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 geometry of the fractals. The classes of fractals include the classical Euclidean self-similar fractals, 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, and various random fractals appearing in the context of Schramm-Loewner evolution, in particular the important two-dimensional random geometry known as the Liouville quantum gravity.