Pomona Research in Mathematics Experience

这个项目的重点是代数几何，这是一个数学领域，涉及由多项式方程定义的几何对象。波莫纳学院将提供为期八周的暑期住宿项目，进行代数几何和数论方面的研究，其明确目标是在推进研究的同时帮助该领域多样化。该项目名为“波莫纳数学经验研究（PRiME）”，将举办全国竞赛中招募的15名本科生，5名研究生，2名初级教师/博士后研究员和3名高级教师。PRiME将展示新的数学思想和技术，突出代数几何和数论方面的最新研究，提供更多的指导机会，确定潜在的角色榜样，并加强所有参与者的专业网络。这些组成部分，单独地和整体地，将通过培养不同参与者群体当前和未来的专业技能，产生重大的更广泛的影响。波莫纳数学经验研究（PRiME）有四个目标。这些是(1)为全国招募的本科生提供为期8周的暑期代数几何和数论密集研究经验，导致值得在全国会议上发表或展示的新结果；(2)安置本科生进入数学科学学士后学位课程；(3)通过纵向整合的研究集群，为研究生、博士后和教师提供密集的指导和导师培训；(4)建立一个扩展的跨代网络和社区，包括代数几何和数论中代表性不足的少数民族。PRiME旨在通过四个关键要素实现这些目标。(a)本科生参与的研究：五个研究小组每天开会，每个小组形成一个类似reu的单位，由一名教员、一名研究生和三名本科生组成。他们的研究项目将深入研究椭圆曲线的排列；为L-Series and Modular Forms Database （LMFDB）计算Belyi map的信息；编写开源软件来可视化Dessin d’enfants；并制作动画来说明单一性对应于曲线分支覆盖的动作。(b)专业发展：每周为本科生和工作人员（教师和研究生）提供专业发展模块。本科生将参加一系列关于未来数学成功所必需的各种主题的每周研讨会。每隔一周，工作人员将举行以文学为基础的重点讨论。(c)指导小组：将有三个指导/研究小组，每周分别举行两次会议，每个小组由研究生、博士后和教师组成。(d)社区建设：每周将举行客座讲座和问答，邀请杰出的教师，包括来自数学科学领域代表性不足的群体的教师。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 focuses on algebraic geometry, a field of mathematics that concerns geometric objects defined by polynomial equations. Pomona College will offer an eight-week summer residential program to conduct research in algebraic geometry and number theory, with an express aim to help diversify the field as it advances research. The program, entitled "Pomona Research in Mathematics Experience (PRiME)," will host fifteen undergraduates recruited in a national competition, five graduate students, two junior faculty/postdoctoral fellows, and three senior faculty members. PRiME will present new mathematical ideas and techniques, highlight recent research in algebraic geometry and number theory, provide enhanced mentoring opportunities, identify potential role models, and strengthen professional networks for all participants in the program. These components, individually and wholly, will produce significant broader impacts by fostering the current and future professional skills of a diverse group of participants.The Pomona Research in Mathematics Experience (PRiME) has four goals. These are to (1) provide a nationally recruited group of undergraduates with an 8-week intensive summer research experience in algebraic geometry and number theory, leading to new results worthy of publication or presentation at national meetings; (2) position undergraduates to enter post-baccalaureate degree programs in the mathematical sciences; (3) provide intensive mentoring and mentor training for graduate students, postdocs, and faculty via vertically integrated research clusters; and (4) establish an extended cross-generational network and community inclusive of underrepresented minorities in algebraic geometry and number theory. PRiME aims to meet these goals through four key elements. (a) Research with Undergraduate Participation: Five research groups meeting daily, each forming an REU-like unit consisting of one faculty member, one graduate student, and three undergraduates. Their research projects will delve into the ranks of elliptic curves; compute information about Belyi maps for the L-Series and Modular Forms Database (LMFDB); write open-source software to visualize Dessin d’Enfants; and create animations to illustrate the action of monodromy corresponding to branched covers of curves. (b) Professional Development: There will be weekly professional development modules for both undergraduates and staff (faculty and graduate students). Undergraduates will attend a series of weekly workshops on various topics necessary for future success in mathematics. Every other week, the staff will hold focused, literature-based discussions. (c) Mentoring Clusters: There will be three mentoring/research clusters that meet separately twice a week, each consisting of graduate students, postdocs, and faculty. (d) Community Building: There will be weekly guest lectures and Q&A featuring distinguished faculty, including those from groups underrepresented in the mathematical sciences.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.