Kenji Kajiwara | Last modified date：2021.06.15 |

Professor /
Division of Applied Mathematics /
Institute of Mathematics for Industry

**Presentations**

1. | Integrable systems and geometric shape generation: Do good equations generate good shapes?. |

2. | Extension of the log-aesthetic curves to space curves and surface and the correspondence of surfaces of pseudospherical type. |

3. | Explicit formulas for the smooth/discrete elastic curves and the theta function solutions to the mKdV hierarchy. |

4. | Shota Shigetomi and Kenji Kajiwara, Explicit formulas for motions of smooth/discrete elasticae, Australia New Zealand Industrial and Applied Mathematics Conference 2021, 2021.02, Elastica is known as the shape of a thin elastic rod on the plane. Mathematically, it is characterised by the differential equation for its curvature. It is also known that traveling wave solutions of the modified KdV equation satisfy the equation for Elastica. Thanks to its integrability, it is possible to construct a discrete version of Elastica characterised by the integrable discrete analog of the modified KdV equation. We construct explicit solutions to the motion of Elastica described by the modified KdV equation. We also construct the explicit solutions to continuous and discrete motions of the discrete Elastica described by the semi-discrete potential modified KdV equation and the discrete potential modified KdV equation, respectively. Explicit formulas in terms of the tau function are presented.. |

5. | Spherical Kaleidocycles on 3-sphere. |

6. | Construction of explicit formula for the isoperimetric deformation of the planar elastic curves in terms of the elliptic theta functions. |

7. | Kenji Kajiwara, Wolfgang Schief, Generation of aesthetic shapes by integrable systems, Australia New Zealand Industrial and Applied Mathematics 2020, 2020.02. |

8. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang Schief, Generation of Aesthetic Shapes by Integrable Geometry, International Congress on Industrial and Applied Mathematics 2019, 2019.07. |

9. | Kenji Kajiwara, Shizuo Kaji, Hyeongki Park, Linkage Mechanisms Governed by Integrable Deformation of Discrete Space Curves, ISLAND V:Integrability, special functions and combinatorics, 2019.06. |

10. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang Schief, The Burgers-type Equations in the Deformation Theory of Curves, Applications of Nonlinear Diffusion Equations 2019, 2019.06. |

11. | Kenji Kajiwara Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang Schief, Application of Integrable Discrete Differential Geometry to Industrial Design, Kyushu University - National Taiwan Normal University Joint Forum, 2019.05. |

12. | Generalization of log-aesthetic curves to space curves by using the integrable similarity geometry II, Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura and Wolfgang K. Schief, JSIAM Activity Groups Union Conference 2019, University of Tsukuba, 2019.3.3-5.. |

13. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang Schief, Space Curve Extensions of Log-Aesthetic Curves in Industrial Design by Integrable Geometry, 55th Annual Meeting of the Australia New Zealand Industrial and Applied Mathematics, 2019.02. |

14. | Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, A hinged linkage mechanism that follows discrete integrable equations, 55th Annual Meeting of the Australia New Zealand Industrial and Applied Mathematics, 2019.02. |

15. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang K. Schief, Extensions of log-aesthetic curves in industrial design, Integrable Systems 2018, 2018.11. |

16. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang K. Schief, A New Framework and Extensions of Log-Aesthetic Curves in Industrial Design by Integrable Geometry, 62nd Annual Meeting of the Australian Mathematical Society, 2018.12. |

17. | Shizuo Kaji, Kenji Kajiwara, Hyeongki Park, Hinged linkage mechanism that follows discrete integrable equations, Forum "Math-for-Industry" 2018, 2018.11. |

18. | Kenji Kajiwara, Nozomu Matsuura, Heyongki Park, Lotka-Volterra flow on discrete centroaffine plane curves, 13th International Conference on Symmetries and Integrability of Difference Equations, 2018.11. |

19. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang K. Schief, Log-aestiethic curves in industrial design as similarity analogue of Euler's elasticae, Geometric Design Meeting at Hokkaido, 2018.10. |

20. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura, Wolfgang K. Schief, Log-aestiethic curves in industrial design as similarity analogue of Euler's elastic curves, Autumn School "Geometric Shape Generation", 2018.10. |

