Park City Mathematics Institute

Institute For Advanced Study, Princeton NJ

Investigators

Abstract

The Park City Mathematics Institute (PCMI) is an annual summer event, held in Park City, Utah, which provides a vertically integrated set of programs, each one focused on students, faculty or researchers in mathematics at a different career stage. PCMI is an outreach program of the Princeton Institute for Advanced Study, and has been held annually since 1991. Each year the program centers around a research theme in the mathematical sciences, chosen to reflect the most active areas in mathematics where new advances are most likely to be stimulated by the type of interaction that PCMI facilitates. The constituent subprograms include: the core Graduate Summer School, a set of 8 minicourses aimed at graduate students, both more advanced and those just starting out; an accompanying Research Program, which is an opportunity for researchers at all levels, ranging from postdocs to the most distinguished leaders in the field, to interact and collaborate; an Undergraduate Summer School, which includes both a lecture course and a small group research experience; the Undergraduate Faculty Program, which brings together a small group of faculty from undergraduate-facing institutions who wish to reengage with the research activities in their field; finally, a small workshop centered on a variety of topics related to Diversity and Inclusion in the mathematics classroom and the general mathematics community. Each group is occupied during the three weeks of the program with their specific activities. PCMI provides a space where interaction between these different groups can happen easily and naturally. These interactions lead to new research collaborations, new mentoring opportunities, and the possibility for the younger participants to learn more about becoming part of the mathematical community. A central goal of PCMI is to bring together a group of students and more senior mathematicians, diverse in as many dimensions as possible, to engage in high level mathematical interactions, with an underlying emphasis on pedagogical excellence and the importance of the interrelationship of the members of this broad mathematical community. The mathematical focus in a PCMI summer session is concentrated on areas of recognized importance with a high level of activity. Programs are typically selected about eighteen months in advance, with a specially designated group of organizers, themselves leading specialists in the field, to guide the intellectual coherence of the session. Upcoming programs are: Motivic Homotopy Theory (2024) and Extremal and Probabilistic Combinatorics (2025). Some of the recent programs include: Quantum Computation (2023), Number Theory Informed by Computation (2022), Quantum Field Theory and Manifold Invariants (2019) and Random Matrix Theory (2018). Attendees have included a number of recent Fields Medalists and other of the most distinguished researchers. The outcomes of each of these sessions includes a volume of lecture notes, published by the AMS, and a professionally produced video archive of the graduate mini-course lectures. The long history of the program, and the variety of fields which it has covered, means that very many mathematicians in the US and abroad have attended PCMI as students or researchers at some point in their careers, and many report that the experience was pivotal in the development of their research program. 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.