KAI ISHIHARA

Last Updated :2025/07/05

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
E-mail
xishiharhiroshima-u.ac.jp

Basic Information

Academic Degrees

  • Saitama University
  • Saitama University

Research Fields

  • Mathematical and physical sciences;Mathematics;Geometry

Research Keywords

  • Knots, Topology

Educational Activity

Course in Charge

  1. 2025, Liberal Arts Education Program1, 2Term, CalculusI
  2. 2025, Undergraduate Education, 3Term, Fundamental Concepts of Mathematics II
  3. 2025, Undergraduate Education, 3Term, Exercises in Fundamental Concepts of Mathematics II
  4. 2025, Undergraduate Education, 1Term, Geometry C
  5. 2025, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  6. 2025, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  7. 2025, Undergraduate Education, First Semester, Special Lectures in Mathematics(On trace-free character varieties)
  8. 2025, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
  9. 2025, Graduate Education (Master's Program) , Year, Topology Seminar
  10. 2025, Graduate Education (Master's Program) , 1Term, Geometry A
  11. 2025, Graduate Education (Master's Program) , 4Term, Geometry B
  12. 2025, Graduate Education (Master's Program) , First Semester, Special Lectures in Mathematics
  13. 2025, Graduate Education (Master's Program) , Year, Exercises in Mathematics
  14. 2025, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  15. 2025, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  16. 2025, Graduate Education (Master's Program) , Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. A first proof of knot localization for polymers in a nanochannel, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 57(38), 20241011
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  2. Complete classification of generalized crossing changes between GOF-knots, Journal of Topology and Analysis, 17(1), 2023
  3. Graph Theoretical and Knot Theoretical Analyses of Multi-cyclic Polymers, Topological Polymer Chemistry, 20220226
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  4. Handlebody decompositions of three-manifolds and polycontinuous patterns, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2260), 20220420
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  5. Neighborhood equivalence for multibranched surfaces in 3-manifolds, Topology and its Applications, 257, 11-21, 201904
  6. Characterising knotting properties of polymers in nanochannels, Soft Matter, 14(28), 5775-5785, 2018
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  7. Enzyme action for topological entanglement in DNA and knot theory, Reactive and Functional Polymers, 132, 74-80, 201811
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  8. Pathways of DNA unlinking: A story of stepwise simplification, SCIENTIFIC REPORTS, 7(1), 201709
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  9. Bounds for minimum step number of knots confined to tubes in the simple cubic lattice, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50(21), 1-28, 201705
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  10. Band surgeries and crossing changes between fibered links, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 94(2), 557-582, 201610
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  11. Coherent band pathways between knots and links, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 24(2), 155006-1-155006-21, 201502
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  12. Site-specific recombination modeled as a band surgery: Applications to Xer recombination, Natural Computing Series, 48, 387-401, 2014
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  13. FtsK-dependent XerCD-dif recombination unlinks replication catenanes in a stepwise manner, Proceedings of the National Academy of Sciences of the United States of America, 110(52), 20906-20911, 20131224
  14. An operator invariant for handlebody-knots, FUNDAMENTA MATHEMATICAE, 217(3), 233-247, 2012
  15. Rational tangle surgery and Xer recombination on catenanes, ALGEBRAIC AND GEOMETRIC TOPOLOGY, 12(2), 1183-1210, 2012
  16. Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(6), 1-26, 201202