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Tsuchioka Lab
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The lab studies symmetry through representation theory in order to discover formulas in the world of numbers.
AboutAbout the lab
Representation theory is the study of symmetry.
The Tsuchioka Lab studies representation theory and quantum algebras.
If number theory is the study of numbers, representation theory is the study of symmetry.
One of the lab's goals is to discover formulas like those of Ramanujan, using Lie theory, quantum algebras, and categorification.
Key terms
- Representation theory
- A field of mathematics that studies symmetry by expressing it as actions on matrices and vector spaces.
- Quantum algebra
- An algebra constructed by deforming the multiplication rule of a conventional algebra. It is connected to research in mathematical physics and knot theory.
- Lie theory
- A theory that studies continuously varying symmetries, such as rotations, through groups and their tangent spaces.
ResearchResearch themes
The lab studies representation theory and quantum algebras. Drawing on Lie theory and categorification as well, it investigates the structure of symmetry.
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MembersFaculty
- Associate ProfessorShunsuke TsuchiokaPublications ↗
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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.
- Top image: “Gosset 1 22 polytope” Tom Ruen / Public domain (cropped)
- Identities for Partitions of Integers: “Young tableaux 1” Arkadipta Sarkar at English Wikipedia / Public domain (cropped)
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- Related lab (鹿島亮研究室): “Formulas on an old blackboard (Unsplash)” Roman Mager roman_lazygeek / CC0 (cropped)
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