My purpose in this fellowship program is to study the recent works of Yusuke Kiriu and Mikami Hirasawa on topology from a point of view of computer graphics, primarily focusing on the visual simulation of clouds.
The themes of my research are the following topics;
Bunraku, also known as Ningyō jōruri, is the traditional Japanese puppet theater founded in Osaka in 1684. In this 14 years, I worked at National Bunraku Theatre to maintain these puppets, and I retired. My main purpose is to discuss the possibilities of character animation in the context of computer graphics.
My purpose in this fellowship program is to assist the recent works of Yusuke Kiriu and Mikami Hirasawa on formal language and formalizations in mathematics, particularly from the view point of geometric structures and combinatorial structures of 3-manifolds.
I study a formalization of mathematics by means of logical methods. Key objects in my research area are mathematical theories, as naive set theories and truth theories, with circularity in non-classical logics. The purposes during this fellowship program are to make a contribution to a studio phones's research project by giving advices from logical point of view, to help an its researcher to formalize non-formalized ideas in terms of logic and category theory, and to give a new insight for them with Yusuke Kiriu.
I study a commutative ring of positive characteristic. Key objects in my research area are a singularity called the F-purity, an invariant called the F-pure threshold, and the test ideal, which are defined for a ring via its Frobenius morphism. The purpose during this fellowship program is to represent them in terms of formal language and category theory, and to give a new insight for them with Yusuke Kiriu.
My purpose in this fellowship program is to assist the recent works of Yusuke Kiriu and Mikami Hirasawa on some formulations in low dimensional topology and computer graphics, particularly from the viewpoint of Morse Theory and the Theory of Singularities of Differentiable Maps.
The theme of my research is to assist the recent works of Yusuke Kiriu and Mikami Hirasawa for some formulations on low dimensional topology, particularly from the viewpoint of Heegaard splittings and Morse functions on 3-manifolds.
Let K be a knotted circle in the 3-space. In the context of low-dimensional topology, it is known that there exists a 2-sided surface whose boundary coincides with K. Using such surfaces, one can calculate various topological invariants of knots, such as Alexander polynomials, determinants, and signatures. Essential algorithms which deal with such objects are desired. For clear understanding of them, we study their algorithm via formal language and category theory.
Following researches about hyperbolic geometry done with Yusuke Kiriu, our interest spreads across several fields of mathematics. Under this fellowship program Yusuke Kiriu and I will put together our current interests into articles.
I defined a new polynomial invariant for a given link diagram in three-dimensional space when I was a student of doctor course in Graduate School of Mathematics, Nagoya University. This link invariant is Poincare polynomial associated to a homology which is a generalization of Khovanov-Rozansky link homology using matrix factorizations. I study a structure of an algorithm to compute this polynomial link invariant in the context of computer language, especially, further possibilities of this algorithm in the context of formal language.