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

该项目将通过研究参与为学生和博士后提供代数、代数几何和数论领域的培训。这些都是数学中最古老的分支。目前在这些领域的研究是一个新旧结合的迷人的混合体：使用非常现代的技术来研究长期存在的具有挑战性的问题，这些技术将这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、四世纪开花；最近的一些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，它的历史甚至比几何学还要早；现在，通过对整数系数多项式的研究，它与代数几何密切相关。这些领域的研究有着广泛的应用，从基本粒子物理到网络安全。这个研究培训小组将有助于向学生传达这些研究领域的兴奋，并促进教师、博士后同事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。为了实现这些目标，研究者们计划举办一系列的学术讨论会，为学生提供主题课程，举办年度研讨会和年度会议，并在学生和博士后之间组织有关当前感兴趣主题的阅读课程。

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.