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/PARK CITY数学研究所（PCMI）是一年一度的三周夏季夏季计划，该计划结合了研究，学生培训以及对数学教育的教育和公平性的卓越表现。 PCMI自1991年以来一直在运行，并开发了一种强大而独特的模型，该模型每年从整个数学专业中汇集了300多名参与者。参与者包括顶级研究人员，大学教职员工和博士后，研究生和本科生。 该计划的影响是巨大的：许多研究数学家在职业生涯的某个时候参加了PCMI会议，许多人报告说，他们在PCMI的经验通过新的指导关系和新的合作对他们的职业生涯产生了很大的影响。每个小组都从事自己的项目，从研究研讨会，研究生和本科讲座系列到小组研讨会和讨论，每个讲座都集中在当前数学研究的某些领域，还是课堂上的教学法和公平性。具体结果包括：在本科生，研究生和博士后水平的深入学科培训中，该阶级是从全国许多不同类型的机构中汲取的广泛组；高级参与者的新研究合作机会和场合为学生和年轻研究人员指导机会的机会；数学家教学论坛教学论坛，以重新关注其数学利益并重新参与研究主题；明确关注数学专业各个部位的教学卓越中心性；强调与公平和访问有关的问题在专业和各种类型的各种层面上都至关重要。每年，研究主题被选为PCMI的数学重点。研究生和研究课程最多绘制了60名初级和高级研究人员以及多达80名研究生。 PCMI的这一部分集中在一系列多达8个短的小型库中，旨在向学生介绍该领域的入门和更高级的主题。 通过视频档案以及这些课程收集的讲座的年度卷的影响，对当年的研究重点提供了最高的介绍。对特定领域中一大批年轻数学家的这种深入培训对该领域产生了重大而持久的影响。本科课程提供的经验与几乎所有其他REU计划不同，因为它以讲座系列为中心，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进行紧密相互互动的机会。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，以应对课堂中的公平，多样性和包容性挑战；他们还有一个论坛，可以将这些课程带给较大的PCMI参与者。 PCMI研究组成部分的最新焦点包括：随机矩阵理论（2017），谐波分析（2018），量子场理论和流形不变式（2019年）以及通过计算得出的即将到来的数字理论（2020年）。本奖颁奖典礼反映了NSF的法定任务，并通过评估了基金会的智力效果，并通过评估了基金会的范围和广泛的范围。