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Algebraic Geometry Lab
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This research field studies the shapes formed by the common zeros of polynomials.
AboutAbout the lab
Untangling the complexity of shapes to discover their mysterious forms
The Algebraic Geometry Lab studies the shapes formed by the common zeros of polynomials.
It is a research field that untangles the complexity of shapes from multiple viewpoints, including algebra and topological analysis, and discovers their mysterious forms.
The field is also deeply connected to commutative algebra, the theory of complex manifolds, and arithmetic geometry.
Faculty research includes rationally connected varieties, the Oka principle, and algebraic K-theory.
Key terms
- Common zeros of polynomials
- The set of points at which the values of several polynomials are all 0. This set is the shape studied in algebraic geometry
- Rationally connected variety
- An algebraic variety that has abundant rational curves. An algebraic variety is a shape formed by the common zeros of polynomials
- Oka principle
- A homotopy principle in complex analysis. It is a heuristic principle stating that analytic problems on Stein manifolds have only topological obstructions
- Algebraic K-theory
- One of the objects studied in arithmetic geometry. It is conjectured to be related to the L-functions of algebraic varieties
ResearchResearch themes
This is a research field that untangles the complexity of shapes formed by the common zeros of polynomials and discovers their mysterious forms. Faculty research includes rationally connected varieties, the Oka principle, and algebraic K-theory.
*Illustrative imageShapes formed by the zeros of polynomials
The lab studies shapes formed by the common zeros of polynomials from multiple viewpoints, including algebra and topological analysis. It untangles the complexity of these shapes and discovers their mysterious forms. The field is also deeply connected to commutative algebra, the theory of complex manifolds, and arithmetic geometry.
*Illustrative imageThe rationality problem for algebraic varieties
Professor Takuzo Okada studies rationally connected varieties, which have abundant rational curves, from the viewpoint of birational geometry. A main challenge is the problem of determining rationality, and the research also works to elucidate the structure of Fano threefolds.
*Illustrative imageThe Oka principle and Gromov ellipticity
Associate Professor Yuta Kusakabe studies the Oka principle, a homotopy principle in complex analysis, and the surrounding area of Gromov ellipticity. Currently, the research examines the Oka principle from a broad perspective that includes algebraic geometry and differential geometry.
*Illustrative imageAlgebraic K-theory and regulator maps
Associate Professor Yuichiro Takeda works within arithmetic geometry, with algebraic K-theory and regulator maps as the main objects of study. The aim is to develop methods for explicitly representing elements of K-theory and to compute their images under the regulator map.
MembersFaculty
- ProfessorLin Weng
- ProfessorTakuzo Okada
- Associate ProfessorYuta Kusakabe
- Associate ProfessorYuichiro Takeda
- Assistant ProfessorJuae Song
- Assistant ProfessorRyo Yamagishi
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: “Heike Kamerlingh Onnes - 29 - Plaster model of a Ψ surface of a mixture of two substances” 作者不詳 / Public domain (cropped)
- Shapes formed by the zeros of polynomials: “Polynomial constant-width curve” Lambiam / CC BY-SA 4.0 (cropped)
- The rationality problem for algebraic varieties: “Algebraic–Geometry1” Jean Constant / CC BY-SA 4.0 (cropped)
- The Oka principle and Gromov ellipticity: “Geometry problem-Sb 13088-IMG 0593-white” Rama / CC BY-SA 2.0 fr (cropped)
- Algebraic K-theory and regulator maps: “A De Morgan algebra” AugPi / CC BY 4.0 (cropped)
- Related lab (Topology Lab): “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
- Related lab (Complex Analysis Lab): “Msltoe - Julia Bulb Mod4 OpenCL HQ 16K 20201222” PantheraLeo1359531 / CC0 (cropped)
- Related lab (Representation Theory and Harmonic Analysis Lab): “Worm's-eye view of Tokyo Skytree with vertical symmetry impression, a sunny day, in Japan” Basile Morin / CC BY-SA 4.0 (cropped)
- Related lab (Differential Geometry Lab): “Schwarz H Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
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