Researcher Information


Associate Professor

Exact WKB analysis

Department of Mathematics, Mathematics


On the exact WKB analysis for Painleve hierarchies with a large parameter

FieldAlgebraic Analysis of Singular Perturbation Theory
KeywordExact WKB analysis, Asymptotic analysis, Stokes geometry, Higher order Painleve equations

Introduction of Research

The exact WKB analysis is a powerful method in studying both linear and non-linear differential equations which contain a large parameter in an appropriate way. Recently, the exact WKB analysis for higher order Painleve equations with a large parameter has been developed. My research interest is to investigate the Stokes geometries and the structure of instanton type solutions so that the Stokes phenomena for solutions of higher order Painleve equations are correctly caught. Moreover, I study holonomic D-modules associated with non-isolated hypersurface singularities in the context of algebraic analysis.

Representative Achievements

General formal solutions for a unified family of PJ-hierarchies (J=I, II, IV, 34), Y.Umeta, Journal of the Mathematical Society of Japan, Vol. 71, No.3 (2019) 979--1003.
On the Stokes geometry of a unified family of PJ-hierarchies (J=I, II, IV, 34), Y.Umeta, Publ. Res. Inst. Math. Sci., 55 (1) (2019) 79-107.
Holonomic D-modules associated with a simple line singularity and vertical monodromy, S.Tajima and Y.Umeta, Funkcialaj Ekvacioj, 64(1) (2021) 17--48.