The Alexander polynomial as a universal invariant

Abstract: I will explain how the reciprocal of the Alexander polynomial of a knot can be viewed as a universal (quantum) invariant associated to the Hopf algebra of regular functions on the group of affine linear transformations of the complex plane. This provides a conceptual interpretation for the Melvin--Morton--Rozansky conjecture proven by Bar-Nathan and Garoufalidis, and Garoufalidis and Le about the relation of the colored Jones polynomials to the reciprocal of the Alexander polynomial in a large color limit.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration