RTG: Applied Algebra at the University of South Florida

该项目将采用多管齐下的方法来招募和留住多样化的国内学生，为他们在应用代数领域从事研究工作做好更好的准备，并特别努力招募女性、代表性不足的少数民族、第一代学生、退伍军人和技术工作者。最终，该项目将增加网络安全和量子劳动力所有分支中受过数学培训的多元化美国公民和永久居民的数量，有助于提高美国的国家安全、经济竞争力和基础设施弹性。该项目的目标是：1)在南佛罗里达大学应用代数领域建立多元化、垂直整合的研究团队，重点研究与密码学、编码理论和量子计算等应用领域的联系；2)培养下一代多样化的美国数学研究人员在其研究生涯中取得成功所需的习惯、思维和专业技能；3)通过广泛的外展和丰富、支持性和富有成效的培训环境，招收和留住多样化的国内学生；4)帮助其他人学习本项目中开发的最佳实践，例如，通过与佛罗里达大西洋大学合作建立一个新的佛罗里达应用代数中心；5)在资助期之后维持项目。为了实现这些目标，RTG项目将整合一些已有的活动，包括最近开发的与密码学和量子科学相关的课程，一个本科研究项目，以及针对8-12年级女孩的推广项目。此外，还将制定一些新的举措，包括：由教师、博士后研究人员、研究生和本科生组成的跨学科研究团队；多层次辅导计划；跨队列同伴辅导；专业技能发展培训；以及校内实习机会。通过该项目，学员将参加三个垂直整合的跨学科研究团队，每个团队专注于以下研究领域之一：1)密码学，研究植根于代数和数论的可用于设计下一代密码系统的难计算问题，包括欧几里得格中的短向量搜索，等基因和群体行为的反转；2)编码理论，涉及用于纠正数据传输过程中出现的错误的数学工具，重点是修复问题和基于代码的密码学；3)量子计算，侧重于设计量子算法来解决经典计算机难以解决的应用代数问题，以及利用计算代数技术改进量子电路设计，并使用纠错码为这些电路带来冗余，以保护它们免受环境引起的误差。除了在这些领域培养下一代多样化的数学研究人员外，该项目还将扩展和垂直整合USF正在开发的应用代数计划，并将加强佛罗里达应用代数社区内的合作关系，首先是佛罗里达大西洋大学（FAU），一个HSI。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.