Seminar by Peter Samuelson (University of Toronto)

Title: Quantizations of character varieties and double affine Hecke algebras

2014.07.30 | Jane Jamshidi

Date Fri 01 Aug
Time 14:15 15:15
Location 1531-215 (Aud. D3)


The skein module of the complement of a knot K can be viewed as a quantization of the character variety of S^3 \ K. It is a module over the double affine Hecke algebra (at t=1), and it also determines classical polynomial invariants of the knot K. We will explain this, and give examples of how representation-theoretic statements on the DAHA side translate into statements about knot invariants. In particular, a representation-theoretic conjecture implies (for each n) the existence of a 3-variable polynomial knot invariant that specializes to the n^th colored Jones polynomials of K. (This is joint work with Yuri Berest.)