### Harmony of Gröbner bases and the modern industrial society

It brings positive contribution of mathematics for solutions of social difficult problems to investigate harmony of the theory of pure mathematics that developed highly and the forefront of technology in the modern industrial society. Our research group consists of algebraists, computer scientists and statisticians who engage in the research of Grobner bases, a trendy topic of modern mathematics. Our goal is to make the progress of the theory together with the development of the algorithm in order to answer the request of realistic questions as well as to apply the latest theory of Grobner bases to the forefront of technology. Especially, we make a breakthrough in the theory together with computer algebra systems on Grobner bases that would be demanded to create softwares which could be effective for statistics such as clinical testing and designs of experiments with discussing the possibility of making marketable packages on algebraic statistics as well as with studying the applications to related research fields such as the cryptographic theory. The complementary development of the theory and society into consideration will yield novel viewpoints of pure mathematics which cannot be obtained in the traditional frame of pure mathematics and, in addition, will stimulate rapid improvement of the ability of the software development in our country.