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Topology and Singularity Theory Lab
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The lab studies the structure of manifolds through singularities of maps, in the field of topology.
AboutAbout the lab
The real answer awaits you at the far end of a freedom with no textbooks.
Prof. Saeki's lab studies the overall structure of manifolds, which are geometric objects, using singularities of differentiable maps as a clue.
By restricting singularity types to simple ones or focusing on low dimensions, the lab investigates the relationship between maps between manifolds and the structure of manifolds.
The lab studies a wide range of areas of topology and also works on DNA knots and visual analysis of multi-valued function data.
Key terms
- Manifold
- An object for treating figures and spaces mathematically, generalizing surfaces and the like.
- Singularity
- A point where the behavior of a map ceases to be simple. The local complexity around the point is what matters.
- Knot
- An object for mathematically studying how a closed loop of string is tangled.
NewsLab news
View More ↗ResearchResearch themes
The lab investigates the overall structure of manifolds using singularities of differentiable functions and maps on them. It studies a wide range of areas of topology and is also interested in applications of topology to other fields.
*Illustrative imageStructure of Manifolds Studied through Singularities of Maps
By restricting singularity types to simple ones or focusing on low dimensions, the lab investigates the relationship between maps between manifolds and the structure of manifolds. Previous research has revealed that singularities carry an essential part of the structure of manifolds.
*Illustrative imageBroad Topology and Applications of Topology
The lab studies a wide range of topology, including isolated singularities of complex hypersurfaces, 4-dimensional manifolds, and unknotting numbers. It also studies visual analysis for DNA knots and multi-valued function data, and is interested in considering the properties of substances and materials from the microscopic level.
MembersFaculty
- ProfessorOsamu Saeki
VoicesStudent voices
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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: “Linkedin maps data visualization” Luc Legay / CC BY-SA 4.0 (cropped)
- Structure of Manifolds Studied through Singularities of Maps: “Caustic with a cusp of reflected lamp light in a plastic bucket, 2022 - 1” Hansmuller / CC BY-SA 4.0 (cropped)
- Broad Topology and Applications of Topology: “Topology joke” Keenan Crane and Henry Segerman / CC BY-SA 3.0 (cropped)
- Related lab (Topology and Singularity Theory Lab): “Bastard Weaver s Knot diagram-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (Applied Algebra and Mathematical Crystallography Lab): “Simple Cubic Lattice (Brillouin zone)” Auro69 at en.wikipedia / Public domain (cropped)
- Related lab (Applied Algebra and Mathematical Crystallography Lab): “Rendering of quasicrystal structure” LinKayser / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory and Random Point Processes Lab): “A boolean model” Tensorproduct / CC BY-SA 4.0 (cropped)
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