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Sakai Lab
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A lab studying special functions and integrable systems, reading the Painlevé equations through the lens of geometry.
AboutAbout the lab
Organizing the properties of equations through geometry.
The Sakai Lab studies differential and difference equations in the complex domain from the perspective of the theory of special functions and integrable systems.
The lab aims to apply the methods and questions developed in the study of elliptic functions and hypergeometric functions to functions defined by nonlinear differential and difference equations.
From an algebro-geometric perspective, the lab works on characterizing integrable systems, including the Painlevé differential equations.
By studying geometric objects called spaces of initial conditions, the lab seeks to understand the various properties of these equations.
Key terms
- Painlevé equations
- Nonlinear differential equations with a special property concerning the singularities of their solutions. Their solutions define new special functions.
- Integrable systems
- Equations and dynamical systems that have many conserved quantities and symmetries and can be solved exactly.
- Difference equations
- Equations expressed as relations among discrete values rather than in terms of continuous variables.
ResearchResearch themes
The lab studies differential and difference equations in the complex domain from the perspective of the theory of special functions and integrable systems. From an algebro-geometric perspective, it characterizes integrable systems, including the Painlevé differential equations.
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MembersFaculty
- Associate ProfessorHidetaka SakaiPublications ↗
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Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Sakai Lab
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Milanov LabFaculty of Science, Department of MathematicsGeometry and integrable systemsThe information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “Modell der Weierstraßschen p-Funktion -Schilling, XIV, 7ab, 8 - 313, 314” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Painlevé Equations and Their Extensions: “Weierstrass p function” Claudio Rocchini / CC BY-SA 4.0 (cropped)
- Related lab (Takada Lab): “Kelvin-Helmholtz instability clouds” Brocken Inaglory / CC BY-SA 3.0 (cropped)
- Related lab (Iwaki Lab): “AiryAi Abs Surface” Inductiveload / Public domain (cropped)
- Related lab (Miyamoto Lab): “TuringPattern” Ex.ungue.leonem / Public domain (cropped)
- Related lab (Milanov Lab): “Periodic waves in shallow water” US Army / Public domain (cropped)
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