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Topology Lab
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A research field that explores the properties of shapes that do not change under continuous deformation.
AboutAbout the lab
Exploring the properties of shapes that remain unchanged under continuous deformation
The Topology field studies geometric objects such as shapes through the properties that do not change under continuous deformation.
It is a relatively new field within mathematics.
Faculty research spans a range of perspectives that vary from professor to professor, including algebraic topology, singularity theory, low-dimensional topology, and applied topology.
At Kyushu University, the Department of Mathematics in the School of Science and the Graduate School of Mathematics introduce the faculty together as one of their research and education fields.
Key terms
- Topology
- A field that studies the properties of shapes and similar objects that remain unchanged under continuous deformation.
- Algebraic topology
- A field that studies the properties of spaces that do not change under continuous deformation by expressing them in terms of numbers and algebra
ResearchResearch themes
This is a field that investigates, from various perspectives, the properties of shapes that do not change under continuous deformation. The approach differs from professor to professor, including algebraic topology, singularity theory, and applied topology.
*Illustrative imageExamining Spaces Through Algebraic Topology
Professor Kishimoto studies the properties of spaces that do not change under continuous deformation by expressing them in terms of numbers and algebra. The objects of study are combinatorially constructed spaces, including the combinatorial and algebraic structures inherent in spaces and arrangements of subspaces.
*Illustrative imageSingularities of Maps and the Structure of Manifolds
Professor Saeki studies how the singularities that appear in differentiable maps between manifolds are related to the structure of the manifolds. The research proceeds by restricting the types of singularities to simple ones or by focusing on low-dimensional cases.
*Illustrative imageApplying Topology to Image and Data Analysis
Associate Professor Moriyama studies topology, configuration spaces of points, and finite-type topological invariants. Attempts are also being made to apply topology to fields such as image analysis and multidimensional data analysis.
*Illustrative imageFundamental Groups, Galois Groups, and Configuration Spaces
Assistant Professor Kodani studies representations of fundamental groups and Galois groups, as well as algebra and geometry related to configuration spaces. Recent work relates to periods expressed as integrals associated with graphs, and to topological invariants.
MembersFaculty
- ProfessorYutaka Ishii
- ProfessorDaisuke Kishimoto
- ProfessorOsamu Saeki
- ProfessorHirofumi Sasahira
- ProfessorToshio Sumi
- ProfessorMasanori Morishita
- Associate ProfessorYasuhiko Asao
- Associate ProfessorYuta Kusakabe
- Associate ProfessorYuichiro Takeda
- Associate ProfessorMitunobu Tsutaya
- Associate ProfessorKazuhiro Hikami
- Associate ProfessorYosuke Morita
- Associate ProfessorTetsuhiro Moriyama
- Assistant ProfessorGeunsu Kim
- Assistant ProfessorHisatoshi Kodani
- Assistant ProfessorNoriyuki Hamada
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
- Examining Spaces Through Algebraic Topology: “NASA-HS201427a-HubbleUltraDeepField” NASA, ESA, H. Teplitz and M. Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst (Arizona State University), and Z. Levay (STScI) / Public domain (cropped)
- Singularities of Maps and the Structure of Manifolds: “Whitney-umbrella” Ag2gaeh / CC BY-SA 4.0 (cropped)
- Applying Topology to Image and Data Analysis: “Example of the Multicover Bifiltration” René Corbet, Michael Kerber, Michael Lesnick & Georg Osang / CC BY 4.0 (cropped)
- Fundamental Groups, Galois Groups, and Configuration Spaces: “Cayley configuration space example” W.sims.ufl / CC BY-SA 4.0 (cropped)
- Related lab (Algebraic Geometry Lab): “Heike Kamerlingh Onnes - 29 - Plaster model of a Ψ surface of a mixture of two substances” 作者不詳 / Public domain (cropped)
- Related lab (Representation Theory and Harmonic Analysis Lab): “Worm's-eye view of Tokyo Skytree with vertical symmetry impression, a sunny day, in Japan” Basile Morin / CC BY-SA 4.0 (cropped)
- Related lab (Differential Geometry Lab): “Schwarz H Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (Number Theory Lab): “SinRiemannSiegelTheta” Chrgue / CC BY-SA 3.0 (cropped)
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