RTG: Applied Algebra at the University of South Florida

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This project will use a multi-pronged approach to recruit and retain diverse domestic students and better prepare them to pursue research careers in Applied Algebra, making a special effort to recruit women, underrepresented minorities, first generation students, veterans, and tech workers. Ultimately, this project will increase the number of mathematically-trained, diverse U.S. Citizens and permanent residents in all branches of the cybersecurity and quantum workforce, helping to improve U.S. national security, economic competitiveness, and infrastructure resilience. The goals of this project are to: 1) establish diverse, vertically-integrated research teams at the University of South Florida in the field of Applied Algebra, focusing on connections with the applied fields of cryptography, coding theory and quantum computing; 2) nurture the Habits and Mind and professional skills that the next generation of diverse U.S. mathematics researchers will need to succeed in their research careers; 3) recruit and retain diverse domestic students through extensive outreach and a rich, supportive, and productive training environment; 4) help others learn the best practices developed in this project, for example, through a new Florida Hub for Applied Algebra, to be established in collaboration with Florida Atlantic University; and 5) sustain the program beyond the funding period. To achieve these goals, this RTG project will bring together a number of pre-existing activities, including recently developed curricula related to cryptography and quantum sciences, an undergraduate research program, and outreach programs for grade 8-12 girls. In addition, a number of new initiatives will be developed, including: interdisciplinary research teams composed of faculty, postdoctoral researchers, graduate students, and undergraduates; a multi-tiered mentoring program; cross-cohort peer tutoring; professional skills development training; and on-campus internship opportunities.Through this project, the trainees will participate in three vertically integrated interdisciplinary research teams, each focusing on one of the following research areas: 1) Cryptography, which investigates hard computational problems rooted in algebra and number theory that can be used to design the next generation of cryptosystems, including the search for short vectors in Euclidean lattices, isogenies, and the inversion of group actions; 2) Coding Theory, which involves mathematical tools for the correction of errors that occur during the transmission of data, with an emphasis on the repair problem and on code-based cryptography; 3) Quantum Computing, focusing on the design of quantum algorithms to solve problems in Applied Algebra that are intractable to classical computers, as well as the improvement of quantum circuit design by computational algebra techniques, and the use of error correcting codes to bring redundancy to these circuits to protect them from the error induced by the environment. In addition to training the next generation of diverse mathematics researchers in these fields, the project will expand and vertically integrate Applied Algebra initiatives that are being developed at the USF, and it will strengthen collaborative ties within the Florida Applied Algebra community, starting with Florida Atlantic University (FAU), an HSI.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.