RTG: Coding Theory, Cryptography, and Number Theory

RTG：编码理论、密码学和数论

• 批准号: 1547399
• 负责人: Felice Manganiello
• 金额: $ 212.7万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1547399&HistoricalAwards=false
• 关键词: RTG; Coding; Theory; Cryptography; Number

The goal of this project is to enhance the development of students in the fields of coding theory, cryptography, and number theory. Activities with strong vertical integration components are introduced at the undergraduate, graduate, and postdoctoral levels to improve recruitment, retention, and training of students in these areas, including those from historically black colleges and universities and small colleges in the region, and to provide research growth and facilitate professional development for postdocs and early career faculty. Activities supported by this grant will give broader access to the latest research methods and results in coding theory, cryptography, and number theory, areas replete with theoretical advances and practical applications.The research problems in this proposal center on automorphic forms and codes, modular forms and algebraic geometry codes, and cryptography and computational number theory. These topics allow entry for students via computation and exploration and offer the opportunity for both theoretical advances and practical applications. Activities in this Research Training Group project include curriculum and condensed research experiences designed to better prepare students transitioning from coursework to research; exam preparation modules to support students entering the graduate school admissions phase as well as those applying for candidacy; and working groups to broaden the research expertise of advanced graduate students and postdocs beyond their dissertation topics in addition to professional development and networking opportunities. The training through research involvement provided by this Research Training Group in Coding Theory, Cryptography, and Number Theory will develop a stronger and more diverse workforce.

该项目的目标是促进学生在编码理论、密码学和数论领域的发展。在本科生、研究生和博士后层面引入具有强大垂直整合成分的活动，以改善这些领域学生的招募、保留和培训，包括来自该地区历史悠久的黑人学院和大学以及小型学院的学生，并提供研究成长并促进博士后和早期职业教师的专业发展。 此项资助支持的活动将让人们更广泛地接触编码理论、密码学和数论等充满理论进展和实际应用的领域的最新研究方法和成果。本提案的研究问题集中在自同构形式和代码、模形式和代数几何代码、密码学和计算数论。这些主题允许学生通过计算和探索进入，并提供理论进步和实际应用的机会。该研究培训小组项目的活动包括课程和浓缩研究经验，旨在更好地准备学生从课程作业过渡到研究；考试准备模块，为进入研究生院招生阶段以及申请候选资格的学生提供支持；和工作组，除了专业发展和交流机会之外，还扩大高级研究生和博士后的研究专业知识，使其超出其论文主题。该研究培训小组在编码理论、密码学和数论方面提供的研究参与培训将培养一支更强大、更多样化的劳动力队伍。