IAS/Park City Mathematics Institute

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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.