Kyushu University [Shizuo Kaji (Professor) Institute of Mathematics for Industry, Division for Intelligent Societal Implementation of Mathmatical Computation]

My research interests are primarily in the areas of algebraic topology. More specifically, I study spaces with group actions, which exhibit a rich connection to algebraic/combinatorial objects such as graphs and polynomials. I am interested in this correspondence between topology and algebra/combinatorics, and I study topological problems through algebro-combinatorial techniques and vice versa. I am also working on applications of topology to various fields such as computer graphics.

Research

Research Interests

My research interests are primarily in the areas of algebraic topology. More specifically, I study spaces with group actions, which exhibit a rich connection to algebraic/combinatorial objects such as graphs and polynomials. I am interested in this correspondence between topology and algebra/combinatorics, and I study topological problems through algebro-combinatorial techniques and vice versa. I am also working on applications of topology to various fields such as computer graphics and data analysis.
keyword : topology, industrial maths, shape processing, data analysis
2008.04～2029.01.

Academic Activities

Reports

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Papers

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Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves, Nonlinear Systems and Their Remarkable Mathematical Structures. Volume 2, CRC Press, https://doi.org/10.1201/9780429263743, 2019.12.

Soojin Cho, Suyoung Choi, Shizuo Kaji, Geometric representations of finite groups on real toric spaces, Journal of the Korean Mathematical Society, 10.4134/JKMS.j180646, 56, 5, 1265-1283, 2019.01, We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces X^R and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of X^R. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties..

Works, Software and Database

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Presentations

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