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Global Mathematics Lab
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A division centered on differential geometry and complex geometry that also studies analysis and algebra.
AboutAbout the lab
Centered on geometry, with work in analysis and algebra as well.
The Global Mathematics Lab is a division of the Department of Mathematics, Graduate School of Science, Osaka University, and its faculty specialize in differential geometry, complex geometry, complex analysis, nonlinear partial differential equations, and algebraic geometry.
Professor Goto studies the geometries known as special geometries, such as Calabi–Yau manifolds, from a viewpoint that treats them in a unified way.
Professor Yamanoi studies problems in complex geometry and complex analysis from the standpoint of Nevanlinna theory.
Associate Professor Iwai investigates the structure of algebraic varieties from the standpoint of complex geometry and algebraic geometry.
Key terms
- Complex geometry
- A field that studies the geometry of spaces with complex numbers as coordinates.
- Special geometry
- A collective name for Calabi–Yau manifolds, hyperkähler manifolds, G2 and Spin(7) manifolds, and similar objects.
- Nevanlinna theory
- A theory that studies the value distribution of functions on the complex plane and similar objects, that is, how often they take each value.
- Tangent bundle
- The object formed by bundling together the tangent vectors at every point of a manifold.
ResearchResearch themes
The faculty of the Global Mathematics Lab specialize in differential geometry, complex geometry, complex analysis, nonlinear partial differential equations, and algebraic geometry. Here we cover the research of Professor Goto, Professor Yamanoi, and Associate Professor Iwai, whose work is described on the department's pages or on their personal pages.
*Illustrative imageA unifying viewpoint on special geometries
The research treats special geometries, such as Calabi–Yau manifolds, hyperkähler manifolds, and G2 and Spin(7) manifolds, from a unifying viewpoint. These objects are related to many fields, including mathematical physics, algebraic geometry, and analysis.
*Illustrative imageHolomorphic curves and Nevanlinna theory
From the standpoint of Nevanlinna theory, the research is interested in the Second Main Conjecture for entire holomorphic curves into projective varieties, and in the behavior of the Kobayashi pseudo-distance on projective varieties of general type. It is also interested in value distribution theory for meromorphic functions on the complex plane.
*Illustrative imageAlgebraic varieties with positive tangent bundles
The research has clarified the structure of algebraic varieties whose tangent bundles or foliations are ample, nef, big, or pseudo-effective. It has also been extended to log versions and to singular varieties (KLT varieties).
*Illustrative imageAlgebraic varieties with positive cotangent bundles
For algebraic varieties with numerical Kodaira dimension at most 1 and nef cotangent bundle, the research has shown that the abundance conjecture holds and has clarified the structure of such varieties.
MembersFaculty
- ProfessorMasashi Ishida
- ProfessorRyushi Goto
- ProfessorKatsutoshi Yamanoi
- Associate ProfessorTakahisa Inui
- Associate ProfessorMasataka Iwai
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: “SqrtRiemann” Auswahlaxiom / CC BY-SA 4.0 (cropped)
- A unifying viewpoint on special geometries: “Calabi-Yau-alternate” The original uploader was Lunch at English Wikipedia. / CC BY-SA 2.5 (cropped)
- Holomorphic curves and Nevanlinna theory: “Domain coloring x2-1 x-2-i x-2-i d x2+2+3i” Djiboun / CC BY-SA 4.0 (cropped)
- Algebraic varieties with positive tangent bundles: “Calabi-Yau” Lunch / CC BY-SA 2.5 (cropped)
- Algebraic varieties with positive cotangent bundles: “Test Configuration” Tazerenix / CC BY-SA 4.0 (cropped)
- Related lab (Analysis Lab): “Graph of argument of square root of complex variable -pi to pi” Dom walden / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Lab): “CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique ( )” Ecole polytechnique Université Paris-Saclay / CC BY-SA 2.0 (cropped)
- Related lab (Geometry Lab): “Schwarz D Surface” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (Algebra Lab): “Geodesics on hyperbolic surface” Café Bene / CC BY-SA 3.0 (cropped)
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