REU Site: Computational Number Theory

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Eight students across the country will participate in an eight-week research experience in computational number theory at Clemson University each year of this project. The goal of this program is to help students attain a higher level of independence in mathematical research by having them take part in significant and interesting research projects. Participants will be introduced to various tools, techniques, and problems from number theory and will work on important and often difficult problems that are suitable for undergraduate work. This program will not only provide the participants with the opportunities to broaden their knowledge in their research area but will also give participants the opportunity to become better expositors of their research. This will be accomplished through student lectures during and at the end of the program that will include two presentations in different formats. The PIs will organize an annual REU conference that will enable the students to interact with and learn from students in other REU programs in the region. The conference will provide the students with a valuable opportunity to deliver their first professional talk in a friendly atmosphere and will also help to disseminate the results obtained by the REU students. This project is jointly funded by the Mathematical Sciences Research Experiences for Undergraduates Sites program and the Established Program to Stimulate Competitive Research program.The theory of modular forms plays an important role in modern number theory, such as Andrew Wiles' proof of Fermat's Last Theorem. In this program, various problems in modular forms will be introduced. These problems will offer a blend of computational investigation with the theoretical pursuit of fundamental problems in modular forms or, more generally, in number theory. The problems are specifically chosen so that the participants will be able to begin investigations almost immediately on computational aspects of the projects, giving them an opportunity to spend the entire time at Clemson working on meaningful research. Potential research projects include but are not limited to studying the distribution of zeros of certain modular forms or period polynomials, investigating properties of higher coefficients of Hecke polynomials, and analyzing traces of Hecke operators on certain types of modular forms. Many of these problems are natural extensions or continuations of the results obtained in the previous REUs. More information can be found at the REU website: https://huixue.people.clemson.edu/REU.html.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.