RTG: Research Training Group in Algebra, Algebraic Geometry, and Number Theory

RTG：代数、代数几何和数论研究培训小组

• 批准号: 1502651
• 负责人: Elham Izadi
• 金额: $ 200万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1502651&HistoricalAwards=false
• 关键词: RTG; Research; Training; Group; Algebra

This project will provide training through research involvement for students and postdoctoral associates in the areas of algebra, algebraic geometry, and number theory. These are some of the oldest branches of mathematics. Current research in these areas is a fascinating mixture of the old and the new: the study of longstanding challenging problems using very modern techniques that intertwine viewpoints from all three areas. Geometry flowered in the third and fourth centuries BC with the study of conic sections by the Greeks; more recent approaches related these geometric objects to quadratic equations. Algebraic geometry is the more general study of geometric objects using polynomials. Number theory is also a very old subject with a history that predates even that of geometry; it is now closely related to algebraic geometry via the study of polynomials with integer coefficients. Research in these fields has had a wide range of applications from elementary particle physics to cybersecurity. This Research Training Group will help to communicate the excitement of these research areas to students and to foster new research among faculty, postdoctoral associates, and students. The focus of this project is to involve undergraduate students, graduate students, and postdoctoral associates in common research. The investigators plan to achieve these goals by running a colloquium series, by offering topics courses to students, by running a yearly workshop and a yearly conference, and by organizing reading courses among students and postdoctoral associates on topics of current interest.

该项目将通过研究参与为代数、代数几何和数论领域的学生和博士后提供培训。 这些是数学的一些最古老的分支。 目前这些领域的研究是新旧研究的迷人结合：使用非常现代的技术来研究长期存在的挑战性问题，这些技术将所有三个领域的观点交织在一起。 随着希腊人对圆锥曲线的研究，几何学在公元前三世纪和四世纪蓬勃发展。最近的方法将这些几何对象与二次方程联系起来。 代数几何是使用多项式对几何对象进行更一般的研究。 数论也是一门非常古老的学科，其历史甚至早于几何学。现在，通过研究具有整数系数的多项式，它与代数几何密切相关。 这些领域的研究具有从基本粒子物理学到网络安全的广泛应用。该研究培训小组将帮助向学生传达这些研究领域的精彩内容，并促进教师、博士后和学生之间的新研究。 该项目的重点是让本科生、研究生和博士后参与共同研究。 研究人员计划通过举办系列研讨会、向学生提供主题课程、举办年度研讨会和年度会议以及在学生和博士后同事中组织当前感兴趣主题的阅读课程来实现这些目标。