IAS/Park City Mathematics Institute

IAS/Park City数学学院(PCMI)是一个为期三周的数学科学暑期住宿项目，它结合了研究、学生培训以及对卓越教育学和数学教育公平性的强调。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，每年聚集了来自整个数学专业的300多名参与者。参与者包括顶尖研究人员、大学教职员工和博士后、研究生和本科生。这个项目的影响是巨大的：许多研究数学家曾在职业生涯的某个时候参加过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强烈的影响。每个小组都致力于自己的项目，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，或关于教育学和课堂公平的研究。具体成果包括：对来自全国许多不同类型机构的广泛群体进行本科、研究生和博士后级别的密集学科培训；高级参与者有机会开展新的研究合作，更有地位的研究人员有机会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，让他们重新关注他们的数学兴趣并重新参与研究主题；明确关注数学专业所有部分的卓越教学的中心地位；以及强调与公平和获取机会有关的问题如何在该专业的各级和每一类机构具有重要意义。每年都选择一个研究主题作为PCMI的数学重点。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个小课程为中心，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，通过视频档案以及每年从这些课程收集的课堂笔记，为当年的研究重点提供了一个最好的介绍。对一大批青年数学家进行特定领域的强化培训，对该领域产生了重大和持久的影响。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在较长一段时间内与研究生和该领域知名研究人员密切互动的机会。数学教育公平讲习班的参与者制定了详细的战略，以加强他们自己的努力，以应对课堂上的公平、多样性和包容性的挑战；还有一个论坛供他们向更多的PCMI参与者传授这些课程。PCMI研究部分最近的焦点包括：随机矩阵理论(2017)、调和分析(2018)、量子场论和流形不变量(2019)，以及即将推出的由计算提供信息的数论(2020)。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。

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.