COLLABORATIVE RESEARCH: EMSW21-RTG: JOINT COLUMBIA-CUNY-NYU RESEARCH TRAINING GROUP IN NUMBER THEORY

合作研究：EMSW21-RTG：哥伦比亚大学-纽约市立大学-纽约大学联合数论研究培训小组

• 批准号: 0739346
• 负责人: Lucien Szpiro
• 金额: $ 87.02万
• 依托单位: CUNY Graduate School University Center
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0739346&HistoricalAwards=false
• 关键词: COLLABORATIVE; RESEARCH; EMSW21; RTG; JOINT

The goal of the RTG proposal is to make the New York metropolitan area a premier world center and model for the study of number theory. The project is a joint training effort involving three universities (Columbia-CUNY-NYU) with eight principal investigators and twenty-five other faculty all working in number theory and related areas. The Columbia-CUNY-NYU team will develop nine new graduate courses for the design of a city-wide graduate number theory curriculum with more active training methods such as workshops, presentations by students, and opportunities to develop technical lecturing, computer programming, and writing skills. The new graduate courses will go beyond the existing first year courses (commutative algebra/algebraic geometry, algebraic number theory) and will cover a broad range of core topics (required for cutting edge research) such as: arithmetic geometry, automorphic representations, spectral theory, and combinatorial number theory. In addition, six new or restructured undergraduate courses will be developed and an annual undergraduate summer research program and graduate summer school (meeting once every 3 years) will be created. The recently created Columbia-CUNY-NYU Number Theory Seminar will be redesigned, making it more accessible to students and more vibrant for seminal research. A central goal is to provide an environment where postdocs, graduate students, undergraduates, and faculty from the entire New York metropolitan area study and work together in a collaborative atmosphere that fosters research and development.Number theory is one of the oldest and most fundamental branches of mathematics. Basic research in number theory has led to important applications in computer science and cryptography. Recent spectacular breakthroughs in the subject such as the proof of Fermat's Last Theorem by Taylor-Wiles require an understanding of an enormous amount of mathematics, much of it outside number theory. It is not sufficient any more for beginning students to study a small segment of number theory. The eight PI's of this proposal (Goldfeld, Kolyvagin, Kramer, Szpiro, Tschinkel, Urban, Venkatesh, Zhang) have extensive overlapping interests but their combined expertise covers all of modern number theory. The scientific research interests of the team include algebraic/arithmetic geometry, hyperbolic geometry, automorphic forms and representations, Langlands program, analytic number theory, spectral theory, ergodic theory, Lie algebras, algebraic number theory, elliptic curves, dynamical systems, and cryptography. This project will be decisive in raising the level of number theory across participating campuses: cross-pollinating successful ideas already in existence, and creating approaches through collective interaction. It is hoped that this RTG will become a national model for other programs of this kind.

RTG提案的目的是使纽约都会区成为最重要的世界中心和数字理论研究的模型。 该项目是一项联合培训工作，涉及三所大学（哥伦比亚 - 纽约尼亚），八名主要研究人员和其他二十五个教师都在数字理论和相关领域工作。哥伦比亚 - 纽约尼亚团队将开发九个新的研究生课程，以设计全市范围的研究生编号理论课程，并​​采用更积极的培训方法，例如研讨会，学生的演讲以及开发技术讲课，计算机编程和写作技能的机会。新的研究生课程将超出现有的第一年课程（交换代数/代数几何，代数数理论），并将涵盖广泛的核心主题（削减边缘研究所需的核心主题），例如：算术几何学，算术几何学，自动形式表示，光谱理论和组合数理论。 此外，还将开发六个新的或重组的本科课程，并将创建一个年度夏季研究计划和研究生暑期学校（每3年一次会议）。最近创建的哥伦比亚 - 纽约尼数理论理论研讨会将重新设计，使学生更容易获得，并且更充满活力。一个核心目标是提供一个环境，在整个纽约大都会地区研究的博士后，研究生，本科生和教职员工中，并在培养研究和发展的协作氛围中共同工作。名单是最古老，最基本的数学分支之一。数字理论的基础研究导致了计算机科学和密码学中的重要应用。该主题最近的壮观突破，例如泰勒 - 韦尔斯（Taylor-Wiles）的Fermat最后一个定理的证明，需要了解大量数学，其中大部分是以外的数字理论。入门学生研究数字理论的一小部分是不够的。该提案的八个PI（Goldfeld，Kolyvagin，Kramer，Szpiro，Tschinkel，Urban，Venkatesh，Zhang）具有广泛的重叠兴趣，但它们的综合专业知识涵盖了所有现代数字理论。团队的科学研究兴趣包括代数/算术几何形状，双曲几何形状，自动形式和表示，兰兰兹计划，分析数理论，光谱理论，梯形理论，lie代数，代数数量理论，椭圆形曲线，动态系统和密码学。该项目将在提高参与校园的数量理论水平上是决定性的：交叉授粉已经存在，并通过集体互动来创造方法。希望该RTG将成为其他此类计划的国家模式。