Quantum Topology and Hyperbolic Geometry

该奖项为美国研究人员提供部分旅行支持，以参加2019年5月27日至5月31日在越南岘港举行的国际会议“量子拓扑和双曲几何III”，以及2019年6月3日至6月7日在奎恩大学举行的研讨会。会议涵盖了量子拓扑学的各个方面及其与双曲几何的关系。它汇集了来自世界各地的参与者，并为研究人员和学生提供了一个分享他们最新想法和相互合作的机会。会议之后是一个研讨会，2019年6月3日至7日，在奎恩。会议的四位演讲者将分别为研究生和最近的博士生提供一个5讲的迷你课程，从而为数学人才的培养和发展做出贡献。 纽结理论一直是拓扑学中一个活跃的分支。在过去的35年里，纽结理论和3-流形拓扑领域出现了令人兴奋的新发展：琼斯多项式、拓扑量子场论、规范理论类型不变量等。这些新发展将纽结理论与其他数学分支联系起来，如数论、李论、统计物理等，并采用了远远超出代数拓扑的传统工具。该学科与生物学、物理学、组合学、代数学和量子计算理论有着重要的应用和关系。这次会议将推动和促进量子拓扑学及其与几何学关系的各个方面的进展。它将提供一个场所，分享量子拓扑学和三维几何学和拓扑学密切相关领域的新成果;它将增加全球研究专家之间的合作和交流;它将向研究人员，特别是学生和早期职业研究人员介绍当前研究的重要问题和领域，特别是位于三维量子和经典拓扑学界面的问题。会议的网站是http://vietnam2019.math.gatech.edu.This奖项反映了NSF的法定使命，并已被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.