REU Site: Research Expericences for Undergraduates in Mathematics at Indiana University

该奖项支持布卢明顿的印第安纳州大学数学系的本科生研究经验（REU）网站。保留一个有价值的传统可以追溯到五十年，该计划将提供一个密集的夏季研究经验，为有才华的本科生与我们的一些国际公认的教师在独特的项目工作。通过提供一个平衡和结构化的环境，以及口头陈述和书面报告结果的里程碑，IU REU为学生在项目中取得成功奠定了基础。参与者的成功是进一步鼓励必要的背景知识，培养一个紧张和协作的工作环境，最重要的是与导师定期工作会议的预备计划。除了抽象的解决问题的技能和参与者获得的智力耐力，他们的专业发展是通过教师，LaTeX写作研讨会，和其他类似的机会定期研究演示增强。印第安纳州大学REU计划提供了一个身临其境的环境，以强大的导师为导向的研究方法。九名学生将与教职员工一对一或小组合作，在IU校园度过八周时间，解决精心挑选的研究问题。这些问题是未解决的，可访问的，数学意义重大。纯数学的主题是从广泛的领域，包括几何群论，微分几何，组合拓扑学和纽结理论，手术理论，逻辑，复杂和符号动力学，范畴理论的各个方面，以及更多的选择。应用数学的主题来自计算机科学领域，如递归理论或同伦类型理论，以及数学生物学和化学领域，从聚合物组织和细胞功能到遗传学。学生们一起住在宿舍里，共享共同的办公空间，他们从集体沉浸在数学中以及自然随之而来的自发合作中受益。学生通过在全州本科数学研究会议上发表演讲，向同行，教师和研究生进行正式讲座，并撰写正式的独立研究报告来传播他们的研究结果。其中一些报告预计将发展成为同行审查的研究论文。最终，该计划将显著帮助参与者成为当今高技术劳动力的领导者，无论是在学术界还是工业界。该奖项反映了NSF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 award supports the Research Experience for Undergraduates (REU) site in the Department of Mathematics at Indiana University, Bloomington. Preserving a valued tradition dating back fifty years, the program will offer an intensive summer research experience for talented undergraduates working with some of our internationally recognized faculty on unique projects. By providing a well-balanced and structured environment together with milestones for both oral exposition and written reports of results, the IU REU lays the groundwork for student success in their projects. Participant success is further encouraged by a preparatory program for necessary background knowledge, the fostering of an intense and collaborative work environment, and most importantly regular working sessions with mentors. In addition to the abstract problem-solving skills and intellectual stamina gained by the participants, their professional development is enhanced through regular research presentations by faculty members, LaTeX writing workshops, and other similar opportunities.The Indiana University REU program provides an immersive environment with a strong mentorship-oriented approach to research. Nine students will work one-on-one or in small groups with faculty members, spending eight weeks on IU campus tackling carefully selected research problems. These problems are unsolved, accessible, and mathematically significant. Topics in pure mathematics are chosen from a broad swath of fields including geometric group theory, differential geometry, combinatorial topology and knot theory, surgery theory, logic, complex and symbolic dynamics, aspects of category theory, and several more. Topics in applied mathematics are drawn from areas in computer science such as recursion theory or homotopy type theory and areas of mathematical biology and chemistry from polymer organization and cell function to phylogenetics. Housed together in a dormitory and sharing common office space, students benefit from being immersed in mathematics collectively and from the spontaneous collaboration that naturally follows. Students disseminate their findings by delivering presentations at a statewide undergraduate mathematics research conference, giving formal lectures to peers, faculty, and graduate students, and writing a formal self-contained research report detailing their findings. Some of these reports are expected to develop into peer-reviewed research papers. Ultimately, the program significantly helps prepare participants to be the leaders in today's highly technical workforce, whether in academia or industry.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.