OSAMU SAEKI | Last modified date：2021.08.28 |

Professor /
Division of Fundamental mathematics /
Institute of Mathematics for Industry

**Presentations**

1. | Osamu Saeki, Data Visualization using Differential Topology, The 25th Annual Meeting in Mathematics: "Mathematics for Innovation Development", 2021.05, First, as director of the Institute of Mathematics for Industry (IMI), KyushuUniversity, I will give a brief introduction of IMI, including various activities in col-laboration with industrial partners. In the second part, I will explain how differentialtopology in Mathematics can provide novel techniques for visualization of large scaledata. In general, scientific data obtained by a simulation or an experiment can berepresented as a discrete set of sample points of a smooth map between manifolds.In computer science, visualization of such data has long been studied, and it hasbeen clarified that differential topological techniques are essential for such visualiza-tion. However, they are encountering various mathematical diﬀiculties for furtherdevelopment. In this talk, we first survey existing techniques based on Morse the-ory. Then, we present recently developed visualization techniques based on singularfibers of generic maps and their Stein factorizations. We also present the reversedirection: in fact, these visualization techniques can also be used for the research ofsingularity theory in Mathematics as a new tool.. |

2. | Osamu Saeki, Simplifying Indefinite Fibrations on 4-manifolds, Fiber Topology Meets Applications, 2021.01. |

3. | Osamu Saeki, Simplifying broken Lefschetz fibrations and trisections of 4-manifolds, Topology Seminar (Online Seminar), Kansas State University, 2020.10, [URL], We present explicit algorithms for simplifying the topology of indefinite fibrations on 4-manifolds, which include broken Lefschetz fibrations and indefinite generic maps, from the viewpoint of singularity theory. These algorithms allow us to give purely topological and constructive proofs of the existence of simplified broken Lefschetz fibrations on general 4-manifolds, and a theorem of Auroux-Donaldson-Katzarkov on the existence of simplified broken Lefschetz pencils on near-symplectic 4-manifolds. We moreover establish a correspondence between broken Lefschetz fibrations and trisections of 4-manifolds, and show the existence of simplified trisections on all 4-manifolds. Based on this correspondence, we provide several examples of simplified trisections.. |

4. | Osamu Saeki, Reeb graphs of smooth functions on manifolds, 研究集会「可微分写像の特異点論とその応用」, 2019.12. |

5. | Osamu Saeki, Data visualization using differential topology, 2019 International Joint Conference on AI & Data Science: Mathematics and Applications, 2019.11. |

6. | Osamu Saeki, Manifolds admitting fold-cusp maps of certain restricted indices, 特異点論とトポロジー, 2019.07. |

7. | Osamu Saeki, PhD Program in Mathematics for Key Technologies - Attempt of Kyushu University, Mathematics for Industry in the Asia Pacific Area - Part 2 of 2, ICIAM2019 Minisymposium, 2019.07. |

8. | Osamu Saeki, Unlinking singular loci from regular fibers and its application to submersions, Lefschetz Pencils and Low dimensional Topology, 2019.06. |

9. | Osamu Saeki, Data visualization using differential topology, 2019 National Taiwan Normal University (NTNU)-Kyushu University Joint Forum, 2019.05, [URL]. |

10. | Osamu Saeki, Examples from our Study Group Activities in Industrial Mathematics, Colloquium, Ajou University, 2019.03. |

11. | Osamu Saeki, Unlinking singular locus from regular fibers and its application to submersions, The 14th Kagoshima Algebra-Analysis-Geometry Seminar, 2019.02. |

12. | Osamu Saeki, Examples from our Study Group Activities, The 2nd NIMS Industrial Math Problem Solving Workshop, 2018.12, [URL]. |

13. | Osamu Saeki, Unlinking singular locus from regular fibers and its application to submersions, Geometry, Topology and Dynamics Seminar, Okinawa Institute of Science and Technology, 2018.10, [URL]. |

