Shingo Takeuchi

I moved to Shibaura Institute of Technology in April 2011. In the northern half of the Omiya campus there is an original forest left, which is a very pleasant environment for me, who is living in a city. Among them, the building of the department of mathematical sciences is located in the closest place to the primeval forest, and it is very exciting to me, who love insects. I am healed by the sound of cicadas that can be heard especially at dusk of the summer. My hobbies include fishing, swimming, history walks, caring for turtles.

I study the p-Laplacian, which generalizes Laplacian. The p-Laplacian is a typical nonlinear operator with degeneracy-singularity and has been studied mathematically since ancient times. I had previously dreamed of building a dynamical system theory of parabolic partial differential equations with degeneracy-singularty and was studying a reaction-diffusion equation with the p-Laplacian as its model case. While studying the influence of degeneracy-singularity on the shape of solution from the viewpoint of free boundary problem and infinite dimensional dynamical system, I came to the idea that the p-Laplacian's eigenvalue problem is essential. Therefore, recently, I am doing something like classical analysis to investigate the properties and applications of generalized trigonometric functions, which are eigenfunctions of the p-Laplacian, and elliptic integrals and Jacobi elliptic functions generalized by using them. Unexpectedly, Ramanujan formulas of hypergeometric function are useful and relationships with number theory are getting visible, and I am feeling that I wandered into "mathematical" primeval forest.