Mathematical Sciences: Research in Commutative Algebra

点击翻译按钮获取中文摘要

Srinivasan 9623141 This proposal supports the work of Professor H. Srinivasan to work on problems in commutative algebra. She intends to study the multiplicity of R/I for a homogeneous ideal I in terms of the shifts in its minimal graded resolution. She also intends to study the finite determinations of the presentations of an ideal. Finally, she intends to construct the minimal algebra resolutions for R/I where I is an ideal in the linkage class of a complete resolution. This research is on the boundary between commutative algebra and algebraic geometry. Both fields arose from the classical problem of studying mathematical objects defined in the plane by the simplest of equations, namely polynomials. Today, the fields use methods not only from algebra, but also from analysis and topology, and conversely are extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.