Learning Seminar 9/29

Speaker: Will Dana

Title: The HOMFLYPT Polynomial of a Knot

Abstract: We introduce the Hoste-Ocneanu-Millett-Freyd-Lickorish-Yetter (Przytycki-Traczyk) or HOMFLY(PT) polynomial of a knot. We start with an overview of its antecedents, the Alexander and Jones polynomials, both of which satisfy recursive "skein relations". The HOMFLYPT polynomial is universal among knot polynomials satisfying such relations, and in particular specializes to the Alexander and Jones polynomial. We'll survey the different constructions of the polynomial, emphasizing its connection to the braid group and Hecke algebra.

Notes for the talk are here.

References:

• https://www.ams.org/journals/bull/1985-12-02/S0273-0979-1985-15361-3/home.html

• https://www.ams.org/journals/tran/1928-030-02/S0002-9947-1928-1501429-1/home.html

• https://math.berkeley.edu/~vfr/jones.pdf