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
基本信息
- 批准号:0838210
- 负责人:
- 金额:$ 129.73万
- 依托单位:
- 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:
- 关键词:
项目摘要
"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
威斯康星大学代数几何和数论研究培训基金将把这一核心教师的研究活动整合到一个统一的培训计划中,涉及来自威斯康星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范围,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。该团队将运营一个合作的本科生研究实验室,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,并轻松过渡到研究生院。对于我们计划之外的美国本科生,我们将提供暑期强化计划,为学生尽快准备资格考试,以便他们的研究可以立即开始。一旦研究开始,我们将为这些拥有RTG奖学金的学生提供教学救济。此外,我们将每年举办研究生会议,每隔一年集中讨论数论和代数几何,来自威斯康星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学科的所有方面的最新发展,并获得演讲和陈述的专业技能。综上所述,这些课程将使我们能够加强我们已经很好的记录,培养出非常优秀的数论和代数几何博士毕业生。我们还将提供新的博士后奖学金,旨在将重点领域的顶尖博士后带到威斯康星州,作为资深教职员工和学生之间的重要桥梁,并使我们能够继续我们精力充沛的博士后导师传统,以及博士后和研究生之间的研究合作。数字理论--研究数字、数字模式和数字性质--是数学中最古老的分支之一,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--研究方程和它们的图形所描绘的形状--要年轻得多,但仍然可以追溯到勒内·笛卡尔时代。但随着亚历山大·格罗森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暴露了出来。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边界几乎完全被抹去了。威斯康星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集成的培训计划,从本科生开始,一直持续到年轻的博士生在其职业生涯的终身教职前阶段
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Jordan Ellenberg其他文献
Jordan Ellenberg的其他文献
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{{ truncateString('Jordan Ellenberg', 18)}}的其他基金
Geometry of Arithmetic Statistics and Related Topics
算术统计几何及相关主题
- 批准号:
2301386 - 财政年份:2023
- 资助金额:
$ 129.73万 - 项目类别:
Continuing Grant
Rational Points and Asymptotics of Distribution
有理点和分布渐进
- 批准号:
2001200 - 财政年份:2020
- 资助金额:
$ 129.73万 - 项目类别:
Continuing Grant
Madison Moduli Weekend - A Conference on Moduli Spaces
麦迪逊 Moduli 周末 - Moduli 空间会议
- 批准号:
1955665 - 财政年份:2020
- 资助金额:
$ 129.73万 - 项目类别:
Standard Grant
Stability Phenomena in Number Theory, Algebraic Geometry, and Topology
数论、代数几何和拓扑中的稳定性现象
- 批准号:
1402620 - 财政年份:2014
- 资助金额:
$ 129.73万 - 项目类别:
Continuing Grant
Moduli Spaces and Algebraic Structures in Homotopy Theory
同伦理论中的模空间和代数结构
- 批准号:
0705428 - 财政年份:2007
- 资助金额:
$ 129.73万 - 项目类别:
Standard Grant
CAREER: Rational points on varieties and non-abelian Galois groups
职业:簇上的有理点和非阿贝尔伽罗瓦群
- 批准号:
0448750 - 财政年份:2005
- 资助金额:
$ 129.73万 - 项目类别:
Standard Grant
Rational points, Galois representations, and fundamental groups
有理点、伽罗瓦表示和基本群
- 批准号:
0401616 - 财政年份:2004
- 资助金额:
$ 129.73万 - 项目类别:
Continuing Grant
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