(joint work with Dror Bar-Natan)
The Alexander polynomial is perhaps the knot invariant that has the greatest number of distinct definitions.
With the help of the audience we will attempt to briefly list at least six such definitions.
We will then zoom in to my favourite definition based on the AX+B group of affine maps from the plane to itself.
This definition has the advantage of allowing many mild generalizations that are still readily computable like Alexander itself.
Applying our computation to a Seifert surface seems to lead to new computable bounds on the knot genus.