Commutative Algebra and Its Applications

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Commutative algebra is a tool in several fields mathematics. Some fundamental problems in those fields are formulated in terms of commutative algebra. These problems stimulate the development of commutative algebra and they are mostly interesing from the purely algebraic viewpoint, too. It is therefore very important for the development of not only the theory of commutative algebra but also mathematics to interchange the ideas between commutative algebra and other fields; algebraic geoemtry, number theory, differential equation erc. We put our stress in this project on arranging the opportunities of interaction, mutual understanding, exchange of ideas and discussions among the specialists of several fields. To accomplish this idea we held several symposia, sent members of our project to conferences whose topics are related to our project and promoted many joint works. We could get many remakable results, for example, study of rings in connection with combinatrics, daterminantal ideals, rings of invariants, classification of algebraic varieties, hodge structures and Torelli problems, study of compactiffications of the moduli space of algebraic vector bundles, study of the algebraic geometric number theoretic aspect of super string theory and so on.