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Staff Introduction

MATSUTANI, Shigeki / Guest Professor

   I have studied numerical computations of physical phenomena associated with Industrial problems, and also investigated algebraic curves, real plane curves, application of number theory to physics, and so on.
   I had studied the industrial mathematics in Canon Inc. for decades, and continue its studies, especially conductivity of percolation systems, mathematical modeling of surfaces of multiphase fluid, geometry of random particle systems, and so on.
   Besides the studies associated with industrial problems, I have investigated the sigma functions related to the algebraic curves including hyperelliptic curves, which are generalization of Weierstrass’s elliptic sigma function. The purpose of this study is to find the algebraic and geometrical properties of the sigma functions so that we can apply the sigma function theory to the other fields, e.g., particle physics, generalized elastic curves, cryptography, coding theory and so on. Recently I have studied the Jacobi inversion problems of strata in the Jacobi varieties, and sigma functions for space curves; the strata and the space curves are related to singularities.
    As an application of the hyperelliptic sigma functions, I have studied the quantized elastica problem which is generalization of Euler’s elastica problem associated with the shape of DNA. I have also considered algebraic properties of conductivity (capacity) of percolation systems by applying the meromorphic function theory to such random systems.  
Furthermore, I am very interested in the algebraic structures and number theoretic structure in physical problems, and studied the relation between Gauss sum and Talbot effects in optics, and sheaf theoretic approach in numerical computations.

   Based on  experiences of research and development in a company and of studying pure mathematics, it is no doubt that Mathematics including pure and applied mathematics has the very strong power to express physical and social phenomena as the same as the era of Euler and Gauss. I would like to proceed the unification of technology, science and mathematics.

Keywords Industrial Mathematics, Mathematical Modeling of Physical Phenomena, Application of Abelian Function Theory, Sigma Functions of Algebraic Curves, Quantized Elastica, Application of Number Theory to Physics
Faculty , Department Institute of Mathematics for Industry , Visitors Section