REU Site: Arithmetic Geometry, Number Theory, and Representation Theory at the University of Virginia

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The University of Virginia (UVA) Research Experiences for Undergraduates in Arithmetic Geometry, Number Theory, and Representation Theory is an intense research activity for undergraduate students. The project provides research experiences for undergraduates interested in arithmetic geometry, combinatorics, and number theory. Organized by the principal investigator with assistance from rotating colleagues, the program plans to train approximately 10 undergraduates annually in the summers of 2022, 2023, and 2024. The participants will be chosen after a nationwide search. Recruitment will target participants from underrepresented groups as well as participants from institutions that do not offer similar STEM research activities for undergraduates. The REU program will enable undergraduate students to enjoy an enhanced learning experience, including research projects and seminars. The overall goal of the UVA REU program is to attract talented undergraduate students to careers in the mathematical sciences, which in turn helps promote progress in science and national security by addressing critical issues in the preparation of the next generation of researchers.Research topics will be accessible to students but will go beyond traditional mathematics coursework, involving cutting-edge studies related to analytic number theory, elliptic curves, Galois representations, modular forms, partitions, prime numbers, and quantum modular forms. These fields have applications to internet security, modeling in physics, and other physical sciences. In addition to pursuing original research, participants will be mentored in various aspects of the mathematics profession. Sessions on grant proposal preparation, graduate school preparation, and careers in industry will be held to help prepare the participants for the "real world" of the mathematical sciences.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.