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Geometry (Futaki) Lab
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Mirror symmetry connects two seemingly different geometries through the language of categories.
AboutAbout the lab
Two geometries that mirror the same thing
Prof. Futaki studies homological mirror symmetry.
It is a field that uses the language of categories to capture a correspondence in which two seemingly different geometries carry the same information.
Its foundation is symplectic geometry, and the approach is more algebraic than that of differential topology.
The professor is also interested in applying higher category theory to geometry and mathematical physics.
Key terms
- Mirror symmetry
- A correspondence in which two seemingly different geometries are thought to give the same quantities
- Symplectic geometry
- A branch of geometry that studies the shape of figures under transformations that preserve quantities such as area
- Category
- A mathematical framework that treats objects and the correspondences between them together as a single whole
ResearchResearch themes
The lab's research centers on homological mirror symmetry, which uses the language of categories to capture a correspondence in which two seemingly different geometries carry the same information.
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MembersFaculty
Doctoral and master's students are enrolled under Prof. Futaki.As of 2026
- Associate ProfessorMasahiro Futaki
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: “Expansion de l'univers dans une variété de Calabi-Yau” N738139 / CC0 (cropped)
- Symplectic Geometry and Mirror Symmetry: “Modell einer Minimalfläche mit einer Lemniskate als geodätischer Linie” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (Geometry (Sanda) Lab): “3D-Cylinder with handle and torus with hole” 作者不詳 / Public domain (cropped)
- Related lab (Algebra Lab (Kenta Sato)): “Chatelet surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (Geometry Lab (Hiroshige Kajiura)): “Kleineigenspace” Joroco246 / CC BY-SA 4.0 (cropped)
- Related lab (Geometry Lab (Jun O'Hara)): “(2,13)-Torus Knot” Bostelk2 / CC BY-SA 4.0 (cropped)
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