Mathematical Sciences

OWe are interested in mathematical sciences, especially mathematics (algebraic geometry, invariant theory, and moduli of representations) and statistics (decision trees, statistics for nursing research, and so on).
Our topics are:
(1)We construct several types of moduli schemes of representations for each group or monoid.
We also describe moduli of representations and investigate (topological) properties of them.
(2)We deal with several problems on statistics or statistics for nursing research. For example, we are going to
make a mathematical formulation on decision trees.

An expression of a given group as matrices is called a group representation.
By regarding a representation as a point, we can consider the set of representations as a geometrical figure.
Such figure is called moduli of representations, which can be constructed in terms of algebraic geometry.
Moduli of representations is our main theme.

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