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Geometry Lab (Hiroshige Kajiura)
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Algebraic topology that explores how geometry relates to algebraic structures.

AboutAbout the lab
Seeing the algebraic structures behind geometry.
Prof. Kajiura specializes in algebraic topology.
The professor is interested in how algebraic structures such as operads and homotopy algebras relate to geometry.
The research keywords include deformation quantization and noncommutative geometry, algebra using categories, and string theory and homological mirror symmetry.
Key terms
- Operad
- An algebraic framework that describes the rules for connecting operations that combine several inputs into one
- Homotopy algebra
- An algebra in which laws such as associativity hold not exactly, but up to deformation
- Mirror symmetry
- A correspondence under which two geometries that look different are thought to give the same quantities
ResearchResearch themes
The lab is interested in viewing the algebraic structures that accompany various geometries as representations of operads, and in viewing deformations of geometry as deformations of those algebraic structures.
View More ↗MembersFaculty
- ProfessorHiroshige Kajiura
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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: “Kleineigenspace” Joroco246 / CC BY-SA 4.0 (cropped)
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(二木 昌宏) ): “Expansion de l'univers dans une variété de Calabi-Yau” N738139 / CC0 (cropped) - Related lab (基礎解析
(岡田 靖則) ): “Anaklasi3” DeRham00 / CC BY-SA 3.0 (cropped)
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