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Ohmoto Lab
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A lab that uses mathematics to understand the singularities that appear in shapes and maps.
AboutAbout the lab
Reading the singularities that appear in surfaces and maps.
Ohmoto Lab studies the properties of singularities that appear in shapes and maps from a mathematical perspective.
Singularities are the places where things stop being smooth, such as where a surface folds or has a sharp point, and the lab classifies them using methods from topology and geometry.
The research covers a wide range of fields, including persistent homology for studying the shape of data, information geometry related to machine learning, and differential line geometry related to robotics.
Key terms
- Singularity
- A part of a shape or map where it stops being smooth, such as a fold or a sharp point
- Topology
- A branch of geometry that studies the properties of shapes that do not change when they are stretched or shrunk
- Persistent homology
- A mathematical method that examines the shape features of a set of data points while varying the scale
NewsLab news
View More ↗ResearchResearch themes
The lab studies the properties of singularities that appear in shapes and maps, using methods from topology and geometry. Building on singularity theory, it also works on applications to a wide range of fields, including enumerative geometry, information geometry, and robotics.
*Illustrative imageTopology of differentiable maps
This research classifies the structure of smooth maps that have singularities, using Thom-Mather theory, invariants of stable maps, and related tools.
*Illustrative imageEnumerative geometry
This is geometry research that counts shapes on which singularities appear, using tools such as Thom polynomials and Hilbert schemes.
*Illustrative imageGeometry of polyhedra
The lab investigates the structure of wavefronts propagating over polyhedra and of their singularities (cut loci), using tools such as discrete Morse theory.
*Illustrative imageApplied topology and applied algebraic geometry
This research applies topology, such as persistent homology that reads the shape of figures from data, to the analysis of images and visual information.
MembersFaculty
The members of Ohmoto Lab consist of faculty, doctoral, master's, and undergraduate students, and joint researchers.As of 2026
- ProfessorToru Ohmoto
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: “Ripples dispersing sunlight into underwater rainbows in Brofjorden” W.carter / CC BY-SA 4.0 (cropped)
- Topology of differentiable maps: “Curving Dune Ridge ( )” Great Sand Dunes National Park and Preserve / Public domain (cropped)
- Enumerative geometry: “Klaus-Orsanka-Stack of firewood-01ASD” Asurnipal / CC BY-SA 4.0 (cropped)
- Geometry of polyhedra: “Rhombidodecadodecahedron - Flickr - fdecomite” fdecomite / CC BY 2.0 (cropped)
- Applied topology and applied algebraic geometry: “Swiss cheese cubes” Christian Bauer / CC BY 2.0 (cropped)
- Related lab (Maruno Lab): “Soliton hydro” Christophe.Finot et Kamal HAMMANI / CC BY-SA 2.5 (cropped)
- Related lab (Toyoizumi Lab): “SocialNetworkAnalysis” Martin Grandjean / CC BY-SA 4.0 (cropped)
- Related lab (Ogita Lab): “U.s.-kilogram-masses” National Institute of Standards and Technology / Public domain (cropped)
- Related lab (Kashiwagi Lab): “Convergence of Iterative Numerical Methods for Poisson System with 16384 elements” ansariddle / CC BY-SA 4.0 (cropped)
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