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Carnahan Lab
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A lab that explores Monstrous Moonshine through representation theory.
AboutAbout the lab
Exploring moonshine through representation theory.
The Carnahan Lab studies representation theory, with an emphasis on low-dimensional physics and number theory.
Its main problem is Monstrous Moonshine, which involves infinite-dimensional Lie algebras, vertex algebras, algebraic curves, and modular functions.
Recently, the lab has also been working on computer-based formalization in the programming language Lean 4, centered on vertex algebras and Lie algebras.
Key terms
- Monstrous Moonshine
- A mysterious correspondence linking the Monster group, a huge finite group, with modular functions. It is the main problem of this lab.
- Vertex algebra
- One of the algebraic structures involved in the study of moonshine. It has also recently become a subject of formalization in Lean 4.
- Modular function
- A function with a specific defining property under certain kinds of transformations. It is involved in the study of moonshine.
- Formalization
- Writing out mathematical definitions and proofs in a form that a computer can verify.
ResearchResearch themes
The lab studies representation theory, with an emphasis on low-dimensional physics and number theory. Its main problem is Monstrous Moonshine, which involves infinite-dimensional Lie algebras, vertex algebras, algebraic curves, and modular functions.
*Illustrative imageMonstrous Moonshine
Monstrous Moonshine, the lab's main problem, involves infinite-dimensional Lie algebras, vertex algebras, algebraic curves, and modular functions. Recently, the lab has also been working on computer-based formalization in Lean 4, centered on vertex algebras and Lie algebras.
*Illustrative imageFormalization in Lean 4
Recently, the lab has been working on computer-based formalization using the language Lean 4, centered on vertex algebras and Lie algebras.
MembersFaculty
- Associate ProfessorScott Carnahan
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: “Math01” MathKnight ✡ (Talk) No machine-readable author provided. MathKnight assumed (based on copyright claims). / CC BY 2.5 (cropped)
- Monstrous Moonshine: “Computational Group Theory” DrRezaZomorrodian / CC BY-SA 4.0 (cropped)
- Formalization in Lean 4: “Closeup of keys” John Snyder / CC BY-SA 4.0 (cropped)
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