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

“这项奖励是根据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与数论研究训练基金将把教员的这一核心部分的研究活动整合到一个统一的培训计划中，包括博士后教员、研究生、威斯康星大学和其他地方的本科生。参与这项资助的八名教员涵盖了数论和代数几何的整个领域，从自同构形式到算术几何，再到与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一起工作，目标是产生可发表的研究成果，并轻松过渡到研究生院。对于在我们项目之外被华盛顿大学录取攻读博士学位的美国本科生，我们将提供夏季增强计划，以便学生尽快准备资格考试，以便他们可以毫不拖延地开始研究。一旦研究开始，我们将为这些学生提供RTG奖学金的教学救济。此外，我们每年都会举办研究生会议，重点关注数论和代数几何，在交替的年份，来自华盛顿大学和其他学院的学生将在协作的环境中了解这一快速变化的学科的各个方面的最新发展，并获得演讲和演示的专业技能。总的来说，这些项目将使我们能够加强我们在数论和代数几何方面培养非常优秀的博士毕业生的良好记录。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，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对博士后的积极指导，以及博士后和研究生之间的研究合作的传统。数论——研究数字、它们的模式和性质的学科——是数学最古老的分支之一，我们至今仍在努力解决困扰希腊人的一些问题。代数几何——研究方程及其图形的形状——要年轻得多，但仍然可以追溯到几个世纪前的勒内·笛卡尔（Rene Descartes）时代。但随着亚历山大·格罗滕迪克（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宏伟统一暴露出来。这种新的范式已经成为现代数学的核心，数论和代数几何之间的界限几乎完全被抹去了。威斯康星大学是这一新型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整合的培训计划，从本科水平开始，一直持续到年轻的博士们在他们职业生涯的终身职位前阶段

"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