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Ozaki Lab
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A lab studying the symmetry of the world of numbers through Iwasawa theory and Galois theory.
AboutAbout the lab
Reading the symmetry of numbers through Iwasawa theory.
Ozaki Lab uses Galois theory to study the structure of number fields, a type of number system.
In particular, the lab centers its research on Iwasawa theory, which concerns extensions of cyclotomic fields, a special kind of number field.
The lab aims to clarify what structure the Galois groups of number fields have, using non-abelian methods as well.
Key terms
- Number field
- A number system obtained by extending the rational numbers with solutions of equations and the like
- Galois group
- A group-theoretic structure that expresses the symmetry of the solutions of an equation
- Iwasawa theory
- A theory that studies the structure of Galois groups when a number system is extended infinitely
ResearchResearch themes
The lab uses a theory called Iwasawa theory to study the structure of the Galois groups of number fields, which are systems of numbers. Its work involves extensions of cyclotomic fields and research using non-abelian methods.
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MembersFaculty
- ProfessorManabu Ozaki
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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: “Minoritenkirche rose window - Vienna” MrPanyGoff / CC BY-SA 3.0 (cropped)
- Non-abelian Iwasawa theory: “Spiral stairs (Art Deco, Nebotičnik, Ljubljana)” Petar Milošević / CC BY-SA 4.0 (cropped)
- Related lab (成田研究室): “Beeswax foundation” Plantsurfer / Public domain (cropped)
- Related lab (楫研究室): “Modell einer Kubik mit vier Doppelpunkten -Schilling VII, 5 - 48” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (永井研究室): “Klein bottle glass2” PaulT (Gunther Tschuch) / CC BY-SA 4.0 (cropped)
- Related lab (池田研究室): “Mathematisches-Gipsmodell.Fläche3.Ordnung - Kopie” Museopedia / CC BY-SA 4.0 (cropped)
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