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Iwaki Lab
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A lab that studies differential equations containing a small parameter using exact WKB analysis.
AboutAbout the lab
Reading the shape of equations through approximation methods from quantum mechanics
The Iwaki Lab studies differential equations containing a small parameter, such as the Planck constant, using a method called exact WKB analysis.
Exact WKB analysis combines the WKB method, long used for approximate calculations in quantum mechanics, with Borel summation, a technique for summing divergent series.
Using this theory, the global structure of solutions to second-order linear differential equations can be described as an infinite sum of certain period integrals on an algebraic curve.
The lab also works on resurgence theory, its relations to cluster algebras and topological recursion, and applications to Painlevé equations.
Key terms
- Exact WKB analysis
- A method for studying solutions of differential equations containing a small parameter, using divergent series and their summation methods
- Borel summation
- A way of summing an infinite series that would otherwise diverge, so as to assign it a meaningful value
- Stokes phenomenon
- A phenomenon in which the form of the expression approximating a solution of an equation switches depending on the direction in the complex plane
ResearchResearch themes
The lab studies singularly perturbed differential equations containing a small parameter, such as the Planck constant, using exact WKB analysis. Paying attention to the many facets of exact WKB analysis, it also works on its relations to cluster algebras and topological recursion.
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MembersFaculty
- Associate ProfessorKohei IwakiPublications ↗
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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: “AiryAi Abs Surface” Inductiveload / Public domain (cropped)
- Analysis of Differential Equations by Exact WKB Analysis: “Plot of the Airy function Ai(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D” WalkingRadiance / CC BY-SA 4.0 (cropped)
- Related lab (Takada Lab): “Kelvin-Helmholtz instability clouds” Brocken Inaglory / CC BY-SA 3.0 (cropped)
- Related lab (Sakai Lab): “Modell der Weierstraßschen p-Funktion -Schilling, XIV, 7ab, 8 - 313, 314” Oliver Zauzig / CC BY-SA 3.0 (cropped)
- Related lab (Miyamoto Lab): “TuringPattern” Ex.ungue.leonem / Public domain (cropped)
- Related lab (Ishige Lab): “Heat Equation 1D BE Color” Gong Chen, Brandon Cloutier, Ning Li, Benson K. Muite and Paul Rigge with contributions from Sudarshan Balakrishnan, Andre Souza and Jeremy West / CC BY-SA 3.0 (cropped)
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