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Algebraic analysis and special functions

Hiroyuki Ochiai
Degree: Doctor of Mathematical Science (the University of Tokyo)
Research Interests: Algebraic Analysis
Unit: Pure Mathematics

Report

Students in elementary schools like mathematics because the solution of the quiz is unique and simple.
This characteristic still has its meaning in the front of mathematical research,
and requires some idealistic circumstance, which we should investigate.
In the `input', we should declare which models we will deal with.
In the `output', we have to develop the mathematical concepts such as; numbers, functions, figures, convergence, and so on.
Without these terminologies, we hardly expect to have an elegant answer.

The field of special functions, which is one of my interest, serves a classical and strong object for such a mathematical terminology and has a ubiquitous role in Science, Technology, and Culture.
Theoretical research on special functions is necessary from the growing computer sciences, especially, symbolic computations. Representation theory is another key word for my research interest. This word is rather new. It can be used to describe the higher dimensional object with symmetry, and to reduce the complication to a simpler situation.
It is a typical method to solve the problem in mathematics. It is also expected to have a significant role to set up the problem in the real world into the mathematical model, such as mathematical physics or solid state chemistry.

I am a new comer to this GCOE program. My past research may show an interface between several fields of mathematics, like algebra, analysis and geometry, of course a part of them. I hope these characteristic will benefit the program.

A feature on an educational activity in the graduate course other than research: Up to September 2009, I've been in Department of Mathematics, Nagoya University, where I took care of a graduate student from an Asian country. In the undergraduate seminar, I treated the probability for the qualification of actuaries.

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