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Geometric Analysis Lab
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The lab analyzes nonlinear partial differential equations on the geometry of spacetime and also investigates the structure of manifolds.
AboutAbout the lab
Exploring how spatial curvature, expansion, and contraction affect solutions.
The Geometric Analysis Lab develops the theory of nonlinear partial differential equations on geometric spacetimes, such as the homogeneous and isotropic spacetimes of general relativity.
It aims to clarify theoretically how spatial curvature, expansion, and contraction affect the solutions of these equations.
The lab also works on clarifying the topological and differentiable structures of manifolds.
The department's page introduces the research topic of Professor Makoto Nakamura as nonlinear partial differential equations, and that of Associate Professor Koichi Yasui as low-dimensional topology.
Key terms
- Nonlinear partial differential equations
- Among equations that express the relationship between an unknown function and its rate of change, those for which the superposition of solutions does not hold.
- Homogeneous and isotropic spacetime
- A spacetime whose properties do not change with location or direction.
- Manifold
- A curved figure or space that looks the same as flat space when viewed in a very small region.
ResearchResearch themes
The lab develops the theory of nonlinear partial differential equations on geometric spacetimes, such as the homogeneous and isotropic spacetimes of general relativity. Its goals are to clarify theoretically how spatial curvature, expansion, and contraction affect the solutions of these equations, and to clarify the topological and differentiable structures of manifolds.
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MembersFaculty
- ProfessorMakoto Nakamura
- Associate ProfessorKoichi Yasui
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: “One-sided spacetime curvatures” Tokamac / CC BY-SA 4.0 (cropped)
- Spacetime geometry and solutions of equations: “Spacetime curvature - Cropped” User:Johnstone / CC BY-SA 3.0 (cropped)
- Related lab (Large-Scale Mathematical Sciences Lab): “Contours in the vector field f(z) = -Cos(z)” Oldtimermath / CC BY-SA 3.0 (cropped)
- Related lab (Applied Analysis Lab): “Lorenz yz x 0” German A. Chernykh & Irina A. Chernykh / CC BY-SA 4.0 (cropped)
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