Graduate Student

Event Information The Jones Polynomial: An Elementary Introduction to Knot Theory
18:10 on Thursday February 04, 2016
19:00 on Thursday February 04, 2016
BA6183, Bahen Center, 40 St. George St.
Huan Vo
https://www.math.toronto.edu/cms/vo-huan/
University of Toronto

Originally discovered in 1984 by Vaughan Jones from his work on operator algebra, the Jones polynomial plays an important role in the development of knot theory. Mathematicians have found many different ways to describe the Jones polynomial ever since and each way gives us a particular insight into the nature of the polynomial. In this talk, I will introduce the Jones polynomial via the Kauffman bracket. The advantage of this approach, besides its elementary nature, is its easy implementation on a computer. I will then reinterpret the Jones polynomial as a quantum invariant. This approach allows one to obtain a generalization of the Jones polynomial, known as the coloured Jones polynomial. We will end with the statement of the volume conjecture, which is a topic of current research.

Prerequisites: linear algebra and mathematical maturity. Pizza and pop provided, pub night to follow the talk.