Tatsuki Hayama Research Group: "Mathematics (Complex Geometry), Application of Mathematics to Design and Art"

2025.06.26

Tatsuki Hayama, Associate Professor, Faculty of Environment and Information Studies; Committee Member, Graduate School of Media and Governance

Area of Specialization: Mathematics (Complex Geometry), Application of Mathematics to Design and Art

I have been researching the theory of what are known as Lie groups in mathematics. In the first year of university, students learn linear algebra, and a Lie group is a collection of matrices with properties such as "preserving length" or "having a determinant of 1." While possessing properties as transformations of geometric figures, they themselves have geometric characteristics, making them a very important subject of study in mathematics at the intersection of algebra, geometry, and analysis.

Separately, I have also been engaged in research applying mathematics to art and design through computer graphics (CG). CG is a field with a high affinity for mathematics, and a wide range of mathematical concepts are utilized within it. For instance, the aforementioned Lie groups are used to express shape deformations and movements. To date, I have been involved in projects such as temple renovations, research and development of Nishijin-ori textiles, and collaborations with artists and designers.

Throughout my university and graduate school years, I received a conventional mathematics education. Mathematics is fundamentally a cumulative discipline, a field where one follows in the footsteps of predecessors stretching back to ancient Greece, only becoming ready for research around the time of a master's degree. In mathematics department seminars, a precise understanding of books and papers is required, and it is common to spend hours discussing at the blackboard to understand a single page of a proof (and often, to continue pondering without fully grasping it...). Furthermore, mathematics is often researched as a solo endeavor. Just as a sage enters a deep spiritual world through meditation, a mathematician delves into the world of mathematics through immersion. The reason many anecdotes about mathematicians seem otherworldly is due to this immersion in the transcendent world of mathematics.

There is generally a large gap between "mathematics for mathematics' sake," which is built upon this traditional history, and "mathematics for application," which is used in technologies like engineering and information science. My research group's mission is to bridge these two by "creating from mathematics." While it is becoming increasingly difficult to find points of contact between modern, highly abstract mathematics and the act of "creating," we unearth the new possibilities dormant within and implement mathematical theories using computers. As a keyword to represent this, we have adopted "xMath." This is derived from XD (X-Design), one of the research areas of the Graduate School of Media and Governance, and it aims to realize the unknown, extreme, experimental, cross-disciplinary, and expressive aspects implied by "x" through mathematics.

SFC is a very unique place, where students with strong mathematical abilities who have studied math independently and go on to graduate school in mathematics coexist with students possessing high technical and expressive skills who are active in the media art scene while still enrolled. Although these two types of students may not seem to interact much in their daily lives, I hope to create a space within the research group where they can intersect and generate something new. As this is only the second year of the research group, and my own experience is limited to mathematics department seminars, I am still finding my way. However, I look forward to shaping the research group together with the students.

In the research group, we have collaborated with the painter Yuki Yamamoto to develop a painting creation system using 3DCG with the UNITY game engine ( Implementation: Reo Tanaka ). This work was exhibited in an off-campus gallery as a collaboration with the Hayama Lab. We have also conducted book-reading circles, paper surveys, and study sessions on 3DCG software. In the spring semester of 2025, we are advancing research and development for an on-campus gallery exhibition in October. Many members of the lab can use 3DCG software at a professional level, and in accordance with the principle of "learning while teaching, teaching while learning," I also learn a great deal from them. We are looking for people who are interested in connecting mathematics with craftsmanship and creative work!

Tatsuki Hayama, Associate Professor, Faculty of Environment and Information Studies; Committee Member, Graduate School of Media and Governance - Faculty Profile