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Matsuo Lab
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The lab studies vertex operator algebras and conformal field theory.
AboutAbout the lab
From Algebra to Conformal Field Theory
Matsuo Lab studies mathematical problems concerning algebraic systems called vertex operator algebras.
Vertex operator algebras are algebraic systems closely related to a physical theory known as two-dimensional conformal field theory.
They are also connected to a wide range of mathematical theories, including affine Lie algebras, modular functions, the Monster simple group, quantum groups, and hypergeometric functions.
In recent years, the lab has been working on constructing the conformal field theory associated with a vertex operator algebra over the moduli space of Riemann surfaces and describing its properties.
Key terms
- Vertex operator algebra
- An algebraic system closely related to two-dimensional conformal field theory. It is connected to a wide range of mathematical theories, such as the Monster simple group.
- Two-dimensional conformal field theory
- A two-dimensional field theory that has symmetry under angle-preserving transformations. It originated in physics.
- Moduli space
- The collection of all geometric objects of the same kind (here, Riemann surfaces), regarded as a single space in its own right.
ResearchResearch themes
The lab's research field is geometry (symmetry and mathematical physics), with themes such as representations of infinite-dimensional Lie algebras, vertex operator algebras, and two-dimensional conformal field theory. The lab studies mathematical problems concerning vertex operator algebras.
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MembersFaculty
- Associate ProfessorAtsushi MatsuoPublications ↗
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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: “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
- Vertex Operator Algebras and Conformal Field Theory: “KleinInvariantJ” Jan Homann / Public domain (cropped)
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