Kyushu University Academic Staff Educational and Research Activities Database
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OSAMU SAEKI Last modified date:2018.08.03



Graduate School
Undergraduate School


Homepage
http://imi.kyushu-u.ac.jp/~saeki/index.html
Osamu Saeki's Home Page .
Academic Degree
Doctor of Science
Country of degree conferring institution (Overseas)
No
Field of Specialization
Topology
Outline Activities
My main research interest is the global singularity theory of differentiable mappings. It has been known that differentiable functions on a manifold can be well used to study its global geometric structures. In the 1950's Thom began to try to generalize such a theory to that of differentiable mappings between manifolds. However, because of the difficulty in controling local singularities, the theory has not been well developed until recently. So I am studying differentiable mappings between manifolds with only mild singularities or those between low dimensional manifolds.

This kind of global study of singularities is fairly new and my recent results have shown that the singularities of differentiable mappings play an essential role in the study of geometric structures of manifolds. In this way, it has been recognized that such a study is important in Topology.

Other than the above mentioned research, I am also interested in the following vast area of Topology and related fields: primary obstruction to topological embeddings, separation properties of codimension 1 maps, topology of complex isolated hypersurface singularities, fibered knots, 4-dimensional manifolds, codimension 1 embeddings, differential geometric invariants of space curves, unknotting numbers of knots, etc. I am also interested in the asymptotic behavior of generalized Fibonacci sequences. Furthermore, I am interested in the application of Topology to other areas in Science and Industry, such as DNA knots, visual data analysis for multivariate functions, analysis of materials from microscopic levels, etc.
Research
Research Interests
  • Mathematical Descriptions of Figures from the Viewpoints of Topology and Differential Geometry
    keyword : Topology, Differential Geometry, Material Science
    2013.04~2014.03.
  • Application of Pure Mathematics to Materials Science
    keyword : Microstructure of Materials, Geometric Features, Mathematical Modeling
    2011.04Research on DNA recombinations by enzymes by using DNA knots and tangles..
  • Low Dimensional Topology, Morse Theory and Computer Graphics
    keyword : low dimensional topology, computer graphics, Morse theory, singularities of differentiable maps
    2011.04Research on DNA recombinations by enzymes by using DNA knots and tangles..
  • Topology-based visual data analysis for multivariate functions
    keyword : multivariate function, data analysis, visualization, differential topology
    2010.10Research on DNA recombinations by enzymes by using DNA knots and tangles..
  • Research on DNA knots
    keyword : DNA recombination, knot theory, tangle, site-specific recombination enzyme, topoisomerase, cyclic surgery theorem
    2007.06Research on DNA recombinations by enzymes by using DNA knots and tangles..
  • Research on separation property of codimension 1 maps, Betti number of generic map images, and primary obstruction to topological embeddings.
    keyword : codimension 1 map, separation property, generic map, Betti number, primary obstruction to topological embeddings
    1991.04~2001.03Research on separation properties of codimension 1 maps, Betti numbers of generic maps, and primary obstruction to topological embeddings..
  • Research on the topology of stable maps
    keyword : stable map, elimination of singularities, manifold, characteristic class, differentiable structure
    1991.04Research on topology of stable maps..
  • Research on generalized Fibonacci sequences.
    keyword : Fibonacci sequence, recurrence, asymptotic behavior, Binet formula, holomorphic function
    1994.04Research on generalized Fibonacci sequences..
  • Research on high dimensional knots
    keyword : knot, codimension 1 embedding, product of spheres, fibered knot, Milnor fibration
    1994.04Research on high dimensional knot theory..
  • Research on contact between curves and 1-parameter orbits in homogeneous spaces
    keyword : homogeneous space, 1-parameter subgroup, contact, orbit, Lie algebra
    1997.04Research on contact between curves and 1-parameter orbits in homogeneous spaces..
  • Research on regular homotopy classes of immersions and embeddings of 3-manifolds into 5-space
    keyword : immersion, embedding, regular homotopy, spin structure, 3-manifold
    2000.04Research on regular homotopy classes of immersions and embeddings of 3-manifolds into 5-space..
Current and Past Project
  • Visual data analysis for multivariate functions
  • Application of Pure Mathematics to Materials Science
  • Studio Phones Fellowship Program (Low Dimensional Topology, Morse Theory and Computer Graphics)
Academic Activities
Books
1. Osamu Saeki, Topology of Singular Fibers of Differentiable Maps, Springer Verlag, Lecture Notes in Math., Vol. 1854, Springer-Verlag, 2004. , 2004.01.
2. Singular Points of Complex Hypersurfaces, J. W. Milnor, Translated into Japanese by O. Saeki and K. Sakuma, Springer Verlag Tokyo, 2003..
3. Characteristic Classes, J. W. Milnor and J. D. Stasheff, Translated into Japanese by O. Saeki and K. Sakuma, Springer Verlag Tokyo, 2001..
4. Geometry and Singularities (in Japanese), S. Izumiya, T. Sano, O. Saeki and K. Sakuma, Kyoritsu Publ., 2001..
Papers
1. Osamu Saeki, Special generic maps on open 4-manifolds, Journal of Singularities, 1, 1-12, 2010.01.
2. O. Saeki and T. Yamamoto, Singular fibers of stable maps and signatures of 4-manifolds, Geometry and Topology , 10, pp. 359-399, 2006.04.
3. Osamu Saeki, Topology of singular fibers of differentiable maps, Lecture Notes in Mathematics, Springer, Vol.1854, 2004.01.
4. Osamu Saeki, Fold maps on 4-manifolds, Comment. Math. Helv., 10.1007/s00014-003-0758-9, 78, 3, 627-647, 78, 627-647, 2003.01.
5. O. Saeki and K. Sakuma, Special generic maps of 4-manifolds and compact complex analytic surfaces, Math. Ann., 313, 617-633, 1999.01.
Presentations
1. 佐伯 修, Topology of singular fibers for visualization, Topology-Based Methods in Visualization 2015, 2015.05, [URL].
2. 佐伯 修, Broken Lefschetz fibrations and their moves, Geometry and topology of smooth 4-manifolds, 2013.06.
3. Cobordism of Morse maps and its application to map germs.
4. Singularities and Characteristic Classes -- important roles played by explicit examples .
5. On 2-knots with total width less than or equal to 8.
6. Morse functions with sphere fibers.
7. Singular fibers of differentiable maps and characteristic classes of surface bundles.
8. Elimination of definite fold.
9. Generic smooth maps with sphere fibers.
10. Theory of singular fibers of differentiable maps and characteristic classes of surface bundles I.
11. Introduction to singular fibers of differentiable maps: theory and examples.
12. Topology of manifolds and singularities of differentiable maps.
13. Universal complex of singular fibers and cobordism of singular maps.
Membership in Academic Society
  • Asia Pacific Consortium of Mathematics for Industry
  • Australian Mathematical Society
  • The Japan Society for Industrial and Applied Mathematics
  • The Mathematical Society of Japan
Awards
  • Stable maps and Topology of Manifolds
Educational
Educational Activities
The numbers of recent master course students that I supervised were 2 (2015), 1 (2014), 4 (2013), 2 (2012), 1 (2011), 2 (2010), 1 (2009), 4 (2008), 2 (2007), 4 (2006), 2 (2005), 1 (2004), 4 (2001), 2 (2000), 2 (1998), 1 (1996) and 1 (1993).

