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Discrete Differential Geometry and Integrable Systems Lab
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The lab creates beautiful shapes from integrable systems and discrete differential geometry.
AboutAbout the lab
Creating beautiful shapes with integrable systems.
Professor Kenji Kajiwara researches the theory of integrable systems and the generation of geometric shapes using discrete differential geometry.
In integrable systems, the lab has pursued algebraic and geometric studies of the Painlevé equations and discrete Painlevé equations, and their applications.
In discrete differential geometry, based on the theory of discrete integrable systems, the lab studies the theory of deformations of discrete curves and the theory of discrete surfaces.
As an application, the lab develops theory and implementations for generating "beautiful" shapes, in collaboration with researchers in architectural design, industrial design, and computational geometry.
Key terms
- Integrable systems
- Systems of differential or difference equations with a special structure that allows their solutions to be studied exactly
- Discrete differential geometry
- A field that treats curves and surfaces as shapes made of discrete points and faces, and studies them with the ideas of differential geometry
- Painlevé equations
- A family of second-order ordinary differential equations. The corresponding family of second-order ordinary difference equations is called the discrete Painlevé equations
ResearchResearch themes
In integrable systems, the lab studies Painlevé systems; in discrete differential geometry, it studies curves and surfaces based on the theory of discrete integrable systems. As an application, it works on the theory and implementation of geometric shape generation, especially the generation of beautiful shapes.
*Illustrative imageGeometry of discrete surfaces for design
Aiming to open up new ways of thinking in design, the lab studies a new geometry of discrete surfaces. Research keywords include geometric shape generation, theory of curves and surfaces, architecture, industrial design, computational geometry, and origami.
*Illustrative imageResearch on Painlevé systems
The lab pursues algebraic and geometric studies of the Painlevé equations and discrete Painlevé equations, and their applications. It focuses on solutions described by hypergeometric-type special functions, such as algebraic function solutions and Gauss's hypergeometric function.
*Illustrative imageFrom discrete integrable systems to discrete differential geometry
Based on the theory of discrete integrable systems, the lab studies the theory of deformations of discrete curves and the theory of discrete surfaces. Research keywords also include discrete systems and soliton equations.
MembersFaculty
- ProfessorKenji Kajiwara
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: “Amper's Geometric Shape Art Project” Neirenz / CC BY-SA 4.0 (cropped)
- Geometry of discrete surfaces for design: “Gridshell” Janine Forbes / CC BY-SA 2.0 (cropped)
- Research on Painlevé systems: “Oceanic nonlinear internal solitary waves from the Lombok Strait (MODIS )” Jeff Schmaltz, MODIS Land Rapid Response Team, NASA GSFC / Public domain (cropped)
- From discrete integrable systems to discrete differential geometry: “Stacked balls with "camera and studio light"” Greg A L / CC BY-SA 3.0 (cropped)
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- Related lab (Topology and Singularity Theory Lab): “Linkedin maps data visualization” Luc Legay / CC BY-SA 4.0 (cropped)
- Related lab (Topology and Singularity Theory Lab): “Bastard Weaver s Knot diagram-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
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