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Kapranov Lab
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The lab explores algebra and algebraic geometry through the language of category theory.
AboutAbout the lab
Understanding space in a broad sense.
The Kapranov Lab studies algebra, algebraic geometry, and category theory.
These fields serve as tools for understanding the concept of space in a broad sense, ranging from the very classical to the highly abstract.
Within algebraic geometry, the lab is also interested in directions such as noncommutative geometry, derived geometry, and infinite-dimensional geometry.
Category theory provides a unified background for all of these fields.
Key terms
- Category theory
- A theory that focuses less on mathematical objects themselves than on how the relations between them (maps) are organized, allowing different fields to be treated across the board.
- Noncommutative geometry
- A branch of geometry that understands space in a broad sense by using algebras in which the order of multiplication cannot be swapped.
- Operad
- An algebraic structure that handles together operations that produce one output from several inputs, and the ways in which those operations can be combined.
ResearchResearch themes
The lab studies algebra, algebraic geometry, and category theory. It is interested in noncommutative geometry and in derived and infinite-dimensional geometry, and uses category theory as a unifying background for them.
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MembersFaculty
- Professorカプラノフ ミハイル
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: “Associahedron K5” Kilom691 / CC BY-SA 3.0 (cropped)
- Algebra, Algebraic Geometry, and Category Theory: “Homotopy with fixed endpoints” Oleg Alexandrov / Public domain (cropped)
- Related lab (Abe Lab): “E8-with-thread” Jlrodri / CC BY-SA 3.0 (cropped)
- Related lab (Oshima Lab): “Weyl chambers for A2” Mathphysman / CC BY-SA 4.0 (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
- Related lab (Oguiso Lab): “Calabi yau” Jbourjai / Public domain (cropped)
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