PCMI 2023 Explored Quantum Computation
The 2023 research topic for Park City Mathematics Institute (PCMI), an annual Institute outreach program held in Park City, Utah, was Quantum Computation. The program, organized by David Gosset (University of Waterloo); Aram Harrow (MIT); Stacey Jeffery (CWI and QuSoft); Ryan O'Donnell, past IAS Member (2003–04) and von Neumann fellow (2010–11), (Carnegie Mellon University); and Thomas Vidick (Caltech), attracted 203 participants from 24 countries.
PCMI is an intensive three-week residential conference and summer school which engages attendees across the entire mathematics community by providing individual courses of study that enrich participants in mathematical topics appropriate for their level. Attendees include undergraduate and graduate students, postdocs, mid-career mathematics researchers as well as the most distinguished senior researchers. Beyond the specific academic activities tailored to each group, cross-program activities provide opportunities for participants from different groups to interact around subject matter, and planned social activities allow for further interaction, which can lead to new collaborations, mentorship opportunities, and more broadly, a chance for participants to better understand people in quite different parts of the world of mathematics.
The choice of Quantum Computation as a research topic in 2023 was motivated by the substantial current activity, both theoretical and practical, in this field. This includes recent experiments that probe the "quantum computing advantage," to understand if and how quantum computers can outperform classical ones at certain tasks. The graduate summer school participants attended a set of minicourses to introduce them to a range of topics at the forefront of this field, delivered by leading experts. The lecturers came from both academic institutions and industry, and provided participants with an in-depth look both at the most recent state of theory in the subject as well as informed views about the current prospects for building and using quantum computers. The undergraduate students received an introduction to the theory of quantum computation with a focus on quantum algorithms. Attendees of the program for mid-career faculty at undergraduate-focused institutions learned about the emerging field of topological quantum computation. Finally, the research program took the form of a traditional research conference, with participants presenting seminar style talks on their current work, but with all activities interlaced among the other contemporaneous activities at PCMI. What sets PCMI apart is the way in which all participants are encouraged to intermingle; this allows the undergraduates and graduate student participants to meet the intellectual leaders of the field as well as early or mid-career researchers in a relaxed setting, which can often lead to key information on graduate programs for the undergraduates, mentorships and postdoctoral opportunities for graduate students, and new opportunities for collaboration for everyone.
PCMI also includes a workshop devoted to the broader goal of equity in mathematics education. This was led in 2023 by Rochelle Gutiérrez (University of Illinois College of Education) with the title of the Workshop for Rehumanizing Mathematics. The goal of this workshop, which counted mathematicians, mathematics teachers, and mathematics education professors among its attendees, was to further the understanding of identity and power issues in mathematical education. Participants discussed practical strategies to help educators expand their goals to consider not only access and achievement but the political and human aspects of teaching and engaging with mathematics. Up through 2023, PCMI also incorporated a professional development program for secondary school teachers; this is currently on hiatus.
Video lectures from this year's program can be viewed on the PCMI YouTube channel. A YouTube playlist is also available for PCMI 2022, which focused on the topic of Number Theory Informed by Computation, organized by Jennifer Balakrishnan (Boston University); Bjorn Poonen (MIT); and Akshay Venkatesh, Robert & Luisa Fernholz Professor in the Institute’s School of Mathematics.
The topic for PCMI 2024 is Motivic Homotopy, organized by Benjamin Antieu (Northwestern University); Marc Levine (Universität Duisburg-Essen); Oliver Röndigs (Universität Osnabruck); Alexander Vishik, past IAS Member (2000, 2002, 2004–05) in the School of Mathematics, (University of Nottingham); and Kirsten Wickelgren (Duke University). It will be held July 7–27, 2024.
PCMI receives major funding from the National Science Foundation (DMS-1915835) and the Simons Foundation, and generous additional support from Math for America and the Clay Mathematics Institute Senior Scholar Program.