Ross Assistant Professor
Department of Mathematics, The Ohio State University
The AJ conjecture for knots
The AJ conjecture was proposed in the mathematics literature by S. Garoufalidis and in the physics literature by S. Gukov about 10 years ago. It predicts a strong connection between two important knot invariants derived from very different background, namely the colored Jones function (a quantum invariant) and the A-polynomial (a geometric invariant). The colored Jones function is a sequence of Laurent polynomials which is known to satisfy a linear q-difference equation. The AJ conjecture states that by writing the linear q-difference equation into an operator form and setting q=1, one gets the A-polynomial. In this talk, I will discuss my joint work with T. Le on a geometric approach to the AJ conjecture which leads to the verification of the conjecture for many classes of knots.
Sponsored by the Department of Mathematical Sciences
Refreshments will be served in the Second Floor Atrium of FO 30 minutes prior to the talk