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Furuhata Lab
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Research that uses differential geometry to study what information determines a shape.
AboutAbout the lab
Exploring “shape” through mathematics
Prof. Furuhata uses the methods of differential geometry to study more general figures that abstract the properties of curves and surfaces.
The study of shape has long been pursued across a wide range of fields, from the natural sciences and engineering to architecture and art.
Even the beautiful curves and surfaces around us have meaningful mathematical structure.
Recently, it has been shown that elegant figures also arise from fields such as statistics, which seem unrelated to shape.
Key terms
- Differential geometry
- A field that studies how figures such as curves, surfaces, and manifolds bend, using the ideas of calculus
- Affine connection
- A rule for comparing the directions (vectors) at neighboring points on a figure
- Statistical manifold
- A collection of probability distributions regarded as a geometric figure. A central concept in information geometry, a new field
ResearchResearch themes
The aim is to shed light on figures that have been overlooked until now and to reconsider them as members of the family of figures that have long attracted interest. The main theme is to investigate what information determines a shape and to clarify what is special about phenomena in the visible world.
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MembersFaculty
- ProfessorHitoshi Furuhata
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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: “Canal-helix” Ag2gaeh / CC BY-SA 3.0 (cropped)
- Geometry of Statistical Manifolds: “Dirichlet distributions” en:User:ThG / Public domain (cropped)
- Related lab (Algebra (Shibukawa) Lab): “Braid 4perm” Claudio Rocchini / CC BY 2.5 (cropped)
- Related lab (Geometry Lab (Inoguchi)): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Related lab (Analysis (Kubo) Lab): “Surface waves” Roger McLassus / CC BY-SA 3.0 (cropped)
- Related lab (Algebra (Daisuke Matsushita) Lab): “K3 surface” BTotaro / CC BY-SA 4.0 (cropped)
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