CAREER: Number Theory Research and Outreach

该奖项资助了与首席研究员在数论方面的研究兴趣有关的广泛的学术和教育项目。至于他自己的研究，这位研究者计划研究除其他主题外，划分和模形式，高斯超几何级数，特征标和，有限域上的变数，多项式-指数方程，以及模形式的因子。除了自己的研究，这位调查员还将在高中和本科生层面开发一些新的外展和教育项目，并将参与更高级的培训项目。具体地说，调查员将指导为高中生和高中教师举办的研讨会，支持有才华的本科生项目，并为研究生和博士后提供更多机会。数论是一个非常古老的数学分支，它植根于对整数的研究。在现代，它已经成为许多应用努力的重要工具。例如，能够在互联网上安全地传输数据的系统是基于数论的，用于可靠数据传输的纠错码也是如此。教师早期职业发展(Career)计划支持学术教师作为教育工作者和研究人员的早期发展。该计划强调全面、平衡的学术生涯的发展。这一奖项将允许研究人员进一步发展他正在进行的数论研究计划。它还将支持研究人员在高中、本科生、研究生和博士后层面的广泛教育和外展努力。

This award funds a wide range of scholarly and educational projects related to the principal investigator's research interests in Number Theory. With regards to his own research, the investigator plans to study, among other topics, partitions and modular forms, Gaussian hypergeometric series, character sums, varieties over finite fields, polynomial-exponential equations, and thedivisors of modular forms. In addition to his own research, the investigator will develop a number of new outreach and educational programs at the high school and undergraduate levels, and will become involved in training programs at more advanced levels. Specifically, the investigator will direct workshops for high school students and high school teachers, will support programs for talented undergraduate students, and will provide enhanced opportunities for graduate students and postdoctoral fellows.Number Theory is a very old branch of mathematics which has its roots in the study of the whole numbers. In modern times it has become an important tool in many applied endeavors. For example, systems which enable secure transmission of data over the internet are based on Number Theory, as are error correcting codes for reliable data transmission. The Faculty Early Career Development (CAREER) Program supports the early development of academic faculty both as educators and as researchers. The program emphasizes the development of full, balanced academic careers. This award will allow the investigator to further develop his ongoing program of research in Number Theory. It will also support the investigator's broadly based educational and outreach efforts at the high school, undergraduate, graduate, and postdoctoral levels.