Mathematical Structures II is divided into two Laboratories. The research subject of (A02-1) Sugawa Laboratory is mainly Complex Analysis. (A02-2) Tanaka Laboratory studies various combinatorial objects, mainly by means of algebraic methods.
This is an introduction to Sugawa Laboratory.
Even if the data and/or functions are described in terms of real variables, hidden structures may emerge when dealing with them as complex variables. For instance, in the classical problems of moments concerning a sequence of real numbers, the power series formed by the sequence (the generating function) gives us many useful visions to tackle the problems. In such a case, Complex Analysis plays an important role.
We are studying analytic functions from the geometric view-point to provide new interpretations to classical results. Moreover, we are interested in quasiconformal mappings, which have recently found many applications in image processing and brain mapping. With the help of computers together with the above knowledge, we are studying modern topics such as Teichmueller spaces, Kleinian groups, Complex Dynamics, and fractals, as well.
If you are interested in the Tanaka Laboratory, please look here.