UMETA Yoko Associate Professor

Analysis

Organization
Department of Mathematics
Research Interest
Algebraic Analysis of Singular Perturbation Theory
Keywords
Exact WKB analysis, Asymptotic analysis, Stokes geometry, Higher order Painleve equations

Research Activities

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.

Papers:

  • S.Tajima and Y.umeta, Holonomic D-modules associated with a simple line singularity and vertical monodromy, Funkcialaj Ekvacioj 64 (1) (2021) 17-48
  • Y.Umeta, On the Stokes geomatry of a unified family of (P_J)-hierarchies (J=I,II,IV,34), Publ. Res. Inst. Math. Sci., 55 (1) (2019) 79-107
  • Y.Umeta, General formal solutions for a unified family of (P_J)-hierarchies (J=I,II,IV,34), Journal of the Mathematical Society of Japan, Vol.71, No.3 (2019) 979-1003
  • Y.Umeta, Instanton-type solutions for the second and the fourth Painleve hierarchies with a large parameter, Journal of the Mathematical Society of Japan, Vol.67, No.3 (2015) 943-978

WebPage

Link

Contact

y-umeta（at）math.sci.hokudai.ac.jp