EMSW21-RTG: Algebraic Geometry and Number Theory at the University of Wisconsin

EMSW21-RTG：威斯康星大学代数几何和数论

• 批准号: 0838210
• 负责人: Jordan Ellenberg
• 金额: $ 129.73万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0838210&HistoricalAwards=false
• 关键词: EMSW21; RTG; Algebraic; Geometry; Number

"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."The University of Wisconsin Algebraic Geometry and Number Theory Research Training Grant will integrate the research activities of this core part of the faculty into a unified training program involving postdoctoral faculty, graduate students, and undergraduates from UW and elsewhere. The eight faculty members involved in the grant cover the entire spectrum of number theory and algebraic geometry, from automorphic forms to arithmetic geometry to interfaces with mathematical physics and theoretical computer science. The team will run a collaborative undergraduate research laboratory in which undergraduates work together with graduate students in the focus areas with the goal of producing publishable research and easing the transition to graduate school. For US undergraduates outside our program who are admitted to UW for Ph.D. study, we will offer a Summer Enhancement Program, in order to prepare the students for qualifiying exams as quickly as possible so that their research can begin without delay. Once the research is underway, we will provide teaching relief to these students with RTG fellowships. In addition, we will run annual graduate student conferences, focusing on number theory and algebraic geometry in alternate years, where students from UW and other schools will get up to speed with currrent developments in all aspects of this rapidly changing subject in a collaborative environment, and gain professional skills in lecturing and presentation. Taken together, these programs will enable us to enhance our already strong record of producing very strong Ph.D. graduates in number theory and algebraic geometry. We will also offer new postdoctoral fellowships, aimed at bringing top new Ph.D.s in the focus areas to Wisconsin to serve as a critical bridge between senior faculty and students, and allowing us to continue our tradition of energetic mentorship of postdocs, and research collaboration between postdocs and graduate students.Number theory -- the study of numbers, their patterns, their properties -- is one of the oldest branches of mathematics, in which we still wrestle with some of the problems that vexed the Greeks. Algebraic geometry -- the study of equations and the shapes traced out by their graphs -- is much younger, but still goes back centuries to the time of Rene Descartes. But with the revolutionary work of Alexander Grothendieck and his collaborators in the 1960s, a magnficent unity between these two seemingly unrelated subjects was exposed. This new paradigm has become so central to modern mathematics that the boundary between number theory and algebraic geometry has been almost entirely erased. The University of Wisconsin is a center of cutting-edge research in this new hybrid subject. The RTG will allow us to leverage our research strength to create a completely integrated training program for new researchers in the area, starting at the undergraduate level and continuing all the way up to young Ph.D.s in the pre-tenure phase of their career

“该奖项是根据 2009 年美国复苏和再投资法案（公法 111-5）资助的。”威斯康星大学代数几何和数论研究培训补助金将把该院系核心部分的研究活动整合到一个统一的项目中。培训计划涉及华盛顿大学和其他地方的博士后教师、研究生和本科生。 参与资助的八名教员涵盖了数论和代数几何的整个领域，从自守形式到算术几何，再到数学物理和理论计算机科学的接口。 该团队将运营一个本科生合作研究实验室，本科生与研究生在重点领域合作，目标是产生可发表的研究成果并简化向研究生院的过渡。 对于我们项目之外被录取到华盛顿大学攻读博士学位的美国本科生在学习期间，我们将提供暑期强化计划，以便学生尽快为资格考试做好准备，以便他们的研究能够立即开始。 一旦研究开始，我们将通过 RTG 奖学金为这些学生提供教学救济。 此外，我们将每隔几年举办一年一度的研究生会议，重点关注数论和代数几何，来自华盛顿大学和其他学校的学生将在协作环境中了解这一快速变化的学科各个方面的当前发展，并获得演讲和演讲的专业技能。 总而言之，这些计划将使我们能够增强我们本已良好的记录，培养出非常优秀的博士。数论和代数几何专业的毕业生。 我们还将提供新的博士后奖学金，旨在将重点领域的顶尖新博士带到威斯康星州，作为高级教师和学生之间的重要桥梁，并使我们能够继续我们积极指导博士后和研究合作的传统数论——对数字、它们的模式和性质的研究——是数学最古老的分支之一，在这个分支中，我们仍然在努力解决一些困扰希腊人的问题。 代数几何——对方程及其图形描绘的形状的研究——要年轻得多，但仍然可以追溯到勒内·笛卡尔时代几个世纪。 但随着亚历山大·格洛腾迪克 (Alexander Grothendieck) 及其合作者在 20 世纪 60 年代的革命性工作，这两个看似无关的主题之间的奇妙统一被暴露出来。 这种新范式已经成为现代数学的核心，以至于数论和代数几何之间的界限几乎被完全消除了。 威斯康星大学是这一新混合学科的前沿研究中心。 RTG 将使我们能够利用我们的研究实力，为该领域的新研究人员创建一个完全综合的培训计划，从本科阶段开始，一直到处于职业生涯前终身职位阶段的年轻博士