7.Mizuki FUKUDASenior Postdoctoral Researcher
(Kotorii Group)

Specially Appointed Associate Professor, Hiroshima University

My research lies in low-dimensional topology, with a particular focus on knot theory in dimensions three and four. A central theme of my work is the interplay between low-dimensional and high-dimensional topology. I study branched twist spins and their generalizations — families of knotted spheres in 4-space constructed via periodic group actions — and investigate how geometric symmetry is encoded in algebraic invariants such as elementary ideals and knot quandles. A guiding question is how classical 3-dimensional knot theory informs, and is informed by, the richer geometry of 4-manifolds. Alongside this, I have a strong interest in the mathematics of textile structures. Weaves — doubly periodic arrangements of strands in 3-space — provide a rich source of topological objects connecting knot theory, surface topology, and the geometry of periodic structures. I am currently developing a framework that relates singly and doubly periodic weaves through boundary-sum constructions, with the aim of bringing topological tools to bear on the classification of textile patterns.

Mentor ：Yuka Kotorii 　　
Co-Mentor ：Katsuya Inoue　
Co-Mentor ： Elisabetta Matsumoto　　

What I like about my science
What I find most exciting in mathematics is the moment when geometric intuition and rigorous theory illuminate each other. A calculation can reveal structure that was invisible to the eye, and a simple physical object — like a woven fabric — can turn out to carry deep topological content. That gap between the tangible and the abstract is what keeps me doing mathematics.