Title: Quantum Plane and Plucking Polynomial of Rooted Trees 

Abstract: Have you ever wondered what would happen if our familiar Cartesian coordinates (x) and (y) did not commute—for example, if yx=qxy? In this talk, I will introduce the noncommutative (quantum) plane and the associated (q)-binomial coefficients. I will then discuss the plucking polynomial of rooted trees, a concept I introduced in 2014 and have since developed with several of my students, including Gabriel. 

I will conclude by describing applications to Knot Theory, focusing on the Kauffman bracket skein module. Along the way, I will explain how the Kauffman bracket is closely related to the Jones polynomial, the celebrated invariant for which Vaughan Jones was awarded the Fields Medal in 1990.