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Ito Lab
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A lab that unravels the sharp points of shapes to connect geometry and algebra.

AboutAbout the lab
Connecting the geometry of singularities with algebra.
The Ito Lab works in algebraic geometry, studying quotient singularities and their resolutions.
Prompted by a problem about singularities arising from superstring theory, the lab has worked on extending the two-dimensional McKay correspondence to three dimensions.
The lab is also interested in the case of non-abelian groups and in methods for proving the existence of resolutions of singularities.
Key terms
- Singularity
- A point on a shape where it is pointed or self-intersecting, so that it is no longer smooth
- Resolution of singularities
- A procedure for studying a shape that has singularities by replacing it with a smooth shape
- McKay correspondence
- A correspondence that connects the properties of a finite group with the geometry of the singularities arising from that group
ResearchResearch themes
The lab's field is algebraic geometry, and it has studied quotient singularities and their resolutions. Its theme is the McKay correspondence, which connects the geometry of singularities with algebra.
View More ↗MembersFaculty
- ProfessorYukari ItoPublications ↗
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: “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
- Quotient Singularities and the McKay Correspondence: “Kummer surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (Oguiso Lab): “Calabi yau” Jbourjai / Public domain (cropped)
- Related lab (Kawakami Lab): “BarthSextic” Mike Williams / Public domain (cropped)
- Related lab (Kelly Lab): “Spectral Sequence Visualization” L.penguu / CC BY-SA 4.0 (cropped)
- Related lab (Gongyo Lab): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
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