The mysterious loop invariants of a knot

https://hu-berlin.zoom.us/j/61686623112 

Contact: Gaetan Borot (HU Berlin)

A main problem in quantum topology is the Volume Conjecture
which asserts that an evaluation of the colored Jones polynomial (known
as the Kashaev invariant) is a sequence of complex numbers that grows
exponentially at the rate of the hyperbolic volume of a knot complement.
This conjecture connects the Jones polynomial with hyperbolic geometry.
The loop invariants are the refinement of the above conjecture to all
orders in perturbation theory, and take values in the trace field of a
knot. Hence, the loop invariants have topological, but also
mysteriously geometric origin. A geometric definition of them is
currently unknown. In the talk we will discuss how these invariants
behave under finite cyclic covers, and give clues about their possible
geometric definition. Joint work with Seokbeom Yoon.