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/.

Project Report

was held in Nha Trang, Vietnam, May 13-17, 2013. Intellectual Merit:The aim of the conference was to understand how Quantum Field Theory in dimension three detects the topology and geometry of the underlying space. The conference focused on the 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 conference emphasized applications of these disciplines to other areas including hyperbolic geometry. The conference intent was to provide opportunities for cross-fertilization of ideas around these areas. The opportunities for young researchers are many, and the conference came in fortunate timing where the old ideas in quantum topology meet the new ones. Approximately 11 US based mathematicians, some of whom were graduate students, recent Ph.D's, and women, were partially supported with travel expenses by this grant. Many of the supported participants gave presentations at the conference. Broader Impacts: The conference brought together participants from all over the world, third-world countries, women, minorities, and provided opportunities for researchers and students to share their latest ideas and to collaborate with each other. The knowledge obtained on this occasion will be disseminated by participants throughout the world. The presentations included plenary talks by distinguished researchers, as well as short talks by other participants. Graduate students and recent Ph.D's gained greatly from the broad exposure of the leading researchers. Particular attention was paid to researchers from developing countries, as well as ways to attract minorities and women into the field. We expect to publish a conference proceedings containing cutting-edge research papers and lecture notes which will be suitable for research mathematicians, students, and readers with backgrounds in other exact sciences, including biology, chemistry, computer science and physics. The conference website can be found at vietnam2013.gatech.edu/.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1251399
Program Officer
Joanna Kania-Bartoszynska
Project Start
Project End
Budget Start
2013-05-01
Budget End
2014-04-30
Support Year
Fiscal Year
2012
Total Cost
$25,000
Indirect Cost
Name
Georgia Tech Research Corporation
Department
Type
DUNS #
City
Atlanta
State
GA
Country
United States
Zip Code
30332