(University of Toronto)
"Algebraic Knot Theory"
Abstract: The right object of study in algebraic topology is not spaces, but rather, "spaces and maps between them". In a similar spirit I will argue that the right things to study in knot theory are not knots, but rather, "knotted trivalent graphs", as in the world of knotted trivalent graphs (and the basic operations between them) many interesting properties of honest knots become "definable". Thus I find myself again studying the good old Kontsevich integral - the best example I know of an algebraic knot theory - but my perspective this time is completely different.