21. | Kenji Kajiwara, Introduction to the discrete integrable systems based on the geometry of plane curves (1), Summer School "Geometric Shape Generation", 2018.09. |

22. | Kenji Kajiwara, Introduction to the discrete integrable systems based on the geometry of plane curves (2), Summer School "Geometric Shape Generation", 2018.09. |

23. | Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura and Wolfgang K. Schief, Log-aesthetic curves in industrial design as similarity analogue of Euler's elastic curves, Summer School "Geometric Shape Generation", 2018.09. |

24. | Genaralization of log-aesthetic curves to space curves by using the integrable similarity geometry, Kenji Kajiwara and W. K. Schief, JSIAM2018 Annual Conference, Nagoya University, 2018.9.3-5.. |

25. | Sebastiàn Elìas Graiff-Zurita, Kenji Kajiwara, Fairing of discrete planar curves with integrable discretization of Euler's elasticae, 日本応用数理学会2018年度年会, 2018.09. |

26. | Lotka-Volterra flow on discrete centroaffine plane curves, @Kenji Kajiwara, @Nozomu Matsuura, #Hyeongki Park, JSIAM2018 Annual Conference, Nagoya University, 2018.9.3-5.. |

27. | Kenji Kajiwara, Integrable Discretization of Log-Aesthetic Curves in Industrial Design, 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications (AIMS2018), 2018.07. |

28. | Kenji Kajiwara, Log-Aesthetic Curves in Industrial Design as Similarity Geometric Analogue of Euler's Elasticae, Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, 2018.04. |

29. | D.Triadis, P. Broadbridge, K. Kajiwara, K. Maruno, An integrable discrete model for soil-water infiltration, ANZIAM Conference 2018, 2018.02. |

30. | Kenji Kajiwara, Log-Aesthetic Curves in Industrial Design as Similarity Geometric Analogue of Euler’s Elastic Curves, ANZIAM Conference 2018, 2018.02. |

31. | Kenji Kajiwara, Log-Aesthetic Curves in Industrial Design as Similarity Geometric Analogue of Euler’s Elastic Curves, Dasan Conference 2017, 2017.12. |

32. | Kenji Kajiwara, Geometric description of discrete power function associated with the sixth Painlevé equation, Painlevé equations and applications in memory of Andrei Kapaev, 2017.08. |

33. | Kenji Kajiwara, Aspects of Integrable discrete differential geometry, Applied Mathematics Seminar, 2017.05. |

34. | Kenji Kajiwara, Soliton equations and deformation of smooth/discrete curves.II. deformation of space curves by mKdV and NLS equations, Applied Mathematics Seminar, 2017.05. |

35. | Kenji Kajiwara, Soliton equations and deformation of smooth/discrete curves.I. deformation of plane curves by mKdV equations , Applied Mathematics Seminar, 2017.05. |

36. | Kenji Kajiwara, dNLS flow on discrete space curves, 10th IMACS Conference on Nonlinear and Evolution Equations and Wave Phenomena: Computation and Theory, 2017.03. |

37. | Kenji Kajiwara, Integrable deformation of plane/space curves, First Kyushu-UNSW Joint Workshop on the Mathematics underpinning Industry and Innovation, 2016.11. |

38. | Kenji Kajiwara, An approach to discrete differential geometry from integrable systems, Applied Mathematics Seminar, 2016.09. |

39. | Kenji Kajiwara, Integrable discrete deformations of space/plane discrete curves, 3rd China-Japan Joint Workshop on Integrable Systems, 2018.06. |

40. | Kenji Kajiwara, Integrable deformation of plane curves, Applied Mathematics Seminar, 2016.08. |

41. | Kenji Kajiwara, An elementary introduction to discrete and ultradiscrete integrable models — disctete and ultradiscrete Burgers equations —, Applied Mathematics Seminar, 2016.08. |

42. | Kenji Kajiwara, An integrable discrte model of vortex filaments, 12th International Conference on Symmetries and Integrability of Difference Equations, 2016.07. |

43. | Kenji Kajiwara, Geometric Aspects of Painlevé Equations: A Brief Introduction. II, NSF/CBMS Regional Research Conference on Discrete Painleve ́ Equations, 2016.05. |