14. | Osamu Saeki, Elimination of definite fold for simple stable maps, Real Algebraic Geometry and Singularity Theory Symposium (Memorial Conference of Masahiro Shiota), 2018.09. |

15. | Osamu Saeki, Simplifying broken Lefschetz fibrations and trisections of 4-manifolds, Four Dimensional Topology, 2018.09, [URL]. |

16. | Osamu Saeki, Singular locus and regular fibers, do they link each other ?, 15th International Workshop on Real and Complex Singularities, 2018.07. |

17. | 佐伯修, Simplified broken Lefschetz fibrations and trisections of 4-manifolds, 研究集会 Intelligence of Low-dimensional Topology, 2018.05. |

18. | Osamu Saeki, Singular set and regular fibers, do they link each other?, 特異点論とその応用【泉屋周一先生退職記念研究集会】, 2018.02. |

19. | Osamu Saeki, Simplifying indefinite fibrations and trisections of 4-manifolds, The 13th Kagoshima Algebra-Analysis-Geometry Seminar, 2018.02. |

20. | Osamu Saeki, Elimination of definite fold II, 可微分写像の特異点論の局所的研究と大域的研究, 2017.11. |

21. | Osamu Saeki, A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces, Australian-Japanese Workshop on Real and Complex Singularities, 2017.09. |

22. | Osamu Saeki, Simplifying indefinite fibrations on 4-manifolds, Geometric and Algebraic Singularity Theory, 2017.09. |

23. | Osamu Saeki, A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces, PRIMA 3rd Congress, Singularities of Spaces and Mappings, 2017.08. |

24. | Osamu Saeki, Indefinite fibrations on differentiable 4-manifolds, Brazil-Mexico 3rd Meeting on Singularities, 2017.08. |

25. | Osamu Saeki, Introduction to singularity theory and fiber topology in multivariate data analysis, Topology, Computation and Data Analysis, Dagstuhl Seminar 17292, 2017.07. |

26. | Osamu Saeki, Indefinite fibrations on 4-manifolds, Differential Geometry, Lie Theory and Low Dimensional Topology, 2016.12. |

27. | Osamu Saeki, A Vassiliev type invariant of order one for stable maps of 3-manifolds into surfaces, 可微分写像の特異点論とその応用, 2016.12. |

28. | Visualizing Singular Fibers － UI & Impacts －. |

29. | 佐伯 修, Singularity theory and data visualization, The 3rd Franco-Japanese-Vietnamese Symposium on Singularities, 2015.12. |

30. | 佐伯 修, Singularity Theory and Data Visualization, 第9回 La Trobe-Kyushu Joint Seminar on Mathematics for Industry, 2015.11. |

31. | 佐伯 修, Singularity theory and data visualization, Geometric Singularity Theory, Polish-Japanese Singularity Theory Working Days, 2015.09. |

32. | 佐伯 修, Cobordism group of Morse functions on surfaces with boundary, Brazil-Mexico 2nd Meeting on Singularities - 2015, 2015.07, [URL]. |

33. | 佐伯 修, New examples of non-trivial real Milnor fibrations, Singularities in Generic Geometry and applications, 2015.06, [URL]. |

34. | 佐伯 修, Topology of singular fibers for visualization, Topology-Based Methods in Visualization 2015, 2015.05, [URL]. |

35. | 佐伯 修, New examples of non-trivial real Milnor fibrations, Workshop on Singularities, Geometry, Topology and Related Topics, 2014.09, We first classify Neuwirth-Stallings pairs of dimension two in the 5-sphere, using the topology of certain configuration spaces. As an appliction, we construct polynomial map germs $(R^6, 0) \to (R^3, 0)$ with an isolated singularity at the origin such that their associated Milnor fibrations are non-trivial, thus putting an end to Milnor's non-triviality question. Furthermore, for certain real polynomial map germs, we study the conditions under which the associated Milnor fiber has the homotopy type of a bouquet of spheres. We then construct, for every pair $(n, p)$ with $n/2 > p > 2$, a new example of a polynomial map germ $(R^n, 0) \to (R^p, 0)$ with an isolated singularity at the origin such that its Milnor fiber has the homotopy type of a bouquet of a positive number of spheres.. |

