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

这个项目将通过参与研究为学生和博士后提供代数、代数几何和数论领域的培训。这些都是一些最古老的数学分支。目前在这些领域的研究是新旧的迷人混合体：使用非常现代的技术研究长期具有挑战性的问题，这些技术将所有三个领域的观点交织在一起。公元前3世纪和4世纪，随着希腊人对圆锥曲线的研究，几何学蓬勃发展；更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；它现在通过研究具有整数系数的多项式而与代数几何密切相关。从基本粒子物理到网络安全，这些领域的研究已经有了广泛的应用。这个研究培训小组将帮助向学生传达这些研究领域的兴奋之情，并在教师、博士后助理和学生中培养新的研究。这个项目的重点是让本科生、研究生和博士后助理参与共同的研究。研究人员计划通过举办一系列座谈会、向学生提供专题课程、举办年度研讨会和年度会议，以及在学生和博士后助理中组织关于当前感兴趣的主题的阅读课程来实现这些目标。

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.