Quantum Topology and Hyperbolic Geometry

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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/.