IAS/Park City Mathematics Institute

IAS/Park City数学研究所（PCMI）是一个为期三周的年度夏季数学科学住宿项目，将研究，学生培训和强调卓越的教学法和数学教育的公平性相结合。PCMI自1991年以来一直在运作，并开发了一个强大而独特的模式，每年汇集300多名来自整个数学专业的参与者。参与者包括顶尖的研究人员、大学教师和博士后、研究生和本科生。这个项目的影响是巨大的：大量的研究数学家在他们职业生涯的某个阶段参加了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强烈的影响。每个小组都有自己的项目，从研究研讨会、研究生和本科生系列讲座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个领域或课堂上的教学法和公平。具体成果包括：为来自全国许多不同类型机构的广泛群体提供本科、研究生和博士后层次的强化学科培训；资深参与者为新的研究合作提供机会，资深研究人员为学生和年轻研究人员提供指导机会；为教学学院的数学家提供一个论坛，让他们重新关注自己的数学兴趣并重新参与研究课题；明确关注卓越教学在数学专业各个部分的中心地位；并强调与公平和机会相关的问题在专业的每一个层次和每一种类型的机构中是多么重要。每年都会选择一个研究主题作为PCMI的数学重点。研究生和研究项目招收60名初级和高级研究人员和80名研究生。PCMI的这一部分集中在一系列多达8个简短的迷你课程上，旨在向学生介绍该领域的入门和更高级的主题。这些材料的影响，通过视频档案以及从这些课程中收集的年度讲义量，提供了对当年研究重点的最高级介绍。在某一特定领域对一大群年轻数学家进行密集培训，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的知名研究人员密切互动的机会。数学教育公平研讨会的参与者制定了详细的策略，以加强他们自己的努力，应对课堂公平、多样性和包容性的挑战；还有一个论坛，让他们把这些经验教训带给更多的PCMI参与者。PCMI最近的研究重点包括：随机矩阵理论（2017），谐波分析（2018），量子场论和流形不变量（2019），以及即将到来的由计算通知的数论（2020）。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。

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.