geometry and arithmetic geometry. For equations with rational coefficients, the field that investigates solutions whose coordinates are rational numbers is called Diophantine geometry, and it has been studied since the time of ancient Greece. In modern mathematics, rational solutions are regarded as points on the geometric object (algebraic variety) defined by the equation, and are studied with the methods of algebraic geometry. The professor has applied methods from higher-dimensional algebraic geometry, which have developed in recent years, to this problem and has achieved results.
Mayu Tsukamoto, Associate Professor
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Prof. Tsukamoto studies the representation theory of algebras. An algebra is a ring that also has the structure of a vector space. Rather than studying an algebra directly, the approach of representation theory is to study the structure of the entire collection of modules that reflects its properties (the module category). Established in the 1970s, this is a relatively new field that continues to develop in close connection with commutative ring theory, algebraic geometry, and the representation theory of Lie algebras and quantum groups.
Yutaka Terasawa, Associate Professor
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Associate Professor Terasawa conducts research that mathematically analyzes the fundamental equations describing the motion of fluids. The main subjects are the Navier–Stokes equations, which describe the motion of incompressible viscous fluids, and their generalizations. Motions described by the generalized equations include those of granular materials and non-Newtonian fluids. Recently, Associate Professor Terasawa has been particularly interested in the two-layer fluid problem for non-Newtonian fluids.
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.
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