Pomona Research in Mathematics Experience

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This project focuses on algebraic geometry, a field of mathematics that concerns geometric objects defined by polynomial equations. Pomona College will offer an eight-week summer residential program to conduct research in algebraic geometry and number theory, with an express aim to help diversify the field as it advances research. The program, entitled "Pomona Research in Mathematics Experience (PRiME)," will host fifteen undergraduates recruited in a national competition, five graduate students, two junior faculty/postdoctoral fellows, and three senior faculty members. PRiME will present new mathematical ideas and techniques, highlight recent research in algebraic geometry and number theory, provide enhanced mentoring opportunities, identify potential role models, and strengthen professional networks for all participants in the program. These components, individually and wholly, will produce significant broader impacts by fostering the current and future professional skills of a diverse group of participants.The Pomona Research in Mathematics Experience (PRiME) has four goals. These are to (1) provide a nationally recruited group of undergraduates with an 8-week intensive summer research experience in algebraic geometry and number theory, leading to new results worthy of publication or presentation at national meetings; (2) position undergraduates to enter post-baccalaureate degree programs in the mathematical sciences; (3) provide intensive mentoring and mentor training for graduate students, postdocs, and faculty via vertically integrated research clusters; and (4) establish an extended cross-generational network and community inclusive of underrepresented minorities in algebraic geometry and number theory. PRiME aims to meet these goals through four key elements. (a) Research with Undergraduate Participation: Five research groups meeting daily, each forming an REU-like unit consisting of one faculty member, one graduate student, and three undergraduates. Their research projects will delve into the ranks of elliptic curves; compute information about Belyi maps for the L-Series and Modular Forms Database (LMFDB); write open-source software to visualize Dessin d’Enfants; and create animations to illustrate the action of monodromy corresponding to branched covers of curves. (b) Professional Development: There will be weekly professional development modules for both undergraduates and staff (faculty and graduate students). Undergraduates will attend a series of weekly workshops on various topics necessary for future success in mathematics. Every other week, the staff will hold focused, literature-based discussions. (c) Mentoring Clusters: There will be three mentoring/research clusters that meet separately twice a week, each consisting of graduate students, postdocs, and faculty. (d) Community Building: There will be weekly guest lectures and Q&A featuring distinguished faculty, including those from groups underrepresented in 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.