REU Site: Computational Number Theory

全国各地的八名学生将参加为期八周的研究经验，在计算数论在克莱姆森大学每年的这个项目。该计划的目标是帮助学生在数学研究中获得更高水平的独立性，让他们参加重要而有趣的研究项目。参与者将被介绍给各种工具，技术和数论问题，并将致力于适合本科工作的重要和困难的问题。该计划不仅为参与者提供了扩大其研究领域知识的机会，而且还将使参与者有机会成为他们研究的更好支持者。这将通过在课程期间和结束时的学生讲座来完成，该课程将包括两种不同格式的演示文稿。PI将组织一次年度REU会议，使学生能够与该地区其他REU项目的学生互动并向他们学习。会议将为学生提供一个宝贵的机会，在友好的气氛中发表他们的第一次专业演讲，也将有助于传播REU学生获得的成果。该项目由数学科学研究经验的本科生网站计划和建立计划，以刺激竞争力的研究计划联合资助。模形式的理论在现代数论中发挥着重要作用，如安德鲁怀尔斯的证明费马大定理。在这个程序中，将介绍各种模块形式的问题。这些问题将提供一个混合的计算调查与理论追求的基本问题，在模块化的形式，或更一般地说，在数论。这些问题是专门选择的，以便参与者将能够开始调查几乎立即对计算方面的项目，让他们有机会花整个时间在克莱姆森工作有意义的研究。潜在的研究项目包括但不限于研究某些模形式或周期多项式的零点分布，调查Hecke多项式的高系数的性质，以及分析Hecke算子在某些类型的模形式上的迹。这些问题中有许多是以前雷乌斯中所得结果的自然延伸或延续。更多信息可以在REU网站上找到：https://huixue.people.clemson.edu/REU.html.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

Eight students across the country will participate in an eight-week research experience in computational number theory at Clemson University each year of this project. The goal of this program is to help students attain a higher level of independence in mathematical research by having them take part in significant and interesting research projects. Participants will be introduced to various tools, techniques, and problems from number theory and will work on important and often difficult problems that are suitable for undergraduate work. This program will not only provide the participants with the opportunities to broaden their knowledge in their research area but will also give participants the opportunity to become better expositors of their research. This will be accomplished through student lectures during and at the end of the program that will include two presentations in different formats. The PIs will organize an annual REU conference that will enable the students to interact with and learn from students in other REU programs in the region. The conference will provide the students with a valuable opportunity to deliver their first professional talk in a friendly atmosphere and will also help to disseminate the results obtained by the REU students. This project is jointly funded by the Mathematical Sciences Research Experiences for Undergraduates Sites program and the Established Program to Stimulate Competitive Research program.The theory of modular forms plays an important role in modern number theory, such as Andrew Wiles' proof of Fermat's Last Theorem. In this program, various problems in modular forms will be introduced. These problems will offer a blend of computational investigation with the theoretical pursuit of fundamental problems in modular forms or, more generally, in number theory. The problems are specifically chosen so that the participants will be able to begin investigations almost immediately on computational aspects of the projects, giving them an opportunity to spend the entire time at Clemson working on meaningful research. Potential research projects include but are not limited to studying the distribution of zeros of certain modular forms or period polynomials, investigating properties of higher coefficients of Hecke polynomials, and analyzing traces of Hecke operators on certain types of modular forms. Many of these problems are natural extensions or continuations of the results obtained in the previous REUs. More information can be found at the REU website: https://huixue.people.clemson.edu/REU.html.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.