For undergraduate students, I am teaching general topology and algebraic topology. The numbers of students that I supervised were 1 (2017), 1 (2016), 1 (2014), 1 (2012), 4 (2011), 4 (2010), 3 (2009), 2 (2008), 4 (2007), 3 (2006), 4 (2005), 3 (2004), 2 (2003), 2 (2001), 3 (2000), 6 (1999), 3 (1998), 3 (1996), 1 (1995), 3 (1993), 3 (1992), 2 (1991) and 4 (1988).

Other than the above mentioned activities, I have given 14 mini-courses in other universities. Furthermore, I have supervised 3 Brazilian students for their PhD.
Other Educational Activities
  • 2010.08, Joint Lecture with Pusan National University for Graduate Students.
Social
Professional and Outreach Activities
I have written the following educational essays (in Japanese).

1. Let us enjoy books on Mathematics
2. Let us look at 4-dimensional spaces by using maps
3. Differential topology and singularities
4. Various ways to topology
5. When I encountered with Mathematics --- fascinated by the mystery
6. Mathematics is interesting
7. Book Review "Introduction to Topology (in Japanese)" by T. Tanaka and H. Murakami.
8. Differential topology and singularities
9. Mathematics, Industry, and Mathematics
10. Mathematics helps in an unexpected way -- Singularity Theory and Data Visualization.