Researcher's Information

Associate Professor

WATANABE, Takuya

Mathematics

Linear differential equations in complex domains/singular perturbation, spectrum, Stokes phenomenon

The subject of our research is to study the spectra (eigenvalues, quantum resonances etc) which relate the quantum mechanics and the classical mechanics. Differential equations which describe typical phenomena have beautiful structures in a mathematical sense. Hence the basic methods in analysis (complex analysis, functional analysis and Fourier analysis) play important roles for problems in Mathematical Physics. 
The students of our laboratory learn deeply such basic techniques selected according to their interests. 
Recently we investigate differential equations including a small parameter (singular perturbation). Its keyword is “Stokes phenomenon”. In order to understand it, we have to treat the differential equations in the complex domain. 
This fact implies that studying natural phenomena require the advanced mathematical technique and interests us in Mathematical Physics.
  • A supernumerary bow can sometimes be seen inside rainbows. This is explained by “Stokes phenomenon” of an Airy’s differential equation.