Conference: Quantum Topology and Hyperbolic Geometry

This award provides partial travel support for U.S.-based researchers to participate in the international conference "Quantum Topology and Hyperbolic Geometry", to be held in Phu Quoc, Vietnam, from June 2–6, 2025, and the associated summer school at the Vietnam Institute for Advanced Study in Mathematics in Hanoi, from June 9–13, 2025. The conference will focus on various aspects of quantum topology, its connections to hyperbolic geometry and other fields in mathematics and theoretical physics. It will gather leading experts, young mathematicians, and graduate students from around the world, offering them a platform to share ideas and to collaborate. The summer school, designed for young mathematicians, will feature five minicourses and brainstorming sessions led by world-renowned experts, contributing to the development and training of new mathematical talent. Significant breakthroughs over the past few decades-such as the discovery of the Jones polynomial, the development of topological quantum field theories, and the introduction of gauge theory invariants, have revolutionized knot theory and three-manifold topology. These developments have forged deep connections between topology and diverse areas including number theory, Lie theory, and statistical physics, utilizing methods that extend beyond traditional algebraic topology. Quantum topology, in particular, has emerged as a pivotal field with substantial applications in biology, physics, combinatorics, algebra, and quantum computation. This conference seeks to build upon these advancements by exploring cutting-edge research in quantum topology and its interplay with hyperbolic geometry and other mathematical disciplines. By addressing a wide range of topics, the conference will promote interdisciplinary collaboration and stimulate innovative approaches that may lead to significant breakthroughs. Additionally, by engaging students and early-career researchers in key problems and frontier research areas, especially at the confluence of quantum and classical topology in three dimensions—the event will enhance their education and contribute to the vitality of the mathematical community. More information about the two events can be found at these websites: https://viasm.edu.vn/hdkh/School-Topo-Geo-2025, https://viasm.edu.vn/hdkh/Conf-Topo-Geo-2025. 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.