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Infinite-Dimensional Integrable Systems Lab
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The lab rigorously analyzes equations by using the mathematical structure of integrable systems.
AboutAbout the lab
Solving hard-to-analyze systems through their underlying mathematical structure
The Infinite-Dimensional Integrable Systems research and education group studies equations and systems that appear in nonlinear waves, statistical physics, and field theory.
Even systems that would normally seem difficult to analyze can sometimes be studied rigorously and in detail thanks to a good underlying mathematical structure, and this field mainly deals with such cases.
The field is described as one where algebra, geometry, analysis, and applications all intersect, letting students experience the original appeal of mathematics.
The faculty specialize in discrete differential geometry, integrable systems, mathematical physics, quantum topology, and more.
Key terms
- Integrable system
- An equation or system that can sometimes be analyzed rigorously and in detail thanks to an underlying mathematical structure.
- Discrete differential geometry
- Differential geometry that treats curves and surfaces as sequences of discrete points.
- Painlevé equations
- A family of second-order ordinary differential equations. The discrete versions are studied as a family of second-order difference equations.
ResearchResearch themes
The field mainly studies those equations and systems appearing in nonlinear waves, statistical physics, and field theory that can be analyzed rigorously thanks to their underlying mathematical structure. The faculty work on applications of integrable systems to discrete differential geometry, Painlevé equations, quantum topology, and more.
*Illustrative imageEquations and Systems That Can Be Analyzed Rigorously
The lab deals with equations and systems in nonlinear waves, statistical physics, field theory, and other areas that would normally seem difficult to analyze. Its main focus is on those that allow rigorous and detailed analysis thanks to their underlying mathematical structure.
*Illustrative imageDiscrete Differential Geometry and Shape Generation
Professor Kajiwara studies discrete curves and discrete surfaces based on the theory of integrable systems, and applies this to the theory and implementation of generating beautiful shapes. The work is carried out in collaboration with researchers in architectural design, industrial design, and computational geometry.
*Illustrative imageResearch on Painlevé Equations
Professor Kajiwara studies Painlevé equations and their discrete counterparts, the discrete Painlevé equations, from algebraic and geometric perspectives. The research also focuses on cases whose solutions are described by special functions of hypergeometric type.
*Illustrative imageKnots and Quantum Invariants
Associate Professor Hikami studies quantum invariants of knots and 3-manifolds. Recently, a paper has also been published on the relationship between skein algebras on surfaces and double affine Hecke algebras.
MembersFaculty
- ProfessorKenji Kajiwara
- Associate ProfessorKazuhiro Hikami
- Assistant ProfessorShota Shigetomi
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: “Jeff Rowley Big Wave Surfer Jaws line up 2 Peahi Maui by Xvolution Media - Flickr - Jeff Rowley Big Wave Surfer” Jeff Rowley / CC BY 2.0 (cropped)
- Equations and Systems That Can Be Analyzed Rigorously: “Soliton 1st order” Alessio Damato / CC BY-SA 3.0 (cropped)
- Discrete Differential Geometry and Shape Generation: “Museum of Anatolian Civilizations Hattian disk with geometric design in 2019 02” Dosseman / CC BY-SA 4.0 (cropped)
- Research on Painlevé Equations: “Gullstrand-Painleve-Freefall-Diagram” Yukterez (Simon Tyran, Vienna) / CC BY-SA 4.0 (cropped)
- Knots and Quantum Invariants: “Good luck knot(ABOK 2437)” Zaripov Rustem / CC BY-SA 4.0 (cropped)
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- Related lab (数論): “SinRiemannSiegelTheta” Chrgue / CC BY-SA 3.0 (cropped)
- Related lab (数理物理): “Crabbers eye knot-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (微分方程式): “Gradient Vector Flow 3D Metasphere Example Result” YoungX2040 / CC BY-SA 4.0 (cropped)
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