Conference: New Frontiers in Gauge Theory, Topology, and Physics

This project supports US-based mathematicians, postdoctoral researchers, and graduate students to participate in an international research event at the Okinawa Institute of Science and Technology (OIST), Okinawa, Japan, August 31–October 30, 2026. The goal of the two-month program is to bring together mathematicians and physicists to investigate fundamental questions about the structure of space, geometric form, and the physical laws governing our universe. The venue will create a sustained and concentrated research environment where insights from one field can inform and accelerate progress in the others. At its core, the program focuses on gauge theory, a theoretical construction originally developed in physics to describe elementary particles and the fundamental forces behind their interactions. Gauge theory has since become a powerful tool in modern mathematics. Using gauge-theoretic ideas, mathematicians can study the properties of curved spaces and uncover deep connections between seemingly disparate areas of mathematics, often suggested by considerations in theoretical physics. In terms of broader impacts, the program places strong emphasis on training and outreach. NSF support will prioritize early-career researchers, including graduate students and postdoctoral fellows, providing them with valuable opportunities for international collaboration and professional development. The program will also feature an autumn school, specialized workshops, and mentoring activities. In addition, public lectures aimed at non-specialist undergraduate audiences will communicate the excitement and significance of modern mathematics and physics to a broader public. Together, these efforts will help cultivate a broad and well-prepared scientific workforce while enhancing public understanding of fundamental research. The focus of the program at OIST will be the following three interconnected research areas: (1) Vafa–Witten invariants in four-dimensional gauge theory and their relation to higher-dimensional gauge theory; (2) Applications of gauge theory to low-dimensional topology; and (3) 3D mirror symmetry and its mathematical foundations. The unifying theme is the study of gauge theoretic moduli spaces arising across geometry, topology, and quantum field theory. These spaces appear in seemingly disparate contexts but share analytic and algebro-geometric features which also admit physical interpretations. Advances in one direction frequently lead to transformative developments in the others. These topics are at the forefront of modern geometry, topology, and mathematical physics. A central goal of the program is to identify and understand common structures that arise across these problems. By fostering close collaboration between mathematicians and physicists, the program aims to accelerate discoveries that advance fundamental knowledge in geometry, topology, and quantum field theory. The program's website is the following: https://sites.google.com/view/new-frontiers-in-gauge-theory/home 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. NSF Award ID: 2621460 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Richard Wentworth | Institution: University of Maryland, College Park, COLLEGE PARK, MD | Award Amount: $20,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2621460 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2621460.html