IWAKI, Kohei

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Associate Professor
Ordinary differential equations, exact WKB analysis, integrable systems, topological recursion
Research interests
Exact WKB analysis of differential equations and related topics
Current research

I'm studying singularly-perturbed differential equations with a small parameter from the view point of the exact WKB analysis. The method is based on the classical WKB (Wentzel-Kramers-Brillouin) method in quantum mechanics and the Borel summation method for divergent series. For second-order linear ODEs, the exact WKB analysis allows us to describe global behaviors (monodromy, Stokes structure etc.) of solutions in terms of certain generating series (called the Voros coefficients) of period integrals over the algebraic curve obtained as the classical limit of the differential equation. I'm also interested in connections among the exact WKB analysis and other research topics, including resurgent analysis, cluster algebras, topological recursion, and Painlevé equations.

Selected publications
  1. Parametric Stokes phenomenon for the second Painlevé equation, Funkcialaj Ekvacioj, 57 (2014), 173-243.
  2. Exact WKB analysis and cluster algebras, J. Phys. A: Math. Theor. 47 (2014) 474009, 98pp (with T. Nakanishi).
  3. Exact WKB analysis and cluster algebras II: Simple poles, orbifold points, and generalized cluster algebras, Int. Math. Res. Not. IMRN2016, no. 14, 4375-4417 (with T. Nakanishi).
  4. Painlevé equations, topological type property and reconstruction by the topological recursion, Journal of Geometry and Physics, 124 (2018), 16-54 (with O. Marchal and A. Saenz).
  5. Voros coefficients for the hypergeometric differential equations and Eynard-Orantin's topological recursion -- Part II : For the confluent family of hypergeometric equations, Journal of Integrable Systems, 4 (2019), (with T. Koike and Y.-M. Takei).
  6. 2-parameter τ-function for the first Painlevé equation --Topological recursion and direct monodromy problem via exact WKB analysis--, Communications in Mathematical Physics, 377 (2020), 1047-1098.

Mathematical Society of Japan