The Department of Mathematics is organized mainly by the staffs in the Faculty of Science and the Faculty of Integrated Arts and Sciences. Research groups are divided into the following five fields: Algebra, Geometry and Topology, Mathematical Analysis, Probability Theory and Mathematical Statistics, and Geometric and Algebraic Analysis. Research subjects of the faculty members are listed below. But student research topics are not necessarily restricted to them. Foreign students receive the Doctor's degree constantly and guest researchers are invited from all over the world. The mathematics library is one of the best in Japan and a well-organized computer network is available.
Admission Policy of Department of Mathematics
We hope to have students who are eager to investigate mathematical truths, who have a strong sense of purpose in mathematical research activities, and who proactively and voluntarily participate in such activities.
This research group investigates the following subjects:
(1) Number Theory : algebraic number theory, arithmetic geometry, arithmetic fundamental groups, arithmetics of moduli spaces.
(2) Algebraic Geometry : positive characteristic geometry, K3 surfaces, derived category of sheaves, Chow groups, motives of algebraic varieties, singularities, moduli space, enumerative geometry.
(3) Applied Algebra : random number generation, coding theory, cryptography, algebraic algorithm.
KIMURA Shun-ichi (Professor) : Algebraic Geometry, Intersecion Theory, Motives.
SHIMADA Ichiro (Professor) : Topology of Algebraic Varieties, K3 Surfaces, Lattice Theory.
MATSUMOTO Makoto (Professor) : Random Number Generation, Quasi-Monte Carlo, Applied Algebra, Arithmetic Fundamental Group.
TAKAHASHI Nobuyoshi (Associate Professor) : Birational Geometry and Enumerative Geometry of Open Algebraic Varieties, Motivic Zeta.
HIRANOUCHI Toshiro (Assistant Professor) : Higher Class Field Theory, Algebraic K-theory, Ramification Theory.
IIJIMA Yu (Assistant Professor (Special Appointment)) : Outer Galois Representation, Algebraic Fundamental Group.
MIYATANI Kazuaki (Assistant Professor (Special Appointment)) : Crystalline Cohomology, Hypergeometric Functions over Finite Fields.
GEOMETRY and TOPOLOGY
Topology is a discipline of mathematics which considers new purposes and new ways of thinking as important. Geometry is deeply related to physics and promotes progress in mathematics. Research subjects of the geometry group are the differential geometry and representation theory in the context of the theory of Lie groups and differentiabl manifolds. The main subject of the topology group is topology of manifolds, in particular surfaces, knots, 3-dimensional manifolds, and 4-dimensional manifolds are studied from various points of view - view from algebra, topology, geometry differential topology. Geometry related to infinite analysis as well as themes from quasi-crystals, information geometry and computational geometry are also studied.
SAKUMA Makoto (Professor) : Knot Theory, Low Dimensional Topology, Hyperbolic Geometry.
TAMARU Hiroshi (Professor) : Differential Geometry, Homogeneous Spaces, Symmetric Spaces, Solvmanifold.
TERAGAITO Masakazu (Professor from the Graduate School of Education) : Topology, 3-manifolds and Knots, Dehn Surgery.
KODA Yuya (Associate Professor): Topology, 3-manifolds and Knots.
DOI Hideo (Lecturer) : Geometry of Field Theory, Representation Theory.
OKUDA Takayuki (Assistant Professor) : Discontinuous Group, Nilpotent orbit, Algebraic Combinatorics on Compact Symmetric Spaces.
YASUI Kouichi (Assistant Professor) : Topology, 4-manifolds, Contact 3-manifolds.
Various phenomena in natural science are described in terms of mathematical analysis such as dynamical systems and differential equations and they are studied by means of the most advanced methods in real analysis, complex analysis, functional analysis, and so on. To be concrete research subjects of this group are dynamical systems, differential equations, nonlinear analysis, complex analysis (including complex dynamics), asymptotic analysis, singular partial differential equation, Borel summability, special function theory, potential theory, and scattering theory.
KAWASHITA Mishio (Professor) : Partial Differential Equations, Scattering Theory.
YOSHINO Masafumi (Professor) : Analytic Partial Differential Equations, Small Denominators, Complex Asymptotic Analysis, Dynamical Systems.
SHIMOMURA Tetsu (Professor from the Graduate School of Education) : Potential Theory, Sobolev Spaces.
TAKIMOTO Kazuhiro (Associate Professor) : Nonlinear Elliptic and Parabolic Partial Differential Equations.
HIRATA Kentaro (Associate Professor) : Potential Theory, Semilinear Elliptie Equation.
KURA Takeshi (Assistant Professor) : Potential Theory on Riemannian Manifolds.
PROBABILITY THEORY and MATHEMATICAL STATISTICS
The purpose of research in this field is to analyze random phenomena in nature and society. The probability theory group studies stochastic processes, stochastic analysis, mathematical finance, insurance mathematics, and the probabilistic approach to mathematical physics. The mathematical statistics group studies multivariate analysis, statistical inference, model selection, design of experiments, asymptotic statistical theory, nonparametric methods, time series, computational methods, data analysis, random number generation and other topics.
INOUE Akihiko (Professor) : Financial and Insurance Mathematics, Stochastic Processes.
WAKAKI Hirofumi (Professor) : High-dimensional Data Analysis, Asymptotic Expansion, Longitudinal Data Analysis.
IWATA Koichiro (Associate Professor) : Probabilistic Method on Mathematical Physics.
YANAGIHARA Hirokazu (Associate Professor) : Sample Distribution Theory under Nonnormality.
YAMATO Yuiti (Assistant Professor) : Real Analysis with Infinite Degree of Freedom, Stochastic Calculus of Variations.
HASHIMOTO Shintaro (Assistant Professor (Special Appointment)) : Bayesian Inference, Asymptotic Theory, Non-regular Estimation.
GEOMETRIC and ALGEBRAIC ANALYSIS
This research group investigates the following subjects:
(1) Algebra : Algebraic Geometry, Derived Category, Number Theory, Iwasawa Theory.
(2) Geometry : Theory of Lie Groups and Homogeneous Spaces, Differential Geometry, Discrete Geometry, Complex Geometry, Exterior Differential Systems.
(3) Analysis : Several Complex Variables, Pluripotential Theory. Differential Equations, Nonlinear Waves.
AGAOKA Yoshio (Professor) : Theory of Riemannian Submanifolds, Connections on Principal Fibre Bundles, Tilings, Discrete Geometry.
ABE Makoto (Professor) : Several Complex Variables, Complex Geometry.
ISHII Akira (Professor) : Algebraic Geometry; Deformation, Moduli and Derived Category of Sheaves.
MIZUMACHI Tetsu (Professor): Nonlinear Partial Differential Equations of Dispersive Type, Nonlinear Waves.
SHIBUYA Kazuhiro (Associate Professor) : Exterior Differential Systems, Finsler Geometry.
KAWAMURA Hisa-aki (Assistant Professor) : Number Theory, Arithmetic Geometry, Hida Theory, Iwasawa Theory.
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