Quantum Topology and Hyperbolic Geometry

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This award provides partial travel support for U.S. based researchers to participate in the international conference "Quantum Topology and Hyperbolic Geometry III" held in Da Nang, Vietnam, May 27-May 31, 2019, and workshop held at Quy Nhon University, Jun 3-June 7, 2019. The conference covers all aspects of quantum topology and its relation to hyperbolic geometry. It brings together participants from all over the world and provides an opportunity for researchers and students to share their latest ideas and to collaborate with each other. The conference is followed by a workshop, June 3-7, 2019, in Quy Nhon. Four of the speakers of the conference will each give a 5-lecture mini-course for graduate students and recent Ph.D's thereby contributing to the training and development of mathematical talent. Knot theory has long been an active branch of topology. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 35 years: the Jones polynomial, topological quantum field theories, gauge theory type invariants, etc. The new developments relate knot theory to other branches of mathematics such as number theory, Lie theory, statistical physics, etc, and employ tools far beyond the traditional ones from algebraic topology. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of quantum computation. This conference will drive and promote progress in all aspects of quantum topology and its relations to geometry. It will provide a venue for sharing new results in the closely related fields of quantum topology and 3-manifold geometry and topology; it will increase collaboration and communication among research experts globally; and it will introduce researchers, especially students and early career researchers, to important problems and areas of current research, especially problems lying at the interface of quantum and classical topology in three dimensions. The website of the conference is at http://vietnam2019.math.gatech.edu.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.