Applications are closed
for this workshop

Quantum invariants and low-dimensional topology

August 14 to August 18, 2023

at the

American Institute of Mathematics, Pasadena, California

organized by

Efstratia Kalfagianni, Christine Ruey Shan Lee, Helen Wong, and Tian Yang

This workshop, sponsored by AIM and the NSF, will be devoted to working on open problems relating quantum invariants to low-dimensional topology and geometry.

The solution to Thurston’s geometrization conjecture established that 3-manifolds decompose into geometric pieces and that hyperbolic geometry is ubiquitous in low dimensional topology. Since the 80’s, low dimensional topology has also been influenced by ideas from quantum physics, which led to subtle structures and invariants. These include the Jones knot polynomial and the Witten-Reshetikhin-Turaev Topological Quantum Field Theories. Understanding the interplay of these quantum invariants to geometric structures from Thurston’s picture is a major goal of low dimensional topology that has received attention in the recent years. Outstanding conjectures predict deep relations between quantum topology and hyperbolic geometry. For example, the volume conjectures assert that certain quantum invariants of hyperbolic 3-manifolds should determine the volume of the hyperbolic structure.

The workshop will bring together experts in quantum topology and in hyperbolic geometry to study the interplay between geometry and TQFT structure on 3-manifolds, with an eye towards developing tools to approach some of these conjectures.

The workshop will focus on the following promising directions:

  • Asymptotics of Quantum Invariants & Volume Conjectures.
  • SL(2)- and SL(3)-Skein Modules of 3-manifolds.
  • Skein Algebras of Surfaces and Teichmuller Space.
  • Quantum representations and non-semisimple TQFT.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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