Curriculum Vitae

Name
Toshiki Usui / 薄井 利基
Current Status
Ph.D. Student in Mathematics
Affiliation
Joint Graduate School of Mathematics for Innovation, Kyushu University
Email
toshiki.940@s.kyushu-u.ac.jp
Website
https://atodenaosu.com/
ORCID
https://orcid.org/atodesyutoku
GitHub
https://github.com/Totti95U

Research Interests

  • Complex Dynamics
  • Symbolic Dynamics

My research concerns the dynamics of complex polynomial maps, with particular interest in the combinatorial and geometric structure of the Mandelbrot set and its analytic continuation into Hénon maps. Especially, I am interested in the relationship between geometric structure of the Mandelbrot set and algebraic structure of shift spaces.

Education

2026–Present Ph.D. in Mathematics, Joint Graduate School of Mathematics for Innovation, Kyushu University. (Advisor: Prof. Ishii Yutaka)
2024–2026 M.Sc. in Mathematics, Joint Graduate School of Mathematics for Innovation, Kyushu University. (Advisor: Prof. Ishii Yutaka)
Thesis: Structure of 2-cascade decomposition for subshifts of finite type and its application to Hénon maps.
2022–2024 B.Sc. in Mathematics, Faculty of Science, Department of Mathematics, Kyushu University. (Advisor: Prof. Ishii Yutaka)
2017–2022 Title of Associate of Engineering, Five-year course in Department of Electrical and Electronic System Engineering, National Institute of Technology, Fukushima College. (Advisor: Prof. Koichi Koizumi)
Graduation Research: A Study on Evolutionary Algorithms for Solving Tangram Puzzles.
(original title: タングラムを解く進化的アルゴリズムに関する研究)

Publications and Preprints

  1. T. Usui, Structure of 2-cascade decomposition for subshifts of finite type and its application to Hénon maps (Submitted).

Other Publications

  1. T. Usui, R. Suzuki, K. Koizumi, and M. Ohtsuki, A Study of Evolutionary Algorithms for Solving Tangram, IPSJ SIG Technical Report, 2022-GI-47(4) (2022), 1–8.

    Abstract

    Tangram is a puzzle that duplicate a shape called silhouette with using other shapes called piece. Solving tangram with simple algorithm is infeasible because combination of each piece position and angle is enormously. Therefore, we made algorithms with evolutionary algorithms for solving tangram. As a result, the algorithms were able to solve simple tangrams that is using 4 pieces. By further research, algorithms solving difficult tangrams will come in front of us.

Talks

  1. Structure of decomposition by 2-cascades for subshifts of finite type and its relation to Hénon maps, 数論・力学系　若手研究集会, Kyushu University, Feb. 2026. Contributed talk.

  2. Structure of decomposition by 2-cascades for subshifts of finite type and its relation to Hénon maps, 2025年度 冬の力学系研究集会, Nihon University Seminar House in Karuizawa (日本大学軽井沢研修所), Jan. 2026. Contributed talk.

  3. Invariants in Symbolic Dynamics, The PNU – Kyushu Young Researchers Workshop on Mathematics for Industry, Kyushu University, Jan. 2026. Contributed talk.

  4. A Study of Evolutionary Algorithms for Solving Tangram, 47th Meeting of the IPSJ Special Interest Group on Game Informatics (GI-47), online, Mar. 2022. Contributed talk.

Awards, Fellowships and Funding

Teaching Experience

Teaching Assistant

  • 2026, Mathematics III (General Topology), Kyushu University.

  • 2025, Mathematics II (Topology of Euclidean and Metric Spaces), Kyushu University.

  • 2024, Fourier and Laplace Transforms and Partial Differential Equations, Kyushu University.

  • 2024, Mathematics II (Topology of Euclidean and Metric Spaces), .

Additional Teaching Experience

  • 2023–present, Programming Instructor, Programming School MiraigotoLab.
    Introductory programming in Minecraft/Scratch/Javascript for elementary and junior high school students.

Service and Outreach

Technical Skills

Programming
Python, Julia, TypeScript, C++
Typesetting
LaTeX, Typst, Microsoft Word
Languages
Japanese (native), English (fluent)