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Algebra (Yuanqing Cai) Lab
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Research that explores how the world of numbers works, using automorphic representations and L-functions as clues.
AboutAbout the lab
Reading the structure of numbers through L-functions.
Prof. Cai studies automorphic representations and their L-functions, in a field spanning number theory and representation theory.
Automorphic representations and L-functions are objects that encode many properties of numbers, and they remain an active area of research today.
In this field, a wealth of results has been found on the theta correspondence and the doubling method.
Prof. Cai works on the theory of L-functions for classical groups, using a recently discovered extension of the doubling method.
Key terms
- Automorphic representation
- A way of viewing the behavior of highly symmetric functions as representations of a group. A central object in number theory.
- L-function
- A function that packages information about integers or representations into an infinite sum or product. It serves as a tool for drawing out properties of numbers.
- Classical group
- Among groups of matrices, those such as the orthogonal groups and symplectic groups that have long been studied.
ResearchResearch themes
Within number theory, the lab studies mainly automorphic representations and their L-functions. Its main settings are a recently discovered extension of the doubling method and the representation theory of covering groups.
*Illustrative imageAutomorphic L-functions of classical groups
Through a recently discovered extension of the doubling method, the lab studies automorphic L-functions of classical groups from both the local and the global sides of the theory.
*Illustrative imageRepresentation theory of covering groups
In recent years, the automorphic representation theory of Brylinski-Deligne covering groups (BD covering groups) of reductive groups has also attracted attention. The lab also studies the L-function theory and automorphic representation theory of BD covering groups.
MembersFaculty
- Associate ProfessorYuanqing Cai
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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: “Dedekind Eta” Jan Homann / Public domain (cropped)
- Automorphic L-functions of classical groups: “Hyperboloid-with-7,3-tiling” PSL27 / CC BY-SA 4.0 (cropped)
- Representation theory of covering groups: “Riemann surface log” Jan Homann / Public domain (cropped)
- Related lab (Algebra (Numata) Lab): “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped)
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