MATHEMATICS

The Mathematics Major is organized mainly by the staffs in the Faculty of Science and the Faculty of Integral Arts and Sciences. Research groups are divided into the following fields : Algebra, Geometry and Topology, Mathematical Analysis, Probability Theory and Mathematical Statistics, and Geometric and Algebraic Analysis. Research subjects are listed below. However, students are not required to choose their research topics from these. Foreign students receive the Doctor's degree constantly and guest professors have been invited from Germany, Finland and China recently. The mathematics library is one of the best in Japan and a well-organized computer network is accessible. Every graduate student may use both freely.

ALGEBRA

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.

ISHII Akira (Associate Professor) : Algebraic geometry; deformation, moduli and derived category of sheaves.

TAKAHASHI Nobuyoshi (Associate Professor) : Birational geometry and enumerative geometry of open algebraic varieties, Motivic zeta.

HIRANOUCHI Toshiro (Assistant Professor) : Arithmetic fundamental groups, Higher class field theory, Algebraic K-theories.

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 differential manifolds. The subjects of the topology group are algebraic topology and topology of manifolds, in particular the theory of 3 and 4 dimensional manifolds, knots, foliations, singularities, and characteristic classes. Geometry related to infinite analysis as well as themes from quasi-crystals, information geometry and computational geometry are also studied.

KAMADA Seiichi (Professor) : Geometric topology, Knot and braid theory.

SAKUMA Makoto (Professor) : Knot theory, Low dimensional topology, Hyperbolic geometry.

TERAGAITO Masakazu (Professor) : Topology, 3-manifolds and knots, Dehn surgery.

TAMARU Hiroshi (Associate Professor) : Differential geometry on homogeneous spaces, symmetric spaces, solvmanifolds, cohomogeneity one actions, Einstein manifolds.

DOI Hideo (Associate Professor (Lecturer)) : Geometric of field theory, Representation theory.

KOWATA Atsutaka (Assistant Professor) : Differential geometry, Spherical functions on homogeneous spaces.

YASUI Kouichi (Assistant Professor) : Topology of 4-manifolds.

MATHEMATICAL ANALYSIS

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, value distribution, special function theory, potential theory, and scattering theory.

NAGAI Toshitaka (Professor) : Differential equations, Nonlinear analysis.

YOSHINO Masafumi (Professor) : Analytic partial differential equations, Small denominators, Complex asymptotic analysis, Dynamical systems.

KAWASHITA Mishio (Associate Professor) : Partial differential equations, Scattering theory.

TAKIMOTO Kazuhiro (Associate Professor) : Nonlinear elliptic and parabolic partial differential equations.

SHIMOMURA Tetsu (Associate Professor) : Potential theory, Sobolev spaces.

KURA Takeshi (Assistant Professor) : Potential theory on Riemannian manifolds.

SASAKI Yoshikatsu (Assistant Professor) : Value distribution, Special function theory.

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, computational methods, data analysis and other topics.

INOUE Akihiko (Professor) : Financial and insurance mathematics, Stochastic processes.

WAKAKI Hirofumi (Professor) : Multivariate statistical analysis, Asymptotic theory.

IWATA Koichiro (Associate Professor) : Probability theory and its application to 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.

KATO Kengo (Assistant Professor) : Mathematical statistics.

SAITO Mutsuo (Assistant Professor) : Pseudorandom number generators, cryptography.

GEOMETRIC and ALGEBRAIC ANALYSIS

This research group investigates the following subjects:
(1) Geometry : Theory of Lie Groups and Homogeneous Spaces, Differential Geometry, Discrete Geometry, Complex Geometry.
(2) Algebra : Representation Theory of Infinite dimensional Lie Algebras and Quantum Groups, Mathematical Physics, Number Theory, Iwasawa Theory.
(3) Analysis : Several complex variables, Harmonic analysis on Homogeneous Spaces, Nonlinear differential equations.

AGAOKA Yoshio (Professor) : Theory of riemannian submanifolds, Connections on principal fibre bundles.

ABE Makoto (Professor) : Function theory of several complex variables, Analytic spaces.

KONNO Hitoshi (Associate Professor) : Representation theory of infinite dimensional Lie algebras and quantum groups, Mathematical physics.

TAKAHASHI Hiroki (Associate Professor) : Number theory, Iwasawa theory.

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