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Hirachi Lab
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The lab studies CR geometry and conformal geometry from the viewpoint of parabolic geometry.
AboutAbout the lab
Two geometries, one viewpoint
The Hirachi Lab studies CR geometry and conformal geometry in the fields of several complex variables and parabolic geometry.
CR geometry is the geometry of real hypersurfaces in complex manifolds.
Using methods from differential geometry, partial differential equations, and representation theory, the lab investigates the two geometries from the unified viewpoint of parabolic geometry.
Key terms
- complex manifold
- A smooth space that can be described by complex-number coordinates around each point
- conformal geometry
- The geometry that studies properties that stay unchanged under transformations preserving angles, rather than lengths
- invariant
- A quantity that does not change when a figure is transformed. It serves as a clue for telling figures apart
ResearchResearch themes
The lab's research fields are several complex variables and parabolic geometry. Using methods from differential geometry, partial differential equations, and representation theory, the lab studies the geometry of real hypersurfaces in complex manifolds (CR geometry) and conformal geometry.
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MembersFaculty
- ProfessorKengo HirachiPublications ↗
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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: “Stereographic projection grid” Henry Segerman / CC BY-SA 3.0 (cropped)
- CR Geometry and Conformal Geometry: “Uniform tiling 433-t12” Tomruen at English Wikipedia / Public domain (cropped)
- Related lab (Shimomura Lab): “Traveling wave” P.wormer / CC BY-SA 3.0 (cropped)
- Related lab (Ishige Lab): “Heat Equation 1D BE Color” Gong Chen, Brandon Cloutier, Ning Li, Benson K. Muite and Paul Rigge with contributions from Sudarshan Balakrishnan, Andre Souza and Jeremy West / CC BY-SA 3.0 (cropped)
- Related lab (Abe Lab): “3-adic integers” LightbulbMEOW / CC BY-SA 4.0 (cropped)
- Related lab (Sakai Lab): “Modell der Weierstraßschen p-Funktion -Schilling, XIV, 7ab, 8 - 313, 314” Oliver Zauzig / CC BY-SA 3.0 (cropped)
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