44. | Kenji Kajiwara, Geometric Aspects of Painlevé Equations: A Brief Introduction. I, NSF/CBMS Regional Research Conference on Discrete Painleve ́ Equations, 2016.05. |

45. | Kenji Kajiwara, A discrete model of vortex filaments, Discrete Integrable Systems, 2016.04. |

46. | 梶原健司, Integrable deformations of discrete curves, Japan-Austria Joint Workshop: Transformations and Singularities, 2016.02. |

47. | 梶原健司, Discrete model of dynamics of vortex filaments, ANZIAM Conference 2016, 2016.02. |

48. | 梶原健司, Integrable discrete deformations of discrete curves , International Congress of Industrial and Applied Mathematics (ICIAM2016), 2015.08. |

49. | 梶原健司, Integrable discrete deformations of discrete curves, Computational and Geometric Approarches for Nonlinear Phenomena, 2015.08, [URL]. |

50. | 梶原健司, Discrete conformal mappings, hypergeometric functions and Painlevé equations, PNU Math Forum, Pusan National University, 2015.07, [URL]. |

51. | , [URL]. |

52. | Kenji Kajiwara, Integrable discrete deformations of discrete curves: geometry and solitons, old and new, Representation theory, special function and Painlevé equation, 2015.03. |

53. | Kenji Kajiwara, Integrable discrete deformations of discrete curves, 2015.01. |

54. | Hisashi Ando, Mike Hay, Kenji Kajiwara, Tetsu Masuda, Explicit formula and extension of the discrete power function associated with circle patterns of Schramm type, Mathematical Progress in Expressive Image Synthesis (MEIS2014), 2014.11. |

55. | Kenji Kajiwara, Torsion-preserving isoperimetric deformation of discrete space curves and its exact solutions, Symmetries and Integrability of Difference Equation X!, 2014.06. |

56. | Kenji Kajiwara, Discrete mKdV and discrete sine-Gordon flows on discrete space curves, Workshop on Integrable Systems, 2014.12. |

57. | Kenji Kajiwara, Discrete mKdV flow on discrete space curves, Symposium “Mathematical Progress in Expressive Image Synthesis” (MEIS2013), 2013.10. |

58. | Kenji Kajiwara, Discrete mKdV flow on discrete space curves, Discrete Integrable Systems – a follow-up meeting, 2013.07. |

59. | Kenji Kajiwara, Some aspects of the Painlevé Systems, Journal of Physics A Editorial Board Meeting, 2013.04. |

60. | Kenji Kajiwara, Some explicit formulas in discrete differential geometry, The 8th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, 2013.03. |

61. | Kenji Kajiwara, Some explicit formulas in discrete differential geometry, The 8th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, 2013.03. |

62. | Kenji Kajiwara, Some explicit formulas in discrete differential geometry, The 2nd China-Japan Joint Workkshop on Integrable Systems, 2013.03. |

63. | Kenji Kajiwara, Is there anything left undone in mathematics?, JSPS-US Alumini Association 3rd Multidisciplinary Science Forum, 2013.02. |

64. | Kenji Kajiwara, Some explicit formulas in discrete differential geometry, Nonlinear Dynamical Systems, 2012.09. |

65. | Kenji Kajiwara, Motion of Discrete Planar Curves in Euclidean and Similarity Geometries, Nonlinear Evolution Equations and Dynamical Systems (NEEDS2012), 2012.07. |

66. | Kenji Kajiwara, Motion of Discrete Planar Curves in Euclidean and Similarity Geometries, Nonlinear Evolution Equations and Dynamical Systems (NEEDS2012), 2012.07. |

67. | Kenji Kajiwara, Discretization of planar curve motions and discrete modified KdV equations, American Mathematical Society 2012 Spring Southeastern Section Meeting, 2012.03. |

68. | 梶原 健司, Discretization of planar curve motions and discrete integrable systems, Winter School for Young Researchers on Mathematical Aspects of Image Processing and Computer Vision, 2011.11. |

69. | Motion and Bäcklund transformations of discrete curves on the Euclidean plane. |

70. | Hankel determinant formula for the solution of the Toda equation and auxiliary linear problem. |

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