TOMO MURAO

Last Updated :2026/09/03

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Associate Professor
Web Site
https://sites.google.com/view/tmurao
E-mail
tmuraohiroshima-u.ac.jp
Self-introduction
My research focuses on low-dimensional topology, in particular knot theory.

Basic Information

Major Professional Backgrounds

  • 2025/.4, Hiroshima University, Mathematics Program, Graduate School of Advanced Science and Engineering, Associate Professor
  • 2022/.1, 2025/.3, Kochi University, Science and Technology Unit, Natural Science Cluster, Research and Education Faculty, Assistant Professor
  • 2020/.9, 2022/.1, Waseda University, Global Education Center, Lecturer
  • 2020/.4, 2020/.8, Waseda University, Global Education Center, Assistant Professor
  • 2018/.8, 2020/.3, University of Tsukuba, JSPS Research Fellow PD
  • 2018/.4, 2018/.7, University of Tsukuba, JSPS Research Fellow DC

Educational Backgrounds

  • University of Tsukuba, Japan, 2016/.4, 2018/.7
  • University of Tsukuba, Japan, 2014/.4, 2016/.3
  • University of Tsukuba, Japan, 2010/.4, 2014/.3

Academic Degrees

  • University of Tsukuba
  • University of Tsukuba

Educational Activity

  • [Bachelor Degree Program] School of Science : Mathematics : Mathematics
  • [Master's Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program
  • [Doctoral Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Geometry

Research Keywords

  • topology, low-dimensional topology, low-dimensional manifold, knot, handlebody-knot, quandle

Affiliated Academic Societies

  • The Mathematical Society of Japan

Educational Activity

Course in Charge

  1. 2026, Liberal Arts Education Program1, 2Term, Linear AlgebraI
  2. 2026, Liberal Arts Education Program1, 1Term, Introductory Seminar for First-Year Students
  3. 2026, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  4. 2026, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  5. 2026, Undergraduate Education, First Semester, Special Lectures in Mathematics(Quandles and knot invariants)
  6. 2026, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
  7. 2026, Graduate Education (Master's Program) , Year, Topology Seminar
  8. 2026, Graduate Education (Master's Program) , 3Term, Topics in Geometry D
  9. 2026, Graduate Education (Master's Program) , First Semester, Special Lectures in Mathematics

Research Activities

Academic Papers

  1. (Co)homology of racks and multiple group racks for compact oriented surfaces in the 3-sphere, Internat. J. Math., 36(2), 2025
  2. 4-move inequivalent handlebody-links and f-twisted Alexander matrices, Osaka J. Math., 61(4), 601-616, 2024
  3. On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots, Beitr. Algebra Geom., 64(3), 689-719, 2023
  4. Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs, Topology Appl, 301, 2021
  5. The tunnel number and the cutting number with constituent handlebody-knots, Topology Appl., 292, 2021
  6. Linear extensions of multiple conjugation quandles and MCQ Alexander pairs, J. Algebra Appl., 20(3), 2021
  7. A multiple group rack and oriented spatial surfaces, J. Knot Theory Ramifications 29, 29(7), 2020
  8. A relationship between multiple conjugation quandle/biquandle colorings, Kobe J. Math., 36(1--2), 57-78, 2019
  9. On connected component decompositions of quandles, Tokyo J. Math., 42(1), 63-82, 2019
  10. The Gordian distance of handlebody-knots and Alexander biquandle colorings, J. Math. Soc. Japan, 70(4), 1247-1267, 2018
  11. On bind maps for braids, J. Knot Theory Ramifications, 25(2), 2016

Invited Lecture, Oral Presentation, Poster Presentation

  1. On quandle cocycle invariants and link homotopy, Tomo Murao, Topology Seminar in Grenoble, 2025/09/26, With Invitation, English, Grenoble Alpes University

External Funds

Acceptance Results of Competitive Funds

  1. 2026/04/01, 2031/03/31
  2. 2021/.4, 2026/.3
  3. 2020/.9, 2023/.3
  4. 2018/.4, 2020/.3