36. | 佐伯 修, Connected components of regular fibers of differentiable maps, 19th Brazilian Topology Meeting, 2014.08. |

37. | 佐伯 修, Singular fibers and visualization of multivariate data, 13th International Workshop on Real and Complex Singularities, 2014.08, In this talk, we first classify singular fibers of stable maps of compact 3-manifolds with boundary into surfaces. Then, we give two applications. One is a construction of a certain cobordism invariant for functions on surfaces with boundary. As the second application, we use the singular fibers to visualize three dimensional multivariate data, by combining a recent technique in computer science, callded the joint contour net.. |

38. | 佐伯 修, Visualizing multivariate data using singularity theory, Visiting Lecture at Center for Advanced Studies, 2014.04. |

39. | 佐伯 修, Singular fibers of differentiable maps and low dimensional topology II, Visiting Lecture at Center for Advanced Studies, 2014.03. |

40. | 佐伯 修, Desingularizing special generic maps, Visiting Lecture at Institute of Mathematics, 2014.03. |

41. | 佐伯 修, Singular fibers of differentiable maps and low dimensional topology I, Visiting Lecture at Center for Advanced Studies, 2014.03. |

42. | 佐伯 修, Topology of manifolds and global theory of singularities, One day workshop on hypersurface singularity and its link manifolds, 2014.01. |

43. | 佐伯 修, Topology of manifolds and global theory of singularities, 可微分写像の特異点論とその周辺, 2013.11. |

44. | 佐伯 修, Visualizing multivariate data using singularity theory, Forum “Math-for-Industry” 2013 -The Impact of Applications on Mathematics-, 2013.11, This is a talk on recent developments in visualization of large data, especially that of multivariate volume data. We present two essential ingredients. The first one is the mathematical background, especially the singularity theory of differentiable mappings, which enables us to capture topological features of given multivariate data in a mathematically rigorous way. The second one is a new development in computer science, called the joint contour net, which can encode topological structures of a given set of multivariate data in an efficient and robust way. Some applications to real data analysis are also presented.. |

45. | 佐伯 修, Desingularizing special generic maps, The 1st Franco-Japanese-Vietnamese Symposium on Singularities (and The 7th Franco-Japanese Symposium on Singularities), 2013.09. |

46. | 佐伯 修, Broken Lefschetz fibrations and their moves, Special Session “Singularities in Geometry and Topology”, The Second Pacific Rim Mathematical Association Congress (PRIMA2013), 2013.06. |

47. | 佐伯 修, Desingularizing special generic maps, Topology Seminar, 2013.06. |

48. | 佐伯 修, Broken Lefschetz fibrations and their moves, Geometry and topology of smooth 4-manifolds, 2013.06. |

49. | Cobordism of Morse maps and its application to map germs. |

50. | Seeking for invariants of manifolds. |

51. | Singularities and Characteristic Classes -- important roles played by explicit examples . |

52. | Morse functions with sphere fibers. |

53. | On 2-knots with total width less than or equal to 8. |

54. | Singular fibres of differentiable maps and their applications. |

55. | Elimination of definite fold. |

56. | Morse functions with sphere fibers. |

57. | On obstructions to the existence of fold maps. |

58. | Singular fibers of differentiable maps and their applications. |

59. | Generic smooth maps with sphere fibers. |

60. | Singular fibers of differentiable maps and characteristic classes of surface bundles. |

61. | Elimination of definite fold. |

62. | Generic smooth maps with sphere fibers. |

63. | Theory of singular fibers of differentiable maps and characteristic classes of surface bundles I. |

