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Kimura Lab
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An algebra lab that studies the K-groups and Chow groups of algebraic varieties.
AboutAbout the lab
Exploring the K-groups and Chow groups of algebraic varieties.
The Kimura Lab studies the K-groups and Chow groups of algebraic varieties in the field of algebra.
In the Degree Program in Mathematics at the University of Tsukuba, the lab belongs to the Algebra Group.
In recent years, the lab has published papers on mixed Tate motives and on integration over semialgebraic sets.
Key terms
- Algebraic variety
- A geometric object defined as the set of solutions of polynomial equations.
- Chow group
- A group formed by classifying the subvarieties of an algebraic variety under a certain equivalence relation.
ResearchResearch themes
The lab studies the K-groups and Chow groups of algebraic varieties. In recent years, it has published papers on mixed Tate motives and on integration over semialgebraic sets.
*Illustrative imageResearch on K-groups and Chow groups
Research on the K-groups and Chow groups of algebraic varieties. The faculty list of the Degree Program in Mathematics also gives this topic as the research of Lecturer Kimura.
*Illustrative imageMixed Tate motives
The lab continues its research on the mixed Tate motives of Bloch-Kriz. In April 2026, it posted to arXiv a preprint on the relationship between Goncharov's conjecture and the Lie coalgebra of the Bloch-Kriz mixed Tate motives.
*Illustrative imageIntegration over semialgebraic sets
Research on integrating logarithmic forms over semialgebraic sets, and on generalized Cauchy formulas. A paper co-authored with Masaki Hanamura and Tomohide Terasoma was published in the Hokkaido Mathematical Journal in 2025.
MembersFaculty
- LecturerKenichiro Kimura
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: “Node (algebraic geometry)” The original uploader was Jakob.scholbach at Wikipedia. / CC BY-SA 3.0 (cropped)
- Research on K-groups and Chow groups: “Clay tablet, mathematical, geometric-algebraic, similar to the Euclidean geometry. From Tell Harmal, Iraq. BCE. Iraq Museum” Osama Shukir Muhammed Amin FRCP(Glasg) / CC BY-SA 4.0 (cropped)
- Mixed Tate motives: “Mathematics lecture at the Helsinki University of Technology” Tungsten / Public domain (cropped)
- Integration over semialgebraic sets: “Mathematics, Lecture notes, Mathematical analysis, Linear algebra, Rostov-on-Don, Russia” Vyacheslav Argenberg / CC BY 4.0 (cropped)
- Related lab (Sakamoto Lab): “Ulam spiral centred on 41” TrulyBlue / CC BY-SA 4.0 (cropped)
- Related lab (Mihara Lab): “Pale cream grey dirty grubby dusty discolored geometric diagonal tile pattern floor texture” Sisters.seamless / CC0 (cropped)
- Related lab (Carnahan Lab): “Math01” MathKnight ✡ (Talk) No machine-readable author provided. MathKnight assumed (based on copyright claims). / CC BY 2.5 (cropped)
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