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

该奖项支持印第安纳大学布鲁明顿数学系本科生研究经验(REU)网站的继续。该项目保留了近50年来的宝贵传统，将为有才华的本科生提供密集的暑期研究体验，与我们的一些国际公认的教师合作开展独特的项目。通过提供一个平衡和结构良好的环境，以及口头阐述和书面结果报告的里程碑，该大学REU为学生在他们的项目中取得成功奠定了基础。通过培养紧张和协作的工作环境，以及最重要的是通过与导师的定期工作会议，进一步鼓励参与者取得成功。除了参与者获得的抽象问题解决技能和智力耐力外，他们的专业发展还通过教员定期的研究报告、乳胶写作研讨会、印第安纳大学图书馆的参观和演示以及向参与者提供的大量计算资源和其他类似机会来加强。印第安纳大学的REU项目提供了一个身临其境的环境，提供了一种以导师为导向的研究方法。八名学生将与教职员工一对一或小组合作，在伊利诺伊大学校园里花八周时间解决精心挑选的研究问题。通常，这些问题是未解决的、可访问的，并且在数学上具有重要意义。纯数学的主题选自广泛的领域，包括：几何群论、微分几何、组合拓扑和纽结理论、外科理论、逻辑、复数和符号动力学、范畴理论的方方面面等等。应用数学的主题来自计算机科学的领域，如递归理论或同伦类型理论，以及数学、生物学和化学的领域，从聚合物组织和细胞功能到系统发育。学生们一起住在一个宿舍里，共享共同的办公空间，从集体沉浸在数学中以及自然地随之而来的自发合作中受益。学生们通过在全州范围内的本科生数学研究会议上发表演讲，给同行、教师和研究生做正式讲座，以及撰写一份详细说明他们发现的正式研究报告来传播他们的发现。其中一些报告预计将发展成同行评议的研究论文。最终，该计划将极大地帮助参与者为成为当今高技术劳动力的领导者做好准备，无论是在学术界还是在行业。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 continuation of the Research Experience for Undergraduates (REU) site in the Department of Mathematics at Indiana University, Bloomington. Preserving a valued tradition dating back nearly 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 the fostering of an intense and collaborative work environment, and most importantly through the 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, tours and demonstrations of Indiana University's libraries and extensive computational resources which are made available to participants, and other similar opportunities. The Indiana University REU program provides an immersive environment with a strong mentorship oriented approach to research. Eight students will work one-on-one or in small groups with faculty members, spending eight weeks on IU campus tackling carefully selected research problems. Typically, 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.