Commutative Algebra (Mathematics)

Sally教授将继续研究交换代数中与局部环及其奇点理论相关的课题。该研究还将借鉴并有助于曲面理论和代数几何中的高维变化。主要议题将包括寻找双等效局部域的有限准则和解析不可约准则。我们的目标是将Zariski的一些关于两族扩展和整体封闭理想的定理扩展（到更高的维度和更一般的环境）。Sally教授每学期将教授一门代数本科课程，积极参加研究生和教师的代数研讨会，并为普渡大学关注女性在科学中的作用的组织提供讲座、非正式谈话和咨询。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

Professor Sally will pursue research in Commutative Algebra on topics related to the theory of local rings and their singularities. The research will also draw from and contribute to the theory of surfaces and higher dimensional varieties in Algebraic Geometry. The primary topics will include the search for finiteness criteria for birationally equivalent local domains and criteria for analytic irreducibility. The goal is the extension (to higher dimension and to more general setting) of some of Zariski's theorems on birational extensions and integrally closed ideals. Professor Sally will teach one undergraduate course in algebra each semester, actively participate in graduate student and faculty seminars in algebra and give lectures, informal talks and counseling to the organizations at Purdue which are concerned with the role of women in science. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.