Various nice functions appearing in several areas in science and engineering
are known as special functions. Gauss hypergeometric function is such a most
fundamental example. The history of the research of special functions is so
long. My way of the research is from the view point of the theory of complex
integrals and the representation theory. The theory of complex integrals, which is originated and developed by Prof. Aomoto,
is regarded as an advanced version of the complex analysis,
in other words, a theory of homology and cohomology with coefficient of
local systems. The representation theory of
quantum groups, Hecke algebras, finite and infinite Lie algebras and
various new algebras, ordinary and partial differential equations in the
sense of complex analysis, topology, algebraic geometry, conformal field theory,solvable lattice model, and random matrices theory play crucial roles in our
research.