REU: Modern Topics in Pure and Applied Mathematics

该项目支持马里兰大学帕克分校数学科学的夏季本科生研究经验。该项目将有助于培养一支精于数学的人才队伍，并扩大本科生对数学科学研究的参与。每年夏天，12名本科生将参加为期8周的住宿暑期项目，之前是为期两周的远程培训课程。每个研究小组将包括一名教师导师和一名研究生助理。这个REU项目有三个主要目标。第一个目标是培养研究能力，促进独立思考，提高本科生参与者的技术和表达能力。第二个目标是为来自STEM领域研究机会有限的学校的本科生提供培训。最终目标是为研究生提供REU项目监督和REU项目管理的实践经验。学生参与者将在当代纯数学和应用数学的各个领域从事前沿研究。该计划还将通过提供多样化的研讨会和讲习班来促进学生的专业发展，并将为学生提供在备受瞩目的国家会议上展示其工作成果的机会。本研究项目的本科生将在经验丰富的教师和研究生导师的指导下进行纯数学和应用数学领域的研究。项目范围将从材料科学的数学建模到研究随机系统中罕见事件的机器学习方法，再到通过神经网络表示数据中的谐波分析应用。其他项目将源于数学领域，如最优输运理论，几何流，凸和微分几何，以及聚类代数。学生参与者还将通过参与一系列的研讨会和研讨会获得宝贵的专业经验：更新研讨会（本科生参与者将发表他们的研究进展），曝光研讨会（来自主办机构和附近大学的教师将对他们的研究进行解释性演讲），以及午餐研讨会（将讨论各种专业发展主题）。在暑期课程结束后，学生将与他们的教师导师保持联系，以获得关于准备期末报告、研究文章和会议演讲的额外指导。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 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.