RTG: Coding Theory, Cryptography, and Number Theory

本计划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、研究生和博士后层面引入了具有强大垂直整合成分的活动，以改善这些领域的学生的招聘、保留和培训，包括来自该地区历史悠久的黑人学院和小型学院的学生，并为博士后和早期职业教师提供研究增长和促进专业发展。该基金支持的活动将使人们更广泛地接触到编码理论、密码学和数论等领域的最新研究方法和成果，这些领域充满了理论进步和实际应用。本文主要研究自同构形式与编码、模形式与代数几何编码、密码学与计算数论。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。这个研究训练小组项目的活动包括课程和浓缩的研究经验，旨在更好地为学生从课程过渡到研究做准备；考试准备模块，以支持学生进入研究生入学阶段以及申请候选人；以及工作组，以扩大高级研究生和博士后的研究专长，除了专业发展和交流机会之外。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。

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.