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.

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