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

“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。“威斯康星州代数几何和数论研究培训补助金的大学将整合到一个统一的培训计划，涉及博士后教师，研究生和本科生从威斯康星大学和其他地方的这一核心部分的研究活动。 参与资助的八名教师涵盖了数论和代数几何的整个范围，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。 该团队将运行一个合作的本科生研究实验室，本科生在重点领域与研究生一起工作，目标是进行可持续的研究，并缓解向研究生院的过渡。 对于我们计划之外的美国本科生谁被录取到华盛顿大学博士学位。研究，我们将提供一个夏季增强计划，以准备学生资格考试尽快使他们的研究可以开始没有延误。 一旦研究正在进行中，我们将提供教学救济与RTG奖学金这些学生。 此外，我们将运行年度研究生会议，专注于数论和代数几何在隔年，在那里来自UW和其他学校的学生将获得速度与当前的发展，在这个迅速变化的主题的各个方面在一个协作的环境，并获得专业技能的演讲和演示。 总之，这些计划将使我们能够提高我们已经很强的记录，生产非常强大的博士学位。数论和代数几何专业毕业。 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的博士后精力充沛的导师传统，以及博士后和研究生之间的研究合作。它们的性质--是数学最古老的分支之一，在这一分支中，我们仍然在努力解决一些困扰希腊人的问题。 代数几何学--研究方程和由它们的图形描绘出的形状--要年轻得多，但仍然可以追溯到几个世纪前的勒内·笛卡尔时代。 但随着亚历山大格罗滕迪克和他的合作者在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巨大统一被暴露出来。 这种新的范式已经成为现代数学的核心，以至于数论和代数几何之间的界限几乎被完全抹去了。 威斯康星州大学是这一新的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，从本科生开始，一直持续到年轻的博士。

"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