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Algebra 1 (Number Theory) Lab (Kaoru Hiraga)
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A lab that studies automorphic forms and trace formulas for algebraic groups.
AboutAbout the lab
Exploring the world of automorphic forms through trace formulas.
The Hiraga Lab studies automorphic forms and automorphic representations in the field of number theory.
Its research theme is trace formulas for algebraic groups.
Key terms
- Automorphic representation
- A representation of an adelic group generated by automorphic forms; automorphic forms viewed as group representations
- Trace formula
- A formula that links, through an equation, information on group representations with information on conjugacy classes of group elements
- Langlands conjectures
- Major conjectures in number theory that aim to generalize class field theory
- Endoscopy
- An important part of the Langlands conjectures: a phenomenon that relates representations of one group to representations of another group
- Covering group
- A group built by extending an original group so that it covers the original group several times over
ResearchResearch themes
The lab studies automorphic forms and automorphic representations, and trace formulas for algebraic groups. It investigates endoscopy, which is related to the Langlands conjectures in number theory, for covering groups of reductive algebraic groups.
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MembersFaculty
- LecturerKaoru Hiraga
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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: “KleinjCont” Empetrisor / CC BY-SA 4.0 (cropped)
- Endoscopy for Covering Groups: “4 21 polytope 2D using H3 basis” Jgmoxness / CC BY-SA 4.0 (cropped)
- Related lab (代数学1
（整数論） （跡部 発） ): “Bruhat-Tits-tree-for-Q-2” 부고 / CC BY-SA 4.0 (cropped) - Related lab (代数学１（整数論，
表現論） （市野 篤史） ): “Dedekindeta” SteJaes / CC BY-SA 4.0 (cropped) - Related lab (代数学1 (整数論, 表現論)
（鈴木 美裕） ): “Cayley graphs of quaternion group” PSL27 / CC BY-SA 4.0 (cropped) - Related lab (代数学１（整数論）
（池田 保） ): “KleinInvariantJ” Jan Homann / Public domain (cropped)
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