REU: Modern Topics in Pure and Applied Mathematics

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This project supports a summer undergraduate research experience in mathematical sciences at the University of Maryland – College Park. The project will contribute to the development of a mathematically sophisticated workforce and broaden the participation of undergraduate students in research in the mathematical sciences. Twelve undergraduates will participate each summer in an eight week residential summer program, preceded by a two week remote training session. Each research team will involve a faculty mentor together with a graduate student assistant. This REU project has three primary goals. The first goal is to nurture research abilities, promote independent thinking, and enhance the technical and presentation skills of the undergraduate participants. The second goal is to provide training to undergraduates from schools with limited research opportunities in STEM fields. The final goal is to provide graduate students with hands-on experience in the supervision of REU projects and administration of REU programs. Student participants will engage in cutting-edge research in a variety of fields within contemporary pure and applied mathematics. The program will also contribute to students’ professional development by offering a diverse array of seminars and workshops, and will provide students with opportunities to present the results of their work at high-profile national conferences.Undergraduate participants in this research program will conduct research in pure and applied mathematical fields under the supervision of experienced faculty and graduate student mentors. Projects will range from mathematical modelling in materials science to machine learning methods for the study of rare events in random systems to applications of harmonic analysis in the representations of data via neural networks. Other projects will originate from mathematical fields such as optimal transport theory, geometric flows, convex and differential geometry, and cluster algebras. Student participants will also gain valuable professional experience through involvement in a series of workshops and seminars: the Update Seminar (where undergraduate participants will give talks on the progress of their research), the Exposure Seminar (where faculty from the host institution and nearby universities will give expository talks on their research), and the Lunchtime Workshop (where a variety of professional development topics will be addressed). Following the conclusion of the summer program, students will remain in contact with their faculty mentors for additional guidance on the preparation of final reports, research articles, and conference presentations.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.