IAS/Park City Mathematics Institute

IAS/帕克城数学研究所

• 批准号: 1915835
• 负责人: Helmut Hofer
• 金额: $ 200万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-15 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1915835&HistoricalAwards=false
• 关键词: IAS; Park; City; Mathematics; Institute

The IAS/Park City Mathematics Institute (PCMI) is an annual three-week residential summer program in the mathematical sciences that combines research, student training, and an emphasis on excellence in pedagogy and equity in mathematics education. PCMI has been in operation since 1991 and has developed a robust and distinctive model that brings together over 300 participants each year from across the entire mathematics profession. Participants include top researchers, university faculty and postdocs, graduate and undergraduate students. The impact of this program is enormous: a large number of research mathematicians have attended a PCMI session at some point in their careers, and many report that their experiences at PCMI have had a strong effect on their career through new mentoring relationships and new collaborations. Each group works on its own projects, ranging from research seminars and graduate and undergraduate lecture series to small group workshops and discussions, each focusing on some area of current research in mathematics or on pedagogy and equity in the classroom. Specific outcomes include: intensive disciplinary training at the undergraduate, graduate and postdoctoral levels for a broad group drawn from many different types of institutions across the country; opportunities for new research collaborations by senior participants and occasions for mentoring opportunities for students and young researchers by more established researchers; a forum for mathematicians at teaching colleges to refocus their mathematical interests and reengage in research topics; a clear focus on the centrality of pedagogical excellence in all parts of the mathematics profession; and an emphasis on how issues related to equity and access are of importance at every level of the profession and in every type of institution.Each year a research theme is chosen as the mathematical focus of PCMI. The graduate and research programs draw up to 60 junior and senior researchers and up to 80 graduate students. This part of PCMI is centered on a series of up to 8 short minicourses designed to introduce students to both introductory and more advanced topics in the field. The impact of this material, through the video archive as well as the annual volume of collected lecture notes from these courses, provides a superlative introduction to that year's research focus. This intensive training of a large group of young mathematicians in a specific area has a significant and lasting impact on that field. The undergraduate program provides a different experience than almost any other REU program in that it is centered around lecture series, but also provides opportunities for these students to interact closely and over an extended period with graduate students and established researchers in the field. Participants in the Workshop for Equity in Mathematics Education develop detailed strategies for enhancing their own efforts to address the challenges of equity, diversity and inclusion in their classrooms; there is also a forum for them to bring these lessons to the larger group of PCMI participants. Recent foci of the research component of PCMI include: Random Matrix Theory (2017), Harmonic Analysis (2018), Quantum Field Theory and Manifold Invariants (2019), and the upcoming Number Theory Informed by Computation (2020).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.

IAS/帕克城数学研究所 (PCMI) 是一项为期三周的数学科学夏季住宿项目，结合了研究、学生培训以及对卓越教学法和数学教育公平性的重视。 PCMI 自 1991 年开始运营，并开发了一个强大且独特的模型，每年汇集来自整个数学行业的 300 多名参与者。参与者包括顶尖研究人员、大学教师和博士后、研究生和本科生。 该计划的影响是巨大的：大量研究数学家在其职业生涯的某个阶段参加过 PCMI 会议，许多人报告说，他们在 PCMI 的经历通过新的指导关系和新的合作对他们的职业生涯产生了重大影响。每个小组都开展自己的项目，从研究研讨会、研究生和本科生讲座系列到小组研讨会和讨论，每个小组都侧重于当前数学研究的某些领域或课堂教学法和公平性。具体成果包括：为来自全国不同类型机构的广大群体提供本科生、研究生和博士后级别的强化学科培训；资深参与者进行新的研究合作的机会，以及更有经验的研究人员为学生和年轻研究人员提供指导的机会；为教学学院的数学家提供一个论坛，让他们重新关注数学兴趣并重新参与研究课题；明确关注数学专业各个领域卓越教学的中心地位；并强调与公平和机会相关的问题在专业的各个层面和各种类型的机构中的重要性。每年都会选择一个研究主题作为 PCMI 的数学焦点。研究生和研究项目吸引了多达 60 名初级和高级研究人员以及多达 80 名研究生。 PCMI 的这一部分以一系列最多 8 个简短的迷你课程为中心，旨在向学生介绍该领域的入门主题和更高级的主题。 通过视频档案以及每年收集的这些课程的讲义，该材料的影响力提供了对当年研究重点的最高级介绍。这种对一大批年轻数学家在特定领域的强化培训对该领域产生了重大而持久的影响。本科课程提供了与几乎任何其他 REU 课程不同的体验，因为它以系列讲座为中心，但也为这些学生提供了与研究生和该领域知名研究人员长期密切互动的机会。数学教育公平研讨会的参与者制定了详细的策略，以加强自己的努力，应对课堂公平、多样性和包容性的挑战；还有一个论坛，供他们将这些经验教训带给更多的 PCMI 参与者。 PCMI 研究部分的最新重点包括：随机矩阵理论（2017 年）、调和分析（2018 年）、量子场论和流形不变量（2019 年）以及即将推出的计算信息数论（2020 年）。该奖项反映了 NSF 的法定奖项使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。