Research

Naotaka Kajino is working on probability theory, with the principal research interest in analysis of Laplacians and their associated diffusion processes on fractals, especially how analytic properties of Laplacians reflect the singular nature of the geometry of the fractals. The classes of fractals include the classical Euclidean self-similar fractals such as the well-known Sierpinski gasket and Sierpinski carpet, and self-conformal fractals appearing naturally in complex function theory such as the limit sets of Kleinian groups and the Julia sets of complex dynamical systems. Recently he has been studying also L^p-type nonlinear energy functionals on fractals and their associated p-harmonic functions and p-energy measures for p > 1.