CAREER: Number Theory Research and Outreach

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

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.