## Math Club

### Thursday, March 22nd, 2018

**Time:** 5:30 p.m. **Place:** Jeffery Hall 118

**Speaker:** Tianyuan Xu (Queen's University)

**Title:** Knot Invariants by Pulling Strings.

**Abstract:** A knot is a smooth closed curve in the 3-dimensional space, and two knots are equivalent if they can be distorted into each other without cutting or gluing. How can we tell whether two knots are equivalent? For example, is the trefoil equivalent to its mirror image? This turns out to be a highly non-trivial problem, and one approach to solving it is to study so-called knot invariants, quantities associated to knots that remain unchanged under equivalences.

We will discuss a knot invariant called the Kauffman bracket of knots. While knots are inherently 3-dimensional objects, in developing this invariant we will simplify their study to the study of 2-dimensional objects called non-crossing pairings. To achieve this, we will need to literally "pull some strings"!