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Geometry Lab
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A geometry lab that creates tools for measuring the shape of things.
AboutAbout the lab
Turning the “shape of things” into measurable quantities
The Geometry Lab approaches geometry as the study of measuring the shape of things.
It extracts quantities that capture the features of a shape, and investigates whether those quantities truly describe the shape well and how they can be computed.
Beyond triangles and surfaces, it treats physical phenomena, complex figures, solution sets of equations, groups, and information as “things that have shape.”
Its research is broad, spanning topology, algebraic geometry, differential geometry, singularity theory, and mathematical physics, and members collaborate while preserving diversity.
Key terms
- Topology
- Geometry that focuses on how a figure is connected, which does not change under stretching or bending
- Differential geometry
- Geometry that investigates how curves and surfaces bend, using the methods of calculus
- Integrable system
- A general term for differential equations (systems) that have a built-in mechanism that makes them solvable. Deeply connected with geometry
NewsLab news
Announcement on the handling of external English proficiency tests in master's program admissions for the Department of Mathematics
Assistant Professor Sakumi Sugawara receives the FY2025 Mathematical Society of Japan Takebe Katahiro Prize for Encouragement of Research
ResearchResearch themes
The lab seeks quantities for measuring the shape of things and studies how to compute them. Both its objects and its methods are wide-ranging, covering topology, algebraic geometry, differential geometry, singularity theory, and mathematical physics.
*Illustrative imageCohomology of Groups
The cohomology of a group is defined algebraically, yet it also coincides with the cohomology of the space determined by the group. The lab mainly studies Coxeter groups, Artin groups, and mapping class groups of closed surfaces.
*Illustrative imageLie Groups and Integrable Geometry
The lab studies differential equations with an underlying geometric structure, using the geometry of Lie groups and homogeneous spaces. It also pursues joint research with various fields, including industrial design, architectural structural design, and the development of teaching materials.
*Illustrative imageConstant Mean Curvature Surfaces
These are surfaces formulated as extrema of the area functional, and they have been studied deeply as objects of geometry. The nonlinear partial differential equation that characterizes them is known to be an integrable system, and recently the lab has been studying geometric structures determined by integrable systems.
*Illustrative imageGeometry of Statistical Manifolds
A manifold equipped with a pair of an affine connection and a Riemannian metric satisfying the Codazzi equation is called a statistical manifold. It is an important concept in information geometry and is closely related to the study of surfaces in affine space.
MembersFaculty
The members of the Geometry Lab are Professors, Associate Professors, and Assistant Professors.As of 2026
- ProfessorToshiyuki Akita
- ProfessorJunichi Inoguchi
- ProfessorShimpei Kobayashi
- ProfessorHitoshi Furuhata
- Associate ProfessorNaohiko Kasuya
- Associate ProfessorMorimichi Kawasaki
- Associate ProfessorYuta Nozaki
- Assistant ProfessorYutaka Kanda
- Assistant ProfessorSakumi Sugawara
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: “Klein bottle translucent” Wridgers / CC BY-SA 3.0 (cropped)
- Cohomology of Groups: “Cayley graph Q8” Sullivan.t.j / Public domain (cropped)
- Lie Groups and Integrable Geometry: “Heptagonal tiling honeycomb ideal surface” Roice3 / CC BY-SA 4.0 (cropped)
- Constant Mean Curvature Surfaces: “7-noid” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Geometry of Statistical Manifolds: “Lidinoid surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (幾何系
（粕谷直彦） ): “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped) - Related lab (代数系
（大内元気） ): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped) - Related lab (幾何系
（古畑仁） ): “Canal-helix” Ag2gaeh / CC BY-SA 3.0 (cropped) - Related lab (代数系
（沼田泰英） ): “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped)
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