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Naito Lab
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The lab studies crystal structures through discrete geometry and also works on variational problems.
AboutAbout the lab
Building good crystal lattices from geometry.
Prof. Naito studies discrete geometric analysis and geometric variational problems.
Viewing the structure of a crystal as a graph of points and lines embedded in space, the lab constructs good crystal lattices from a geometric standpoint and studies them.
Nonlinear partial differential equations on manifolds, derived from variational problems originating in differential geometry, are also objects of study.
For small graduate-level classes, the professor wants to take computers and the mathematics related to them as themes, and hopes students will study with a balance of "theory and practice," realizing theory on the computer.
Key terms
- Graph
- A structure made of points and the lines (edges) connecting them. It represents only how the points are connected and carries no information about their positions.
- Manifold
- A shape, such as a sphere, in which the neighborhood of every point can be regarded as flat space.
- Minimal surface
- A surface, like a soap film, whose area is locally minimal once the surrounding frame is fixed.
ResearchResearch themes
The lab's research themes are discrete geometric analysis and geometric variational problems. It works on research that treats crystal structures as graph embeddings, and on nonlinear partial differential equations related to geometric variational problems.
*Illustrative imageCrystal structures and discrete geometric analysis
From a mathematical viewpoint, the crystal structures that appear in materials science can be regarded as highly symmetric graphs embedded in space. The lab defines an energy for graphs and realizes crystal structures as its minimizers, constructing good crystal lattices and studying their properties.
*Illustrative imageGeometric variational problems and nonlinear partial differential equations
Geometric variational problems deal with geometric objects formulated through variational principles; harmonic maps and minimal surfaces are representative examples. The lab studies nonlinear partial differential equations related to them.
MembersFaculty
- ProfessorHisashi Naito
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: “Carbon lattice diamond” GYassineMrabetTalk✉ This structure was created with PyMOL. / Public domain (cropped)
- Crystal structures and discrete geometric analysis: “Natural Mineral Crystal Display” QueenCityCebu / CC BY-SA 4.0 (cropped)
- Geometric variational problems and nonlinear partial differential equations: “Soap Films” Ryan Somma / CC BY-SA 2.0 (cropped)
- Related lab (微分幾何・複素幾何・力学系・
大域解析学 （松尾 信一郎） ): “Minimal surface curvature planes-nl” ChristiaanPR / CC BY-SA 4.0 (cropped) - Related lab (代数幾何・微分幾何・複素幾何
（久本 智之） ): “Peano intersection” Salix alba / CC BY-SA 4.0 (cropped) - Related lab (フーリエ解析・偏微分方程式
（加藤 淳） ): “Ocean waves water” Jon Sullivan / Public domain (cropped) - Related lab (フーリエ解析・偏微分方程式・流体力学
（寺澤 祐高） ): “Flow separation” Jaganath at English Wikipedia / CC BY-SA 3.0 (cropped)
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