Mathematical Sciences: Applications of Linkage

链接技术有助于攻击 交换代数中的一组不同的问题。 教授 Kustin和米勒将集中在这项研究主要是在 理论的各个方面涉及联系的相互作用， 完美理想的有限自由分解的结构， 特别强调乘法结构 支持这些决议。 他们还将扩展这项研究 更灵活的剩余交线关系， 以前的技术可以扩展到更广泛的代数类。 他们特别感兴趣的里斯代数，代数 由不定式的序列和矩阵定义。 Poincare级数合理性判定的应用 以及某些K-群的计算。

The technique of linkage has been instrumental in attacking a diverse group of problems in commutative algebra. Professors Kustin and Miller will concentrate in this research mainly on the aspects of the theory that involve the interplay of linkage with the structure of finite free resolution of perfect ideals, putting particular emphasis on the multiplicative structures supported on these resolutions. They will also extend this study to the more flexible relation of residual intersection, so that previous techniques can be extended to a wider class of algebras. They are particularly interested in Rees algebras, and algebras defined by sequences and matrices of indeterminates. Applications to determination of rationality of Poincare series and the computation of certain K-groups are expected.