Differential Equations in Complex Domain, Special Functions, Twisted de Rham Theory, Mathematical Physics

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 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.