CAREER: Number Theory Research and Outreach

该奖项资助了广泛的学术和教育项目，这些项目与主要研究者在数论方面的研究兴趣有关。关于他自己的研究，研究人员计划研究，除其他主题外，分区和模块化形式，高斯超几何级数，字符和，有限域上的品种，多项式指数方程，以及模块化形式的因子。 除了他自己的研究之外，研究人员还将在高中和本科阶段开发一些新的推广和教育计划，并将参与更高级的培训计划。 具体来说，调查员将直接讲习班的高中学生和高中教师，将支持计划，为有才华的本科生，并将提供增强的机会，研究生和博士后研究员。数论是一个非常古老的分支的数学有其根源的研究，整个数字。 在现代，它已成为许多应用领域的重要工具。 例如，能够通过互联网安全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。 该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。 它还将支持研究者在高中、本科、研究生和博士后水平上的广泛教育和推广工作。

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.