Quantum Topology and Hyperbolic Geometry

量子拓扑与双曲几何会议将于2013年5月13日至5月17日在越南芽庄举行。会议的目的是了解三维量子场论如何检测底层空间的拓扑结构和几何结构。作为一个例子，我们将研究双曲3流形（一个著名的Dimofte-Gaiotto-Gukov的q级数，Garoufalidis和Garoufalidis- hodgson - rubinstein - segerman也研究过）的指标与有色琼斯多项式的渐近性及其整数系数的分类之间的联系。我们还将研究上述q系列的递推性及其与AJ猜想和Slope猜想的关系，以及上述q系列的Nahm型与Garoufalidis-Le证明的交替环节的彩色Jones多项式的稳定性的关系。会议将集中讨论数学物理的这一令人兴奋的新发展及其对三维几何和拓扑的影响。这是一块肥沃的土地，充满了具体的、可测试的猜想、符号计算机实验、物理学、代数和低维拓扑。年轻研究人员的机会很多，这次会议恰逢量子拓扑学的旧思想与新思想相遇的幸运时机。会议的网址是http://vietnam2013.gatech.edu/。

The conference Quantum Topology and Hyperbolic Geometry will be held in Nha Trang, Vietnam, May 13-May 17, 2013. The aim of the conference is to understand how Quantum Field Theory in dimension three detects the topology and geometry of the underlying space. As an example, we will study the connection of the index of a hyperbolic 3-manifold (a remarkable q-series of Dimofte-Gaiotto-Gukov, also studied by Garoufalidis and Garoufalidis-Hodgson-Rubinstein-Segerman) with the asymptotics of the colored Jones polynomial, and with categorification of its integer coefficients. We will also study the recursions of the above q-series and their relation to the AJ and Slope Conjectures, and the relation of the above q-series of Nahm type with thestability of the colored Jones polynomial of alternating links, proven by Garoufalidis-Le.The conference will focus on this new and exciting developments of mathematical physics and their implications to geometry and topology in dimension 3. This is a fertile land of concrete, testable conjectures, symbolic computer experimentation, physics, algebra and low dimensional topology. The opportunities for young researchers are many, and the conference would come in a fortunate timing where the old ideas in quantum topology meet the new ones. The conference website can be found at http://vietnam2013.gatech.edu/.