64. | Introduction to singular fibers of differentiable maps: theory and examples. |

65. | Concordance of 4-dimensional knots. |

66. | Universal complex of singular fibers and cobordism of singular maps. |

67. | Topology of manifolds and singularities of differentiable maps. |

68. | Universal complex of singular fibers and cobordism of singular maps. |

69. | Generic smooth maps with sphere fibers. |

70. | Cobordism of surfaces embedded in S^4. |

71. | Cobordism of surface knots. |

72. | Pull back relation for non-spherical knots. |

73. | Fold maps on 4-dimensional manifolds. |

74. | Singular fibers of stable maps and signatures of 4-manifolds, Osamu Saeki, 4-Dimensional Topology, Hiroshima University, 2003.. |

75. | Fold maps on 4-manifolds, Osamu Saeki, Topology of Real and Complex Singularities II, Kagoshima, December 2002.. |

76. | Open book structures on highly connected manifolds, Osamu Saeki, Mathematical Society of Japan, Shimane University, September 2002.. |

77. | Fold maps on 4-manifolds, Osamu Saeki, International Conference on Topology in Matsue 2002 joined with The Second Japan-Mexico Topology Symposium, Shimane University, June 2002.. |

78. | On fold maps on 4-manifolds, Osamu Saeki, Meeting on 4-dimensional topology, Hiroshima, January 2002.. |

79. | Stable maps and 4-dimensional topology, Osamu Saeki, Mathematical Society of Japan, Tokyo, March 2001.. |

80. | Open books and isotopy of 4-manifolds, Osamu Saeki, XII Encontro Brasileiro de Topologia, Niteroi, August 2000.. |

81. | Stable maps and their singular fibers, Osamu Saeki, The 6th Workshop on Real and Complex, Sao Carlos, July 2000.. |

82. | Topology of singular fibers of stable maps, Osamu Saeki, Singularities and Dynamical Systems, Kyoto, June 2000.. |

83. | Euler characteristic formulas for singular surfaces and its application, Osamu Saeki, Surface, Line Congruence and PDE, Kagoshima, January 2000.. |

84. | Topics from global theory of singularities of differentiable mappings I, II, Osamu Saeki, Seminar on Differential Analysis in Kwansai, Kinki University, November 1999.. |

85. | Generic maps into the plane which lift to standard embeddings in codimension two, Osamu Saeki, Topology of manifolds and singularities in various categories, Wakayama, September 1999.. |

86. | On algebraic unknotting numbers of knots, Osamu Saeki, Mathematical Society of Japan, Tokyo, March 1999.. |

87. | On punctured 3-manifolds in S^5, Osamu Saeki, Mathematical Society of Japan, Tokyo, March 1999.. |

88. | Application to differential topology, Osamu Saeki, 10th Encounter with Mathematics, Chuo University, February 1999.. |

89. | A primary obstruction to topological embeddings and its applications, Osamu Saeki, 25th Symposium on Group Actions, Yamagata, October 1998.. |

90. | Embedding of quaternion space in S^4, Osamu Saeki, Mathematical Society of Japan, Osaka, October 1998.. |

91. | Gluck surgery along a 2-sphere in a 4-manifold is realized by surgery along a projective plane, Osamu Saeki, XI Brazilian Meeting of Topology, Rio Claro, August 1998.. |

92. | Euler characteristic formulas for simplicial maps and their applications, Osamu Saeki, 5th Workshop on Real and Complex Singularities, Sao Carlos, July 1998.. |

93. | Euler characteristic formulas for simplicial maps and their applications, Osamu Saeki, Topology of singularities, Kochi, February 1998.. |

94. | Elimination of singularities of differentiable maps, Osamu Saeki, Topology Symposium, Yamaguchi, July 1998.. |

95. | Finiteness results for knots and singularities, Osamu Saeki, Singularities in Geometry and Topology, Sapporo, July 1998.. |

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