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Taguchi Lab
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The lab studies number theory, with a focus on Galois representations.
AboutAbout the lab
Exploring the world of numbers through Galois representations
Taguchi Lab studies number theory.
In its papers to date, the lab has dealt with Galois representations and with the moduli spaces that classify them.
The lab's website also offers explanations of topics such as Fermat's Last Theorem, class field theory, and p-adic numbers.
Key terms
- Number theory
- A field of mathematics that studies the properties of integers and prime numbers. Also called higher arithmetic.
- Galois representation
- A way of writing the ways the roots of an equation can be permuted (the Galois group) in the form of matrices.
- p-adic number
- A number system that measures how close numbers are to each other by looking at how many times they are divisible by a prime p.
ResearchResearch themes
*Illustrative imageGroups of Rational Points on Elliptic Curves and Related Objects
The rational points on elliptic curves and similar objects form a group, and the structure of this group is a major theme in number theory. The lab determines what this group (the Mordell-Weil group) looks like when considered over very large number fields.
MembersFaculty
- ProfessorYuichiro TaguchiPublications ↗
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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: “Ulam spiral with prime numbers and divisor-based dot sizes” Marianoju / CC BY-SA 4.0 (cropped)
- Groups of Rational Points on Elliptic Curves and Related Objects: “ECClines-2.0” IlyaP111 / CC BY-SA 4.0 (cropped)
- Related lab (馬研究室): “Kummer surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Related lab (プルカイト研究室): “J-inv-phase” Linas Vepstas / CC BY-SA 3.0 (cropped)
- Related lab (鈴木研究室): “Complex zeta” Jan Homann / Public domain (cropped)
- Related lab (内藤研究室): “E8 edgeoverlap” Tom Ruen / Public domain (cropped)
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