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Algebra Lab (Kenta Sato)
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Algebraic geometry that reads the shapes defined by equations through their singularities.
AboutAbout the lab
Looking at the singularities of shapes in the world of positive characteristic.
Prof. Sato studies algebraic geometry.
It is a field that regards the set of solutions of equations as a shape and investigates its form and properties.
The lab's research centers on singularities that appear in the world known as positive characteristic.
The professor is also interested in higher-dimensional algebraic geometry related to the minimal model program.
Key terms
- Algebraic geometry
- A field of mathematics that regards the set of solutions of equations as a shape and investigates its form and properties
- Singularity
- A point on a shape where it is not smooth, because it has a sharp point or crosses itself
- Positive characteristic
- A world of numbers in which adding the same number a certain number of times gives 0. It is determined for each prime number and behaves differently from ordinary numbers
- Invariant
- A quantity attached to a shape that serves as a clue for telling shapes apart
ResearchResearch themes
Within algebraic geometry, the lab's research centers on singularities in positive characteristic. The keywords are commutative ring theory, singularity theory, and F-singularities.
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MembersFaculty
- Associate ProfessorKenta Sato
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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: “Chatelet surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Singularities in positive characteristic and invariants: “Algebraic–Geometry1” Jean Constant / CC BY-SA 4.0 (cropped)
- Related lab (幾何
（梶浦 宏成） ): “Kleineigenspace” Joroco246 / CC BY-SA 4.0 (cropped) - Related lab (幾何
（三田 史彦） ): “3D-Cylinder with handle and torus with hole” 作者不詳 / Public domain (cropped) - Related lab (幾何
（二木 昌宏） ): “Expansion de l'univers dans une variété de Calabi-Yau” N738139 / CC0 (cropped) - Related lab (基礎解析
（岡田 靖則） ): “Anaklasi3” DeRham00 / CC BY-SA 3.0 (cropped)
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