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年的《美国回收与再动投资法》（公法111-5）资助的。”威斯康星大学代数几何学和数字理论研究培训培训赠款将将该核心部分的研究活动整合到统一的研究活动中培训计划涉及大学教师，研究生和大学生的本科生。 参与赠款的八位教职员工涵盖了数量理论和代数几何的整个范围，从自动形式到算术几何形状到与数学物理学和理论计算机科学的接口。 该小组将开设一个合作的本科研究实验室，该实验室与重点领域的研究生一起工作，目的是进行可发布的研究并放松向研究生院的过渡。 对于我们计划以外的我们的本科生，他们被大学获得博士学位。研究，我们将提供一个夏季增强计划，以便尽快为学生准备预选考试，以便他们的研究可以毫不拖延地开始。 一旦进行研究，我们将通过RTG奖学金为这些学生提供教学救济。 此外，我们还将举办年度研究生会议，重点介绍数字理论和代数几何的几何学，在此期间，UW和其他学校的学生将在这个迅速变化的主题的各个方面与Currrent的发展一起加快，在协作环境中，这一方面的各个方面，并获得讲课和演讲方面的专业技能。 综上所述，这些计划将使我们能够增强我们本来已经有很强的博士学位记录。数量理论和代数几何学的毕业生。 我们还将提供新的博士后奖学金，旨在将重点领域的顶级新博士学位带到威斯康星州，以作为高级教师和学生之间的关键桥梁，并允许我们继续我们在博士后的充满活力的指导和研究合作的传统。在博士后和研究生之间。数字理论 - 数字，模式，其特性的研究 - 是数学最古老的分支之一，我们仍然与一些困扰希腊人感到困扰的问题。 代数几何形状 - 方程式和图形所追踪的形状的研究 - 还年轻得多，但仍然可以追溯到雷内笛子时代。 但是，随着亚历山大·格罗伦迪克（Alexander Grothendieck）的革命性工作及其在1960年代的合作者，这两个看似无关的主题之间的宏伟统一被暴露出来。 这种新的范式已经成为现代数学的核心，以至于数字理论与代数几何形状之间的界限几乎被完全删除了。 威斯康星大学是这个新混合主题的尖端研究中心。 RTG将使我们能够利用我们的研究力量为该地区的新研究人员创建一项完全集成的培训计划，从本科级别开始，并一直持续到他们职业生涯的预期阶段的年轻博士学位