Kashaev's conjecture and the Chern-Simons invariants of knots and links.
Knot theory with the Lorentz group
We analyse perturbative expansions of the invariants defined from unitary representations of the Quantum Lorentz Group in two different ways, namely using the Kontsevich Integral and weight systems, and the R-matrix in the Quantum Lorentz Group defined by Buffenoir and Roche. The two formulations are proved to be equivalent; and they both yield ℂ[[h]]h-valued knot invariants related with the Melvin-Morton expansion of the Coloured Jones Polynomial.