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Introduction of Laboratory ( Mathematics / Language )

MAEDA Lab.

Research Field: [Mathematics] Algebraic Geometry

Algebraic Variety/Singular Points/Ramification

Analyse the arithmetic and geometric structure via singularities

Every conic section, i.e. ellipse, parabola or hyperbola, is a plane curve defined by a quadratic equation. The geometric object defined by some algebraic equations is called algebraic variety. Sometimes the defining equations may have multiple roots and these cause singular locus on the variety.
We study the relation between the global structre of the variety and the singular locus including its very infinitely near structure.

MAEDA Hironobu Associate Professor
MAEDA Hironobu

NAOI Lab.

Research Field: [Mathematics] Representation theory

quantum group  symmetry  matrices

Analyze symmetries via matrices

Representation theory is the field of mathematics in which symmetries are studied by representing them in forms of matrices.
In Naoi LAB, we study the mysterious symmetries called "quantum groups" in the view of representation theory.

NAOI Katsuyuki Associate Professor
NAOI Katsuyuki

NAKAZONO Lab.

Research Field: [Mathematics] Integrable Systems

Symmetry  Recurrence Relation  Special Functions
NAKAZONO Lab. Image1
Circle Patterns of Schramm Type
NISHIDA Lab. Image2
Solitons

Symmetries and geometric structures of difference equations

Differential and difference equations, which have symmetries or an infinite number of conserved quantities, can be reduced to liner problems, etc. are called integrable systems.
In NAKAZONO Lab., we study symmetries and geometric structures of integrable systems.

NAKAZONO Nobutaka Lecturer
NAKAZONO Nobutaka