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Algebra Lab
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The lab is an algebra group that studies number theory and algebraic geometry.
AboutAbout the lab
Research in algebra, including number theory and algebraic geometry
The Algebra Lab belongs to the Department of Mathematics in the Graduate School of Science and the School of Science at The University of Osaka. Its faculty members work in fields such as number theory and algebraic geometry.
In number theory, there is a faculty member who studies automorphic representations.
In algebraic geometry, there are faculty members who study Fano varieties and the singularities of shapes defined by algebraic equations.
The research areas listed by faculty members also include complex geometry, mathematical physics, representation theory, topology, and combinatorics.
Key terms
- Algebraic geometry
- A branch of geometry that studies shapes defined by algebraic equations. Its objects of study include singularities and Fano varieties
- Automorphic representations
- Representations of reductive groups, which are a kind of matrix group. They are a broad generalization of classical modular forms
- Fano varieties
- A special class of algebraic varieties that is studied as a distinct object
ResearchResearch themes
Faculty members of the Algebra Lab work in number theory, algebraic geometry, complex geometry, mathematical physics, representation theory, topology, combinatorics, and other fields. This section presents the research of faculty members whose work is described on the university's faculty profile pages.
*Illustrative imageSingularities of Algebraic Varieties
Professor Takehiko Yasuda focuses on singularities of algebraic varieties, which he studies using tools such as motivic integration and jet schemes. Recently, he has been studying the wild McKay correspondence, in which number theory and singularities are closely connected.
*Illustrative imageAutomorphic Representations and the Theta Correspondence
Associate Professor Shuichiro Takeda studies automorphic representations, which are representations of reductive groups, using a method called the theta correspondence. This method constructs representations of one reductive group from those of another, which makes it possible to compare representations of different groups.
*Illustrative imageResearch on Fano Varieties
Associate Professor Kento Fujita studies Fano varieties, a special class of algebraic varieties, mainly from the viewpoint of birational geometry. Recently, his main focus has been the K-stability of Fano varieties.
MembersFaculty
- ProfessorAtsushi Takahashi
- ProfessorHiroaki Nakamura
- ProfessorTakehiko Yasuda
- ProfessorMasahiko Yoshinaga
- Associate ProfessorShuichiro Takeda
- Associate ProfessorKento Fujita
- Assistant ProfessorKoji Ohno
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: “Geodesics on hyperbolic surface” Café Bene / CC BY-SA 3.0 (cropped)
- Singularities of Algebraic Varieties: “Algebraic–Geometry1” Jean Constant / CC BY-SA 4.0 (cropped)
- Automorphic Representations and the Theta Correspondence: “Representation of SU(3)” Arkadipta Sarkar at English Wikipedia / CC BY-SA 3.0 (cropped)
- Research on Fano Varieties: “Algebraic surfaces” Ashton Bradley Aspir8 / CC BY-SA 4.0 (cropped)
- Related lab (実験数学): “Watts-Strogatz small-world model 100nodes” Keiono / CC BY-SA 3.0 (cropped)
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- Related lab (応用数理学): “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique ( )” Ecole polytechnique Université Paris-Saclay / CC BY-SA 2.0 (cropped)
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